Appendix

I. Tables of the Kubelka-Munk-Function

Roo F(Roo) logF(R",) Roo F(Roo) logF(Roo)

0,0010 499,00 +2,6981 0,0020 249,00 +2,3962 0,0030 165,67 +2,2192 0,0040 124,00 +2,0934 0,0050 99,003 +1,9956 0,0060 82,336 +1,9156 0,0070 70,432 + 1,8478 0,0080 61,504 +1,7889 0,0090 54,560 + 1,7369 0,0100 49,005 +1,6902 0,0110 44,460 +1,6480 0,0120 40,673 +1,6093 0,0130 37,468 + 1,5737 0,0140 34,721 +1,5406 0,0150 32,341 +1,5098 0,0160 30,258 +1,4808 0,0170 28,420 +1,4536 0,0180 26,787 +1,4279 0,0190 25,325 +1,4036 0,0200 24,010 + 1,3804

0,0210 22,820 + 1,3583" 0,0220 21,738 + 1,3372 0,0230 20,751 +1,3170 0,0240 19,845 +1,2977 0,0250 19,013 +1,2790 0,0260 18,244 +1,2611 0,0270 17,532 +1,2438 0,0280 16,871 + 1,2271 0,0290 16,256 + 1,2110 0,0300 15.682 + 1,1954 0,0310 15,145 +1,1803 0,0320 14,641 + 1,1656 0,0330 14,168 + 1,1513 0,0340 13,723 +1,1374 0,0350 13,303 + 1,1240 0,0360 12,907 +1,1108 0,0370 12,532 +1,0980 0,0380 12,177 + 1,0855 0,0390 11,840 +1,0734 0,0400 11,520 +1,0615

0,0410 11,216 +1,0498 0,0420 10,926 + 1,0385 0,0430 10,649 +1,0273 0,0440 10,386 +1,0164 0,0450 10,134 + 1,0058 0,0460 9,8926 +0,9953 0,0470 9,6618 +0,9851 0,0480 9,4407 +0,9750 0,0490 9,2286 +0,9651 0,0500 9,0250 +0,9554 0,0510 8,8294 +0,9459 0,0520 8,6414 +0,9366 0,0530 8,4605 +0,9274 0,0540 8,2863 +0,9184 0,0550 8,1184 +0,9095 0,0560 7,9566 +0,9007 0,0570 7,8004 +0,8921 0,0580 7,6497 +0,8836 0,0590 7,5041 +0,8753 0,0600 7,3633 +0,8671

22 Kortiim, Reflectance Spectroscopy

338 Appendix

1. (continued)

~ F(Roo) logF(~) ~ F(Roo) logF(Roo)

0,0610 7,2272 +0,8590 0,0620 7,0955 +0,8510 0,0630 6,9680 +0,8431 0,0640 6,8445 +0,8353 0,0650 6,7248 +0,8277 0,0660 6,6088 +0,8201 0,0670 6,4962 +0,8127 0,0680 6,3869 +0,8053 0,0690 6,2809 +0,7980 0,0700 6,1779 +0,7908 0,0710 6,0778 +0,7837 0,0720 5,9804 +0,7767 0,0730 5,8858 +0,7698 0,0740 5,7938 +0,7630 0,0750 5,7042 +0,7562 0,0760 5,6169 +0,7495 0,0770 5,5320 +0,7429 0,0780 5,4493 +0,7363 0,0790 5,3686 +0,7299 0,0800 5,2900 +0,7235

0,0810 5,2133 +0,7171 0,0820 5,1386 +0,7108 0,0830 5,0656 +0,7046 0,0840 4,9944 +0,6985 0,0850 4,9249 +0,6924 0,0860 4,8570 +0,6864 0,0870 4,7906 +0,6804 0,0880 4,7258 +0,6745 0,0890 4,6625 +0,6686 0,0900 4,6006 +0,6628 0,0910 4,5400 +0,6571 0,0920 4,4808 +0,6514 0,0930 4,4228 +0,6457 0,0940 4,3661 +0,6401 0,0950 4,3107 +0,6345 0,0960 4,2563 +0,6290 0,0970 4,2031 +0,6236 0,0980 4,1510 +0,6182 0,0990 4,1000 +0,6128 0,1000 4,0500 +0,6075

