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Unclassified Round Robin Final Report PAGE: DATE:

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Round Robin Refractive Index Measurements of Fused Silica and Zinc Selenide

Round Robin Final Report PAGE: DATE:

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Summary This report summarizes the results of refractive index measurements performed on samples of fused silica and zinc selenide. The measurements were performed in round robin style, with three independent laboratories measuring the same samples at 20⁰C. Each laboratory

measured the refractive indices multiple times and fitted the average measured values to Sellmeier dispersion formulas. The refractive indices were then compared on the basis of the values computed from the dispersion formulas.


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1.0 Background Knowledge of the refractive index of infrared optical materials is essential for the design of state-of-the-art electro-optical systems. Fairly precise values for the most commonly used materials have been published occasionally in the scientific literature since at least the 1970’s. These have been incorporated in the materials databases of optical design programs and applied successfully for decades. However, there are small differences in the refractive index values in optical design software databases that raise some questions, including: (1) Which values are “correct”?

(2) Do the differences indicate actual variability in the indices, or measurement uncertainty?

(3) What index tolerances should be used for optical design?

(4) Have the indices of material changed over time, due to improvements in material purity

and manufacturing processes?

(5) Would modern improvements in metrology equipment (e.g., automation) produce

different values than obtained in early measurements?

Materials suppliers are unable to shed any light on these questions, since none has yet committed the capital and labor necessary to establish statistical process control over manufacturing processes. The consensus of most manufacturers (and many users) appears to be that the physicochemical nature of IR materials – at least the crystalline and CVD materials – minimizes the variability of refractive index. However, the manufacturing processes likely leave trace impurities in the materials that can affect the optical properties. There is a need for a study of infrared optical materials that establishes (1) the refractive index values for materials manufactured under current processes, and

measured with current measurement technology.

(2) the blank-to-blank variability in the refractive index.

The Round Robin measurements described in this report were performed in preparation for this study, to help establish the available measurement precision and to help select a laboratory for the study. 2.0 Index Measurement Methods Several methods have been used to measure the refractive index of optical materials. These are described in ASTM C 1648. Because of the high refractive indices and/or opacity of many IR materials, most of these methods are not easily adaptable for IR materials. Others are insufficiently precise. The two methods best suited for measuring the refractive indices of IR materials are illustrated in Figures 1 and 2. 2.1 Prism Refractometer

In the Prism Refractometer, the sample is in the form of a prism with apex angle . The

prism apex angle and the deviation angle produced by the prism sample are measured.


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min

= Minimum Deviation Angle

2sin

2sin

n

min

p

Sample

min

np

Figure 1. Prism Refractometer Method

Obviously, the highest possible precision is required in the measurement of these angles. Many variables must be controlled to obtain high precision, including prism surface power and irregularity, prism pyramidal error, temperature (especially for materials with high dn/dT), monochromator slit imaging optics, and rotation stage accuracy. Wavelength must also be measured precisely. Traditionally, the highest-precision measurements have used the minimum deviation method,

in which the prism is rotated relative to the input beam so as to minimize angle . At this angle, the beam traverses the prism symmetrically (the incidence angle at the input face equals the angle of refractive at the output face) and the refractive index is given by the simple expression shown in Figure 1. 2.2 Prism Coupler In the Prism Coupler, the sample is in the form of a thin plate. The measurement consists of determining the critical angle at the interface between the plate sample and a reference prism of known refractive index.

Reference Prism

np

ns

= npsin

c

Detector

c

c = Critical Angle

Sample

Figure 2. Prism Coupler Method

The sample must be thin and flexible enough that it can be brought into intimate contact with the reference prism. Both the reference prism and sample must be clean. There are some practical issues in a prism coupler measurement. Since the measurement depends on detecting the angle at which the transition between high and low detector signal


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occurs, high signal-to-noise ratio is desirable. This is accomplished by using lasers as the source of the input beam and by taking care that the beam intersects the interface between the reference prism and the sample in the region of intimate contact. A fair amount of trial and error is involved to accurately position the beam in the contact region, especially when the materials are opaque. This complicates automation of the measurement. It should be noted that a prism coupler instrument operating at wavelengths in the LWIR was not identified (Pacific Northwest National Laboratory) until after the measurements had already commenced with prism refractometers. To include prism coupler measurements would have required additional funding. Also, since the prism coupler uses a different sample configuration than the prism refractometer, commonality between the sample material properties could not be assured. In the future, it may be beneficial to make samples of both configurations, taking care that both types come from the same region of the material batch. In any case, the prism refractometer has several advantages over the prism coupler: (1) The prism refractometer results do not require calibration of a reference prism. Coupler

reference prisms are, in fact, calibrated using a prism refractometer.

(2) The prism refractometer can make measurements over a continuous range of

wavelengths, as opposed to a few laser wavelengths.

(3) Available laser wavelengths for the prism coupler are limited on the long end of the IR

range.

(4) Because of the operator intervention currently required to properly position the

measurement beam, the prism coupler is less readily automated.

3.0 Participating Laboratories Three laboratories were available that could provide the prism refractometer measurements: (1) M3 Measurement Solutions, Inc. of Escondido, CA (2) NASA Goddard Space Flight Center of Green Belt, MD (3) U.S. Air Force Research Laboratory, Materials and manufacturing Directorate, Wright

Patterson AFB, OH. All three participated in the Round Robin. NIST and the National Physical Laboratory in the UK formerly had prism refractometer instruments. Inquires were made at both laboratories. However, neither laboratory currently has an operational refractometer. In this report, M3 Measurements Solutions is referred to as “M3M”, the U.S. Air Force Research Laboratory is referred to as “AFRL”, and NASA Goddard SFC is referred to as “NASA”. The NASA refractometer is referred to using NASA’s acronym “CHARMS” (Cryogenic High-Accuracy Refraction Measuring System). 4.0 Measurements 4.1 Sample Configuration


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The samples were fabricated to the specifications shown in Figures 3 and 4. Before finalizing the sample specifications, the specifications were reviewed by all three participating laboratories and final specifications were adjusted so that the samples would be compatible with all participants. Two samples of each material were fabricated, but only one of each was measured. The other samples were retained as backups. It should be noted that the fabricator misinterpreted the surface figure requirements on surface A and B. The drawings call for 1 fringe of power and ¼ fringe irregularity. However, the fabricator read these as 1 wave and ¼ wave, respectively. Therefore, surface figure was not as good as it might have been, particularly for the ZnSe prisms. Inspection reports for the prisms are shown in Appendices A and B. Prism apex angle is among the most important parameters for accurate index measurements, and all laboratories have implemented hardware designs and measurement procedures to enhance the precision of the apex angle measurement. The reported apex angles were as follows:

Table 1. Prism Apex Angles

Laboratory Reported Apex Angle (degrees)

Fused Silica ZnSe

M3M 59.17156 28.99852

AFRL 59.17048 28.9982

NASA 59.17143 28.99851

It should be noted that the ZnSe prism angle initially reported by M3M was 29.00122⁰. However, after reporting the ZnSe refractive indices, M3M discovered a calibration error in one of their rotation stages. By that time, the ZnSe prism had moved on to NASA and was unavailable for immediate re-measurement. Therefore, M3M recomputed their index values using the angle shown in Table 1 and issued a revised report. (This report shows these recomputed M3M index values.) Ostensibly, M3M intended to use the exact NASA angle. It isn’t clear how, but the NASA value of 28.99851⁰ became 28.99852⁰ when M3M recomputed

their index values. The estimated effect of the small difference of 0.00001⁰ (0.036 arc

second) on the refractive index is less than 1x10-6. This is much smaller than the estimated measurement uncertainties and is therefore considered negligible. 4.2 Measurement Protocol A generalized measurement protocol was defined in a Statement of Work (SOW) issued to all the participating laboratories. The salient provisions of the protocol are as follows: (1) Use the minimum deviation method

(2) Measure two sample materials – ZnSe (high index) and Fused Silica (low index)

(3) Room temperature only (20±0.5⁰C).

