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Simulation and Correction of Spectral Smile Effect and its Influence on Hyperspectral

Mapping

Md. Aktaruzzaman

March, 2008

Course Title: Geo-Information Science and Earth Observation

for Environmental Modelling and Management

Level: Master of Science (MSc)

Course Duration: September 2006 - March 2008

Consortium partners: University of Southampton (UK)

Lund University (Sweden) University of Warsaw (Poland) International Institute for Geo-Information Science and Earth Observation (ITC) (The Netherlands)

GEM thesis number: 2006-17

Simulation and Correction of Spectral Smile Effect and its Influence on Hyperspectral Mapping

by

Md. Aktaruzzaman Thesis submitted to the International Institute for Geo-information Science and Earth Observation in partial fulfilment of the requirements for the degree of Master of Science in Geo-information Science and Earth Observation for Environmental Modelling and Management Thesis Assessment Board Chairman: Prof. Freek van der Meer External examiner: Prof. Katarzyna Dabrowska External examiner: Dr. Martin Schlerf First supervisor: Dr. Harald van der Werff Second supervisor: Mr. Chris Hecker

International Institute for Geo-Information Science and Earth Observation Enschede, the Netherlands

Disclaimer This document describes work undertaken as part of a programme of study at the International Institute for Geo-information Science and Earth Observation. All views and opinions expressed therein remain the sole responsibility of the author, and do not necessarily represent those of the institute.

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Abstract

The spectral smile, also known as ‘smile’ or ‘frown’ curve, is a spectral distortion that is typically found in push-broom sensors. It is a shift in wavelength in the spectral domain, which is a function of across-track pixel (column) in the swath. The Hyperion instrument is susceptible to smile effect because of the arrangement of its two-dimensional detector arrays. The pre-launch smile model of Hyperion was characterized by TRW INC., a US based spacecraft contractor. Most people use this TRW information to correct smile effect. But recent research has revealed enough evidences which showed that pre-launch smile calibration has been changed after launching the sensor. It is suspected that due to mechanical vibration at the time of launching and decaying of sensors over the time are probable reasons that triggered this change. So it is more realistic to correct smile effect on the information of post-launch calibration. The smile effect alters the pixel spectra and reduces classification accuracies. So development of a technique to quantify smile effect per column of hyperspectral image is one of the main objectives of this study. Hyperion and SEBASS sensors were taken as case study. In case of Hyperion, which is a space born sensor, pre-launch smile model and some literatures treating this problem are available. On the contrary, SEBASS which is an air-borne sensor, lacks any kind of information regarding smile problem. In this research, a smile quantification model (SQM) has been developed and validated for Hyperion. This new model produced a curving pattern smile model for Hyperion which was slightly different from pre-launch calibration. This is consistent with available literature suggesting pre-launch and post-launch differences in smile calibration model. Later, the model was adapted to SEBASS and a smile curve was produced. This curve looked like a mixture of ‘frown’ and ‘smile’ resulting in ‘wave’ shapes. The shape of this newly quantified smile curve was consistent with the brightness gradients of SEBASS image. After gathering up-to-date information on smile models of both sensors, a new smile correction technique was adopted to correct the effect. After applying this correction technique, both images showed reduced brightness gradients. Only Hyperion, however, showed improved hyperspectral mapping. There has been hype about smile problem of Hyperion. Little has been talked about the possibility of smile problems of other push-broom sensors. This research work has opened up a new horizon of thinking about smile problem of any existing and future pushbroom hyperspectral sensor.

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Acknowledgements

Al-hamdulillah, all the praise to ALLAH, the almighty, who gave me His divine grace to successfully accomplish this study. I would like to express my deepest gratitude to my supervisors Dr. Harald van der Werff and Mr. Chris Hecker for their continuous guidance, suggestions and contributions throughout the research. I am grateful to Erasmus Mundus Consortium for awarding me the fellowship to pursue such an exciting course in four universities. My sincere gratitude to the four coordinators of the program: Prof. P.M Atkinson, University of Southampton; Prof. P. Pilesjö, Lund University; Prof. Katarzyna Dabrowska, University of Warsaw and Prof. A. Skidmore, ITC. I am really grateful to them for their continuous support during the whole period. I would like to thank all the teachers of four institutions for their valuable contribution in bestowing the best knowledge. I would also like to extend my sincere gratitude to the staff of four institutions specially Ms. Stef Web, Ms. Eva Kovacs and Ms. Jorien Terlouw for their help with logistics. Special thanks to Prof. Steve Mackin, University of Surrey ; Prof. Wouter Verhoef, ITC; Prof. F. Van der Meer, ITC; Roshanak Darvishzadeh, ITC; Dr. Tom Cudahy, CSIRO and Prof. Rudolf Richter, DLR, for their logistic support, inspiration and criticism about my research. My humble admiration goes to all my fellow classmates who have offered me splendid time and cheerful life during the whole period of study. My special thanks to our class representative Mr. Robert Johns for many of his volunteer services. I must mention the name of Mr. Manoj Pant, Mr. Niladri Gupta and Mr. Sam Varghese for their valuable assistance in different aspects. Finally my deepest gratitude goes to my parents and little sweet sister who have always inspired me in my all vision and mission of life.

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Table of contents

1. Introduction........................................................................................................ 7 1.1. Problem statement ................................................................................... 7 1.2. Influence of Smile Effect......................................................................... 9

1.2.1. Influence on red-edge position (REP) of vegetation........................... 9 1.2.2. Influence on surface characterization ............................................... 10

1.3. Research Problem.................................................................................. 10 1.4. Motivation of the study ......................................................................... 11 1.5. Research Objectives ..............................................................................11 1.6. Research Questions ...............................................................................11 1.7. Research Methodology.......................................................................... 12 1.8. Thesis Layout ........................................................................................ 12

2. Model Development ........................................................................................ 14 2.1. Simulated Spectral Response Functions................................................ 15 2.2. High resolution atmospheric feature...................................................... 16 2.3. Simulation of resampled spectrum ........................................................ 17 2.4. Simulation of smile effect...................................................................... 18 2.5. Calculation of spectral products ............................................................ 20

2.5.1. Slope calculation............................................................................... 20 2.5.2. Asymmetry calculation ..................................................................... 21 2.5.3. Spectral angle calculation ................................................................. 22 2.5.4. Choice of spectral product for smile quantification.......................... 24

2.6. Spectral smile quantification ................................................................. 24 2.7. Smile correction..................................................................................... 25 2.8. Chapter summery................................................................................... 27

3. Application to Hyperion .................................................................................. 28 3.1. Response function adaptation................................................................ 28 3.2. High resolution MODTRAN 4 data adaptation..................................... 28 3.3. Similarity in real image and simulated resampled spectrum ................. 29 3.4. Smile quantification............................................................................... 31 3.5. Pre-launch and post-launch calibration ................................................. 33 3.6. Smile correction..................................................................................... 34 3.7. Chapter summary................................................................................... 36

4. Effect of MODTRAN 4 resolution on smile calibration.................................. 37 4.1. Influence of transmittance spectra resolution on Hyperion ................... 37 4.2. Implications for determining smile in SEBASS................................... 39 4.3. Chapter summary................................................................................... 39

5. Application to SEBASS................................................................................... 40

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5.1. Response function adaptation................................................................ 40 5.2. MODTRAN 4 data adaptation............................................................... 41 5.3. Similarity in real image and simulated resampled spectrum ................ 42 5.4. Smile quantification in SEBASS sensor................................................ 43 5.5. Smile correction of SEBASS sensor...................................................... 44 5.6. Chapter summary................................................................................... 46

6. Validation and discussion ................................................................................ 47 6.1. Influence on Hyperion........................................................................... 47 6.2. Influence on SEBASS ........................................................................... 49 6.3. Chapter summary................................................................................... 52

7. Conclusion and recommendation..................................................................... 53 7.1. Summary ............................................................................................... 53 7.2. Conclusion............................................................................................. 53 7.3. Recommendation...................................................................................54

References ................................................................................................................ 56 Appendices ............................................................................................................... 58

Appendix –A ( MATLAB code of general SQM )............................................... 58 Appendix-B ( MATLAB code for SQM adaptation to Hyperion ) ...................... 59 Appendix-C ( MATLAB code for SQM adaptation to SEBASS )....................... 62 Appendix-D ( Smile correction model for Hyperion ) ......................................... 65 Appendix-E ( Smile correction model for SEBASS ) .......................................... 68 Appendix-F ( Amount of shift per column of Hyperion ) ................................... 71 Appendix-G (Amount of shift per column of SEBASS)...................................... 73

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List of figures

Figure 1-1 Pre-launch smile calibration curves of band 10 (blue), band 30 (magenta) and band 55 (green) for Hyperion (Courtesy CSIRO)................................................ 8 Figure 1-2 Hyperion image of resolution 30m (left) and SEBASS image of resolution 3m (right) exhibiting clear brightness gradient.......................................... 9 Figure 2-1 Components of SQM; simulated spectral response function (bottom), simulated high resolution atmospheric feature (middle) and simulated resampled spectrum (top)........................................................................................................... 15 Figure 2-2 High resolution atmospheric feature which is simulated to oxygen absorption region in VNIR and Hyperion reflectance value..................................... 17 Figure 2-3 Graphical presentation of the formation of single resampled spectrum resulting from scalar product between two vectors containing values of Gaussian response function and real world absorption feature respectively. ........................... 17 Figure 2-4 Formation of resampled spectrum for a series of response functions, which ultimately leads to complete resampled spectrum.......................................... 18 Figure 2-5 Simulation of smile effect; resampled spectrum without any shift in response function (top left), resampled spectra with 1 nm shift (top right), with 1+ 2 nm shift (bottom left) and with 1+2+3 nm shift (bottom right). ............................... 19 Figure 2-6 Graphical presentation to determine ‘x’ and ‘y’ coordinates of two points A and B on a resampled spectrum to calculate slope of the points........................... 20 Figure 2-7 Relationship between slopes and shifts.................................................. 21 Figure 2-8 Graphical presentation to calculate asymmetry of a resampled spectrum................................................................................................................................... 21 Figure 2-9 Relationship between asymmetry and shifts .......................................... 22 Figure 2-10 Graphical presentation of spectral angle calculation............................. 23 Figure 2-11 Relationship between spectral angle and shifts..................................... 23 Figure 2-12 Flow chart of Spectral smile quantification ......................................... 25 Figure 2-13 Flow chart of smile correction .............................................................. 26 Figure 3-1 Model adaptation to Hyperion; simulated spectral response function adapted to Hyperion bands (bottom), high resolution MODTRAN data containing oxygen absorption (middle) and resampled spectrum (top)...................................... 29 Figure 3-2 Simulated resampled spectrum (left) and real image spectrum (right) around Oxygen absorption feature at 762 nm........................................................... 30 Figure 3-3 Image at left shows spectral profile of four different Hyperion image columns (Column 2, 30, 60 and 90) around oxygen absorption feature. Image at right shows simulated resampled spectra around oxygen feature for three different amounts of shift (1, 2 and 3 nm)............................................................................... 31 Figure 3-4 Smile curve for Hyperion (Band 41) produced from SQM..................... 33