0,1010 4,0010 +0,6022 0,1020 3,9530 +0,5969 0,1030 3,9059 +0,5917 0,1040 3,8597 +0,5866 0,1050 3,8144 +0,5814 0,1060 3,7700 +0,5763 0,1070 3,7264 +0,5713 0,1080 3,6836 +0,5663 0,1090 3,6417 +0,5613 0,1100 3,6005 +0,5564 0,1110 3,5600 +0,5515 0,1120 3,5203 +0,5466 0,1130 3,4813 +0,5417 0,1140 3,4430 +0,5369 0,1150 3,4053 +0,5322 0,1160 3,3683 +0,5274 0,1170 3,3320 +0,5227 0,1180 3,2963 +0,5180 0,1190 3,2612 +0,5134 0,1200 3,2267 +0,5088

0,1210 3,1927 +0,5042 0,1220 3,1594 +0,4996 0,1230 3,1265 +0,4951 0,1240 3,0943 +0,4906 0,1250 3,0625 +0,4861 0,1260 3,0313 +0,4816 0,1270 3,0005 +0,4772 0,1280 2,9703 +0,4728 0,1290 2,9405 +0,4684 0,1300 2,9112 +0,4641 0,1310 2,8823 +0,4597 0,1320 2,8539 +0,4554 0,1330 2,8259 +0,4512 0,1340 2,7983 +0,4469 0,1350 2,7712 +0,4427 0,1360 2,7445 +0,4385 0,1370 2,7181 +0,4343 0,1380 2,6922 +0,4301 0,1390 2,6666 +0,4260 0,1400 2,6414 +0,4218

Tables of the Kubelka-Munk-Function 339

1. (continued)

Rx, F(R",) logF(Rx,) Rx, F(Rx,) logF(Rx,)

0,1410 2,6166 +0,4177 0,1420 2,5921 +0,4137 0,1430 2,5680 +0,4096 0,1440 2,5442 +0,4056 0,1450 2,5208 +0,4015 0,1460 2,4977 +0,3975 0,1470 2,4749 +0,3936 0,1480 2,4524 +0,3896 0,1490 2,4302 +0,3856 0,1500 2,4083 +0,3817 0,1510 2,3868 +0,3778 0,1520 2,3655 +0,3739 0,1530 2,3445 +0,3700 0,1540 2,3238 +0,3662 0,1550 2,3033 +0,3624 0,1560 2,2831 +0,3585 0,1570 2,2632 +0,3547 0,1580 2,2436 +0,3509 0,1590 2,2242 +0,3472 0,1600 2,2050 +0,3434

0,1610 2,1861 +0,3397 0,1620 2,1674 +0,3359 0,1630 2,1490 +0,3322 0,1640 2,1308 +0,3285 0,1650 2,1128 +0,3249 0,1660 2,0950 +0,3212 0,1670 2,0775 +0,3175 0,1680 2,0602 +0,3139 0,1690 2,0431 +0,3103 0,1700 2,0262 +.0,3067 0,1710 2,0095 +0,3031 0,1720 1,9930 +0,2995 0,1730 1,9767 +0,2959 0,1740 1,9606 +0,2924 0,1750 1,9446 +0,2888 0,1760 1,9289 +0,2853 0,1770 1,9134 +0,2818 0,1780 1,8980 +0,2783 0,1790 1,8828 +0,2748 0,1800 1,8678 +0,2713

0,1810 1,8529 +0,2679 0,1820 1,8383 +0,2644 0,1830 1,8237 +0,2610 0,1840 1,8094 +0,2575 0,1850 1,7952 +0;2541 0,1860 1,7812 +0,2507 0,1870 1,7673 +0,2473 0,1880 1,7536 +0,2439 0,1890 1,7400 +0,2405 0,1900 1,7266 +0,2372 0,1910 1,7133 +0,2338 0,1920 1,7002 +0,2305 0,1930 1,6872 +0,2272 0,1940 1,6743 +0,2238 0,1950 1,6616 +0,2205 0,1960 1,6490 +0,2172 0,1970 1,6366 +0,2139 0,1980 1,6243 +0,2107 0,1990 1,6121 +0,2074 0,2000 1,6000 +0,2041