(4) Measure each sample a minimum of three times. Each measurement was to include the

removal and remounting of the prism in the instrument.

(5) Average the measurements and fit the average data to a 3-term Sellmeier formula

(6) Wavelength ranges: 400nm to 4000nm for fused silica and 550nm to 12000nm for ZnSe.


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Figure 3. Fused Silica Sample Drawing

Figure 4. Zinc Selenide Sample Drawing


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Wavelength ranges and maximum wavelength sampling intervals were prescribed in the SOW, but the participating laboratories were allowed some latitude in selecting the final measurement wavelengths. In particular, it was known that the NASA refractometer is limited to a maximum wavelength of approximately 5500nm. The SOW required that each laboratory measure the largest feasible portion of the prescribed wavelength ranges. 4.3 Measurement Implementation Details It was understood from the outset that the detailed measurement procedures of the three participating laboratories would not be identical. The SOW permitted each laboratory to use its own established measurement processes for operations such as calibration, temperature control and measurements, and angular measurements. There are also differences in the combinations of sources, detectors, and gratings used to cover the full wavelength ranges. Within the constraints of the overall protocol, there were also differences among the laboratories with respect to the measurement wavelengths and the number of measurement runs. For example, M3M provided data from three runs for each prism, representing one measurement for each of three separate mountings of the prism as required by the SOW. Each data set contained index values over the full range of prescribed wavelengths (400-4000 nm for fused silica and 550-12000 nm for ZnSe). AFRL provided data from 15 runs for each prism, corresponding to five measurements for each of three separate mountings of the prism. The fused silica prism was measured from 404.6-4600 nm, and the ZnSe prism was measured from 550-11000 nm. Both M3M and AFRL held the temperature as near 20⁰C as

possible during the measurements and corrected for temperature variations by monitoring the temperature during each run and extrapolating their raw measurements to 20⁰C.

NASA provided data from five runs of the fused silica prism, representing five separate mountings of the prism. Five runs were performed using CHARMS’s Si CCD detector covering wavelengths from 461.9-1054.7 nm, and four measurement runs were performed using CHARMS’s Merlin InSb infrared camera covering wavelengths from 1054.7-3563.6 nm. All runs satisfy roughly the specified wavelength sampling; the wavelength ranges covered are slightly truncated by limitations in the combined spectral properties of CHARMS’s light source, monochromator grating efficiency, and detectors. NASA intended a similar set of measurements for the ZnSe. Unfortunately, because of the failure of a rotation stage and scheduling complications, NASA completed the measurements for three separate mountings over a period of several months (roughly August 2011 – February 2012), providing data in a series of partial data sets covering portions of the prescribed wavelength range. This resulted in varying amounts of data in various wavelengths regions: four data sets for the 542.41nm-1054.7nm region, five data sets for the 1054.7nm-3796.8nm region, three data sets for the 4890.3nm-5433.7nm region, and eight data sets for the 4157.5nm-4751.5nm region. In aggregate, this data spans the full CHARMS wavelength range for each of the three separate mountings. NASA noted that for the three longest wavelengths for the run of the ZnSe prism with the InSb detector and their quartz-tungsten-halogen source (the second mounting of the prism), measured data exist for only a few temperatures just above 20.0 C, so index values for those wavelengths were derived by extrapolating each measured index value to 20.0 C using


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dn/dT = 6.3 X 10-5/K from previous NASA work on ZnSe and averaging those extrapolated values. The maximum, minimum, and standard deviation for each laboratory’s data were separately computed by the laboratories, and independently by Lockheed Martin based on the measured data reported. Each laboratory provided Sellmeier dispersion curve fits to the averaged data in accordance with the SOW, using the curve fitting software of their choice. In this regard, two aspects of the NASA measurements deserve special mention. First, unlike most refractometers, the NASA CHARMS refractometer is not set up to measure refractive index at fixed temperatures. Instead, sample temperature is lowered to a starting temperature and allowed to drift upward during the course of a measurement set while sample temperature is tracked continuously, resulting in a large data set at a variety of wavelengths and temperatures. The index data tabulated for each measurement run reported by in NASA had been interpolated to 20⁰C. For the final Sellmeier fit, the entire large set of raw data for all runs, at all

wavelengths and temperatures, is fitted to a temperature-dependent Sellmeier dispersion formula in which each Sellmeier coefficient is fitted to a 4th-order function of temperature. This approach is obviously quite convenient for computing the refractive index at any temperature. Second, the NASA measurements are always performed in an evacuated chamber, so the NASA values are absolute (relative to vacuum). To facilitate comparison to other measurements, the refractive index values shown in this report have been converted to values relative to air by dividing them by the refractive index of air at 20ºC. A value of 1.00027 was used (Reference 1). 5.0 Results 5.1 Measurements The data provided by the participating laboratories are summarized in the tables in Appendices C through H. The first two columns of each table list the wavelength and the average measured index. The next two columns list the peak-valley (PV) variation of the measurements and standard deviation (SD) of the measurements – important measures of measurement repeatability. The next column lists the error between the average measurement and the Sellmeier fit. The last two columns list the index computed from the Handbook of Optics Vol. II (1995) (References 2 and 3) and the difference between the average measurement and the Handbook value. Handbooks of Optics values are included primarily as a common reference for comparing the results from the laboratories to each other. A variation between the measured data and the Handbook of Optics values does not necessarily indicate error in the measured data. Small differences would not be surprising, given the age of the Handbook data and likely differences in sample material characteristics. For example, our fused silica sample was made of Heraeus Infrasil to provide enhanced transmission in the midwave IR; the seven samples in Reference 3 were made from material obtained from four different suppliers (General Electric, Heraeus, Nieder Fused Quartz, and Corning) that were probably similar to modern standard grades of fused silica. Heraeus lists slightly different index values for Suprasil versus Homosil and Infrasil in its product information, with Infrasil and Homosil indices being generally 0.00010-0.00015 greater than Suprasil indices. The refractive indices of the two CVD ZnSe samples in Reference 2 varied


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from each other by as much as 0.0004 at the shorter wavelengths (over 600nm – 12000nm), with an RMS variation of 0.000135. 5.1.1 Fused Silica Referring to Appendices C, D, and E, the PV values for the M3M and NASA data show no obvious trends with respect to wavelength. The AFRL data in Table D-1 shows a slight increase in PV at the longer wavelengths. Table 2 shows the averages of the PV and SD over wavelength for the three labs, as well as the RMS fit error the Sellmeier formula to the average measurements. Repeatability is excellent for all labs, with the NASA data showing exceptionally good repeatability. It should be noted that two outlier measurements (one at 1420 nm in run #1 and the other at 4400 nm in run #9) were removed from the calculation of the repeatability measures for AFRL in Table 2.