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Figure 3-5 Pre-launch (Courtesy CSIRO) and post-launch (result of this research) smile curve for Hyperion (Band 41)......................................................................... 33 Figure 3-6 Smile correction model (SCM); simulated response function of Hyperion sensor (bottom), spline corrected image spectrum (middle) , resampled spectra (top) before (Thin blue line with red open circle) and after (Thick red line with asterisk mark) smile correction.............................................................................................. 35 Figure 3-7 Close view of resampled spectrum in SCM; resampled spectrum before (blue) and after (red) smile correction ...................................................................... 35 Figure 4-1 High resolution MODTRAN data in VNIR region................................. 37 Figure 4-2 Coarse resolution MODTRAN 4 data in TIR region ............................. 38 Figure 4-3 Effect of different resolutions on Smile calibration of Hyperion............ 38 Figure 5-1 Model adaptation to SEBASS; simulated spectral response function of SEBASS sensor (bottom), MODTRAN 4 data in TIR containing water absorption (middle) and resampled spectrum (top). ................................................................... 41 Figure 5-2 A resampled MODTRAN spectrum (left) and a real image spectrum (right) around water absorption feature at 12541.4 nm. ........................................... 42 Figure 5-3 Image at left shows spectral profile of three different SEBASS image columns (Column 30, 60 and 90) around water absorption feature. Image at right shows simulated resampled MODTRAN spectra around oxygen feature for three different amounts of shift (1, 3 and 4 nm). ............................................................... 43 Figure 5-4 Smile curve for SEBASS (Band 102) ..................................................... 44 Figure 5-5 Smile correction model for SEBASS; simulated response curve of the SEBASS sensor (bottom), spline corrected image spectrum (middle), resampled spectrum (top) before (Thin blue line with open circle) and after (Thick red line with asterisk mark) smile correction................................................................................. 45 Figure 5-6 Close view of resampled spectrum in SCM for SEBASS; resampled spectrum before (blue) and after (red) smile correction ........................................... 45 Figure 6-1Hyperion image before (left) and after (right) smile correction............... 47 Figure 6-2 Spectral angle mapping along a line of Hyperion image before smile correction.................................................................................................................. 48 Figure 6-3 Spectral angle mapping along a line of Hyperion image after smile correction.................................................................................................................. 49 Figure 6-4 SEBASS image before (left) and after (right) smile correction .............. 50 Figure 6-5 Spectral angle mapping along a line of SEBASS image before smile correction.................................................................................................................. 50 Figure 6-6 Spectral angle mapping along a line of SEBASS image after smile correction.................................................................................................................. 51

SIMULATION AND CORRECTION OF SPECTRAL SMILE EFFECT

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1. Introduction

1.1. Problem statement

The spectral smile, also known as ‘smile’ or ‘frown’ curve is a push-broom technology effect. The Hyperion instrument is susceptible to smile effect because of the arrangement of its two-dimensional detector arrays. The consequence of this effect is that the central wavelength of a band varies with spatial position across the width of the image in a smoothly curving pattern. Very often the peak of the smooth curve tends to be in the middle of the image and gives it a shape of “smile” or “frown”. That is why this spectral misalignment is termed as smile effect. Many popular push-broom sensors such as Hyperion and SEBASS suffer from this problem which reduces their performance. While there is some literature available on the smile effect of Hyperion, very little has been studied for the case of SEBASS. In this work, it has been proposed to quantify and correct the smile effect on Hyperion and SEBASS datasets. Hyperion is a satellite-based hyperspectral sensor which was launched in November 2000, on the Earth Observing 1 (EO-1) platform. It is a push-broom type sensor that measures the incoming radiation in 242 spectral bands in the 400–2500 nm wavelength range. This sensor acquires data with two spectrometers; one in the VNIR range (400-1000 nm) and another in the SWIR range (900-2500 nm). The prominent problem that has been noticed in Hyperion data processing and applications is smile effect. According to pre-launch calibration this effect produces variation between 2.6-3.6 nm in the spectral dimension of VNIR array while in SWIR array this is less than 1 nm (Liao et al., 2000). SEBASS (Spatially Enhanced Broadband Array Spectrograph System) is a push-broom imaging hyperspectral thermal infrared (TIR) system that uses two helium cooled 128 by 128 detector element arrays and measure within the 2.9 to 5.2 µm and 7.5 to 13.6 µm wavelength regions (Hackwell et al., 1996). In the 8- to 12-µm TIR atmospheric window region, mineral groups such as silicates, carbonates, sulphates, and phosphates have spectral features related to the fundamental vibrational frequencies of their interatomic bonds. So wavelength shift due to smile effect in this region will undoubtedly lead to misclassification of minerals in geologic applications.


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Pre-launch smile model for Hyperion was characterized by TRW INC., a US based spacecraft contractor, and is shown in figure-1.1. TRW used 25 points on the 242 (No of bands) by 256 detector array. A polynomial was chosen to model the smile. Each polynomial was linear in the spectral dimension and quadratic in wavelength dimension. The spectral dimension showed a variation of less than 1 nm. However, in the spectral dimension of the VNIR array they detected a variation of up to 2.7 nm (Liao et al., 2000).

Figure 1-1 Pre-launch smile calibration curves of band 10 (blue), band 30

(magenta) and band 55 (green) for Hyperion (Courtesy CSIRO).

The effect of smile is not obvious in the individual bands. Therefore, an indicator is needed to make evident whether or not a given image suffers from smile problem. Smile becomes observable when the image is transformed into Minimum Noise Fraction (MNF) space (Green et al., 1988). For Hyperion images with significant smile, a brightness gradient appears in the first eigenvalue image of MNF space. There is no brightness gradient in MNF for images without significant smile. . Apart from MNF transformation, another way to check for the smile effect is to look at the band difference images around atmospheric absorption feature such as Oxygen A feature near 762 nm (Jupp et al., 2002). Figure-1.2 shows brightness gradient of Hyperion (image at left) and SEBASS (image at right) after applying band difference technique.


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Figure 1-2 Hyperion image of resolution 30m (left) and SEBASS image of resolution 3m (right) exhibiting clear brightness gradient.

1.2. Influence of Smile Effect

Smile effect implies shift in wavelength which is actually a kind of spectral distortion as well. So it is most likely that extracted information from “smiled” Hyperion data will be faulty.

1.2.1. Influence on red-edge position (REP) of vegetation

The region of red-near infrared (NIR) transition has high information content of vegetation spectra. This region is generally called “red-edge” (670-780 nm) and the wavelength point is known as red-edge position (REP) (Horler et al., 1983; Clevers et al., 2002). REP is a good indicator of chlorophyll concentration. Increase in amount of vegetation causes shift in red-edge slope and REP towards longer wavelengths. In contrast, low chlorophyll concentration causes shift in red-edge slope towards shorter wavelengths. The smile effect is acute due to sharp absorption of Oxygen-A feature (760 nm) in band 41 of Hyperion which is within the red-edge region. Atmospheric correction of that feature will be incorrect on “smiled” data. As a result, REP has got potential vulnerability to exact indexation due to smile effect.


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1.2.2. Influence on surface characterization

The application of satellite hyperspectral data for subtle surface classification and mineral exploration has got immense importance. The smile effect alters the pixel spectra and reduces classification accuracies. A variation of 2.6-3.6 nm in VNIR and around 1 nm in SWIR does not seem to be a serious problem because the wavelength step is about 10 nm and the FWHM widths of the bands are also about 10 nm. But in SWIR when it comes to the identification of minerals, this small variation might matter. Cairns et al. (2003), discussed that in case of sharp “spikes” of many atmospheric spectra a variation of FWHM/100 or 0.1 nm can be significant. For mineral identification this small shift do play a role, even give the risk of misidentifications & classifications. So, it is better to consider the smile effect in SWIR region for Hyperion sensor where shift in wavelength is 1 nm.

1.3. Research Problem

Although some research has been done on Hyperion dataset to solve the smile problem, the researchers have yet not come up with a complete solution. The methodologies developed so far can only reduce the intensity of the smile effect but can not remove it entirely. These all are correcting the symptoms and not the cause and lead to spectral artifacts in data. Another problem is pre-launch and post-launch smile calibration is not the same. It is most likely that after launching the sensor suffered mechanical vibration and its calibration got altered. Pearlman et al. (2003) and Khurshid et al. (2006) show sufficient results in support of this assumption. Goodenough et al. (2003) explained the reason why post-launch calibration might be different from the pre-launch smile calibration. An experiment was conducted on artificially created smiled AVIRIS and Hyperion data by applying linear fitting method. But it could only remove smile for AVIRIS. The reason could be the spectral calibration data might have changed after the sensor was launched into orbit. Another bunch of supporting documents discussed by Pearlman et al. (2003) and Cairns et al. (2003) who showed how the measured smile based on spatial variations in the position of the Oxygen-A feature does not match the pre-launch smile (polynomial) model by up to 1 nm. Performing atmospheric correction for each column can remove smile effect on the basis of pre-launch calibration information. Qu, et al. (2003) described a modified HATCH-2D atmospheric model which can atmospherically correct each column separately. In principle this should have removed smile if the pre and post-launch


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calibration remain same. But unfortunately this modified model did not provide a satisfactory solution for smile and pointed to the difference of pre and post-launch calibration for smile. So formulation of a new research approach is necessary that would attempt to remove the cause of smile effect.

1.4. Motivation of the study

It is known that Hyperion sensor suffers from smile problem. But little is known to what degree smile problem can affect hyperspectral mapping. Some techniques are available to correct this problem based on pre-launch calibration information while there has been evidences that pre-launch and post-launch calibration differ. The smile correction techniques are not available in existing software and very often people ignore this problem. Other push-broom hyperspectral sensor such as in SEBASS the effect of smile is visible and it appears stronger than Hyperion. It is believed that detection and correction of smile problem for SEBASS would increase the accuracy of mineral classification in thermal infrared region.

1.5. Research Objectives

• To quantify smile effect per column of Hyperion image.

• To develop a technique for correcting smile effect for Hyperion.

• To adapt this smile quantifying and correcting technique to SEBASS sensor which also suffers from strong smile effect.

• To assess the improvement achieved by this correction technique.

1.6. Research Questions

• How does the shift in central wavelength of a particular waveband vary across the width of a hyperspectral image?

• Do spectral products (Slope, asymmetry and spectral angle) of image spectrum of a specific waveband around sharp absorption features vary across the width of the image?


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• Can a relationship between spectral products and amount of shifts in central wavelength be made?

• How can this relationship be transformed into a technique to detect shift in Hyperion image?

• How to adapt this technique that is developed on Hyperion to the SEBASS sensor in order to reduce its smile as well?

• To what degree of accuracy can we detect smile effect in Hyperion data as compared to existing calibration information?

• How is the improvement in classification accuracy before and after the smile correction?

1.7. Research Methodology

Smile quantifying model (SQM) was developed using software package MATLAB (www.mathworks.com). The model had three components. Technical cause of smile effect of pushbroom scanner was simulated in the model. The components were simulated spectral response function, high resolution real world absorption feature and simulated resampled spectrum. Artificial shift was created in response function which resulted in different resample spectra. These reference spectra were matched with real image spectra to determine the spectral similarity. From the best matching, amount of shift was determined. In this way, for Hyperion image, model was run across the 256 columns and for SEBASS image it was 128 columns. Shift in wavelengths for each column for both images were plotted. For Hyperion, the curve was “frown” shape while for SEBASS it was mixture of “frown” and “wave” shapes.

1.8. Thesis Layout

The contents of different chapters are summarized below:

• Introduction: Includes background of the research (research problem and research scope), research questions, research objectives and methodology of the research.

• Model development: includes detailed description of different parts of Smile quantification model (SQM), idea of smile simulation and smile correction approaches.


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• Application to Hyperion: includes adaptation of SQM to HYPERION image, smile quantification curve and mechanism of correction techniques in details.

• Effect of different resolution MODTRAN data on smile calibration: includes graphical presentation of various resolution MODTRAN data of Hyperion smile curve and discuss probable uncertainty that might occur during quantification of SEBASS smile curve.

• Application to SEBASS: includes adaptation of SQM to SEBASS sensor, smile quantification curve and correction mechanism.

• Validation and discussion: includes discussion of improvement achieved after smile correction.

• Conclusion and recommendation: includes summary of the whole research, answering research questions and recommendation for future research.