0,2010 1,5881 +0,2009 0,2020 1,5762 +0,1976 0,2030 1,5646 +0,1944 0,2040 1,5530 +0,1912 0,2050 1,5415 +0,1880 0,2060 1,5302 +0,1847 0,2070 1,5190 +0,1815 0,2080 1,5078 +0,1784 0,2090 1,4968 +0,1752 0,2100 1,4860 +0,1720 0,2110 1,4752 +0,1688 0,2120 1,4645 +0,1657 0,2130 1,4539 +0,1625 0,2140 1,4434 +0,1594 0,2150 1,4331 +0,1563 0,2160 1,4228 +0,1531 0,2170 1,4126 +0,1500 0,2180 1,4026 +0,1469 0,2190 1,3926 +0,1438 0,2200 1,3827 +0,1407

22*

340 Appendix

1. (continued)

Rx, F(Rx,) logF(Rx,) Rx, F(Rx,) logF(Rx,)

0,2210 1,3729 +0,1377 0,2220 1,3633 +0,1346 0,2230 1,3537 +0,1315 0,2240 1,3441 +0,1284 0,2250 1,3347 +0,1254 0,2260 1,3254 +0,1223 0,2270 1,3161 +0,1193 0,2280 1,3070 +0,1163 0,2290 1,2979 +0,1132 0,2300 1,2889 +0,1102 0,2310 1,2800 +0,1072 0,2320 1,2712 +0,1042 0,2330 1,2624 +0,1012 0,2340 1,2538 +0,0982 0,2350 1,2452 +0,0952 0,2360 1,2366 +0,0922 0,2370 1,2282 +0,0893 0,2380 1,2198 +0,0863 0,2390 1,2116 +0,0833 0,2400 1,2033 +0,0804

0,2410 1,1952 +0,0774 0,2420 1,1871 +0,0745 0,2430 1,1791 +0,0716 0,2440 1,1712 +0,0686 0,2450 1,1633 +0,0657 0,2460 1,1555 +0,0628 0,2470 1,1478 +0,0599 0,2480 1,1401 +0,0570 0,2490 1,1325 +0,0541 0,2500 1,1250 +0,0512 0,2510 1,1175 +0,0483 0,2520 1,1101 +0,0454 0,2530 1,1028 +0,0425 0,2540 1,0955 +0,0396 0,2550 1,0883 +0,0367 0,2560 1,0811 +0,0339 0,2570 1,0740 +0,0310 0,2580 1,0670 +0,0282 0,2590 1,0600 +0,0253 0,2600 1,0531 +0,0225

0,2610 1,0462 +0,0196 0,2620 1,0394 +0,0168 0,2630 1,0326 +0,0139 0,2640 1,0259 +0,0111 0,2650 1,0193 +0,0083 0,2660 1,0127 +0,0055 0,2670 1,0062 +0,0027 0,2680 0,9997 -143.47 0,2690 0,9932 -0,0029 0,2700 0,9869 -0,0057 0,2710 0,9805 -0,0085 0,2720 0,9742 -0,0113 0,2730 0,9680 -0,0141 0,2740 0,9618 -0,0169 0,2750 0,9557 - 0,0197 0,2760 0,9496 -0,0225 0,2770 0,9436 -0,0252 0,2780 0,9376 -0,0280 0,2790 0,9316 -0,0308 0,2800 0,9257 -0,0335

0,2810 0,9199 -0,0363 0,2820 0,9140 -0,0390 0,2830 0,9083 -0,0418 0,2840 0,9026 -0,0445 0,2850 0,8969 -0,0473 0,2860 0,8913 -0,0500 0,2870 0,8857 -0,0527 0,2880 0,8801 -0,0555 0,2890 0,8746 -0,0582 0,2900 0,8691 -0,0609 0,2910 0,8637 -0,0636 0,2920 0,8583 -0,0663 0,2930 0,8530 -0,0691 0,2940 0,8477 -0,0718 0,2950 0,8424 -0,0745 0,2960 0,8372 -0,0772 0,2970 0,8320 -0,0799 0,2980 0,8269 -0,0826 0,2990 0,8217 -0,0853 0,3000 0,8167 -0,0880