Table 2. Repeatability of Fused Silica Measurements

Laboratory PV (average) SD (average) RMS Fit Error

M3M 0.000039 0.000021 0.000019

AFRL 0.000080 0.000022 0.000058

NASA 0.000016 0.000006 0.000005

A significant component of the difference between the measured data and the Handbook of Optics values is a constant offset. 5.1.2 Zinc Selenide The fact that NASA measurements span a much smaller wavelength range than the M3M and AFRL measurements makes it difficult to make a definitive comparison of the results from the three labs. Nevertheless, Table 3 shows the averages of the PV and SD over wavelength for the three labs, plus the RMS fit error over wavelength between the Sellmeier fit and the average measurement. Repeatability is again very good for the M3M and NASA data. The AFRL data is somewhat less repeatable. It should be noted that the measurements at the longest two wavelengths (10500nm and 11000nm) account for much of the variability in the AFRL data. AFRL has pointed out that the very low signal at these two wavelengths may have resulted in a substantial error in measuring the beam deviation angle, and has recommended that these data points be removed. (Indeed, AFRL’s uncertainty estimate degrades significantly at these wavelengths.) For the 550nm-10000nm range, the PV, SD, and RMS fit error are only 0.000401, 000117, and 0.000077, respectively.

Table 3. Repeatability of Zinc Selenide Measurements

Laboratory PV (average) SD (average) RMS Fit Error

M3M 0.000095 0.000049 0.000022

AFRL 0.000500 0.000157 0.000848

NASA 0.000068 0.000031 0.000023

As with the fused silica measurements, part of the difference between the measured data and the Handbook of Optics values is in the form of a constant offset, at least for the M3M and AFRL measurements. There is also a noteworthy trend at the short end of the wavelength range near the ZnSe absorption edge. Here, all three labs’ data trends higher than the Handbook values. Although not provable, this trend may be due to a real difference


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in absorption between the samples used for the round robin measurements and the Handbook measurements. As noted earlier, the index values of the two ZnSe prisms reported in Reference 3 vary relative to each other by as much as 0.0004. The degraded irregularity of the ZnSe prism surfaces (due to misinterpretation of the prism specifications) may also play a minor role here. 5.2 Comparison of Fitted Values The following curve fitting software was used by the laboratories: NASA DataFit 2.0 (Oakdale Engineering) AFRL Kaleidagraph (Synergy Software) M3M TableCurve 2D (Systat Software) Appendices I and J show the differences among the three laboratories at common sets of wavelengths, based on the values computed with the Sellmeier formulas. Basically, the comparisons in the tables indicate the reproducibility of the measurements. Shaded cells indicate wavelengths that were outside the wavelength range measured by one lab or another, and therefore the Sellmeier fits are likely not valid. At the bottom of each column, the Worst Case and RMS differences are shown. Since these differences are based on the Sellmeier fits, the Worst Case and RMS difference values were computed only over the regions of validity of the fits. The differences of the Sellmeier fits and the dispersion formulas in the Handbook of Optics are plotted in Figures 5 and 6. It should also be noted that in the interest of saving space in the tables, the wavelength increments are not uniform. The worst case and RMS differences were determined using a uniform wavelength increment of 0.05 micron. Therefore, the worst case and RMS values shown may not agree with worst case and RMS values computed using only the values listed in the tables. 5.2.1 Fused Silica Referring to table I-2 and Figure 5, it can be seen that over most of the measured wavelength range, the Sellmeier-based fused silica index values are higher than the Handbook of Optics values (Reference 2) by approximately 0.0001-0.0002. Over the entire common 450nm-3600nm region, where all labs’ measurements overlap, the Worst Case differences vary from about 0.000222 (AFRL) to about 0.000243 (NASA), and the RMS differences vary from about 0.000151 (AFRL) to about 0.000189 (M3M). The differences tend to be largest near the ends of the wavelength ranges, where the peak-to-valley variability of the measurements for each lab also tends to be largest. This could be due to any of several influences: (1) curve fitting errors at the ends of the wavelength range (2) reduced signal/noise at the edge of the transmission band (3) higher sensitivity to wavelength uncertainty long-wave near absorption edge of the

material, where the index is changing most rapidly


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Figure 5. Differences between fitted refractive index values and Optics

Handbook values for Fused Silica (Infrasil 301) Table I-1 and figure 5 shows that the best agreement is between the M3M and NASA results, particularly between 600nm and 3400nm. 5.2.2 Zinc Selenide The measured indices of the ZnSe sample are also consistently higher than the Handbook of Optics values. Worst Case differences are generally about 0.0005 or less, with larger difference in some wavelength regions, especially wavelengths below 1 micron and above 7 microns for the AFRL measurements. RMS differences are less than about 0.0003. As with fused silica, the trends in the plots suggest that perhaps the Handbook values are low. Where the laboratories disagree, the disagreement tends to be in the form of a nearly constant offset. The natural assumption is that this may be due to differences in the measurement of prism apex angle. However, Table 1 indicates excellent agreement among the apex angle measurements. The largest differences tend to be largest near the ends of the wavelength ranges, where the peak-to-valley variability of the measurements also tends to be largest. This could be due to any of several influences: (1) curve fitting errors at the ends of the wavelength range (2) reduced signal/noise at the edge of the transmission band (3) higher sensitivity to wavelength uncertainty near absorption edge of the material, where

the index is changing most rapidly


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Figure 6. Differences between fitted refractive index values and Optics

Handbook values for Zinc Selenide 6.0 Observations, Conclusions, and Recommendations The observation and conclusions below are aimed at the selection of a laboratory to perform a larger measurements program comprising measurements of multiple samples of multiple materials. Some of these were known at the outset of the round robin, and were pointed out earlier, but are included here for completeness. 1) The repeatability of the measurements is significantly influenced by the ability to maintain

sufficient signal-to-noise ratio (SNR) across the wavelength range of interest. SNR is a function of both the material transmittance and refractometer characteristics (source, gratings, and detectors). The M3M refractometer is the only laboratory currently able to cover reliably the entire LWIR wavelength range of interest out to 12000nm.

2) Given sufficient SNR, the average repeatability of measurements is on the order of 0.000039 or better for VIS/MWIR material (e.g., fused silica), and 0.000095 or better for VIS/MWIR/LWIR material (e.g., ZnSe). The NASA refractometer provides exceptionally good repeatability and Sellmeier fits over its operational wavelength range.