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2. Model Development

One of the main objectives of this research is to quantify smile effect per column of hyperspectral image. To address this problem, a model was developed using software package MATLAB (www.mathworks.com). The specialty of this model is that its different parts are the mimic of the technical cause and atmospheric environment that are responsible for smile effect in push-broom scanner. As there is no existing solution in the available software, the building blocks of different components of the model were ventured to construct in a unique manner by using required programming codes. MATLAB offers a very strong numerical computing environment and programming language. The model that has been developed using MATLAB is known as ‘Smile Quantification Model’ (SQM). The SQM consists of three parts (figure 2.1), namely

1) Simulated spectral response function 2) Simulated high resolution atmospheric feature 3) Simulated resampled spectra

The SQM was developed in two phases. Firstly, all the components of SQM were constructed on a generic scenario. At this stage, elements of the model such as spectral response functions were simulated to an imaginary Full width half maximum (FWHM) Gaussian curve. This response functions were qualitatively similar to Hyperion and SEBASS sensor channels but not quantitatively. Similarly, high resolution atmospheric absorption was constructed by fitting a Gaussian curve in a synthetic dataset to represent a sharp absorption and its interaction with spectral response functions. In the second stage, each element of the model was adapted to Hyperion and SEBASS scenario while dealing with spectral smile problem of the sensors respectively. In this chapter the first stage of SQM development has been discussed. The motivation behind constructing SQM on a generic platform is to get idea about the general behaviour of resampled spectrum due to artificial shift caused to SRF (Spectral response function) and subsequent calculation of spectral products (slopes, asymmetry and spectral angle). This calculation was performed to see if there exists any relation between spectral product and amount of shift. Both Hyperion and SEBASS have different spectral channel widths and atmospheric features of interest


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for quantifying smile effect for both sensors are also different. So it is more logical to develop SQM on generic scenario and then go for its adaptation for both sensors successively.

Figure 2-1 Components of SQM; simulated spectral response function

(bottom), simulated high resolution atmospheric feature (middle) and simulated resampled spectrum (top).

2.1. Simulated Spectral Response Functions

The spectral response functions of Hyperion and SEBASS were assumed to be Full width half maximum (FWHM) Gaussian curves. The mathematical equation for this FWHM function is:

2( )x uy e − −=------------------------------------------------------- (2.1)


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Where, x = Range of vector values where to construct Gaussian curve y = Output Gaussian curve u = Parameter to move the Gaussian curve The width of the Gaussian function was controlled by a constant value ‘a’. This value was either divided (x/a) or multiplied with (a*x) vector ‘x’. By performing trial and error method, the value of ‘a’ was calculated. It was found that to maintain FWHM of 10nm the required ‘a’ value is 6.11 while to maintain FWHM of 40 nm required ‘a’ was 23.7. The model contains fifteen spectral response functions. These functions partly overlap with each other and intersect at half of the height of Gaussian curve fulfilling the requirement of ‘Full width half maximum’. Above mentioned equation (2.1) was coded to construct fifteen consecutive Gaussian response functions. The width of Gaussian curve was made 10 units by diving vector ‘x’ of equation (2.1) by 6. The parameter ‘u’ of equation (2.1) was multiplied by 1.67 to make neighbouring curves intersect at half width. The MATLAB code looks: z=zeros(1,n); % Vector to contain y values of one G aussian curve

v=zeros(n,15);% Vector to contain y values of fifte en Gaussian curve

x1= 1:0.5:170;% Range of a Gaussian curve along x a xis

for j=1:15 % Loop to run through fifteen Gaussia n curve

for i=1:n % Loop to construct y values for Gaus sian curve

z(i)=exp(-((x1(i)/6)- (1.67*j))^2); % Equation to construct Gaussian

% curve

end % End of second loop

v(:,j)=z;

end % End of first loop

2.2. High resolution atmospheric feature

High resolution atmospheric feature was constructed from synthetic dataset. Region of oxygen absorption in VNIR was mimicked in the synthetic data. From available literature the width ‘W’ of this absorption region was found 732 nm to 782 nm. The depth ‘H’ of the oxygen absorption was simulated to Hyperion reflectance. Figure 2.2 shows the setup of high resolution atmospheric feature simulated to oxygen absorption. After fixing the width and depth, a smooth Gaussian curve was fit to the absorption feature.


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732 nm 782 nm

50 nm

H =Simulated to Hyperion

Reflectance

W = Simulated to oxygen absorption

Figure 2-2 High resolution atmospheric feature which is simulated to oxygen

absorption region in VNIR and Hyperion reflectance value.

2.3. Simulation of resampled spectrum

Resampled spectra are low resolution spectra resulting from interaction between response function’s sensitivity and high resolution real world spectra. In the model the resampled spectra were simulated by dot product of two vectors containing data of response function and high resolution absorption feature respectively.

Figure 2-3 Graphical presentation of the formation of single resampled

spectrum resulting from scalar product between two vectors containing values of Gaussian response function and real world absorption feature respectively.


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In figure-2.3 it has been schematically shown that how resampled spectrum of a single band is formed after combining two vectors under the definition of scalar product. One vector Z contains value of a Gaussian response function while other vector Y contains real world absorption feature. As per the requirements of scalar product, two vectors must have same length. In this case same length means same number of vector elements. In the SQM, construction of one sensor channel (also known as response function) needed 341 interval points. It is to mention here that this number is changeable. The idea is whatever number of points the response function has got, the high resolution atmospheric feature must contain same number of points. This is the precondition to get scalar product of two vectors. Figure 2.4 shows how a resampled spectrum look for a series of response functions.

Figure 2-4 Formation of resampled spectrum for a series of response functions, which ultimately leads to complete resampled spectrum.

2.4. Simulation of smile effect

As smile effect is a shift in wavelength, so the simulation was done in SQM (Smile Quantification Model) by causing artificial shift in response function which directly induced variation in resampled spectra in their shapes, sizes and slopes.


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Figure 2-5 Simulation of smile effect; resampled spectrum without any shift in response function (top left), resampled spectra with 1 nm shift (top right), with

1+ 2 nm shift (bottom left) and with 1+2+3 nm shift (bottom right). The idea of simulation is actually an attempt to simulate the technical cause of spectral smile effect. In the image it is not possible to directly measure the shift in wavelength per column. Rather it is only possible to observe spectral change in shapes and sizes around any sharp absorption feature. These changes are symptom of smile effect. The main purpose to run the simulation model is to produce similar types and trends of resampled spectra as real image spectra having various shapes around absorption feature, where the shifts are known for resampled spectra. So, various shapes of absorption feature in an image column will be attempted to relate to that of SQM. In this way, simulation approach will open up ways to quantify shift in real image columns.


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2.5. Calculation of spectral products

Spectral products such as slopes, asymmetry and spectral angle of resampled spectra were calculated for different amount of shifts. Each of the spectral products had characteristic relationship with varying amount of shifts.

2.5.1. Slope calculation

The slope of a resampled spectrum was calculated using following geometric equation; ----------------------------------------------------------------- (2.2) Figure 2-6 shows the method of determining ‘x’ and ‘y’ coordinates of two points A and B which will be placed in above mentioned equation (2.2).

Figure 2-6 Graphical presentation to determine ‘x’ and ‘y’ coordinates of two points A and B on a resampled spectrum to calculate slope of the points

In this way slopes of all the resampled spectra for different amount of shifts were calculated. Then shifts versus slopes were plotted in figure-2.7 to see if there exists any relationship.

2 1tan

2 1

y y

x xθ −=

−


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Figure 2-7 Relationship between slopes and shifts

2.5.2. Asymmetry calculation

Asymmetry is the ratio of areas located at both sides of minimum absorption band. The equation of asymmetry; ------------------------------------------------------ (2.3) Figure 2.8 shows the method of obtaining area (left) and area (right) after defining boundary of minimum absorption.

Figure 2-8 Graphical presentation to calculate asymmetry of a resampled spectrum.

( )

( )

Area LeftAsymmetry

Area Right=


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Asymmetry of all the resampled spectra were calculated and then plotted against shifts in figure 2-9.

Figure 2-9 Relationship between asymmetry and shifts

2.5.3. Spectral angle calculation

Spectral angle calculates the spectral similarity between a test spectrum and a reference spectrum (Kruse et al., 1993; Van der Meer et al., 1997). In this approach, the spectra are treated as vectors in a space with dimensionality equal to the number of bands being considered. The outcome of the spectral angle mapping for each pixel is an angular difference measured in radians ranging from zero to П/2. The equation of spectral angle is,

------------------------------------------- (2.4)

Where, = test spectrum

= reference spectrum

Figure-2.10 shows the setup of spectral angle and its components such as test and reference spectrum.

1cos ( )| | | |

t rSpectralAngle

t r−=� �

�� i

t�

r�


23

Figure 2-10 Graphical presentation of spectral angle calculation

Spectral angle of all the resampled spectra were calculated. It is to mention that different shifted spectra acted as test spectra while unshifted spectrum acted as reference spectrum. Later all the angle values were plotted against shifts in figure-2.11.

Figure 2-11 Relationship between spectral angle and shifts


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2.5.4. Choice of spectral product for smile quantification

Among the above mentioned relationships (in fig-2.7, fig-2.9 and fig-2.11), spectral angle had the most convincing and linear characteristic behaviour with respect to shifts (figure-2.11). In the SQM, spectral angle was taken as indicator to determine spectral similarity. Spectral similarity was determined between resampled spectra simulated from SQM and real image (Hyperion and SEBASS) spectra. The less the spectral angle the more the similarity between those spectra.

2.6. Spectral smile quantification

Smile quantification refers to measurement of shifts per column of hyperspectral image (Hyperion and SEBASS). An average spectrum of a particular image column was extracted first. For Hyperion image, spectra of five consecutive bands around 762.6 nm (Hyperion bands 39-43 nm) were chosen as test spectra. Band 41 has the deepest oxygen absorption whereas the remainders act as shoulders of sharp absorption and exhibit significant variation in shapes due to shift in wavelength. The reference spectra were taken from simulated model. Response functions in the model were shifted 6 nm in both directions with an increment of 0.1 nm. In this way simulated model produce 120 spectra due to different shifts ranging from 0 to 6 nm and one spectrum without any shift. So the total number of reference spectra was 121.

To determine the smile of a particular image column, the average spectrum from that column was matched against 121 reference spectra. Spectral angle (SA) of 121 reference spectra against one test spectrum was calculated. The lowest SA was taken as best similarity between test and reference spectra. From the model, position of best reference spectra and corresponding amount of shift were noted down. The shift of the model is the shift of image spectra of a particular column. For SEBASS image, spectra of five consecutive bands around 12541.4 nm (SEBASS bands 100-104) were chosen as test spectra. Band 102 has the deepest water absorption feature. The other steps to quantify smile curve for SEBASS remain same as Hyperion. In this way smile i.e. shifts in wavelength were determined for each column of Hyperion and SEBASS image. After measuring shift per column of image, corrective measures were followed. Figure-2.12 shows the flow chart of spectral smile quantification.


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HyperspectralImage

Smile model

Image spectra With unknown shift

(Test Spectra)

Resampled spectraWith known shift

(Reference spectra)

Spectral angle (SA) calculation

Determination ofMinimum SA

Identification of particular reference spectrum

producing minimum SA

Determination of shift from corresponding reference

spectra

HyperspectralImage

Smile model

Image spectra With unknown shift

(Test Spectra)

Resampled spectraWith known shift

(Reference spectra)

Spectral angle (SA) calculation

Determination ofMinimum SA

Identification of particular reference spectrum

producing minimum SA

Determination of shift from corresponding reference

spectra

Figure 2-12 Flow chart of Spectral smile quantification

2.7. Smile correction

The smile effect can be corrected by moving linear fitting and interpolation with the help of Hyperion ground spectral calibration data provided by TRW. Other existing methods for correcting smile are “Column Mean Adjusted in Radiance Space” and “Column Mean Adjusted in MNF Space” (Goodenough, et al., 2003). In the first


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method, for each individual band of the original Hyperion data, each column mean value was set equal to the band mean value. The underlying assumption is that the image is sufficiently homogeneous. This method removes the gradient caused by the smile but unfortunately creates false spectra. In latter method, instead of adjusting the column means in radiance space, the column means are adjusted in MNF space. Apart from this CSIRO (Commonwealth Scientific and Industrial Research Organization) and CCRS (Canada Centre for Remote Sensing) have developed their own technique to correct smile effect. CSIRO has developed their technique based on spline interpolation technique (Jupp et al., 2002) whereas CCRS has developed based on convolution-deconvolution technique (Khurshid et al., 2006). But they did not disclose the details of their respective correction technique.

