john r. jensen department of geography university of south carolina columbia, south carolina 29208

John R. JensenJohn R. JensenDepartment of GeographyDepartment of Geography

University of South CarolinaUniversity of South CarolinaColumbia, South Carolina 29208Columbia, South Carolina 29208

Image Preprocessing:Image Preprocessing: Radiometric and Geometric CorrectionRadiometric and Geometric Correction

Jensen 2003Jensen 2003

Image Preprocessing: Image Preprocessing: Radiometric CorrectionRadiometric Correction


Solar and Heliospheric Observatory (SOHO)Solar and Heliospheric Observatory (SOHO)Image of the Sun Obtained on September 14, 1999Image of the Sun Obtained on September 14, 1999


Sources of Electromagnetic EnergySources of Electromagnetic Energy

Thermonuclear fusion on the surface of the Sun yields a continuous spectrum of electromagnetic Thermonuclear fusion on the surface of the Sun yields a continuous spectrum of electromagnetic energy. The 6,000 K temperature of this process produces a large amount of short wavelength energy energy. The 6,000 K temperature of this process produces a large amount of short wavelength energy (from 0.4 - 0.7 (from 0.4 - 0.7 m; blue, green, and red light) that travels through the vacuum of space at the speed of m; blue, green, and red light) that travels through the vacuum of space at the speed of light. Some energy is intercepted by the Earth where it interacts with the atmosphere and surface light. Some energy is intercepted by the Earth where it interacts with the atmosphere and surface materials. The Earth may reflect some of the energy directly back out to space or it may absorb the materials. The Earth may reflect some of the energy directly back out to space or it may absorb the short wavelength energy and then re-emit it at a longer wavelength. short wavelength energy and then re-emit it at a longer wavelength.


Blackbody Radiation Blackbody Radiation CurvesCurves

Blackbody radiation curves for several Blackbody radiation curves for several objects including the Sun and the Earth objects including the Sun and the Earth which approximate 6,000 K and 300 K which approximate 6,000 K and 300 K blackbodies, respectively. Notice that as blackbodies, respectively. Notice that as the temperature of the object increases, the temperature of the object increases, its dominant wavelength shifts toward its dominant wavelength shifts toward the short wavelength portion of the the short wavelength portion of the spectrum.spectrum.


Radiant Intensity Radiant Intensity of the Sunof the Sun

The Sun approximates a 6,000 K The Sun approximates a 6,000 K blackbody with a dominant blackbody with a dominant wavelength of 0.5 wavelength of 0.5 m (green light). m (green light). Earth approximates a 300 K Earth approximates a 300 K blackbody with a dominant blackbody with a dominant wavelength of 9.7 wavelength of 9.7 m . The 6,000 K m . The 6,000 K Sun produces 41% of its energy in Sun produces 41% of its energy in the visible region from 0.4 - 0.7 the visible region from 0.4 - 0.7 m m (blue, green, and red light). The other (blue, green, and red light). The other 59% of the energy is in wavelengths 59% of the energy is in wavelengths shorter than blue light (<0.4 shorter than blue light (<0.4 m) and m) and longer than red light (>0.7 longer than red light (>0.7 m). Eyes m). Eyes are only sensitive to light from the are only sensitive to light from the 0.4 to 0.7 0.4 to 0.7 m. Remote sensor m. Remote sensor detectors can be made sensitive to detectors can be made sensitive to energy in the non-visible regions of energy in the non-visible regions of the spectrum.the spectrum.


Electromagnetic Electromagnetic SpectrumSpectrum

The Sun produces a The Sun produces a continuous spectrum of energy continuous spectrum of energy from gamma rays to radio from gamma rays to radio waves. The visible portion of waves. The visible portion of the spectrum may be the spectrum may be measured using wavelength measured using wavelength (measured in nanometers or (measured in nanometers or micrometers, i.e. nm or micrometers, i.e. nm or m) m) or electron volts (eV) or electron volts (eV) terminology. All units are terminology. All units are interchangeable.interchangeable.

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

violet limit

blue

green limit yellow orange red

Photon energy of visible light in

electron volts (eV) Photon wavelength in nanometers (nm)

400

450

550 580 600 650

10 -14

10 -8

10 -6

10 -2

10

Sun Earth

Gamma and x-ray

Ultraviolet

Infrared

Microwave and radio waves

Wavelength in meters (m)

Electromagnetic Spectrum and the Photon Energy of Visible Light

Visible

10 -12

3.10

2.75

2.252.142.061.91

10001.24

1.77 700 red limit

30k0.041

2.48 green 500

near-infrared

far infrared

ultraviolet


Irradiance and ExitanceIrradiance and Exitance

The amount of radiant flux incident per unit area of a plane surface is The amount of radiant flux incident per unit area of a plane surface is called called IrradianceIrradiance ( (EE), where:), where:

EE

• • The amount of radiant flux leaving per unit area of the plane surface is The amount of radiant flux leaving per unit area of the plane surface is called called ExitanceExitance ( (MM).).