3) Based on a comparison of the Sellmeier fits, reproducibility is better than about 0.0005 over a large part of the wavelength range of interest, but degrades significantly when SNR degrades. This suggests the need for SNR standards for refractive index measurements.

5) The typical index repeatability variation is good (i.e., small) enough to provide meaningful measurements of index for optical design and tolerancing. When developing standards on refractive index and dispersion, we should anticipate spectral variations in standard tolerances due to spectral variations in repeatability and reproducibility of the measurements.

6) To minimize Sellmeier fit errors at the ends of the wavelength range of interest, the measurement range should exceed the wavelength range of interest. The amount of excess is a consideration to be addressed during program planning.


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7) The NASA refractometer would require upgrades to extend its operation into the LWIR. It appears that the AFRL refractometer would also require upgrades to improve SNR and repeatability above 10000nm. The cost of these upgrades is a key consideration.

8) Another practical consideration for a large measurements program is the availability of personnel to execute the program. All the labs have small staffs, generally with one to at most a few personnel trained and available to run the instruments. Both AFRL and NASA personnel are primarily dedicated to priorities other than performing IR material measurements. A high degree of automation is desirable to help mitigate this.

19) The NASA method for gathering index data over wavelength and temperature has great appeal for efficiently and cost-effectively generating dispersion and dn/dT values.

10) Protocols must be in place to ensure that equipment is calibrated and remains calibrated. 11) The potential for equipment failures is a concern that must be taken into account in

program planning. References 1. S. L. Valley, “Handbook of Geophysics and Space Environments”, McGraw-Hill, 1976 2. W. S. Rodney and R. J. Spindler, “Index of Refraction of Fused-quartz Glass for Ultraviolet, Visible, and Infrared Wavelengths”, Journal of Research of the National Bureau of Standards, 53: 185-189, (1954). 3. A. Feldman, D. Horowitz, R. M. Walker, and M. J. Dodge, “Optical Materials Characterization Final Technical Report, February 1, 1978 – September 30, 1978.


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Appendix A – Prism Sample Inspection Report, Fused Silica Prisms


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Appendix B – Prism Sample Inspection Report, Zinc Selenide Prisms


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Appendix C – M3M Measured Data, Fused Silica

Table C-1. M3M Fused Silica Measurements

Wavelength (nm)

Refractive Index at 20ºC

Average of Measurements

Peak-Valley

Std Dev Avg Meas-

Fit Handbook

Value Avg Meas-Handbook

400 1.469941 0.000079 0.000042 -0.000048 1.470116 -0.000175

450 1.465626 0.000020 0.000011 0.000056 1.465566 0.000060

500 1.462418 0.000029 0.000016 0.000022 1.462326 0.000092

550 1.460016 0.000023 0.000013 0.000002 1.459911 0.000105

600 1.458156 0.000018 0.000010 -0.000003 1.458038 0.000118

650 1.456651 0.000016 0.000009 -0.000015 1.456535 0.000116

700 1.455419 0.000014 0.000008 -0.000011 1.455292 0.000126

750 1.454362 0.000016 0.000009 -0.000015 1.454237 0.000125

800 1.453446 0.000016 0.000009 -0.000012 1.453317 0.000129

900 1.451891 0.000030 0.000015 -0.000006 1.451754 0.000137

1000 1.450557 0.000028 0.000014 -0.000004 1.450417 0.000140

1100 1.449358 0.000039 0.000022 0.000010 1.449204 0.000155

1200 1.448219 0.000046 0.000026 0.000022 1.448050 0.000169

1300 1.447084 0.000047 0.000026 0.000017 1.446918 0.000166

1400 1.445949 0.000049 0.000027 0.000017 1.445779 0.000170

1500 1.444782 0.000059 0.000031 0.000008 1.444618 0.000164

1600 1.443582 0.000056 0.000028 0.000002 1.443419 0.000163

1700 1.442327 0.000063 0.000032 -0.000012 1.442174 0.000153

1800 1.441028 0.000057 0.000029 -0.000016 1.440874 0.000155

1900 1.439674 0.000056 0.000028 -0.000014 1.439513 0.000161

2000 1.438250 0.000051 0.000026 -0.000016 1.438085 0.000164

2500 1.430006 0.000050 0.000026 -0.000003 1.429802 0.000204

3000 1.419487 0.000053 0.000027 0.000017 1.419247 0.000241

3500 1.406104 0.000014 0.000007 0.000002 1.405886 0.000217

4000 1.389179 0.000047 0.000027 -0.000004 1.389028 0.000151

Dispersion Formula (Fitted to averaged data)

3

2

2

3

2

2

2

2

1

2

2

12

C

B

C

B

C

BAn

A =0.80300401 B1 = 0.57506344 C1 = 0.0066392199 B2 = 0.72632302 C2 = 0.0069614779 B3 = 0.86417928 C3 = 94.958104


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Appendix D – AFRL Measured Data, Fused Silica

Table D-1. AFRL Fused Silica Measurements

Wavelength (nm)