HyperspectralImage

Choice of a column

Determination of shift From smile curve

Shift of response functionin reverse direction

Spline corrected exactimage spectrum

Calculation of newresampled spectra

HyperspectralImage

Choice of a column

Determination of shift From smile curve

Shift of response functionin reverse direction

Spline corrected exactimage spectrum

Calculation of newresampled spectra

Figure 2-13 Flow chart of smile correction


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This research has ventured to develop a new technique of smile correction. The correction was done on the spectral and spatial subset of the whole image. Smile correction refers to re-establishment of wavelength to its original position. In the image it is not possible to shift the position of wavebands but it is possible to change the reflectance value of each waveband. The shift per column of image was corrected by re-writing the new reflectance value of the wavebands in the image. This new reflectance value was obtained from smile correction model (SCM). The idea of SCM is when the position of response functions are shifted reverse direction as required, there would be changes in reflectance in resampled spectra. Horizontal movement of response functions cause vertical movements in the resampled spectra. Figure-2.13 shows flow chart of general smile correction procedure.

2.8. Chapter summery

Different components of SQM have been discussed here. Calculation of spectral products and their relationship with varying amount of shifts have been shown. Spectral angle (SA) has most convincing and linear relationship and it is taken as an indicator to determine spectral similarity. Through flow-charts, the principle of smile quantifying procedures has been discussed and a new smile correction technique has been proposed.


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3. Application to Hyperion

3.1. Response function adaptation

The SQM model was adapted to the Hyperion sensor to quantify the ‘shift’ per column of the image. The first step of adaptation was simulating Hyperion response functions. According to the header file information associated with each Hyperion image, bands have an average of 10.19 nm FWHM (Full Width Half Maximum). In smile quantifying model (SQM) the 10.19 nm FWHM of each Gaussian curve was defined by the following empirical equation;

2( / 6.11 )x uy e− −= ---------------------------------------------------------- (3.1)

The implementation of equation (3.1) through MATLAB code looks; x1=670:0.1:860; % Width of atmospheric window

for j=1:15 % Loop to construct 15 response fun ctions

for i = 1:n % Loop to construct y values of eac h response function

z(i)= exp(-(x1(i)/6.11-(111.46+2*j*0.834))^2); % Main equation


v(:,j)= z; % Vector to contain 15 response fun ctions


The width of response function was defined 10.19 nm by dividing the vector ‘x’ with a constant value 6.11. This value was calculated by trial and error process. The parameter ‘u’ in equation (3.1) was replaced by an empirical constant value 111.46 to define the fifteen series of response functions in the atmospheric region 670 to 860 nm. The reason of choosing this region is oxygen absorption falls here.

3.2. High resolution MODTRAN 4 data adaptation

The general SQM contains a synthetic Gaussian fit to represent high resolution atmospheric absorption. This synthetic absorption feature was replaced by high resolution (0.1 nm) MODTRAN 4 data to adapt the model to Hyperion sensors. MODTRAN 4 is an atmospheric radiative transfer model (RTM). This model


29

calculates atmospheric transmittance, single and multiple scattered solar and thermal radiances.

Figure 3-1 Model adaptation to Hyperion; simulated spectral response function

adapted to Hyperion bands (bottom), high resolution MODTRAN data containing oxygen absorption (middle) and resampled spectrum (top).

MODTRAN 4 data with 0.1 nm resolution was taken as high resolution real world spectra within the atmospheric window of 670 nm to 860 nm. The third component of the model, the resampled spectra was calculated by performing dot product between spectral response function and MODTRAN high resolution data. The details of calculating resampled spectra have been discussed in Chapter 2, Section 2.3. Figure-3.1 shows the adaptation of general SQM model to Hyperion sensor.

3.3. Similarity in real image and simulated resampled spectrum

After performing adaptation to Hyperion, the model requires a region of interest around a sharp absorption feature to detect shift in wavelength per column of Hyperion image. Oxygen has sharp absorption at 760 nm wavelength and this dip is present at 762.6 nm of Hyperion band 41.


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Figure 3-2 Simulated resampled spectrum (left) and real image spectrum

(right) around Oxygen absorption feature at 762 nm.

In figure 3.2, simulated resampled spectrum (left) and real image spectrum (right) of oxygen absorption feature at 762 nm has been presented. Visually both of the spectral profiles show a clear resemblance. But a close look into the figures would reveal difference in slopes of both sides of oxygen absorption. The reason is real image spectrum contains both ground and atmospheric reflectance while simulated spectrum contains only atmospheric reflectance. As the purpose of the model is to quantify smile effect which is shift in wavelength, it is important for the model to exhibit as similar changing pattern of resampled spectra as in real image due to artificial shift caused to model. However the authenticity of the quantified smile value depends not only on the interior mathematical mechanism of the model, but also on the output 2D visualization of resampled spectra. In figure-3.3, image at left shows spectral profile of four different Hyperion image columns (Column 2, 30, 60 and 90) around oxygen absorption feature. The four spectral profiles do not coincide exactly with each other. This incidence is symptom of smile problem. It also tells that the four column positions have four different amounts of shifts which are unknown. In figure-3.3, image at right shows simulated resampled spectra for three different amounts of shift (1, 2 and 3 nm). The simulated spectral profiles (image at right) are very much similar to that of real image (image at left). So, the Smile quantification model gives a firsthand mimicking impression of original image.


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Figure 3-3 Image at left shows spectral profile of four different Hyperion image columns (Column 2, 30, 60 and 90) around oxygen absorption feature. Image at

right shows simulated resampled spectra around oxygen feature for three different amounts of shift (1, 2 and 3 nm).

3.4. Smile quantification

The idea of smile quantification is quite simple. There are image spectra with unknown amount of shifts in the real image. There are also resampled spectra from model with known shifts. An image spectrum from each column has to be matched with all the resampled spectra from model to determine the best match. The main steps of smile quantification are discussed below with a little detail of model and programming code. The first step was to extract test spectra from Hyperion image from each column. More specifically a subset of Hyperion image containing 256 columns, 10 lines and 15 bands were created first on a visually homogeneous area. The homogeneity of the subset image was tested by calculating the mean standard deviation of reflectance value of all the bands. The calculated mean standard deviation value was 108.19 for visually homogeneous area. The homogeneity test was also carried out on a visually relatively heterogeneous area and on the whole image and the mean standard deviations were found 774.43 and 934.55 respectively. So it can be said that visually homogeneous area had better homogeneity. The test spectra from each column with 10 lines were collected and mean of 10 lines were calculated to choose representative spectrum of this particular column. It is worth mention that out of 15


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spectral bands, 5 of them namely band 39,40,41,42 and 43 were considered for SA calculation, where band 41 has oxygen absorption. Once the test spectra have been collected from each of image column, next step is to match each of them with reference spectra. Reference spectra are the output from SQM model due to artificial shift caused to model response function. The mechanism to construct reference spectrum has been discussed in Chapter 2, section 2.3. It is to mention here that resampled spectrum of SQM are known as reference spectrum. Once the setup of test and reference spectra are done, the next stage comes to determine similarity between those spectra. The scale of measuring similarity between test and reference spectra is calculation of ‘Spectral Angle’ (SA). The definition and mathematical equation of SA have been included in Chapter 2, Section 2.5.3. Application of SA in Hyperion image spectra to determine best spectral match in MATLAB code looks; theta=zeros(256,401); % Declaration of 401 spectra l angle

w=zeros(256,401); % Spectral angle in degree

for r=1:256 % Loop through columns

for i=1:401 % Loop through reference spe ctra

alpha=sqrt(sum(M(:,i).*M(:,i))); % Reference spect rum vector

beta=M(:,i)/alpha; % Absolute value of referenc e spectrum

chi=sqrt(sum(L(:,r).*L(:,r))); % Test spectrum vec tor

phi=L(:,r)/chi; % Absolute value of test spe ctrum

theta(r,i)=acos(sum(beta.*phi)); % Spectral angle in radian

theta;

w(r,i)=(theta(r,i)*180/pi); % Spectral angle in de gree



After adapting the SQM model to Hyperion, it produced 121 resampled spectra after shifting response functions in both directions up to 6 nm with an increment of 0.1 nm. A test spectrum from a particular image column was matched with each of 121 reference spectra. In this way 121 SA were calculated .The minimum SA value was the best spectral match and pointed to a particular reference spectrum and the corresponding amount of shift in the model. The SQM calculated amount of shift for


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256 columns of Hyperion image. This shift per column which is smile effects looks like following figure- 3.4.

Figure 3-4 Smile curve for Hyperion (Band 41) produced from SQM

3.5. Pre-launch and post-launch calibration

Figure 3-5 Pre-launch (Courtesy CSIRO) and post-launch (result of this

research) smile curve for Hyperion (Band 41)

The smile curve produced from SQM for band 41 of Hyperion image looked very much similar to pre-launch smile curve. But when plotted together, deviation was


34

noticed between them. Figure 3.5 shows difference in pre-launch and post-launch smile calibration for band 41 of Hyperion image. This result is also supported by existing literatures such as Pearlman et al. (2003) and Khurshid et al. (2006) that have shown clear difference in pre-launch and post-launch smile calibration.

3.6. Smile correction

Smile correction was done pixel by pixel basis on the subset image. The subset image contains 256 columns, 1000 lines and 10 bands. From smile calibration there is information about amount of shift per column of Hyperion image. The treatment of a particular column would be to shift the spectral response function of that column in the reverse direction the same amount shift it suffers. The exact spectrum was approximated by a spline corrected line passing through all the bands (10 subset bands) around atmospheric absorption. To say more specifically the spline corrected line passed through the reflectance value of the wavebands of a particular pixel. The interaction between shifted response function and spline corrected line produced corrected resampled spectrum.

For example, if column 240 suffers from smile effect of -2 nm (‘-’ indicates shift in left-hand direction) then as for correction of that particular column the series of spectral response functions around oxygen absorption (band 41) have to be shifted 2 nm right-hand direction. Now the new position of response functions is known. Spline interpolation technique was deployed to approximate exact image spectrum. This approximation is important because of its being use as high resolution spectrum in the smile correction model (SCM). In the image it is not possible to move the bands. The only option left is the scope of changing (or rewriting) the reflectance/transmittance value in the image. The objective of SCM is to see the change in reflectance/transmittance after moving the response functions as required. Figure-3.6 shows the set up and mechanism behind smile correction model (SCM) and figure-3.7 shows close view of output part (i.e. resampled spectra before and after smile correction) of SCM. Difference in resampled spectrum before and after smile correction was calculated for each pixel of an image subset containing 256 columns, 1000 lines and 10 bands. This difference was added to the existing image to correct smile problem. The whole process was implemented through a totally automated program.


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Figure 3-6 Smile correction model (SCM); simulated response function of

Hyperion sensor (bottom), spline corrected image spectrum (middle) , resampled spectra (top) before (Thin blue line with red open circle) and after

(Thick red line with asterisk mark) smile correction.

Figure 3-7 Close view of resampled spectrum in SCM; resampled spectrum

before (blue) and after (red) smile correction


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3.7. Chapter summary

General SQM was adapted to Hyperion sensor. Smile curve of band 41 of Hyperion produced from SQM had a smooth curving pattern. This curve was also slightly different from pre-launch calibration. A new smile correction technique has been explained and applied to Hyperion image.


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4. Effect of MODTRAN 4 resolution on smile calibration

4.1. Influence of transmittance spectra resolution on Hyperion

The input to SQM was atmospheric transmittance from the MODTRAN 4 radiative transfer model. For smile quantification of Hyperion, the wavelength region of 670 nm to 860 nm was chosen as the region of interest because ‘oxygen absorption’ falls in this range. In the VNIR, MODTRAN 4 generates atmospheric transmittance with as high resolution as 0.01 nm. But this is not the case in the Thermal infrared (TIR), which ranges for the SEBASS sensor from 8000 nm to 13000 nm. Here, MODTRAN 4 generates atmospheric transmittance with a resolution as coarse as 10 to 13 nm.

