杂散光分析

EO-1 Stray Light Analysis Report No. 3 Submitted to: MIT Lincoln Laboratory 244 Wood Street Lexington, MA 02173 P.O. # AX-114413 May 4, 1998 Prepared by: Lambda Research Corporation 80 Taylor Street P.O. Box 1400 Littleton, MA 01460-4400 Tel. (978) 486-0766 FAX (978) 486-0755 EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation TABLE OF CONTENTS 1. SUMMARY...........................................................................................................................1 2. MEASURED BRDFS AND BRDF MODELS.....................................................................1 3. PREDICTED TIS, MTF DEGRADATION, AND STRAY LIGHT ...................................1 3.1 TIS........................................................................................................................................1 3.2 MTF DEGRADATION..............................................................................................................2 3.3 STRAY LIGHT.........................................................................................................................2 3.4 RESULTS................................................................................................................................4 4. TRACEPRO SIMULATIONS AND STRAY RADIATION SCENE INTEGRATION .....5 4.1 TRACEPRO MODEL................................................................................................................5 4.2 TRACEPRO SIMULATIONS AND PST PREDICTIONS...................................................................6 4.3 EXTENDED SOURCE INTEGRATION..........................................................................................8 5. EDGE RESPONSE DEGRADATION.................................................................................9 6. APPENDIX A - ETM+ STRAY LIGHT REQUIREMENT ..............................................11 7. APPENDIX B - SCHMITT MEASUREMENT BRDF DATA .........................................12 EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation 1 1. Summary This study is a detailed follow-up to two previous studies concerning stray light in the EO-1 telescope (see EO-1 Stray Light Analysis Reports 1 and 2). Following coating of the EO-1 flight mirrors, the BRDF was measured by SSG, then re-measured by Schmitt Measurement Systems. The stray spectral radiance from the Stray Radiation Scene described in the LANDSAT 7 specification was recalculated using the Schmitt BRDF measurements and a simple spreadsheet calculation. This calculation assumes the Point Source Transmittance (PST) is rotationally symmetric, and does an integration over the Stray Radiation Scene. To refine this estimate of stray radiance, ray-trace simulations were done using TracePro to better predict the PST. The PST was used to calculate the stray spectral radiance using a C++ computer program written for this purpose. The stray spectral radiance was computed by integrating over the LANDSAT 7 Stray Radiation Scene, weighed by the PST. 2. Measured BRDFs and BRDF models The measured BRDF data for mirrors M1, M2, M3, and F1 measured by Schmitt were curve- fitted using the ABg BSDF model to allow easier calculation of TIS, MTF degradation, and stray light, and for use in the TracePro simulations. This BSDF model has the form BSDF A B g( ) , r r r rb b b b - = + - 0 0 where A, B, and g are fitting parameters. Per the Harvey-Shack BSDF model, r b is the projection of the unit vector in the scattering direction onto the surface, and r b 0 is a projection of the specular direction unit vector onto the surface. This BSDF model has the advantage that it does not have a singularity at r r b b- =0 0 , as some other models do. It also adequately fits a wide variety of measured BSDFs. The fitted BRDF curves are shown in Appendix B. 3. Predicted TIS, MTF Degradation, and Stray Light Using these fitted BRDFs, we have computed the total integrated scatter (TIS), the MTF degradation, and the stray light according to the “Stray Radiation Scene.” We have computed the contribution to each of these quantities from each mirror as well as the result for the whole system. 3.1 TIS The TIS for each mirror was calculated by simply integrating the BRDF over a hemisphere, TIS BRDF d d= òò ( , )cos sin / q f q q q f pp 0 2 0 2 . EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation 2 Again, the BRDF has the form of the ABg BSDF model as described above. In this model, the BRDF scales as 1/l4, and the angular dependence of the BRDF scales linearly with angle. Therefore, for a 1/sin2q dependence (i.e. g = 2), the BRDF will scale as 1/l4 for small angles and 1/l4-g for large angles, and the TIS scales by a factor between 1/l4 and 1/l4-g. 3.2 MTF Degradation The MTF degradation factor was calculated by first assuming that the scattered light causes a uniform haze when the instrument is presented with an extended scene. This in turn causes the