Peak-Valley

Std Dev Avg Meas-

Fit Handbook


404.6 1.469729 0.000039 0.000012 -0.000094 1.469623 0.000106

420 1.468205 0.000048 0.000014 -0.000087 1.468094 0.000111

440 1.466456 0.000020 0.000005 -0.000087 1.466350 0.000106

460 1.464937 0.000010 0.000004 -0.000082 1.464833 0.000104

480 1.463614 0.000025 0.000007 -0.000067 1.463502 0.000112

500 1.462455 0.000026 0.000006 -0.000042 1.462326 0.000129

520 1.461399 0.000015 0.000005 -0.000043 1.461280 0.000119

540 1.460462 0.000029 0.000010 -0.000035 1.460344 0.000118

560 1.459620 0.000029 0.000008 -0.000025 1.459500 0.000120

580 1.458852 0.000030 0.000009 -0.000021 1.458735 0.000117

600 1.458170 0.000014 0.000003 0.000001 1.458038 0.000132

620 1.457523 0.000035 0.000009 -0.000001 1.457399 0.000124

640 1.456944 0.000010 0.000003 0.000013 1.456812 0.000132

660 1.456387 0.000037 0.000008 0.000005 1.456268 0.000119

680 1.455882 0.000027 0.000008 0.000010 1.455764 0.000118

700 1.455404 0.000088 0.000023 0.000008 1.455292 0.000112

740 1.454542 0.000088 0.000023 0.000011 1.454436 0.000106

780 1.453784 0.000222 0.000056 0.000023 1.453671 0.000113

820 1.453076 0.000064 0.000018 0.000012 1.452979 0.000097

860 1.452453 0.000064 0.000015 0.000028 1.452344 0.000109

900 1.451872 0.000135 0.000044 0.000040 1.451754 0.000118

940 1.451294 0.000068 0.000017 0.000019 1.451199 0.000095

980 1.450789 0.000077 0.000019 0.000042 1.450672 0.000117

1020 1.450282 0.000052 0.000015 0.000040 1.450167 0.000115

1060 1.449786 0.000132 0.000033 0.000032 1.449679 0.000107

1100 1.449286 0.000080 0.000020 0.000007 1.449204 0.000082

1140 1.448821 0.000060 0.000020 0.000006 1.448738 0.000083

1180 1.448365 0.000054 0.000015 0.000008 1.448278 0.000087

1220 1.447918 0.000059 0.000017 0.000014 1.447823 0.000095

1260 1.447451 0.000041 0.000012 -0.000003 1.447370 0.000081

1300 1.446994 0.000080 0.000020 -0.000010 1.446918 0.000076

1340 1.446527 0.000038 0.000012 -0.000027 1.446464 0.000063

1380 1.446062 0.000085 0.000024 -0.000040 1.446008 0.000054

1420 1.445592 0.000080 0.000018 -0.000055 1.445549 0.000043

1460 1.445130 0.000106 0.000027 -0.000058 1.445086 0.000044

1500 1.444638 0.000081 0.000026 -0.000086 1.444618 0.000020

1540 1.444164 0.000077 0.000020 -0.000090 1.444143 0.000021

1580 1.443657 0.000117 0.000037 -0.000120 1.443662 -0.000005

2200 1.435102 0.000141 0.000045 -0.000102 1.435014 0.000088

2400 1.431764 0.000203 0.000048 -0.000070 1.431625 0.000139

2600 1.428094 0.000229 0.000070 -0.000014 1.427888 0.000206


23 OF 35 April 9, 2012

2800 1.423919 0.000115 0.000037 -0.000074 1.423773 0.000146

3000 1.419408 0.000076 0.000023 -0.000044 1.419247 0.000161

3200 1.414503 0.000181 0.000048 0.000060 1.414273 0.000230

3400 1.409042 0.000187 0.000047 0.000121 1.408812 0.000230

3600 1.402840 0.000154 0.000036 0.000007 1.402820 0.000020

3800 1.396034 0.000118 0.000032 -0.000084 1.396245 -0.000211

4000 1.388709 0.000110 0.000033 0.000004 1.389028 -0.000319

4200 1.380546 0.000173 0.000050 0.000035 1.381100 -0.000554

4400 1.371450 0.000159 0.000046 0.000012 1.372381 -0.000931

4600 1.361227 0.000222 0.000053 -0.000141 1.362779 -0.001552


3

2

2

3

2

2

2

2

1

2

2

12

C

B

C

B

C

BAn

A = 1.000000 B1 = 0.69705 C1 = 0.006612 B2 = 0.4069 C2 = 0.010737 B3 = 0.77958 C3 = 86.867


24 OF 35 April 9, 2012

Appendix E – NASA Measured Data, Fused Silica

Table E-1. NASA Fused Silica Measurements

Wavelength (nm)



Peak-Valley

Std Dev Avg Meas-

Fit Handbook


461.94 1.464799 0.000016 0.000006 0.000002 1.464696 0.000102

474.61 1.463951 0.000018 0.000007 -0.000002 1.463844 0.000106

509.09 1.461943 0.000018 0.000007 -0.000002 1.461836 0.000107

519.69 1.461399 0.000017 0.000006 0.000001 1.461296 0.000104

542.41 1.460343 0.000016 0.000006 0.000000 1.460237 0.000105

593.93 1.458347 0.000017 0.000006 0.000000 1.458243 0.000105

632.82 1.457122 0.000016 0.000006 0.000000 1.457017 0.000104

692.92 1.455559 0.000017 0.000006 0.000000 1.455456 0.000103

712.72 1.455113 0.000017 0.000006 -0.000001 1.455008 0.000105

759.38 1.454158 0.000017 0.000006 0.000000 1.454055 0.000103

791.03 1.453577 0.000018 0.000006 0.000000 1.453474 0.000103

831.50 1.452895 0.000017 0.000006 -0.000001 1.452791 0.000103

890.90 1.451990 0.000017 0.000006 -0.000002 1.451885 0.000105

949.23 1.451179 0.000018 0.000006 -0.000001 1.451075 0.000104

1039.38 1.450032 0.000018 0.000006 0.000001 1.449929 0.000104

1054.70 1.449851 0.000018 0.000007 -0.000003 1.449743 0.000108

1582.00 1.443760 0.000014 0.000006 0.000000 1.443638 0.000122

1781.80 1.441249 0.000011 0.000005 -0.000003 1.441114 0.000134

1898.40 1.439670 0.000015 0.000006 0.000003 1.439535 0.000135

2078.80 1.437055 0.000015 0.000006 0.000004 1.436911 0.000144

2375.70 1.432217 0.000016 0.000007 0.000005 1.432055 0.000163

2531.20 1.429386 0.000016 0.000006 0.000006 1.429215 0.000171

2847.60 1.422927 0.000017 0.000006 0.000006 1.422734 0.000192

3164.00 1.415439 0.000011 0.000005 -0.000018 1.415203 0.000236

3563.60 1.404186 0.000014 0.000006 0.000004 1.403953 0.000233

TL

TS

TL

TS

TL

TS1T,n

2

3

2

2

3

2

2

2

2

2

2

1

2

2

12

where

4

14

3

13

2

1211101 TSTSTSTSSTS

4

14

3

13

2

1211101 TLTLTLTLLTL

4

24

3

23

2

2221202 TSTSTSTSSTS

4

24

3

23

2

2221202 TLTLTLTLLTL

4

34

3

33

2

3231303 TSTSTSTSSTS

4

34

3

33

2

3231303 TLTLTLTLLTL


25 OF 35 April 9, 2012

Temperature is in K and wavelength is in microns.

S10 = 1.1124172E+00 L10 = 1.2401627E-01 S11 = 3.5984489E-05 L11 = -2.5680246E-04 S12 = -4.2778573E-07 L12 = -4.0077614E-08 S13 = -4.5873500E-10 L13 = 3.5799926E-09 S14 = 2.9267428E-12 L14 = -6.4767094E-12 S20 = -2.6420403E-02 L20 = 4.1642588E-01 S21 = 1.1555705E-04 L21 = 1.0304456E-03 S22 = 1.0796702E-07 L22 = -1.3934022E-05 S23 = 1.5012903E-10 L23 = 2.7230271E-08 S24 = -1.5329819E-12 L24 = 1.9526834E-13 S30 = 9.8894839E-01 L30 = 1.3390885E+01 S31 = -5.0955228E-04 L31 = -2.0121920E-02 S32 = 4.5308093E-06 L32 = -2.9980441E-05 S33 = -3.6137518E-08 L33 = 3.1405721E-07 S34 = 7.5925712E-11 L34 = -4.0717227E-10 At 293.16K (20ºC),

096260931.1TS1 0879273758.0TL1 009194934.0TS2 208491255.0TL2 879273758.0TS3 820567142.9TL3


26 OF 35 April 9, 2012

Appendix F – M3M Measured Data, Zinc Selenide

Table F-1. M3M Zinc Selenide Measurements

Wavelength (nm)