Figure 4-1 High resolution MODTRAN data in VNIR region

The coarse resolution causes a less accurate modelling of spectral shift, therefore the spectral angle will show coarser steps in the determination of shift and thus the smile calibration curve will be less accurate. It is very logical concern that this coarse resolution might not produce accurate smile calibration curve for SEBASS. There is no research activity existing on the pre-flight calibration of SEBASS against which the modelled smile calibration can be verified.


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Figure 4-2 Coarse resolution MODTRAN 4 data in TIR region

Before adapting the SQM to SEBASS, an experimental study on Hyperion with different resolutions of the transmittance spectrum was done. The resolution was lowered gradually from 0.1 nm to 10 nm in step of 1 nm. These coarse resolution MODTRAN data were fit to SQM model successively and smile calibration curves were produced for each resolution (figure-4.3).

Figure 4-3 Effect of different resolutions on Smile calibration of Hyperion From figure-4.3, it is clear that despite the difference in resolution, the ‘smile’ or ‘frown’ shape of the curves remains the same. However, there clearly is an absolute


39

shift of the smile curve. Smile calibration produced from the SQM model using 9 and 10 nm MODTRAN data showed the maximum absolute shift (In figure the top two curves, magenta and blue) from authentic high resolution (0.1 nm) smile curve of approximately 2 nm. Surprisingly, lower resolution MODTRAN transmittance spectra up to 8nm showed a very similar smile calibration of original one. Nonetheless, the approximate deviations were +0.5 nm to -0.5 nm.

4.2. Implications for determining smile in SEBASS

On average, Hyperion has a channel width of 10 nm. MODTRAN resolutions of 3 nm width, which is a third of Hyperion's channel resolution, produced quite good results. In the same way, 10-12 nm MODTRAN resolutions in TIR region, which is almost one-third (1/3) of SEBASS channel width (In average SEBASS has got 40 nm channel width), is believed to produce an acceptable smile curve. From the experience of Hyperion, a deviation of -0.5 to +0.5 nm might occur during the absence of high resolution MODTRAN transmittance data in TIR region.


Different resolution of MODTRAN 4 transmittance spectra has influence on smile curve of Hyperion. The smile curve suffers absolute shift due to absence of high resolution transmittance spectra. This incident points to the concern of coarser resolution MODTRAN 4 transmittance in TIR during its adaptation to SEBASS sensor.


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5. Application to SEBASS

This chapter is a reiteration of chapter 3, as the main steps of SQM application to SEBASS are the same as Hyperion. Of course, the width of spectral response function of SEBASS, choice of atmospheric feature and region of atmospheric window differs from Hyperion.

5.1. Response function adaptation

The SQM model was adapted to the SEBASS sensor to quantify the shift per column of the image. The first step of adaptation was simulating SEBASS response functions. SEBASS has varying width of response function ranging from 30 nm to 50 nm. The region around band 102 (12541.1 nm) contains water absorption feature where each band has an average 39 nm FWHM Gaussian response function. In SQM the width of each waveband was defined 39 nm by the following empirical equation,

( / 23.7 )x uy e− −= ------------------------------------------------------------ (5.1)

In Chapter 2, section 2.1, it has been discussed how to control width of Gaussian curve by manipulating the variable ‘x’ mentioned in equation (5.1). The implementation of the above mentioned equation through MATLAB code looks, x1=12138.6:1:12888.6; % Width of atmospheric window

for j=1:15 % Loop through fifteen Gaussian curve

for i = 1:n % Loop to produce y values

z(i)= exp(-(x1(i)/23.7-(515.8+2*j*0.834))^2);% Main equation


v(:,j)= z; % Vector to contain 15 response funct ion



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In equation (5.1), parameter ‘u’ was replaced by constant value 515.8 which helps the equation to stay within desired atmospheric window from 12138.6 nm to 12888.6 nm.

5.2. MODTRAN 4 data adaptation

At this stage, the high resolution synthetic data of general SQM was replaced by MODTRAN 4 data available in thermal infrared region (TIR). MODTRAN 4 provides 10 nm spectral resolutions in TIR region which is much lower than the case of Hyperion where it has 0.1 nm resolution. Figure 5.1 shows adaptation of general SQM model to SEBASS environment.

Figure 5-1 Model adaptation to SEBASS; simulated spectral response function

of SEBASS sensor (bottom), MODTRAN 4 data in TIR containing water absorption (middle) and resampled spectrum (top).

The third component of the model, the resampled spectrum was calculated by performing dot product between sensor’s response function and MODTRAN data. The details of calculating resampled spectra have been discussed in Chapter 2, Section 2.3.


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5.3. Similarity in real image and simulated resampled spectrum

After performing the adaptation to SEBASS sensor, the model requires a region of interest around a sharp absorption feature to detect shift in wavelength per column of SEBASS image. Water has a sharp absorption at 12541.4 nm wavelength and this is present at SEBASS band 102, which is equivalent to this wavelength. In figure 5.2, real image spectrum (left) and MODTRAN resampled spectrum (right) of water absorption feature at 12541.4 nm has been presented. Visually both of the spectral profiles show a clear resemblance but still there are small differences in overall shapes and slopes. The reason is that the real image spectrum contains both ground and atmospheric reflectance while simulated spectrum contains only atmospheric reflectance.

Figure 5-2 A resampled MODTRAN spectrum (left) and a real image

spectrum (right) around water absorption feature at 12541.4 nm.

The importance of visual similarity between various simulated shifts and real image spectra of different columns has been discussed in chapter 3, section 3.3. In figure- 5.3, image at right shows simulated resampled spectra for three different amounts of shift (1, 2 and 3 nm). The simulated spectral profiles (image at right) are very much similar to that of real image (image at left). In figure-5.3, image at left shows spectral profile of three different SEBASS image columns (Column 30, 60 and 90) around water absorption feature. The three spectral profiles do not coincide exactly with each other. This incidence is symptom of smile problem. It also tells that the three column positions have three different amounts of shifts, which are unknown.


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So, the SQM gives a firsthand mimicking impression of original image also in case of SEBASS.

Figure 5-3 Image at left shows spectral profile of three different SEBASS image

columns (Column 30, 60 and 90) around water absorption feature. Image at right shows simulated resampled MODTRAN spectra around oxygen feature

for three different amounts of shift (1, 3 and 4 nm).

5.4. Smile quantification in SEBASS sensor

The first step was to extract test spectra from SEBASS image from each column. More specifically a subset of SEBASS image containing128 columns, 10 lines and 10 bands were created first on a homogeneous area. The homogeneity test was similar to Hyperion (Chapter 3, section 3.4). The test spectra from each column with 10 lines were collected and mean of 10 lines were calculated to choose representative spectrum of this particular column. It is worth mention that each spectral profile contains 15 wavebands and 5 of them namely band 100,101,102,103 and 104 were taken for SA calculation, where band 102 has water absorption. Once the test spectra have been collected from each of image column, next step was to match each of them with reference spectra. Reference spectra are the output from SQM model due to artificial shift caused to model sensors. The mechanism to construct reference spectrum has been discussed in Chapter 2, section 2.3. It is to mention here that resampled spectrum of SQM are known as reference spectrum.


44

Once the setup of test and reference spectra are done, the next stage comes to determine similarity between those spectra. The scale of measuring similarity between test and reference spectra is calculation of ‘Spectral Angle’ (SA) (Chapter 2, Section 2.5.3). The SQM model calculated amount of shift for 128 columns of SEBASS image. This shift per column which is smile is shown in figure-5.4.

Figure 5-4 Smile curve for SEBASS (Band 102)

5.5. Smile correction of SEBASS sensor

Smile correction was done on a pixel by pixel basis on a spectral and spatial subset of SEBASS image. The subset image had 124 columns, 500 lines and 10 bands. From smile calibration curve there is information about amount of shift per column of SEBASS image. The treatment for this particular column would be to shift the response functions of that column in the reverse direction the same amount shift it suffers. The smile correction procedures remain the same as Hyperion discussed in Chapter3, section 3.5. The new reflectance value of resampled spectrum after correction (after moving the response function as desired) was calculated for each pixel and stored in a 3D array through an automated program to re-write new image.


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Figure 5-5 Smile correction model for SEBASS; simulated response curve of

the SEBASS sensor (bottom), spline corrected image spectrum (middle), resampled spectrum (top) before (Thin blue line with open circle) and after

(Thick red line with asterisk mark) smile correction.

Figure 5-6 Close view of resampled spectrum in SCM for SEBASS; resampled

spectrum before (blue) and after (red) smile correction


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Figure-5.5 shows the set up and mechanism of SCM adapted to SEBASS and figure-5.6 shows close view of output part (i.e. resampled spectra before and after smile correction) of SCM.


Smile curve of SEBASS sensor of band 102 did not look like that of Hyperion; rather it looked like ‘wave’ shape. This ‘wave’ shape was consistent with the brightness gradient of SEBASS image. Same smile correction technique as Hyperion was applied to SEBASS.


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6. Validation and discussion

This chapter will be discussing the outcome of smile correction model (SCM) applied to existing Hyperion and SEBASS image and the following consequences on hyperspectral mapping.

6.1. Influence on Hyperion

As discussed in chapter 1, section 1.1, appearance of brightness gradient in MNF space or by image difference technique is the symptom of smile effect of a hyperspectral image. It is a pushbroom technology effect of the sensor. So removal of brightness gradient completely or partially is the testimony of success of smile correction technique. Information of smile effect per column of Hyperion image was obtained from SQM. Based on this information smile correction technique through SCM was applied to Hyperion image. Figure-5.1 shows appearance of brightness gradient in Hyperion image before (left) smile correction and absence of brightness gradient after (right) smile correction.

Figure 6-1Hyperion image before (left) and after (right) smile correction


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Removing brightness gradient is one aspect to show improvement achieved through new smile correction technique. More insight into internal image structure and quality is important to explore other aspects of improvement achieved after smile correction of Hyperion image. The concept of soft image classification was applied to the image to see influence of smile effect on Hyperion mapping. For this purpose a particular line of image containing 256 columns on a homogeneous area was taken. The homogeneity of the subset image was tested by calculating the mean standard deviation of reflectance value of all the bands. The calculated mean standard deviation value was 96.28 on a visually homogeneous area. On a visually heterogeneous area the value was 1000. It is to be mentioned that the image to be corrected was spectral and spatial subset containing 10 wavebands and 1000 lines.

Figure 6-2 Spectral angle mapping along a line of Hyperion image before smile correction

One pixel spectra was collected as reference spectrum from the centre column of Hyperion image before smile correction was performed. Along one single line of image on a homogeneous area 256 test spectra were collected and later matched with the only reference spectrum to calculate spectral angle for 256 test spectra. Fig-6.2 shows spectral angle mapping along a single line of Hyperion image on a homogeneous area before smile correction.

Fig-6.3 shows spectral angle mapping along a single line of Hyperion image on a homogeneous area after smile correction. From the concept of soft classification, if a threshold value of spectral angle between 0-1 is assigned to classify a pixel as a particular class, then from figure-6.2 it can be seen that all the pixels after column


49

200 will be exempted from this particular classification. In figure-6.3 the situation improved after smile correction and all the pixels up to column 248 can be brought into same particular classification.

Figure 6-3 Spectral angle mapping along a line of Hyperion image after smile correction

The improvement achieved through smile correction technique can be related to a particular field of application such as determination of red-edge position (REP) of vegetation. Guyot and Baret (1998) and Chao and Skidmore (2006) have shown correlation between chlorophyll content and red edge position and calculated R2 of 0.71 and 0.72 respectively. A shift in REP can easily change the information of amount of chlorophyll (mg/g). In the model of Chao and Skidmore (2006), smile effect of 2 nm can increase (When shift is ‘+’) or decrease (When shift is ‘-’) the amount of chlorophyll by 0.2 mg/g which is 20% of the total chlorophyll ranged from 2.8 to 3.8 mg/g. In Guyot and Baret (1998) model, smile effect of 1 nm can change the exact amount of chlorophyll by 40%. This difference is not worth neglecting. So people interested in vegetation will be undoubtedly benefitted while working with smile free Hyperion image.

