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A phase function can be determined from Mie theory if given the particle size distribution, particle phase, optical depth, and wavenumber. If a particle size distribution is assumed under cirrus conditions for a given microwindow region, the optical depth remains the only unknown.
Reflectance was calculated for a series of optical depths for each microwindow region; where the IR optical depth varied from 0.01 through 5.0. The upper limit is beyond the capabilities of the lidar and is an acceptable cut-off.
Figure 39 shows a plot of reflectance as a function of the
IR optical depth; which is subsequently fit with a sixth-order polynomial to
determine a parameterization for the reflectance for the given optical
depth range. Data shown is at 772 cm
. The calculated reflectance for
the given assumptions varies from 0 to 0.52%, among all microwindows.
Figure 39: Reflectance as a function of IR optical depth and a sixth-order
polynomial fit for the microwindow region centered at 722 cm. The fit
is required to parameterize reflectance to allow optical depth
inversion from the IR RTE.
The coefficients for each microwindow region are given in Table 9 for completeness, such that
where the reflectance is valid for infrared optical depths between 0 and 5, and the spectral dependence is implied.
 window (cm ) | a 10  | b 10  | c 10
| d 10 | e 10  | f 10
| g 10 
|
| 773 | 3.9556 | 7.8733 | -6.1774 | 2.8969 | -7.8505 | 1.1149 | -6.3747 |
| 788 | 3.8503 | 7.6638 | -6.0055 | 2.8156 | -7.6313 | 1.0839 | -6.1990 |
| 811 | 3.6348 | 7.1907 | -5.6321 | 2.6428 | -7.1704 | 1.0194 | -5.8339 |
| 820 | 3.5399 | 6.9738 | -5.4638 | 2.5656 | -6.9656 | 0.9908 | -5.6724 |
| 831 | 3.5093 | 6.6325 | -5.2271 | 2.4700 | -6.7406 | 0.9624 | -5.5254 |
| 846 | 3.2853 | 6.1136 | -4.8293 | 2.2878 | -6.2555 | 0.8944 | -5.1399 |
| 862 | 3.0069 | 5.4711 | -4.3383 | 2.0628 | -5.6558 | 0.8102 | -4.6621 |
| 875 | 2.7645 | 4.9264 | -3.9209 | 1.8710 | -5.1439 | 0.7382 | -4.2533 |
| 894 | 2.3410 | 3.9045 | -3.1262 | 1.4978 | -4.1250 | 0.5921 | -3.4095 |
| 902 | 2.1395 | 3.4956 | -2.8113 | 1.3524 | -3.7352 | 0.5372 | -3.0979 |
| 935 | 1.2622 | 1.8554 | -1.5322 | 0.7510 | -2.0987 | 0.3041 | -1.7628 |
| 962 | 1.3547 | 1.9466 | -1.6173 | 0.7948 | -2.2233 | 0.3223 | -1.8688 |
| 992 | 1.9235 | 2.8994 | -2.3775 | 1.1578 | -3.2208 | 0.4653 | -2.6902 |
| 1081 | 2.4633 | 4.0218 | -3.2373 | 1.5550 | -4.2874 | 0.6158 | -3.5472 |
| 1096 | 2.4832 | 4.0746 | -3.2745 | 1.5712 | -4.3288 | 0.6214 | -3.5784 |
| 1115 | 2.5223 | 4.1853 | -3.3529 | 1.6056 | -4.4185 | 0.6338 | -3.6486 |
| 1129 | 2.5462 | 4.2579 | -3.4040 | 1.6281 | -4.4778 | 0.6422 | -3.6958 |
| 1145 | 2.5693 | 4.3299 | -3.4540 | 1.6498 | -4.5338 | 0.6499 | -3.7389 |
| 1159 | 2.5818 | 4.3689 | -3.4799 | 1.6607 | -4.5613 | 0.6536 | -3.7596 |