Tables of the Kubelka-M unk -Function 341

1. (continued)

Roo F(~) logF(~) ~ F(~) logF(~)

0,3010 0,8116 -0,0906 0,3020 0,8066 -0,0933 0,3030 0,8017 -0,0960 0,3040 0,7967 -0,0987 0,3050 0,7918 -0,1014 0,3060 0,7870 -0,1040 0,3070 0,7822 -0,1067 0,3080 0,7774 -0,1094 0,3090 0,7726 -0,1120 0,3100 0,7679 -0,1147 0,3110 0,7632 -0,1174 0,3120 0,7586 -0,1200 0,3130 0,7539 -0,1227 0,3140 0,7494 -0,1253 0,3150 0,7448 -0,1280 0,3160 0,7403 -0,1306 0,3170 0,7358 -0,1332 0,3180 0,7313 -0,1359 0,3190 0,7269 -0,1385 0,3200 0,7225 -0,1412

0,3210 0,7181 -0,1438 0,3220 0,7138 -0,1464 0,3230 0,7095 -0,1491 0,3240 0,7052 -0,1517 0,3250 0,7010 -0,1543 0,3260 0,6967 -0,1569 0,3270 0,6926 -0,1595 0,3280 0,6884 -0,1622 0,3290 0,6843 -0,1648 0,3300 0,6802 -0,1674 0,3310 0,6761 -0,1700 0,3320 0,6720 -0,1726 0,3330 0,6680 -0,1752 0,3340 0,6640 -0,1778 0,3350 0,6600 -0,1804 0,3360 0,6561 -0,1830 0,3370 0,6522 -0,1856 0,3380 0,6483 -0,1882 0,3390 0,6444 -0,1908 0,3400 0,6406 -0,1934

0,3410 0,6368 -0,1960 0,3420 0,6330 -0,1986 0,3430 0,6292 -0,2012 0,3440 0,6255 -0,2038 0,3450 0,6218 -0,2064 0,3460 0,6181 -0,2090 0,3470 0,6144 -0,2115 0,3480 0,6108 -0,2141 0,3490 0,6072 -0,2167 0,3500 0,6036 -0,2193 0,3510 0,6000 -0,2218 0,3520 0,5965 -0,2244 0,3530 0,5929 -0,2270 0,3540 0,5894 -0,2296 0,3550 0,5860 -0,2321 0,3560 0,5825 -0,2347 0,3570 0,5791 -0,2373 0,3580 0,5756 -0,2398 0,3590 0,5723 -0,2424 0,3600 0,5689 -0,2450

0,3610 0,5655 -0,2475 0,3620 0,5622 -0,2501 0,3630 0,5589 -0,2527 0,3640 0,5556 -0,2552 0,3650 0,5524 -0,2578 0,3660 0,5491 -0,2603 0,3670 0,5459 -0,2629 0,3680 0,5427 -0,2654 0,3690 0,5395 -0,2680 0,3700 0,5364 -0,2706 0,3710 0,5332 -0,2731 0,3720 0,5301 -0,2757 0,3730 0,5270 -0,2782 0,3740 0,5239 -0,2808 0,3750 0,5208 -0,2833 0,3760 0,5178 -0,2858 0,3770 0,5148 -0,2884 0,3780 0,5118 -0,2909 0,3790 0,5088 -0,2935 0,3800 0,5058 -0,2960

342 Appendix

1. (con tin ued)

~ F(Roc,) logF(R",) ~ F(~) logF(~)