wings of the point spread function to increase uniformly. Since the MTF is the Fourier transform of the PSF, and the Fourier transform of a constant value is a delta function, we expect the effect on the MTF to be addition of a delta function at zero frequency. Since the MTF is always normalized to the DC value, this has the effect of lowering the MTF uniformly, by a multiplicative factor, at all non-zero spatial frequencies. An MTF degradation factor can be computed as approximately d = 1 - TIS . The fact the scattered light is not uniform, but falls off with increasing angle, has little effect on this approximation, because it is nearly uniform compared to the Airy pattern, which falls off as 1/q3. This departure from uniformity is manifested as a slight broadening of the delta function, but the multiplicative factor is not affected. This approximation will predict a worse degradation than will actually be observed for another reason: the scatter at large angles will miss the image plane. Furthermore, the mirrors are shaded from light incident at large angles by the baffles and by the finite field of view of the system. A more accurate calculation would integrate over a solid angle corresponding to the observable angle in object space as seen from each mirror. 3.3 Stray Light The stray light was computed by first calculating the stray irradiance from the “stray radiation scene.” The stray radiation scene consists of a small circular target region of low radiance surrounded by a large annular region of scene radiance. The stray light is specified as a ratio of the spectral radiance from this composite scene to the nominal full-scale spectral radiance for each band. We have calculated the stray spectral radiance as an equivalent scene radiance for direct comparison with the specification. With a spectral radiance MlFOV incident on the instrument from the target, the spectral irradiance focused on the detector by the instrument is E M Fd FOVl l p = 4 2 , where F is the F-number of the system. A differential element of spectral irradiance incident on the instrument from a differential element of solid angle outside the target (i.e. from the stray radiation scene) is dE M dSCENE0 l l= W , EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation 3 where is dW is the differential solid angle. The stray spectral irradiance resulting at the detector from the differential solid angle of the scene is dE PST dEstray l l= × 0 , where we model the PST as PST f S f S f S f S F = + + +[ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )]1 1 2 2 3 3 4 4 24 q q q q q q q q p . Here the f functions are the BRDFs of the mirrors, and the S functions are the shading functions for each mirror. For this analysis, the shading functions are simply triangle-shaped functions of the form S=1-(sinq/sinqmax), and truncated to zero at angles larger than qmax. The shading values are the same as used by Wally Wong of SSG, namely 26.6, 9.5, 9.5, and 4.75 degrees for mirrors M1- F1, respectively. The total stray spectral irradiance is the integral over the differential spectral irradiance, E PST M dstray SCENE strayscene l l= ×ò W , which expands to E F M f S f S f S f S dstray SCENE strayscene l l p q q q q q q q q= + + +ò4 2 1 1 2 2 3 3 4 4[ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )] W . Here we have taken the (annular) angular dependence of the scene spectral radiance out of M and put it into the integration limits, allowing us to treat M as a constant. Finally, there is a contribution to the stray light due to the target itself. This is identical in form to the scene stray light, except that the target spectral radiance is used and the integral is performed over the circular region comprising the inside of the stray radiation scene (i.e., the target). The sum of these two stray light terms give the total stray spectral irradiance. Noting that the signal light collected by the instrument from the target is E M Fd FOVl l p = 4 2 , we can get an expression for the equivalent stray spectral radiance, M E F M f S d M f S dstrayeqivalent stray SCENE i i strayscene FOV i i t et l l l lp = = +åò åò 4 2 ( ) ( ) arg W W . The target integration region is the small 768 mr diameter hole in the annular stray radiation scene. It has a small contribution to the stray light, but we include it for the sake of completeness. The above integrals have been calculated for each of the 8 bands in the LANDSAT 7 System Specification Revision K (July 1997). EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation 4 3.4 Results The results of the above calculations are summarized in the tables below. Table 1 shows the predicted TIS and MTF degradation factor due to each mirror, and the composite or system predictions. Table 1 Predicted TIS and MTF degradation factors TIS - Schmitt BRDF data MTF Multiplier - from Schmitt BRDF data BAND M1 M2 M3 F1 Composite M1 M2 M3 F1 Composite