MM

• • Both quantities are measured in Both quantities are measured in watts per meter squared (W mwatts per meter squared (W m-2-2))..


AE

AM

The concept of radiant flux The concept of radiant flux density for an area on the density for an area on the surface of the earth. surface of the earth. IrradianceIrradiance is is a measure of the amount of a measure of the amount of incoming energy in Watts mincoming energy in Watts m-2-2..

ExitanceExitance is a measure of the is a measure of the amount of energy leaving in amount of energy leaving in Watts mWatts m-2-2..

Irradiance

Area, A

Radiant flux, Concept of Radiant Flux Density

E =

Area, A

Exitance

Radiant flux,

M =

Jensen 2003

Radiant Flux DensityRadiant Flux Density

Radiance Radiance

Radiance (LRadiance (L) ) is the radiant flux per unit solid angle leaving an extended is the radiant flux per unit solid angle leaving an extended source in a given direction per unit projected source area in that direction source in a given direction per unit projected source area in that direction and is measured in watts per meter squared per steradian (W mand is measured in watts per meter squared per steradian (W m-2 -2 sr sr -1 -1 ). We ). We are only interested in the radiant flux in certain wavelengths (are only interested in the radiant flux in certain wavelengths (LL) leaving ) leaving the projected source area (the projected source area (AA) within a certain direction () within a certain direction () and solid angle ) and solid angle ((): ):

LLcoscos

This is the most precise remote sensing radiometric measurement.This is the most precise remote sensing radiometric measurement.

Jensen 2003

cosAL

The conceptconcept of radiance leaving a specific projected source area on the ground, in a specific direction, and within a specific solid angle.This is the most precise radiometric measurement used in remote sensing.

Side view of Source

Area, A

Projected Source Area =

Normal to Surface Radiant flux,

Solid Angle,

L

Concept of Radiance

A Cos

A Cos

Jensen 2003

Radiometric QuantitiesRadiometric Quantities

Hemispherical reflectance (rHemispherical reflectance (r)) is defined as the dimensionless is defined as the dimensionless ratio of the radiant flux reflected from a surface to the radiant ratio of the radiant flux reflected from a surface to the radiant flux incident to it:flux incident to it:

reflectedreflected

rr


Radiometric QuantitiesRadiometric Quantities

We often take the hemispherical reflectance equation and We often take the hemispherical reflectance equation and multiply it by 100 to obtain an expression for multiply it by 100 to obtain an expression for percent spectral percent spectral reflectance (reflectance (pprr)),,

reflectedreflected

pprrx 100x 100

This quantity is used in remote sensing research to describe This quantity is used in remote sensing research to describe the general spectral reflectance characteristics of various the general spectral reflectance characteristics of various phenomena.phenomena.


100

Ireflectedpr

ReflectanceReflectance

Perfect Specular Reflector Near-Perfect Specular Reflector

Perfect Diffuse Reflector A Lambertian Surface

Specular Versus Diffuse Reflectance

d.

Angle of Incidence

Angle of Exitance

Angle of Incidence

Angle of Exitance

a. c. smooth water

Near-Perfect Diffuse Reflector

b.


Spectral Reflectance Curves of Selected MaterialsSpectral Reflectance Curves of Selected Materials


Spectral Bandwidths of Landsat and SPOT Sensor SystemsSpectral Bandwidths of Landsat and SPOT Sensor Systems

JensenJensen 2003

AtmosphericAtmosphericScatteringScattering

The type of scattering is a The type of scattering is a function of:function of:

• • the wavelength of the the wavelength of the incident radiant energy, and incident radiant energy, and

• • the size of the gas molecule, the size of the gas molecule, dust particle, or water vapor dust particle, or water vapor droplet encountered.droplet encountered.

Atmospheric Scattering

Diameter

Rayleigh Scattering

Mie Scattering

Non-Selective Scattering

Gas molecule

Smoke, dust

Water vapor

Photon of electromagnetic energy modeled as a wave

a.

c.

b.


RayleighRayleighScatteringScattering

The intensity of Rayleigh The intensity of Rayleigh scattering varies inversely scattering varies inversely with the fourth power of with the fourth power of the wavelength (the wavelength (-4-4).).