0,3810 0,5028 -0,2986 0,3820 0,4999 -0,3011 0,3830 0,4970 -0,3037 0,3840 0,4941 -0,3062 0,3850 0,4912 -0,3087 0,3860 0,4883 -0,3113 0,3870 0,4855 -0,3138 0,3880 0,4827 -0,3164 0,3890 0,4798 -0,3189 0,3900 0,4771 -0,3214 0,3910 0,4743 -0,3240 0,3920 0,4715 -0,3265 0,3930 0,4688 -0,3290 0,3940 0,4660 -0,3316 0,3950 0,4633 -0,3341 0,3960 0,4606 -0,3367 0,3970 0,4579 -0,3392 0,3980 0,4553 -0,3417 0,3990 0,4526 -0,3443 0,4000 0,4500 -0,3468

0,4010 0,4474 -0,3493 0,4020 0,4448 -0,3519 0,4030 0,4422 -0,3544 0,4040 0,4396 -0,3569 0,4050 0,4371 -0,3595 0,4060 0,4345 -0,3620 0,4070 0,4320 -0,3645 0,4080 0,4295 -0,3670 0,4090 0,4270 -0,3696 0,4100 0,4245 -0,3721 0,4110 0,4220 -0,3746 0,4120 0,4196 -0,3772 0,4130 0,4172 -0,3797 0,4140 0,4147 -0,3822 0,4150 0,4123 -0,3848 0,4160 0,4099 -0,3873 0,4170 0,4075 -0,3898 0,4180 0,4052 -0,3924 0,4190 0,4028 -0,3949 0,4200 0,4005 -0,3974

0,4210 0,3981 -0,4000 0,4220 0,3958 -0,4025 0,4230 0,3935 -0,4050 0,4240 0,3912 -0,4076 0,4250 0,3890 -0,4101 0,4260 0,3867 -0,4126 0,4270 0,3845 -0,4151 0,4280 0,3822 -0,4177 0,4290 0,3800 -0,4202 0,4300 0,3778 -0,4227 0,4310 0,3756 -0,4253 0,4320 0,3734 -0,4278 0,4330 0,3712 -0,4304 0,4340 0,3691 -0,4329 0,4350 0,3669 -0,4354 0,4360 0,3648 -0,4380 0,4370 0,3627 -0,4405 0,4380 0,3606 -0,4430 0,4390 0,3585 -0,4456 0,4400 0,3564 -0,4481

0,4410 0,3543 -0,4506 0,4420 0,3522 -0,4532 0,4430 0,3502 -0,4557 0,4440 0,3481 -0,4583 0,4450 0,3461 -0,4608 0,4460 0,3441 -0,4633 0,4470 0,3421 -0,4659 0,4480 0,3401 -0,4684 0,4490 0,3381 -0,4710 0,4500 0,3361 -0,4735 0,4510 0,3341 -0,4761 0,4520 0,3322 -0,4786 0,4530 0,3303 -0,4812 0,4540 0,3283 -0,4837 0,4550 0,3264 -0,4862 0,4560 0,3245 -0,4888 0,4570 0,3226 -0,4913 0,4580 0,3207 -0,4939 0,4590 0,3188 -0,4964 0,4600 0,3170 -0,4990

Tables of the Kubelka-Munk-Function 343

I. (continued)

Roo F(Roo) logF(Roo) Roo F(Roo) logF(Roo)

0,4610 0,3151 -0,5016 0,4620 0,3133 -0,5041 0,4630 0,3114 -0,5067 0,4640 0,3096 -0,5092 0,4650 0,3078 -0,5118 0,4660 0,3060 -0,5143 0,4670 0,3042 -0,5169 0,4680 0,3024 -0,5195 0,4690 0,3006 -0,5220 0,4700 0,2988 -0,5246 0,4710 0,2971 -0,5271 0,4720 0,2953 -0,5297 0,4730 0,2936 -0,5323 0,4740 0,2919 -0,5348 0,4750 0,2901 -0,5374 0,4760 0,2884 -0,5400 0,4770 0,2867 -0,5425 0,4780 0,2850 -0,5451 0,4790 0,2833 -0,5477 0,4800 0,2817 -0,5503