6.2. Influence on SEBASS

After applying smile correction technique to SEBASS image, the condition of brightness gradient and spectral angle mapping was investigated. Figure-5.4 shows


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Figure 6-4 SEBASS image before (left) and after (right) smile correction

Figure 6-5 Spectral angle mapping along a line of SEBASS image before smile correction.


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the appearance of brightness gradient in SEBASS image before (left) smile correction and absence of brightness gradient after (right) smile correction. It is apparent from above figure-6.4 (right) that after smile correction not only brightness gradient disappeared but also the image became noisy. To see the effectiveness of smile correction technique spectral angle mapping was calculated along a single line of image and was plotted against a reference spectra pixel collected from middle column of SEBASS image. Fig-6.5 shows spectral angle mapping along a single line of SEBASS image on a homogeneous area before smile correction. Values of spectral angle vary along the width of the image consistent with the wavy smile curve determined by SQM adapted to SEBASS (Chapter 5, figure-5.4). Fig-6.6 shows spectral angle mapping along a single line of SEBASS image on a homogeneous area after smile correction. The plotting of spectral angle along the width of image seemed to have created random noise instead of showing any regular pattern or coming into a horizontal line to show improvement in smile correction. There might be several reasons behind this incident. Firstly, smile correction technique might have removed only the systematic gradient error caused by smile effect.

Figure 6-6 Spectral angle mapping along a line of SEBASS image after smile correction

The reason might be inadequate depth of water absorption feature and its influence on the sensitivity of resampled spectra. It pointed to the ineffectiveness of spline corrected image spectrum for SEBASS when the absorption feature is not as prominent as oxygen absorption of Hyperion. When systematic error is removed from total noise, then only random noise get exposed which is caused by sensor


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noise due to lack of sensor’s sensitivity. Second reason might be the presence of the 12541 nm water absorption feature, which scatters light and makes the image look noisy. The last reason might be the coarser resolution MODTRAN 4 data in thermal infrared region. This results in an inadequate simulation of the depth of the water absorption feature which influences the sensitivity of SCM. Chapter 4, figure-4.3 discussed how different resolution MODTRAN 4 data influenced smile curve of Hyperion. It was noticeable that due to different resolution of MODTRAN 4 data the shapes of smile curves were almost same but there were remarkable absolute vertical shift among them. From the experience of Hyperion it can be said that although the shape of smile curve for SEBASS was consistent with its brightness gradient, the actual smile model might be somewhere else (most probably vertically upward) due to coarse MODTRAN 4 data.

Many minerals such as quartz, feldspar and chalcedony cannot be always mapped uniquely with VNIR/SWIR hyperspectral data. But they can be identified easily with SEBASS data (Vaughan et al., 2003). SEBASS spectral bandwidth is critical for differentiating mineral species such as calcite vs. dolomite and identifying mixed minerals such as feldspar and gypsum. It is believed that up-to-date smile information of SEBASS and its correction would definitely increase the accuracy of mineral classification.


Smile correction technique has removed brightness gradient and improved hyperspectral mapping for Hyperion image. In case of SEBASS image, smile correction technique removed brightness gradient but also the image became noisy. The reasons could be sensor’s sensitivity noise, scattering noise form water absorption, coarser resolution MODTRAN 4 data in TIR or ineffectiveness of spline corrected image spectrum.


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7. Conclusion and recommendation

7.1. Summary

Quantification of smile effect per column of Hyperion image was done successfully with the SQM. It produced a curving pattern smile model for Hyperion which was slightly different from pre-launch calibration. This is in consistent with available literatures suggesting pre-launch and post-launch difference in smile calibration model. Pearlman et al. (2003) and Khurshid et al. (2006) have shown with enough evidence that pre-launch and post-launch smile calibration of Hyperion differs up to 2 nm for various bands. The objective to develop SQM was to get up-to-date information of smile effect to correct the problem instead of looking into pre-launch calibration. The smile correction technique which assumes a spline interpolated surface to approximate exact spectrum was effective on spectral (10 bands) and spatial (1000 lines) subset of Hyperion image. In this research SQM model only calculated smile curve of band 41. Later smile information of this band was assigned to the surrounding bands to correct smile problem. After gaining confidence on Hyperion platform, SQM was adapted to SEBASS sensor. It was challenging in the sense that no information exists about smile problem of SEBASS. The smile calibration curve of SEBASS looked like a ‘wave’ shape. The justification of this ‘wave’ shape is its consistency with brightness gradient of SEBASS image in MNF space. The same smile correction technique as Hyperion was applied to SEBASS. But the outcome of this correction technique did not exhibit desired improvement.

7.2. Conclusion

• Smile effect i.e. shift in central wavelength of band 41 of Hyperion image

varies like smooth curving pattern (Chapter 3, Fig-3.4) while smile effect of


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band 102 of SEBASS image varies like ‘wave’ shape along the width of the image (Chapter 5, figure-5.4).

• Each spectral product such as slope, asymmetry and spectral angle has characteristic relationship with amount of shift (Chapter 2, Fig-2.7, Fig-2.9 and Fig-2.11).

• The magnitude of spectral angle was taken as indicator to determine similarity between real image spectrum and resampled spectrum (Chapter 2, section 2.5.4). Amount of shift for a particular Hyperion image column was determined from the best matched resampled spectrum.

• SQM components were adapted to SEBASS by simulating spectral response function to SEBASS channel width, atmospheric absorption as water absorption around 12541.4 nm and region of atmospheric window in TIR (Chapter 5).

• SQM produces smile curve as accurately as to distinguish it from existing pre-launch calibration within the limit of acceptable deviation supported by existing literatures (Chapter 3, Fig-3.5).

• After applying correction technique hyperspectral mapping improved for Hyperion. Correction of 1 nm smile problem can improve chlorophyll concentration (mg/g) in vegetation from 20% to 40% depending on the model used to estimate chlorophyll from reflectance spectra and the vegetation type to which it is applied.

• For SEBASS, correction technique reduced brightness gradient but did not clearly improve hyperspectral mapping (Chapter 6, section 6.1 and 6.2). The reasons could be sensor’s sensitivity noise, scattering noise form water absorption, coarser resolution MODTRAN 4 data in TIR or ineffectiveness of spline corrected image spectrum.

7.3. Recommendation

• Smile calibration curve for more than one band over the entire wavelength range needs to be quantified by SQM model to get the exact impression of smile behaviour of the hyperspectral image.

• Smile correction technique based on spline interpolation is not the best choice when atmospheric feature is not prominent. Some more advanced and robust interpolation technique such as thin-plate spline, adaptive


55

normalized convolution and discrete fourier transformation can be applied in smile correction model (SCM).

• Coarse resolution MODTRAN 4 data in thermal infrared region was a

problem for SQM model during its adaptation to SEBASS. Newly released MODTRAN 5 data can be used as it has got 10 times higher resolution than the previous version.


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References

Cairns, B., Carlson, B.E., Ruoxian, Y., Lacis, A.A. and Oinas, V., “Atmospheric correction and its application to an analysis of Hyperion data”, IEEE Trans. Geosci. Remote Sensing, vol. 41, No. 6, June 2003, pp.1232-1245 Chao, M.A. and Skidmore, A.K., “A new technique for extracting the red edge position from hyperspectral data: the linear extrapolation method”. Remote Sensing of the Environment, Vol. 101, 2006, pp. 181-193. Clevers, J.G.P.W., De Jong, S.M., Epema, G.F., Van der Meer, F., Bakker W.H., Skidmore, A.K., Scholte, K.H., “Derivation of the red edge index using MERIS standard band setting”. International Journal of Remote sensing, vol.23, No. 16, August 2002, pp. 3169-3184. Green, A.A., Berman, M., Switzer, P. and Craig, M.D., “A transformation for ordering multispectral data in terms of image quality with implications for noise removal,” IEEE Trans. Geosci. Remote Sensing, Vol. 26, No. 1, January 1988, pp. 65–74. Goodenough, D.G., Dyk, A., Niemann, K.O., Pearlman, J.S., Hao Chen, Han, T., Murdoch, M., and West, C., “Processing Hyperion and ALI for Forest Classification”, IEEE Trans. Geosci. Remote Sensing, Vol. 41, No. 6, June 2003, pp. 1321-1331 Guyot, G. and Baret, F, “Utilisation de la haute resolution spectrale pour suivre l'tetat des couverts vegetaux”, Proceedings 4th International Colloquium on Spectral Signatures of Objects in remote sensing, 1988,Aussois,France. Hackwell, J. A., Warren, D. W., Bongiovi, R. P., Hansel, S. J., Hayhurst, T. L., Mabry, D. J., Sivjee, M. G., & Skinner, J. W., “LWIR/MWIR imaging hyperspectral sensor for airborne and ground-based remote sensing”. Proc. SPIE, Vol. 2819, Nov. 1996, pp. 102– 107.


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Horler, D.N.H., Dockray, M. and Barber, J., “The red edge of plant leaf reflectance”. International Journal of remote Sensing, 1983a, Vol. 4, No. 2, pp. 273-288. Jupp, D.L.B, B. Datt, J. Lovell, S.Campbell, E.A. King, et al. (2002) “Discussions around Hyperion Data: Background Notes for the Hyperion Data users Workshop”, CSIRO Earth Observation Centre, Canberra. Khurshid, K.S., Staenz, K., Sun, L., Neville, R., White, H.P., Bannari, A., Champagne, C.M. and Hitchcock, R., “Pre-processing of EO-1 Hyperion data”, Can. J. Remote Sensing, Vol. 32, No. 2, 2006, pp. 84-97. Kruse, F.A., Boardman, J.W., Lefkoff, A.B., Heidebrecht, K.B., Shapiro, A.T., Barloon, P.J., and Goetz, A.F.H. (1993). “The Spectral Image Processing System (SIPS) – Interactive Visualization and Analysis of Imaging Spectrometer Data”. Remote Sensing of Environment, Vol. 44, p.145-163. Liao, L., Jarecke, P., Gleichauf, D. and Hedman, T., “Performance characterization of the Hyperion imaging spectrometer instrument”, Proceedings of the SPIE, Vol. 4135, 2000, pp. 264-275. Pearlman, J.S., Barry, P.S., Segal, C.C., Shepanski, J., Beiso, D. and Carman, S.L., “Hyperion, a space-based imaging spectrometer”, IEEE Trans. Geosci. Remote Sensing, Vol. 41, No. 6, June 2003, pp. 1160-1173. Qu, Z., B.C. Kindel, A.F.H. Goetz, 2003, The High Accuracy Atmospheric Correction for Hyperspectral Data (HATCH) Model, IEEE Transactions on Geoscience and Remote Sensing, vol.41, 1223-1231.

Van der Meer, F., Vasquez-Torres, M., and Van Dijk, P.M., “Spectral Characterization of Ophiolite Lithologies in the Troodos Ophiolite Complex of Cyprus and its Potential in Prospecting for Massive Sulphide Deposits”. International Journal of Remote Sensing, 1997, Vol. 18, No.6, p. 1245-1257.

Vaughan, R.G., Calvin, W.M. and Taranik, J.V., “SEBASS hyperspectral thermal infrared data: surface emissivity measurement and mineral mapping”, Remote Sensing of Environment, 2003, Vol. 85, pp. 48-63.