0.4 0.5 0.6 0.7

100

20

40

60

80

0

Inte

nsity

of S

catt

ered

Lig

ht

3 2.75 2.5 2.25 2 1.75

Wavelength in Micrometers

Intensity of Rayleigh Scattering Varies Inversely with -4

V B G Y O R

Energy in electron volts (eV)


Absorption of the Sun's Incident Electromagnetic Energy in the Absorption of the Sun's Incident Electromagnetic Energy in the Region from 0.1 to 30 Region from 0.1 to 30 m by Various Atmospheric Gasesm by Various Atmospheric Gases


Energy-matter Energy-matter Interactions in the Interactions in the

Atmosphere, at the Study Atmosphere, at the Study Area, and at the Remote Area, and at the Remote

Sensor DetectorSensor Detector

Solar irradiance

Reflectance from study area,

Various Paths of Satellite Received Radiance

Diffuse sky irradiance

Total radiance at the sensor

L L

L

Reflectance from neighboring area,

1

2

3

Remote sensor

detector

Atmosphere

5

4 1,3,5

E

L

90Þ

0T

v T

0

0

v

p T

S

I

nr r

Ed


Path 1:Path 1: EMR from the Sun EMR from the Sun that was attenuated very little that was attenuated very little before illuminating the terrain before illuminating the terrain within the IFOVwithin the IFOV

Path 2:Path 2: EMR that may never EMR that may never reach the Earth’s surface reach the Earth’s surface because of scattering in the because of scattering in the atmosphere. Unfortunately, atmosphere. Unfortunately, such energy is often scattered such energy is often scattered into the FOV of the sensor into the FOV of the sensor systemsystem

Solar irradiance





L L

L


1

2

3

Remote sensor

detector

Atmosphere

5

4 1,3,5

E

L

90Þ

0T

v T

0

0

v

p T

S

I

nr r

Ed

JensenJensen 2003

Path 3:Path 3: Contains energy from Contains energy from the Sun that has undergone the Sun that has undergone some Rayleigh, Mie, and/or some Rayleigh, Mie, and/or Non-selective scattering and Non-selective scattering and perhaps some absorption and perhaps some absorption and re-emission before re-emission before illuminating the study area. illuminating the study area. Thus, its spectral composition Thus, its spectral composition and polarization may be and polarization may be somewhat different than the somewhat different than the energy in Path 1.energy in Path 1.

Path 4: Path 4: Radiation that was Radiation that was reflected or scattered by reflected or scattered by nearby terrain such as snow, nearby terrain such as snow, concrete, soil, water,and/or concrete, soil, water,and/or vegetation into the IFOV of vegetation into the IFOV of the sensor system. The energy the sensor system. The energy does not actually illuminate does not actually illuminate the study area.the study area.

Solar irradiance





L L

L


1

2

3

Remote sensor

detector

Atmosphere

5

4 1,3,5

E

L

90Þ

0T

v T

0

0

v

p T

S

I

nr r

Ed

Path 5: Path 5: Energy that was Energy that was reflected from nearby terrain reflected from nearby terrain into the atmosphere and then into the atmosphere and then scattered or reflected onto the scattered or reflected onto the study area.study area.

Path 2 and Path 4 combine to Path 2 and Path 4 combine to produce what is commonly produce what is commonly referred to as referred to as Path Radiance, Path Radiance, LLpp..

Solar irradiance





L L

L


1

2

3

Remote sensor

detector

Atmosphere

5

4 1,3,5

E

L

90Þ

0T

v T

0

0

v

p T

S

I

nr r

Ed


Solar irradiance





L L

L


1

2

3

Remote sensor

detector

Atmosphere

5

4 1,3,5

E

L

90Þ

0T

v T

0

0

v

p T

S

I

nr r

Ed

pdooovS LETETRL cos1

The total The total radiance radiance

reaching the reaching the sensor is:sensor is:

Sometimes the remote sensing system simply does not function properly. Several Sometimes the remote sensing system simply does not function properly. Several of the more common radiometric errors include of the more common radiometric errors include line drop-outsline drop-outs, , stripingstriping or or bandingbanding, and , and line-startline-start problems. problems.

Correction for Sensor System Detector ErrorCorrection for Sensor System Detector Error

2,,1,,1 kjikji

ijk

BVBVIntBV

Correction for a Correction for a line drop-outline drop-out problem: problem:

This is performed for every pixel in a bad scan line.This is performed for every pixel in a bad scan line.