PAN 0.0321 0.0014 0.0270 0.0042 0.0647 0.9679 0.9986 0.9730 0.9958 0.9353 1 0.0756 0.0034 0.0647 0.0113 0.1551 0.9244 0.9966 0.9353 0.9887 0.8449 2 0.0533 0.0023 0.0454 0.0076 0.1086 0.9467 0.9977 0.9546 0.9924 0.8914 3 0.0377 0.0016 0.0319 0.0051 0.0764 0.9623 0.9984 0.9681 0.9949 0.9236 4 0.0222 0.0009 0.0185 0.0028 0.0444 0.9778 0.9991 0.9815 0.9972 0.9556 5 0.0048 0.0002 0.0038 0.0005 0.0093 0.9952 0.9998 0.9962 0.9995 0.9907 6 5.4E-05 1.8E-06 1.9E-05 1.7E-06 7.7E-05 0.9999 1.0000 1.0000 1.0000 0.9999 7 0.0025 0.0001 0.0018 0.0002 0.0046 0.9975 0.9999 0.9982 0.9998 0.9954 Table 2 shows the equivalent stray spectral radiance for all eight bands. The results are expressed both as equivalent spectral radiance values and as a percentage of the saturation signal for all eight bands in the LANDSAT 7 Spec. Rev. K, and for both gain settings. The numbers in this table compare directly with the 2% requirement stated in the specification. In Table 3, the contribution for each mirror is shown. Clearly, the stray light from M1 is the major contributor in all bands, due to its high BRDF and relatively full illumination by the stray radiation scene. These predictions are probably slightly pessimistic. A more accurate calculation could be done by simulating the telescope with a ray tracing program such as TracePro to generate a three- dimensional PST, then integrating over the stray radiation scene. Table 2 Equivalent stray spectral radiance from the Stray Radiation Scene. Low gain High gain Stray spectral spectral Spectral percent of Spectral Radiance represent. Band radiance radiance Radiance lo gain hi gain FOV Scene bFOV bGAP bSCENE wavelength PAN 23.50 15.63 1.20 5.12% 7.70% 2.285 44.05 0.000256 0.000768 0.436 0.71 1 28.57 19.00 4.03 14.09% 21.19% 4.000 57.32 0.000256 0.000768 0.436 0.48 2 29.13 19.37 2.64 9.06% 13.63% 3.000 55.17 0.000256 0.000768 0.436 0.57 3 22.50 14.96 1.58 7.02% 10.56% 2.167 48.31 0.000256 0.000768 0.436 0.66 4 22.50 14.96 0.65 2.89% 4.34% 1.375 35.72 0.000256 0.000768 0.436 0.84 5 4.73 3.15 0.043 0.92% 1.38% 0.400 12.97 0.000256 0.000768 0.436 1.65 6 (cond 1) 1.50E-03 7.70E-04 2.0E-08 0.0013% 0.0026% 8.50E-04 8.50E-04 0.000682 0.000682 0.436 11.45 6 (cond 2) 1.50E-03 7.70E-04 3.3E-08 0.0022% 0.0043% 8.50E-04 1.42E-03 0.000682 0.000682 0.436 11.45 7 1.67 1.11 0.0094 0.56% 0.85% 0.170 5.93 0.000256 0.000768 0.436 2.22 Table 3 Contributions of each mirror to the equivalent stray spectral radiance. Stray Spectral Radiance by Mirror- Schmitt data % contribution by mirror BAND M1 M2 M3 F1 M1 M2 M3 F1 PAN 0.8887 0.0215 0.2821 0.0121 73.79% 1.78% 23.42% 1.00% 1 2.7991 0.0710 1.1015 0.0544 69.53% 1.76% 27.36% 1.35% 2 1.8794 0.0468 0.6821 0.0317 71.19% 1.77% 25.84% 1.20% 3 1.1527 0.0281 0.3828 0.0168 72.94% 1.78% 24.22% 1.06% 4 0.4923 0.0117 0.1399 0.0056 75.79% 1.79% 21.54% 0.87% 5 0.0366 0.0008 0.0058 0.0002 84.47% 1.83% 13.26% 0.44% 6 (cond 1) 1.92E-08 3.24E-10 2.40E-10 7.00E-12 97.11% 1.64% 1.21% 0.04% 6 (cond 2) 3.20E-08 5.41E-10 4.00E-10 1.17E-11 97.11% 1.64% 1.21% 0.04% 7 8.27E-03 1.73E-04 9.30E-04 2.91E-05 87.96% 1.84% 9.89% 0.31% EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation 5 4. TracePro Simulations and Stray Radiation Scene Integration In order to refine the estimates of stray light by more accurately modeling the shading functions (view factors) of the mirrors, the EO-1 instrument was simulated using TracePro, a Monte Carlo ray-tracing program developed and marketed by Lambda Research. In TracePro, rays or photons are traced through an optical system and the interactions of these rays with optical surfaces are modeled according to probability distributions. The probability distributions are used to model the directions in which light scatters. Variance reduction techniques are used to improve the efficiency of the Monte Carlo process. These variance reduction techniques include ray splitting and importance sampling. In ray splitting, a ray may be split into several components when it strikes a surface. For example, reflected, refracted, absorbed, and scattered components may be produced. In importance sampling, a ray may be selected to go along an unlikely path that is of interest to the user (e.g., toward the detector or an image of the detector) thereby increasing the probability to one, and the flux of the ray component is renormalized to compensate for the increased probability. TracePro has its Monte Carlo roots in the GUERAP stray light analysis program which has been used for almost 30 years to analyze stray light in a large number of aerospace optical systems. 