0,4810 0,2800 -0,5528 0,4820 0,2783 -0,5554 0,4830 0,2767 -0,5580 0,4840 0,2751 -0,5606 0,4850 0,2734 -0,5632 0,4860 0,2718 -0,5657 0,4870 0,2702 -0,5683 0,4880 0,2686 -0,5709 0,4890 0,2670 -0,5735 0,4900 0,2654 -0,5761 0,4910 0,2638 -0,5787 0,4920 0,2623 -0,5813 0,4930 0,2607 -0,5839 0,4940 0,2591 -0,5865 0,4950 0,2576 -0,5891 0,4960 0,2561 -0,5917 0,4970 0,2545 -0,5943 0,4980 0,2530 -0,5969 0,4990 0,2515 -0,5995 0,5000 0,2500 -0,6021

0,5010 0,2485 -0,6047 0,5020 0,2470 -0,6073 0,5030 0,2455 -0,6099 0,5040 0,2441 -0,6125 0,5050 0,2426 -0,6151 0,5060 0,2411 -0,6177 0,5070 0,2397 -0,6203 0,5080 0,2383 -0,6230 0,5090 0,2368 -0,6256 0,5100 0,2354 -0,6282 0,5110 0,2340 -0,6308 0,5120 0,2326 -0,6335 0,5130 0,2312 -0,6361 0,5140 0,2298 -0,6387 0,5150 0,2284 -0,6414 0,5160 0,2270 -0,6440 0,5170 0,2256 -0,6466 0,5180 0,2243 -0,6493 0,5190 0,2229 -0,6519 0,5200 0,2215 -0,6546

0,5210 0,2202 -0,6572 0,5220 0,2189 -0,6598 0,5230 0,2175 -0,6625 0,5240 0,2162 -0,6651 0,5250 0,2149 -0,6678 0,5260 0,2136 -0,6705 0,5270 0,2123 -0,6731 0,5280 0,2110 -0,6758 0,5290 0,2097 -0,6784 0,5300 0,2084 -0,6811 0,5310 0,2071 -0,6838 0,5320 0,2058 -0,6864 0,5330 0,2046 -0,6891 0,5340 0,2033 -0,6918 0,5350 0,2021 -0,6945 0,5360 0,2008 -0,6972 0,5370 0,1996 -0,6998 0,5380 0,1984 -0,7025 0,5390 0,1971 -0,7052 0,5400 0,1959 -0,7079

344 Appendix

I. (continued)

Ra, F(Roo) logF(Roo) Roo F(Ra,) logF(Roo)

0,5410 0,1947 -0,7106 0,5420 0,1935 -0,7133 0,5430 0,1923 -0,7160 0,5440 0,1911 -0,7187 0,5450 0,1899 -0,7214 0,5460 0,1888 -0,7241 0,5470 0,1876 -0,7268 0,5480 0,1864 -0,7295 0,5490 0,1852 -0,7322 0,5500 0,1841 -0,7350 0,5510 0,1829 -0,7377 0,5520 0,1818 -0,7404 0,5530 0,1807 -0,7431 0,5540 0,1795 -0,7459 0,5550 0,1784 -0,7486 0,5560 0,1773 -0,7513 0,5570 0,1762 -0,7541 0,5580 0,1751 -0,7568 0,5590 0,1740 -0,7596 0,5600 0,1729 -0,7623

0,5610 0,1718 -0,7651 0,5620 0,1707 -0,7678 0,5630 0,1696 -0,7706 0,5640 0,1685 -0,7733 0,5650 0,1675 -0,7761 0,5660 0,1664 -0,7789 0,5670 0,1653 -0,7816 0,5680 0,1643 -0,7844 0,5690 0,1632 -0,7872 0,5700 0,1622 -0,7900 0,5710 0,1612 -0,7928 0,5720 0,1601 -0,7955 0,5730 0,1591 -0,7983 0,5740 0,1581 -0,8011 0,5750 0,1571 -0,8039 0,5760 0,1561 -0,8067 0,5770 0,1551 -0,8095 0,5780 0,1541 -0,8123 0,5790 0,1531 -0,8151 0,5800 0,1521 -0,8180