Single Image Normalization Using Histogram AdjustmentSingle Image Normalization Using Histogram Adjustment

Radiometric Correction Using theRadiometric Correction Using theATATmosphere mosphere REMREMoval (ATREM) Programoval (ATREM) Program

22origorigerror yyxxRMS

ATREMATREM calculates scaled surface reflectance values from hyperspectral radiance data calculates scaled surface reflectance values from hyperspectral radiance data using an approximate atmospheric radiative transfer modeling technique. Radiative using an approximate atmospheric radiative transfer modeling technique. Radiative transfer modeling is used to calculate the atmospheric transmittance of gases and transfer modeling is used to calculate the atmospheric transmittance of gases and molecular and aerosol scattering. The water vapor amount is derived on a pixel by molecular and aerosol scattering. The water vapor amount is derived on a pixel by pixel basis using the pixel basis using the 0.94 0.94 mm and and 1.14 1.14 mm water absorption bands and a three channel water absorption bands and a three channel ratioing technique where several bands in the water absorption feature are averaged ratioing technique where several bands in the water absorption feature are averaged and ratioed against two sets of averaged window channels adjacent to the water and ratioed against two sets of averaged window channels adjacent to the water absorption feature.absorption feature.

Additional inputs: Additional inputs: - Select up to 7 atmospheric gases that may be modeled and - Select up to 7 atmospheric gases that may be modeled and

removed during the reflectance calculationremoved during the reflectance calculation- An aerosol model.- An aerosol model.

- Visibility conditions during the overflight (e.g., 10 km)- Visibility conditions during the overflight (e.g., 10 km)- Standard atmospheric model- Standard atmospheric model

- Average surface elevation (km)- Average surface elevation (km)- Scene center latitude and longitude- Scene center latitude and longitude

- Aircraft altitude above sea level (km)- Aircraft altitude above sea level (km)Jensen 2003Jensen 2003

Radiometric Correction Using Radiometric Correction Using Empirical Line CalibrationEmpirical Line Calibration

22origorigerror yyxxRMS

Empirical Line calibration forces remote sensing spectral data Empirical Line calibration forces remote sensing spectral data ((radianceradianceimageimage ) to match selected field reflectance spectra () to match selected field reflectance spectra (FieldFieldspectraspectra). ). A linear regression is developed A linear regression is developed for each bandfor each band to equate the to equate the brightness value in the imagery with the brightness value in the imagery with the in situin situ reflectance reflectance measurements. This is equivalent to removing the solar irradiance and measurements. This is equivalent to removing the solar irradiance and the atmospheric path radiance. The following equation shows how the atmospheric path radiance. The following equation shows how the empirical line the empirical line gaingain and and offsetoffset values are collected: values are collected:

offsetradiancegainField imagespectra

Typically, the analyst chooses a dark and a bright region in the image Typically, the analyst chooses a dark and a bright region in the image for use in the empirical line calibration. Of course, for use in the empirical line calibration. Of course, in situin situ reference reference calibration data must be available for these areas. Using as many calibration data must be available for these areas. Using as many paired data/field spectra as possible improves the calibration. At least paired data/field spectra as possible improves the calibration. At least one spectral pair is necessary.one spectral pair is necessary.

FieldFieldspectraspectra

Band 1Band 1

Band 2Band 2

Band 3Band 3OneOne

Bright TargetBright Target

4848 4949

48484747

50504848

5555 5454

57575454

56565555

4040 4040

39394040

41414242

RadianceRadianceimageimage (e.g., Band 1) (e.g., Band 1)

Band 1Band 1

Band 2Band 2

Band 3Band 3One One

Dark TargetDark Target

99 1010

11111010

1010121255 44

5566

6644

00 00

4400

1122

Wavelength, nmWavelength, nm

Rad

ianc

eR

adia

nce

Fie

ldF

ield

spec

tra

spec

tra

offsetradiancegainField imagespectra

Paired Relationship:Paired Relationship:

Band 1Band 1 Band 2Band 2 Band 3Band 3

Dark Dark TargetTarget

Dark Dark TargetTarget

Bright Bright TargetTarget

Bright Bright TargetTarget


Remote Remote measurementmeasurement

FieldFieldspectraspectra= 55= 55Remote Measurement Remote Measurement = 49 = 49

= 55= 55FF = = 5959

= 41= 41FF = = 4848

FieldFieldspectraspectra= 13= 13Remote Measurement Remote Measurement = 11 = 11

= 5= 5FF = = 77 = 3= 3

FF = = 44

Multiple Date Image Normalization Using Regression Multiple Date Image Normalization Using Regression

Jensen 20032003

Example based on SPOT imagery obtained over

Water Conservation 2A in South Florida

Cosine Correction Cosine Correction for Terrain Slope for Terrain Slope

i

oTH LL

coscos

where:where:

LLHH = radiance observed for a horizontal = radiance observed for a horizontal surface (i.e., slope-aspect corrected surface (i.e., slope-aspect corrected remote sensor data).remote sensor data).LLTT = radiance observed over sloped terrain = radiance observed over sloped terrain (i.e., the raw remote sensor data)(i.e., the raw remote sensor data)00 = sun’s zenith angle = sun’s zenith angle ii = sun’s incidence angle in relation to the = sun’s incidence angle in relation to the normal on a pixel normal on a pixel

Jensen 2003