Peak-Valley

Std Dev Avg Meas-

Fit Handbook


550 2.663612 0.000694 0.000366 0.000005 2.662458 0.001154

600 2.614761 0.000662 0.000334 -0.000031 2.613804 0.000957

650 2.581288 0.000441 0.000222 0.000059 2.580539 0.000749

700 2.557135 0.000261 0.000135 -0.000049 2.556358 0.000777

750 2.538654 0.000168 0.000088 0.000050 2.538038 0.000616

800 2.524379 0.000116 0.000058 -0.000034 2.523732 0.000647

900 2.503513 0.000058 0.000030 -0.000007 2.502983 0.000530

1000 2.489266 0.000086 0.000043 0.000007 2.488824 0.000442

1100 2.479059 0.000053 0.000027 -0.000003 2.478668 0.000391

1200 2.471457 0.000100 0.000050 -0.000014 2.471104 0.000352

1300 2.465608 0.000084 0.000042 -0.000009 2.465301 0.000306

1400 2.461002 0.000062 0.000032 0.000000 2.460739 0.000263

1500 2.457318 0.000095 0.000048 -0.000007 2.457076 0.000242

1600 2.454307 0.000085 0.000043 -0.000011 2.454084 0.000223

1700 2.451787 0.000035 0.000019 0.000006 2.451601 0.000186

1800 2.449662 0.000072 0.000036 0.000025 2.449512 0.000150

1900 2.447866 0.000062 0.000033 0.000026 2.447732 0.000134

2000 2.446323 0.000034 0.000019 0.000023 2.446198 0.000125

2500 2.440970 0.000048 0.000025 0.000005 2.440867 0.000103

3000 2.437655 0.000032 0.000017 0.000011 2.437579 0.000076

3500 2.435248 0.000046 0.000025 0.000000 2.435170 0.000078

4000 2.433247 0.000038 0.000021 -0.000013 2.433159 0.000088

4500 2.431414 0.000040 0.000021 -0.000018 2.431318 0.000096

5000 2.429627 0.000032 0.000017 -0.000017 2.429527 0.000100

6000 2.425952 0.000010 0.000006 -0.000007 2.425844 0.000108

6500 2.424013 0.000013 0.000007 -0.000018 2.423881 0.000132

7000 2.421937 0.000017 0.000010 0.000002 2.421809 0.000127

7500 2.419764 0.000010 0.000005 -0.000003 2.419613 0.000151

8000 2.417471 0.000004 0.000002 -0.000021 2.417283 0.000188

8500 2.415007 0.000009 0.000005 -0.000009 2.414807 0.000200

9000 2.412382 0.000004 0.000002 0.000015 2.412179 0.000203

9500 2.409621 0.000003 0.000002 0.000018 2.409392 0.000229

10000 2.406693 0.000008 0.000004 0.000025 2.406437 0.000256

10500 2.403589 0.000006 0.000003 0.000038 2.403309 0.000280

11000 2.400389 0.000001 0.000001 -0.000029 2.399999 0.000389

11500 2.396919 0.000007 0.000004 -0.000010 2.396502 0.000417

12000 2.393276 0.000006 0.000003 -0.000007 2.392810 0.000466


27 OF 35 April 9, 2012


3

2

2

3

2

2

2

2

1

2

2

12

C

B

C

B

C

BAn

A = 0.0067610305 B1 = 5.2547552 C1 = 0.17238533 B2 = 0.66432241 C2 = 0.37838092 B3 = 3.0505036 C3 = 48.394409


28 OF 35 April 9, 2012

Appendix G – AFRL Measured Data, Zinc Selenide

Table G-1. AFRL Zinc Selenide Measurements

Wavelength (nm)



Peak-Valley

Std Dev Avg Meas-

Fit Handbook


550 2.663177 0.000624 0.000151 0.000019 2.662458 0.000719

600 2.614398 0.000218 0.000074 -0.000091 2.613804 0.000594

650 2.581107 0.000292 0.000088 -0.000110 2.580539 0.000567

700 2.557071 0.000271 0.000072 0.000049 2.556358 0.000714

750 2.538785 0.000247 0.000068 0.000099 2.538038 0.000748

800 2.524502 0.000236 0.000067 0.000140 2.523732 0.000771

850 2.512969 0.000251 0.000061 0.000060 2.512297 0.000672

900 2.503478 0.000554 0.000171 -0.000101 2.502983 0.000494

950 2.495860 0.000411 0.000113 0.000001 2.495280 0.000580

1000 2.489328 0.000184 0.000055 -0.000060 2.488824 0.000504

1050 2.483772 0.000217 0.000070 -0.000129 2.483352 0.000421

1100 2.479155 0.000232 0.000057 -0.000050 2.478668 0.000487

1150 2.475103 0.000204 0.000047 -0.000046 2.474624 0.000480

1200 2.471655 0.000238 0.000064 0.000036 2.471104 0.000551

1250 2.468521 0.000223 0.000055 -0.000006 2.468021 0.000500

1300 2.465793 0.000314 0.000086 -0.000005 2.465301 0.000492

1350 2.463350 0.000383 0.000091 -0.000028 2.462889 0.000461

1400 2.461214 0.000210 0.000072 -0.000006 2.460739 0.000475

1450 2.459230 0.000302 0.000080 -0.000055 2.458811 0.000419

1500 2.457535 0.000341 0.000114 -0.000009 2.457076 0.000458

1550 2.455960 0.000213 0.000052 -0.000010 2.455508 0.000452

1600 2.454550 0.000152 0.000040 0.000009 2.454084 0.000465

2200 2.444022 0.000404 0.000104 -0.000074 2.443687 0.000334

2400 2.442021 0.000360 0.000121 -0.000085 2.441710 0.000311

2600 2.440381 0.000446 0.000164 -0.000104 2.440099 0.000282

2800 2.439031 0.000511 0.000151 -0.000093 2.438747 0.000284

3000 2.437868 0.000330 0.000114 -0.000078 2.437579 0.000289

3200 2.436851 0.000338 0.000108 -0.000053 2.436545 0.000306

3400 2.436000 0.000430 0.000113 0.000040 2.435609 0.000391

3600 2.435228 0.000496 0.000127 0.000139 2.434745 0.000482

3800 2.434388 0.000294 0.000104 0.000118 2.433933 0.000455

4000 2.433552 0.000367 0.000095 0.000063 2.433159 0.000393

4200 2.432792 0.000220 0.000069 0.000057 2.432411 0.000381

4400 2.431950 0.000428 0.000159 -0.000049 2.431679 0.000270

4600 2.431280 0.000417 0.000166 0.000006 2.430959 0.000321

4800 2.430536 0.000387 0.000152 -0.000018 2.430243 0.000293

5000 2.429879 0.000529 0.000153 0.000044 2.429527 0.000352

5200 2.429177 0.000450 0.000155 0.000063 2.428808 0.000369

5400 2.428447 0.000468 0.000145 0.000058 2.428083 0.000364

5600 2.427744 0.000601 0.000186 0.000089 2.427348 0.000396


29 OF 35 April 9, 2012

7500 2.419802 0.001006 0.000299 -0.000215 2.419613 0.000189

8000 2.417611 0.000851 0.000225 -0.000140 2.417283 0.000328

8500 2.415386 0.000711 0.000178 0.000024 2.414807 0.000579

9000 2.412818 0.000503 0.000125 -0.000028 2.412179 0.000639

9500 2.410255 0.001071 0.000277 0.000054 2.409392 0.000863

10000 2.407433 0.000502 0.000148 0.000011 2.406437 0.000995

10500 2.407358 0.003606 0.001488 0.002850 2.403309 0.004049

11000 2.406571 0.001973 0.000639 0.005115 2.399999 0.006571


2

3

2

2

2

2

1

2

2

12 BC

B

C

BAn

A =1.000000 B1 = 4.3366 C1 = 0.037755 B2 = 0.59112 C2 = 0.14534 B3 = .0013454


30 OF 35 April 9, 2012

Appendix H – NASA Measured Data, Zinc Selenide

Table H-1. NASA Zinc Selenide Measurements

Wavelength (nm)