0,5810 0,1511 -0,8208 0,5820 0,1501 -0,8236 0,5830 0,1491 -0,8264 0,5840 0,1482 -0,8293 0,5850 0,1472 -0,8321 0,5860 0,1462 -0,8349 0,5870 0,1453 -0,8378 0,5880 0,1443 -0,8406 0,5890 0,1434 -0,8435 0,5900 0,1425 -0,8463 0,5910 0,1415 -0,8492 0,5920 0,1406 -0,8520 0,5930 0,1397 -0,8549 0,5940 0,1388 -0,8578 0,5950 0,1378 -0,8606 0,5960 0,1369 -0,8635 0,5970 0,1360 -0,8664 0,5980 0,1351 -0,8693 0,5990 0,1342 -0,8722 0,6000 0,1333 -0,8751

0,6010 0,1324 -0,8780 0,6020 0,1316 -0,8809 0,6030 0,1307 -0,8838 0,6040 0,1298 -0,8867 0,6050 0,1289 -0,8896 0,6060 0,1281 -0,8925 0,6070 0,1272 -0,8954 0,6080 0,1264 -0,8984 0,6090 0,1255 -0,9013 0,6100 0,1247 -0,9042 0,6110 0,1238 -0,9072 0,6120 0,1230 -0,9101 0,6130 0,1222 -0,9131 0,6140 0,1213 -0,9160 0,6150 0,1205 -0,9190 0,6160 0,1197 -0,9219 0,6170 0,1189 -0,9249 0,6180 0,1181 -0,9279 0,6190 0,1173 -0,9309 0,6200 0,1165 -0,9339

Tables of the Kubelka-Munk-Function 345

1. (continued)

~ F(Roo) logF(Roo) ~ F(~) logF(Roo)

0,6210 0,1157 -0,9368 0,6220 0,1149 -0,9398 0,6230 0,1141 -0,9428 0,6240 0,1133 -0,9458 0,6250 0,1125 -0,9488 0,6260 0,1117 -0,9519 0,6270 0,1109 -0,9549 0,6280 0,1102 -0,9579 0,6290 0,1094 -0,9609 0,6300 0,1087 -0,9640 0,6310 0,1079 -0,9670 0,6320 0,1071 -0,9701 0,6330 0,1064 -0,9731 0,6340 0,1056 -0,9762 0,6350 0,1049 -0,9792 0,6360 0,1042 -0,9823 0,6370 0,1034 -0,9854 0,6380 0,1027 -0,9884 0,6390 0,1020 -0,9915 0,6400 0,1013 -0,9946

0,6410 0,1005 -0,9977 0,6420 0,0998 -1,0008 0,6430 0,0991 -1,0039 0,6440 0,0984 -1,0070 0,6450 0,0977 -1,0101 0,6460 0,0970 -1,0133 0,6470 0,0963 -1,0164 0,6480 0,0956 -1,0195 0,6490 0,0949 -1,0227 0,6500 0,0942 -1,0258 0,6510 0,0935 -1,0290 0,6520 0,0929 -1,0321 0,6530 0,0922 -1,0353 0,6540 0,0915 -1,0385 0,6550 0,0909 -1,0416 0,6560 0,0902 -1,0448 0,6570 0,0895 -1,0480 0,6580 0,0889 -1,0512 0,6590 0,0882 -1,0544 0,6600 0,0876 -1,0576

0,6610 0,0869 -1,0608 0,6620 0,0863 -1,0641 0,6630 0,0856 -1,0673 0,6640 0,0850 -1,0705 0,6650 0,0844 -1,0738 0,6660 0,0838 -1,0770 0,6670 0,0831 -1,0803 0,6680 0,0825 -1,0835 0,6690 0,0819 -1,0868 0,6700 0,0813 -1,0901 0,6710 0,0807 -1,0934 0,6720 0,0800 -1,0967 0,6730 0,0794 -1,0999 0,6740 0,0788 -1,1033 0,6750 0,0782 -1,1066 0,6760 0,0776 -1,1099 0,6770 0,0771 -1,1132 0,(\780 0,0765 -1,1165 0,6790 0,0759 -1,1199 0,6800 0,0753 -1,1232