4.1 TracePro Model The TracePro model used for the simulations was based on a previous model of the instrument developed under contract to SSG. This earlier model included the GIS spectrometer, which was deleted from the model for this study. The model was then modified to include the correct location of baffle edges in the as-built flight unit. The shape of the entrance port was also modified to match drawings supplied by MITLL, while the M1, M3, and F1 mirror shapes were left as rectangular approximations to the true shapes. The latches for the instrument cover were added, as was the stop on the secondary mirror. The ABg models of BRDF that were fitted to the 0.6328 mm data measured by Schmitt Measurement Systems were applied to the mirrors. A small image surface of radius 0.01 mm was defined at six degrees off axis in the cross-track direction. Finally, importance sampling was defined for the mirrors, stop, baffles and instrument structure to enhance sampling to this small image. An isometric view of the completed model is shown in Figure 1. The TracePro coordinate system is also shown in Figure 1, with the z axis pointing to the right along the optical axis, the y axis pointing up, and the x axis pointing “into the page.” This coordinate system is used for the discussions of point source transmittance and edge response in subsequent sections. EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation 6 Figure 1 Isometric view of TracePro model of EO-1 telescope 4.2 TracePro Simulations and PST predictions In order to characterize the PST over the angles needed for the extended source integration over the Stray Radiation Scene, ray-traces were done using the TracePro model. Collimated light was simulated in a polar array of directions, with the pole of the array passing through the center of the six-degree-off-axis image surface. The polar angles simulated were 0.01, 0.1, 1, 2, 5, 10, 15, 20, and 25 degrees, while the azimuth angles were 0 through 315 degrees in 45-degree increments. This grid of 9 polar by 8 azimuth angles means a total of 72 simulations were done. As expected, the stray light in all cases is dominated by mirror scatter, with M1 being the greatest contributor. The PST values resulting from the simulations are summarized in Figure 2. Also shown in Figure 2 are a simplified calculation of "unbaffled" PST as a point of reference and the equivalent PST due only to aperture diffraction. The unbaffled PST is what would occur if there were no baffles or instrument structure whatsoever. It was calculated from the mirror BRDFs using the formula )( 4 43212 ffff F PST +++= p where F is the f-number of the optical system and f1 through f4 are the mirror BRDFs. An additional assumption implicit in this formula is that the BRDFs have a 1/sin2q dependence. EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation 7 The predicted PST closely matches the earlier predicted PST at small off-field angles and shows the expected asymmetry at larger angles. EO1 Point Source Transmittance TracePro ray-trace simulation 1.00E-08 1.00E-07 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00 1.00E+01 0 5 10 15 20 25 Off-field angle P S T -y PST +y PST -x PST +x PST +x -y PST -x +y PST -x -y PST +x +y PST Unbaffled PST Diffraction PST Figure 2 PST predicted by TracePro for EO-1 band 3 There are some problematic angles for this telescope that, if it were not for the large amount of light scattered from M1, would emerge as stray light problems at large off-axis angles. One such case is illustrated in Figure 3. In this picture, light is incident at a y angle of +25 degrees and strikes M3 directly, from where is scatters directly toward the image of the detector. In a well- EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation 8 baffled telescope, this light would be largely absorbed by the baffles, and only light scattered from baffles would reach M3. Ironically, M1 is completely shaded at this angle. This angle corresponds to the 25° point for the +y curve in Figure 2. Figure 3 Light incident at y angle of +25 degrees reaches M3 directly. 4.3 Extended Source Integration A special-purpose computer program was written to perform the integration over the annular source. The program performs a simple trapezoidal rule integration over the Stray Radiation Scene. The PST is interpolated between the calculated points using a semi-logarithmic interpolation - this is equivalent to drawing straight lines between the points on a semi-log graph of the PST as shown above. The resulting stray spectral radiance, calculated for Band 3 (a close match to 0.6328 um) was scaled to the other bands by a simple multiplicative factor. The results for all bands are summarized in the table below, along with the results calculated above using spreadsheet calculations. The results are in close agreement with the earlier results predicted by the spreadsheet calculation. EO-1 Stray Light Analysis Report No 3 4-May-98 Lambda Research Corporation 9 Table 4 Stray Spectral Radiance predicted by TracePro Previous TracePro Low gain High gain results results spectral spectral percent of Band radiance radiance radiance radiance lo gain hi gain PAN 1.20 1.14 23.5 15.63 4.83% 7.27% 1 4.03 3.80 28.57 19 13.2