Peak-Valley

Std Dev Avg Meas-

Fit Handbook


542.41 2.673270 0.000080 0.000057 -0.000009 2.671906 0.000642

593.93 2.619813 0.000090 0.000047 0.000017 2.618711 0.000396

632.82 2.591830 0.000170 0.000076 0.000016 2.590718 0.000413

692.92 2.560517 0.000080 0.000042 0.000012 2.559371 0.000455

712.72 2.552445 0.000110 0.000048 -0.000052 2.551231 0.000525

759.38 2.536280 0.000090 0.000039 -0.000031 2.535089 0.000506

791.03 2.527255 0.000100 0.000042 -0.000045 2.526060 0.000513

831.50 2.517370 0.000060 0.000027 0.000008 2.516247 0.000444

890.90 2.505650 0.000080 0.000035 -0.000006 2.504546 0.000428

949.23 2.496440 0.000060 0.000027 0.000010 2.495388 0.000378

1012.5 2.488365 0.000010 0.000007 0.000030 2.487372 0.000321

1039.4 2.485413 0.000050 0.000022 0.000034 2.484440 0.000301

1054.7 2.483855 0.000100 0.000065 0.000023 2.482881 0.000319

1187.9 2.472827 0.000060 0.000032 0.000012 2.471913 0.000246

1265.6 2.467992 0.000090 0.000036 0.000034 2.467136 0.000190

1385.8 2.462138 0.000080 0.000031 0.000030 2.461325 0.000148

1582.0 2.455358 0.000050 0.000026 0.000008 2.454581 0.000113

1781.8 2.450622 0.000040 0.000020 -0.000014 2.449867 0.000093

1898.4 2.448485 0.000070 0.000033 -0.000006 2.447759 0.000065

2078.8 2.445825 0.000030 0.000021 0.000002 2.445131 0.000034

2375.7 2.442618 0.000060 0.000025 -0.000023 2.441928 0.000030

2531.2 2.441285 0.000060 0.000026 -0.000009 2.440620 0.000006

2847.6 2.439090 0.000040 0.000020 0.000004 2.438454 -0.000023

3164.0 2.437374 0.000070 0.000027 -0.000021 2.436723 -0.000007

3563.6 2.435554 0.000060 0.000029 -0.000031 2.434898 -0.000002

3796.8 2.434592 0.000050 0.000022 -0.000021 2.433946 -0.000011

4157.5 2.433206 0.000060 0.000018 -0.000009 2.432568 -0.000018

4346.9 2.432511 0.000030 0.000011 -0.000005 2.431872 -0.000017

4429.6 2.432208 0.000060 0.000020 0.000001 2.431572 -0.000021

4751.5 2.431070 0.000090 0.000028 -0.000006 2.430416 -0.000002

4890.3 2.430587 0.000080 0.000046 -0.000013 2.429920 0.000011

5062.5 2.429960 0.000090 0.000046 0.000006 2.429303 0.000001

5345.4 2.428913 0.000040 0.000021 0.000048 2.428281 -0.000024

5433.7 2.428603 0.000030 0.000015 0.000043 2.427960 -0.000012

TL

TS

TL

TS

TL

TS1T,n

2

3

2

2

3

2

2

2

2

2

2

1

2

2

12

where


31 OF 35 April 9, 2012

4

14

3

13

2

1211101 TSTSTSTSSTS

4

14

3

13

2

1211101 TLTLTLTLLTL

4

24

3

23

2

2221202 TSTSTSTSSTS

4

24

3

23

2

2221202 TLTLTLTLLTL

4

34

3

33

2

3231303 TSTSTSTSSTS

4

34

3

33

2

3231303 TLTLTLTLLTL

Temperature is in K and wavelength is in microns.

S10 = 4.2152533E+00 L10 = -2.0356047E+-01 S11 = 8.2999384-04 L11 = -5.9842123E-05 S12 = 1.9934043E-07 L12 = 4.4328993E-07 S13 = -1.5493287-09 L13 = -3.8221735E-12 S14 = 5.6574651E-12 L14 = -2.5019857E-12 S20 = 4.9401662E-01 L20 = 2.9958665E-01 S21 = 3.1453306E-04 L21 = 4.0887524E-04 S22 = -4.2033359E-07 L22 = 2.7181198E-07 S23 = -5.4733151E-09 L23 = -2.9503563E-09 S24 = 5.1221106E-12 L24 = 3.4010549E-12 S30 = 1.9241728E+04 L30 = -6.4070433E+03 S31 = -2.3562990E+01 L31 = 1.1605261E+01 S32 = 3.8969236E-01 L32 = 2.6360228E-02 S33 = -1.4378066E-03 L33 = -2.1345224E-04 S34 = 1.7563791E-06 L34 = 2.664831E-07 At 293.16K (20ºC),

478457805.4TS1 201582588.0TL1

450033130.0TS2 393599349.0TL2 6314.22572TS3

01223.4149TL3


32 OF 35 April 9, 2012

Appendix I – Comparison of Fitted Values, Fused Silica

Table I-1. Comparison among laboratories, Fused Silica

Wavelength (nm)