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Appendices

Appendix –A ( MATLAB code of general SQM )

x= 672:0.5:842; % Width of atmospheric window n=length(x); % length of vector x y2=3500:-57:1200; % Declaration of synthetic dat a y3=1257:57:3500; y1 = ones(1,138)*3500; y4 = ones(1,122)*3500; y = [y1,y2,y3,y4]; % combining vectors into one length(y); % Length of vector y subplot(3,1,2), % sub plot window plot(x,y) hold on t=zeros(15,61); % Declaration of reference spe ctra x1=zeros(1,n); for m = 0:1:60 % Loop to produce 60 reference spectra x1= m*0.1:0.5:170+m*0.1; z=zeros(1,n); % declaration of one response function v=zeros(n,15); % declaration of 15 response f unction for j=1:15 for i=1:n z(i)=exp(-((x1(i)/6)- (1.67*j))^2); % equation f or FWHM Gaussian end % curve v(:,j)=z; end for k=1:15 % Loop to plot 15 response funct ion subplot(3,1,3), plot(x1,v(:,k)) hold on end % End of loop a=zeros(1,15); % Declaration of resampled spect ra for i = 1:15 % Loop to calculate each resampl ed spectrum a(i)=y*v(:,i);% Dot product between response functi on and end % high resolution data x2=692:10:816; % Declaration of x axis for resa mpled spectra subplot (3,1,1), plot((x2),a(:,2:end-1)/74443*3450) hold on subplot(3,1,1), plot((x2),a(:,2:end-1)/74443*3450,'ro') t(:,1+m)=a/74443*3450; % Transferring value to refe rence spectra % matrix end % End of loop


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Appendix-B ( MATLAB code for SQM adaptation to Hyperion )

I=imread('subset_1.tif'); % To read the image to quantify smile aimg=zeros(10,256,5); % Declaration of 3D ar ray for j=1:256 % Loop through the col umn for i=1:10 % Loop through the lin es aimg(i,j,:)=I(i,j,6:10); % transferring value end % End of second loop end % End of first loop k=zeros(256,5); % Declaration of 2D ma trix for i=1:256 % Loop through columns b=reshape(aimg(1:10,i,:),10,5,1); % transform 3D in to 1D k(i,:)=mean(b(:,1:5)); % Calculation of mean end % End of loop L=k'; % transpose of matrix k %---------------------------------------------------------------------------------------------------------------- x=670:.1:860; % Declaration of atmos pheric window n=length(x); % Length of x G=load('new_ydata.txt'); % Loading ascii file y=G(:,2); % Extract column 2 z=zeros(1,n); % declaration of respo nse function v=zeros(n,15); t1=zeros(15,201); % Reference spectra du e to positive shift t2=zeros(15,201); % Reference spectra du e to negative shift for m=0:1:200 % Loop for causing po sitive shift x1=670+m*0.1:.1:860+m*0.1; for j=1:15 % loop through each re sponse function for i = 1:n % loop to construct Ga ussian y values z(i)= exp(-(x1(i)/6.11-(111.46+2*j*0.834))^2);% main equation end % end of loop v(:,j)= z; end % end of loop a=zeros(1,15); % declaration of resam pled spectra for i = 1:15 % loop through respons e function a(i)=y'*v(:,i); % calculating scalar p roduct end % End of loop rua=max(a); % determine maximum of a t1(:,1+m)=a/rua*3400; % Value transferring a nd rescaling


60

end % End of loop M1=t1(6:end-5,:); % Extracting only five bands

%-------------------------------------------------- ---------

for m=0:-1:-200 %loop for negative shi ft x1=670+m*0.1:.1:860+m*0.1; for j=1:15 %loop through response function for i = 1:n %loop through Gaussian points z(i)= exp(-(x1(i)/6.11-(111.46+2*j*0.834))^2); % Main equation end % end of loop v(:,j)= z; end % end of loop a1=zeros(1,15); % declaration of resam pled spectra % for negative shifts for i = 1:15 % loop through respons e function a1(i)=y'*v(:,i); % calculating scalar p roduct end % end of loop t2(:,1-m)=a1/86*3400; % Value transferring a nd rescaling end % End of loop M2=t2(6:end-5,:); % extracting only five bands M3=M2(:,2:end); % protecting duplicate of zero shift M4=fliplr(M3); % flipping left to rig ht M=[M4,M1]; % combining into one m atrix size(M); % size of M matrix theta=zeros(256,401); % declaration of SA in degree w=zeros(256,401); % declaration of SA in radian for r=1:256 % loop through columns for i=1:401 % loop through referen ce spectra alpha=sqrt(sum(M(:,i).*M(:,i))); % multiplication o f reference spectra beta=M(:,i)/alpha; % absolute value of re ference spectra chi=sqrt(sum(L(:,r).*L(:,r))); % multiplication of test spectra phi=L(:,r)/chi; % absolute value of te st spectra theta(r,i)=acos(sum(beta.*phi)); % calculation of S A theta; w(r,i)=(theta(r,i)*180/pi); % SA in degree end % end of first loop end % end of second loop [value,pos]=min(w'); % locating position of best matched % spectrum f=-20:0.1:20; indp=1:401; % declaration of index ing for i=1:401 % loop through index


61

indp(i)=f(i); % separation of ‘+’ an d ‘-’ index end % end of loop shift=zeros(1,256); % declaration of 1D ar ray for i=1:256 % loop through columns q=pos(i); % determine position shift(i)=indp(q); % corresponding shift end % end of loop fid=fopen('smile_cali.txt','wt'); % writing new tex t file for i=1:256 % loop through co lumn col(i)=i; fprintf(fid,'%6.2f %12.2f\n',col(i),shift(i)); % command to write % shift and column end % end of loop fclose(fid) % file close


62

Appendix-C ( MATLAB code for SQM adaptation to SEBASS )

I=imread('seabass1.tif'); % read image to quantif y smile % for SEBASS aimg=zeros(10,128,9); % 3D array declaration for j=1:128 % loop through column for i=1:10 % loop through line aimg(i,j,:)=I(i,j,4:12); % transfer value end % end of loop end % end of loop k=zeros(128,9); % declaration of 2D mat rix for i=1:128 % loop through columns b=reshape(aimg(1:10,i,:),10,9,1);% transforming int o 2D k(i,:)=mean(b(:,1:9)); % mean of waveband end % end of loop L=k'; % transpose of k matrix %-------------------------------------------------- --------- x=12138.6:1:12888.6; % atmospheric window in TIR n=length(x); % length of x G=load('new_102.txt'); % read ascii file y=G(:,2); % extract MODTRAN data length(y) % length of y z=zeros(1,n); % declaration RF for m = 0:1:200 % loop to cause positiv e shift x1=12138.6+m*0.1:1:12888.6+m*0.1; v=zeros(n,15); % matrix for 15 RF for j=1:15 % loop through RFs for i = 1:n z(i)= exp(-(x1(i)/23.7-(515.8+2*j*0.834))^2); end v(:,j)= z; end % end of loop a=zeros(1,15); % declaration of resamp led spectra for i = 1:15 a(i)=y'*v(:,i); % scalar product end t1(:,1+m)=a/23.94*1079.5; % transfer to matrix end % end of loop M1=t1(4:end-3,:); % transferring into mat rix


63

%-------------------------------------------------- ------ for m=0:-1:-200 % loop to cause negativ e shift x1=12138.6+m*0.1:1:12888.6+m*0.1; v1=zeros(n,15); % matrix for 15 RF for j=1:15 % loop through RFs for i = 1:n z(i)= exp(-(x1(i)/23.7-(515.8+2*j*0.834))^2); end % end of loop v1(:,j)= z; end % end of loop a1=zeros(1,15); % declaration of resampl ed spectra for i = 1:15 % loop through RFs a1(i)=y'*v1(:,i); % scalar product end % end of loop a1; t2(:,1-m)=a1/23.94*1079.5; % transfer to reference spectra end % end of loop M2=t2(4:end-3,:); % extracting desired ban ds M3=M2(:,2:end); % protect duplicate zero shift M4=fliplr(M3); % flipping left to right M=[M4,M1]; % combine into matrix M; size(M); theta=zeros(128,401);%(961)% declaration of SA in d egeree w=zeros(128,401); % declaration of AS in r adian for r=1:128 % loop through columns for i=1:401 % loop through reference spectra alpha=sqrt(sum(M(:,i).*M(:,i))); beta=M(:,i)/alpha; % absolute value of refe rence spectra chi=sqrt(sum(L(:,r).*L(:,r))); % multiplication of image spectra phi=L(:,r)/chi; % absolute value of real spectra theta(r,i)=acos(sum(beta.*phi)); % SA in radians theta; w(r,i)=(theta(r,i)*180/pi); % SA in degree end % end of loop end % end of loop [value,pos]=min(w'); % locating position of best matched % spectrum f=-20:0.1:20; indp=1:401; % declaration of index ing for i=1:401 % loop through index indp(i)=f(i); end % end of loop shift=zeros(1,128); % declaration of 1D a rray


64

for i=1:128 % loop through column s q=pos(i); % determine position shift(i)=indp(q); % corresponding shift end % end of loop

fid=fopen('sebass_cali_1.txt','wt'); % writing new file for i=1:124 col(i)=i; fprintf(fid,'%6.2f %12.2f\n',col(i),shift(i)); end % end of loop fclose(fid) % close of file


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Appendix-D ( Smile correction model for Hyperion )

I=imread('sub_hypw1.tif'); % image read for correct ion aimg=zeros (1000,256,10); % declaration of 3D arr ay for i=1:1000 % loop through lines of image for j= 1:256 % loop through columns aimg(i,j,:)=I(i,j,1:10); % transferring value end % end of loop end % end of loop reposit=zeros(1000,256,10);% declaration of correct ed image for t=1:1000 % loop through the lines b=reshape(aimg(t,:,:),10,256,1); % transforming 3D to 2D c=[711.5 721.86 731.98 742.1 752.4 762.6 772.72 782 .84 793.2 803.33]; % center wavelength of 10 wavebands smfile= load ('auto_cali.txt'); % read smile calibr ation file sm=smfile(:,2); % extract column 2 s=zeros(256,1); % declaration shift v ector c1=zeros(256,10); % shift for 10 bands for l= 1:256 % loop through column s(l)=sm(l); % transferring shift c1(l,:)=c-s(l); end % end of loop %-------------------------------------------------- --------------

H=load('hyp_cor.txt'); % read ascii file xx=H(:,1); % read spline interpo lated surface length(xx); % length of xx vector xx1=zeros(751,256); % declaration for 256 columns for l=1:256 % loop through column s xx1(:,l)= xx-s(l); % shift of response f unction end % end of loop yy=zeros(751,256); % declaration spline correction surface for l=1:256 % loop through column s yy(:,l)=spline(c,b(:,l),xx); % spline interpolatio n end % end of loop

x1=670:.253:860; % atmospheric window n=length(x1); % length of window z=zeros(1,n); % vector of one RF


66

v=zeros(n,15); % matrix of 15 RF for j=1:15 % loop through 15 RF for i = 1:n z(i)= exp(-(x1(i)/6.11-(111.46+2*j*0.834))^2); % main equation end % end of loop v(:,j)= z; end % end of loop a=zeros(256,15); % resampled spectral f or 256 columns for l=1:256 % loop through columns for i = 1:15 % loop through RFs a(l,i)=yy(:,l)'*v(:,i); % scalar product end % end of loop end % end of loop a; quar=max(a'); % maximum of a transpo se bfsm = zeros(256,10); % reflectance before c orrection for l=1:256 % loop through columns bfsm(l,:) = a(l,3:12)/quar(:,l)*max(b(:,l)); % scal ar product end % end of loop m=zeros(256,1); % smile effect declara tion afcor=zeros(256,10); % reflectance after co rrection z2=zeros(1,n); for l=1:256 % loop through columns m=-sm(l); x1=670+m:.253:860+m; % shift of RF v2=zeros(n,15); for j=1:15 % loop through RF for i = 1:n z2(i)= exp(-(x1(i)/6.11-(111.46+2*j*0.834))^2); % main equation end % end of loop v2(:,j)=z2; end % end of loop a1=zeros(256,15); % declaration of corre cted reflectance for l=1:256 % loop through columns for i = 1:15 a1(l,i)=yy(:,l)'*v2(:,i);% scalar product end % end of loop end % end of loop a1; afcor(l,:) = a1(l,3:12)/quar(:,l)*max(b(:,l)); % co rrected reflectance end difference=zeros(256,10); % change in reflectanc e keep=zeros(256,10); % matrix for new value for l=1:256 % loop through columns difference(l,:)= afcor(l,:)-bfsm(l,:);% change in r eflectance keep(l,:)= difference(l,:); % storage of new value