Refractive Index Difference at 20ºC

M3M-AFRL NASA-M3M AFRL-NASA

0.400 -0.000320 0.000224 0.000096

0.450 -0.000179 0.000093 0.000086

0.500 -0.000094 0.000029 0.000065

0.550 -0.000040 -0.000005 0.000044

0.600 -0.000004 -0.000023 0.000027

0.650 0.000021 -0.000033 0.000012

0.700 0.000039 -0.000039 0.000000

0.750 0.000051 -0.000042 -0.000009

0.800 0.000060 -0.000044 -0.000016

0.900 0.000071 -0.000046 -0.000025

1.000 0.000075 -0.000046 -0.000029

1.100 0.000075 -0.000045 -0.000030

1.200 0.000073 -0.000045 -0.000028

1.300 0.000068 -0.000044 -0.000024

1.400 0.000063 -0.000044 -0.000019

1.500 0.000056 -0.000044 -0.000013

1.600 0.000049 -0.000043 -0.000006

1.700 0.000042 -0.000043 0.000002

1.800 0.000034 -0.000043 0.000009

1.900 0.000027 -0.000043 0.000016

2.000 0.000019 -0.000042 0.000023

2.200 0.000007 -0.000041 0.000034

2.400 -0.000001 -0.000039 0.000040

2.600 -0.000003 -0.000035 0.000038

2.800 0.000004 -0.000029 0.000025

3.000 0.000024 -0.000021 -0.000003

3.200 0.000060 -0.000010 -0.000050

3.400 0.000117 0.000005 -0.000122

3.600 0.000202 0.000025 -0.000227

3.800 0.000321 0.000051 -0.000372

4.000 0.000484 0.000084 -0.000568

WC 0.000484 0.000093 -0.000331

RMS 0.000139 0.000037 0.000085


33 OF 35 April 9, 2012

Table I-2. Comparison vs. Optics Handbook, Fused Silica

Wavelength (nm)

Refractive Index Difference at 20ºC

M3M-Hdbk NASA-Hdbk AFRL-Hdbk

0.400 -0.000120 0.000104 0.000200

0.450 0.000011 0.000104 0.000190

0.500 0.000076 0.000105 0.000170

0.550 0.000110 0.000105 0.000149

0.600 0.000128 0.000105 0.000131

0.650 0.000137 0.000104 0.000116

0.700 0.000143 0.000104 0.000104

0.750 0.000145 0.000103 0.000094

0.800 0.000147 0.000103 0.000087

0.900 0.000148 0.000103 0.000078

1.000 0.000149 0.000104 0.000075

1.100 0.000151 0.000105 0.000076

1.200 0.000153 0.000108 0.000080

1.300 0.000155 0.000111 0.000087

1.400 0.000158 0.000114 0.000096

1.500 0.000162 0.000118 0.000106

1.600 0.000166 0.000123 0.000117

1.700 0.000171 0.000128 0.000129

1.800 0.000176 0.000133 0.000142

1.900 0.000181 0.000138 0.000154

2.000 0.000186 0.000144 0.000167

2.200 0.000197 0.000156 0.000190

2.400 0.000207 0.000169 0.000209

2.600 0.000217 0.000182 0.000220

2.800 0.000224 0.000195 0.000220

3.000 0.000229 0.000208 0.000205

3.200 0.000230 0.000220 0.000170

3.400 0.000226 0.000230 0.000108

3.600 0.000214 0.000239 0.000012

3.800 0.000194 0.000244 -0.000127

4.000 0.000161 0.000245 -0.000323

WC 0.000230 0.000243 -0.000323

RMS 0.000188 0.000166 0.000159


34 OF 35 April 9, 2012

Appendix J – Comparison of Fitted Values, Zinc Selenide

Table J-1. Comparison among laboratories, Zinc Selenide

Wavelength (nm)


M3M-AFRL NASA-M3M AFRL-NASA

0.55 0.000458 -0.000561 0.000104

0.60 0.000241 -0.000492 0.000251

0.65 0.000130 -0.000347 0.000217

0.70 0.000064 -0.000243 0.000179

0.75 0.000018 -0.000177 0.000159

0.80 -0.000018 -0.000137 0.000155

0.90 -0.000073 -0.000101 0.000174

1.00 -0.000115 -0.000091 0.000206

1.10 -0.000149 -0.000091 0.000240

1.20 -0.000177 -0.000093 0.000270

1.30 -0.000200 -0.000097 0.000296

1.40 -0.000218 -0.000100 0.000318

1.50 -0.000233 -0.000102 0.000335

1.60 -0.000245 -0.000104 0.000349

1.70 -0.000255 -0.000106 0.000360

1.80 -0.000262 -0.000106 0.000369

1.90 -0.000269 -0.000106 0.000375

2.00 -0.000274 -0.000106 0.000380

2.50 -0.000284 -0.000100 0.000384

3.00 -0.000280 -0.000089 0.000369

3.50 -0.000269 -0.000079 0.000348

4.00 -0.000255 -0.000072 0.000327

4.50 -0.000239 -0.000073 0.000312

5.00 -0.000226 -0.000085 0.000311

5.50 -0.000216 -0.000113 0.000329

6.00 -0.000211 -0.000162 0.000374

6.50 -0.000229 -0.000350 0.000579

7.50 -0.000257 -0.000502 0.000759

8.00 -0.000301 -0.000706 0.001006

8.50 -0.000364 -0.000970 0.001334

9.00 -0.000449 -0.001308 0.001758

9.50 -0.000561 -0.001733 0.002294

10.00 -0.000703 -0.002260 0.002964

10.50 -0.000880 -0.002908 0.003788

11.00 -0.001097 -0.003697 0.004794

11.50 -0.001357 -0.004653 0.006010

12.00 -0.001667 -0.005803 0.007470

WC -0.001097 -0.000603 0.000394

RMS 0.000406 0.000135 0.000338


35 OF 35 April 9, 2012

Table J-2. Comparison vs. Optics Handbook, Zinc Selenide

Wavelength (nm)


M3M-Hdbk NASA-Hdbk AFRL-Hdbk

0.55 0.001158 0.000597 0.000700

0.60 0.000925 0.000433 0.000685

0.65 0.000807 0.000460 0.000677

0.70 0.000729 0.000486 0.000665

0.75 0.000666 0.000489 0.000648

0.80 0.000613 0.000475 0.000630

0.90 0.000522 0.000421 0.000595

1.00 0.000448 0.000357 0.000564

1.10 0.000388 0.000297 0.000537

1.20 0.000338 0.000245 0.000515

1.30 0.000297 0.000201 0.000497

1.40 0.000263 0.000164 0.000481

1.50 0.000235 0.000133 0.000468

1.60 0.000211 0.000107 0.000456

1.70 0.000192 0.000086 0.000446

1.80 0.000175 0.000068 0.000437

1.90 0.000160 0.000054 0.000429

2.00 0.000148 0.000042 0.000421

2.50 0.000107 0.000008 0.000391

3.00 0.000087 -0.000002 0.000368

3.50 0.000078 0.000000 0.000347

4.00 0.000076 0.000004 0.000330

4.50 0.000077 0.000005 0.000317

5.00 0.000083 -0.000002 0.000308

5.50 0.000091 -0.000023 0.000306

6.00 0.000101 -0.000061 0.000312

6.50 0.000129 -0.000220 0.000359

7.50 0.000147 -0.000355 0.000404

8.00 0.000168 -0.000538 0.000468

8.50 0.000191 -0.000779 0.000555

9.00 0.000218 -0.001091 0.000667

9.50 0.000247 -0.001486 0.000809

10.00 0.000281 -0.001979 0.000984

10.50 0.000318 -0.002590 0.001199

11.00 0.000360 -0.003337 0.001457

11.50 0.000407 -0.004246 0.001764

12.00 0.000458 -0.005345 0.002126

WC 0.001158 0.000555 0.001457

RMS 0.000269 0.000163 0.000592

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