67

reposit(t,:,:)=keep; % write new image end % end of loop end % end of loop cant1=reposit(:,:,1); save 1layer.txt cant1 -ascii cant2=reposit(:,:,2); save 2layer.txt cant2 -ascii cant3=reposit(:,:,3); save 3layer.txt cant3 -ascii cant4=reposit(:,:,4); save 4layer.txt cant4 -ascii cant5=reposit(:,:,5); save 5layer.txt cant5 -ascii cant6=reposit(:,:,6); save 6layer.txt cant6 -ascii cant7=reposit(:,:,7); save 7layer.txt cant7 -ascii cant8=reposit(:,:,8); save 8layer.txt cant8 -ascii cant9=reposit(:,:,9); save 9layer.txt cant9 -ascii cant10=reposit(:,:,10); save 10layer.txt cant10 -ascii


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Appendix-E ( Smile correction model for SEBASS )

I=imread('124seab.tif'); % image read for correc tion aimg=zeros(500,124,10); % declaration of 3D arr ay for i=1:500 % loop through lines for j= 1:124 % loop through columns aimg(i,j,:)=I(i,j,1:10); % transfer value end % end of loop end % end of loop reposit=zeros(500,124,10); % declaration of correc t image for t=1:500 % loop through lines b=reshape(aimg(t,:,:),10,124,1); % transform into 2 D matrix c=[ 12343.9 12383.7 12423.3 12462.8 12502.1 12541.4 12580.5 12619.5 12658.3 12697 ]; % center wavelength of 10 bands smfile= load('sebass_cali.txt'); % read smile calib ration file sm=smfile(:,2); % extract shift column s=zeros(124,1); % declaration shift ve ctor c1=zeros(124,10); for l= 1:124 % loop through columns s(l)=sm(l); c1(l,:)=c-s(l); end % end of loop H=load('sea_102.txt'); % read ascii file xx=H(:,1); % read spline surface length(xx); % length of xx xx1=zeros(751,124); % exact spectra for 12 4 columns for l=1:124 % loop through columns xx1(:,l)= xx-s(l); % shift in RF end % end of loop yy=zeros(751,124); % declaration spline c orrection % surface for l=1:124 % loop through columns yy(:,l)=spline(c,b(:,l),xx); % spline interpolation end % end of loop %-------------------------------- x1=12138.6:1:12888.6; % atmospheric window i n TIR n=length(x1); % length of x1 z=zeros(1,n); % declaration one RF v=zeros(n,15); % declaration 15 RFs


69

for j=1:15 % loop through for i = 1:n z(i)= exp(-(x1(i)/23.7-(515.8+2*j*0.834))^2); end v(:,j)= z; end % end of loop a=zeros(124,15); % matrix declaration fo r resampled % spectra for l=1:124 % loop through column for i = 1:15 % loop through a(l,i)=yy(:,l)'*v(:,i); % scalar product end % end of loop end % end of loop quar=max(a'); % maximum of a transpos e bfsm = zeros(124,10); % reflectance before co rrection for l=1:124 % loop through columns bfsm(l,:) = a(l,3:12)/quar(:,l)*max(b(:,l)); % scal ar product end % end of loop %------------------------------------------------ v2=zeros(n,15); % declaration of RFs m=zeros(124,1); z2=zeros(1,n); afcor=zeros(124,10); % reflectance declarati on for l=1:124 % loop through columns m=-sm(l); x1=12138.6+m:1:12888.6+m; % shift in RFs for j=1:15 for i = 1:n z2(i)= exp(-(x1(i)/23.7-(515.8+2*j*0.834))^2); end v2(:,j)= z2; end % end in loop a1=zeros(124,15); % resampled spectra for all columns for l=1:124 % loop through columns for i = 1:15 % loop through RFs a1(l,i)=yy(:,l)'*v2(:,i); % scalar product end % end of loop end % end of loop afcor(l,:) = a1(l,3:12)/quar(:,l)*max(b(:,l)); % sc alar product end % end of loop difference=zeros(124,10); % change in new reflect ance keep=zeros(124,10); % new reflectance for l=1:124 % loop through columns difference(l,:)= afcor(l,:)-bfsm(l,:); keep(l,:)= difference(l,:); % storage of new reflec tance reposit(t,:,:)=keep; % new image end % end of loop end % end of loop


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cant1=reposit(:,:,1); save 1layer.txt cant1 -ascii cant2=reposit(:,:,2); save 2layer.txt cant2 -ascii cant3=reposit(:,:,3); save 3layer.txt cant3 -ascii cant4=reposit(:,:,4); save 4layer.txt cant4 -ascii cant5=reposit(:,:,5); save 5layer.txt cant5 -ascii cant6=reposit(:,:,6); save 6layer.txt cant6 -ascii cant7=reposit(:,:,7); save 7layer.txt cant7 -ascii cant8=reposit(:,:,8); save 8layer.txt cant8 -ascii cant9=reposit(:,:,9); save 9layer.txt cant9 -ascii cant10=reposit(:,:,10); save 10layer.txt cant10 -ascii


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Appendix-F ( Amount of shift per column of Hyperion )

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

1 -0.1 52 -0.5 103 -0.6 154 -0.2 205 0.5 2 -0.1 53 -0.5 104 -0.6 155 -0.2 206 0.5 3 -0.1 54 -0.5 105 -0.6 156 -0.2 207 0.5 4 -0.1 55 -0.6 106 -0.6 157 -0.1 208 0.6 5 -0.1 56 -0.5 107 -0.5 158 -0.1 209 0.6 6 -0.1 57 -0.5 108 -0.6 159 -0.1 210 0.6 7 -0.2 58 -0.5 109 -0.5 160 -0.1 211 0.7 8 -0.1 59 -0.6 110 -0.5 161 -0.2 212 0.6 9 -0.2 60 -0.5 111 -0.5 162 -0.1 213 0.7

10 -0.2 61 -0.6 112 -0.6 163 -0.1 214 0.6 11 -0.2 62 -0.5 113 -0.5 164 -0.1 215 0.7 12 -0.1 63 -0.5 114 -0.6 165 -0.1 216 0.8 13 -0.2 64 -0.6 115 -0.5 166 0.0 217 0.8 14 -0.2 65 -0.5 116 -0.5 167 0.0 218 0.8 15 -0.1 66 -0.6 117 -0.5 168 0.0 219 0.8 16 -0.2 67 -0.6 118 -0.6 169 0.0 220 0.8 17 -0.3 68 -0.6 119 -0.5 170 0.0 221 0.9 18 -0.2 69 -0.6 120 -0.5 171 -0.1 222 0.9 19 -0.2 70 -0.7 121 -0.5 172 0.0 223 0.9 20 -0.2 71 -0.6 122 -0.5 173 0.0 224 0.9 21 -0.2 72 -0.6 123 -0.5 174 0.0 225 1.0 22 -0.3 73 -0.6 124 -0.5 175 0.0 226 1.0 23 -0.3 74 -0.6 125 -0.5 176 0.1 227 1.0 24 -0.3 75 -0.6 126 -0.4 177 0.2 228 1.0 25 -0.3 76 -0.5 127 -0.4 178 0.1 229 1.1 26 -0.3 77 -0.6 128 -0.4 179 0.0 230 1.1 27 -0.3 78 -0.6 129 -0.5 180 0.1 231 1.1 28 -0.3 79 -0.6 130 -0.4 181 0.1 232 1.1 29 -0.4 80 -0.6 131 -0.5 182 0.1 233 1.2 30 -0.4 81 -0.6 132 -0.4 183 0.1 234 1.3 31 -0.4 82 -0.6 133 -0.5 184 0.2 235 1.3 32 -0.4 83 -0.6 134 -0.4 185 0.2 236 1.3


72

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

33 -0.4 84 -0.6 135 -0.4 186 0.1 237 1.3 34 -0.4 85 -0.6 136 -0.3 187 0.2 238 1.4 35 -0.4 86 -0.7 137 -0.3 188 0.2 239 1.5 36 -0.5 87 -0.6 138 -0.4 189 0.2 240 1.4 37 -0.4 88 -0.6 139 -0.3 190 0.2 241 1.6 38 -0.4 89 -0.6 140 -0.3 191 0.3 242 1.6 39 -0.4 90 -0.6 141 -0.4 192 0.3 243 1.6 40 -0.4 91 -0.6 142 -0.3 193 0.3 244 1.6 41 -0.4 92 -0.6 143 -0.3 194 0.3 245 1.7 42 -0.4 93 -0.6 144 -0.3 195 0.3 246 1.7 43 -0.4 94 -0.5 145 -0.3 196 0.3 247 1.7 44 -0.4 95 -0.6 146 -0.3 197 0.4 248 1.8 45 -0.4 96 -0.6 147 -0.3 198 0.4 249 1.9 46 -0.4 97 -0.6 148 -0.3 199 0.4 250 1.9 47 -0.5 98 -0.5 149 -0.2 200 0.4 251 2.0 48 -0.5 99 -0.6 150 -0.2 201 0.4 252 2.0 49 -0.5 100 -0.6 151 -0.2 202 0.4 253 2.1 50 -0.5 101 -0.6 152 -0.3 203 0.4 254 2.0 51 -0.5 102 -0.6 153 -0.3 204 0.5 255 2.1 256 2.2


73

Appendix-G (Amount of shift per column of SEBASS)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

Col

umn

Shi

ft (n

m)

1 -1.1 27 -3.1 53 -1.8 79 -2.3 105 -3.2 2 -1.3 28 -3 54 -1.8 80 -2.4 106 -3.2 3 -1.4 29 -3 55 -1.8 81 -2.4 107 -3.1 4 -1.6 30 -3 56 -1.8 82 -2.5 108 -3 5 -1.8 31 -2.9 57 -1.8 83 -2.6 109 -2.9 6 -2 32 -2.9 58 -1.8 84 -2.6 110 -2.8 7 -2.1 33 -2.8 59 -1.8 85 -2.7 111 -2.7 8 -2.3 34 -2.7 60 -1.7 86 -2.7 112 -2.6 9 -2.5 35 -2.6 61 -1.7 87 -2.8 113 -2.5

10 -2.6 36 -2.6 62 -1.7 88 -2.9 114 -2.3 11 -2.7 37 -2.5 63 -1.7 89 -2.9 115 -2.2 12 -2.8 38 -2.4 64 -1.7 90 -3 116 -2 13 -2.9 39 -2.4 65 -1.7 91 -3.1 117 -1.9 14 -3 40 -2.4 66 -1.8 92 -3.1 118 -1.7 15 -3.1 41 -2.3 67 -2 93 -3.2 119 -1.5 16 -3.1 42 -2.2 68 -2 94 -3.2 120 -1.4 17 -3.2 43 -2.2 69 -2 95 -3.2 121 -1.2 18 -3.2 44 -2.1 70 -2 96 -3.2 122 -1.1 19 -3.3 45 -2.1 71 -2.1 97 -3.3 123 -0.9 20 -3.3 46 -2.1 72 -2.1 98 -3.3 124 -0.8 21 -3.2 47 -2 73 -2.1 99 -3.3 125 -0.8 22 -3.3 48 -2 74 -2.1 100 -3.3 126 -0.7 23 -3.2 49 -2 75 -2.2 101 -3.3 127 -0.6 24 -3.2 50 -1.9 76 -2.2 102 -3.3 128 -0.5 25 -3.2 51 -1.9 77 -2.3 103 -3.3 26 -3.1 52 -1.8 78 -2.3 104 -3.3

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