0,6810 0,0747 --1,1266 0,6820 0,0741 -1,1300 0,6830 0,0736 -1,1333 0,6840 0,0730 -1,1367 0,6850 0,0724 -1,1401 0,6860 0,0719 -1,1435 0,6870 0,0713 -1,1469 0,6880 0,0707 -1,1503 0,6890 0,0702 -1,1537 0,6900 0,0696 -1,1572 0,6910 0,0691 -1,1606 0,6920 0,0685 -1,1640 0,6930 0,0680 -1,1675 0,6940 0,0675 -1,1709 0,6950 0,0669 -1,1744 0,6960 0,0664 -1,1779 0,6970 0,0659 -1,1814 0,6980 0,0653 -1,1849 0,6990 0,0648 -1,1884 0,7000 0,0643 -1,1919

346 Appendix

I. (continued)

Roo F(Roo) logF(Roo) ~ F(Roo) logF(~)

0,7010 0,0638 -1,1954 0,7020 0,0633 -1,1989 0,7030 0,0627 -1,2025 0,7040 0,0622 -1,2060 0,7050 0,0617 -1,2096 0,7060 0,0612 -1,2131 0,7070 0,0607 -1,2167 0,7080 0,0602 -1,2203 0,7090 0,0597 -1,2239 0,7100 0,0592 -1,2275 0,7110 0,0587 -1,2311 0,7120 0,0582 -1,2347 0,7130 0,0578 -1,2384 0,7140 0,0573 -1,2420 0,7150 0,0568 -1,2456 0,7160 0,0563 -1,2493 0,7170 0,0559 -1,2530 0,7180 0,0554 -1,2567 0,7190 0,0549 -1,2603 0,7200 0,0544 -1,2640

0,7210 0,0540 -1,2678 0,7220 0,0535 -1,2715 0,7230 0,0531 -1,2752 0,7240 0,0526 -1,2790 0,7250 0,0522 -1,2827 0,7260 0,0517 -1,2865 0,7270 0,0513 -1,2902 0,7280 0,0508 -1,2940 0,7290 0,0504 -1,2978 0,7300 0,0499 -1,3016 0,7310 0,0495 -1,3054 0,7320 0,0491 -1,3093 0,7330 0,0486 -1,3131 0,7340 0,0482 -1,3170 0,7350 0,0478 -1,3208 0,7360 0,0473 -1,3247 0,7370 0,0469 -1,3286 0,7380 0,0465 -1,3325 0,7390 0,0461 -1,3364 0,7400 0,0457 -1,3403

0,7410 0,0453 -1,3442 0,7420 0,0449 -1,3482 0,7430 0,0444 -1,3522 0,7440 0,0440 -1,3561 0,7450 0,0436 -1,3601 0,7460 0,0432 -1,3641 0,7470 0,0428 -1,3681 0,7480 0,0424 -1,3721 0,7490 0,0421 -1,3762 0,7500 0,0417 -1,3802 0,7510 0,0413 -1,3843 0,7520 0,0409 -1,3883 0,7530 0,0405 -1,3924 0,7540 0,0401 -1,3965 0,7550 0,0398 -1,4006 0,7560 0,0394 -1,4048 0,7570 0,0390 -1,4089 0,7580 0,0386 -1,4131 0,7590 0,0383 -1,4172 0,7600 0,0379 -1,4214

0,7610 0,0375 -1,4256 0,7620 0,0372 -1,4298 0,7630 0,0368 -1,4341 0,7640 0,0365 -1,4383 0,7650 0,0361 -1,4426 0,7660 0,0357 -1,4468 0,7670 0,0354 -1,4511 0,7680 0,0350 -1,4554 0,7690 0,0347 -1,4597 0,7700 0,0344 -1,4641 0,7710 0,0340 -1,4684 0,7720 0,0337 -1,4728 0,7730 0,0333 -1,4772 0,7740 0,0330 -1,4816 0,7750 0,0327 -1,4860 0,7760 0,0323 -1,4904 0,7770 0,0320 -1,4948 0,7780 0,0317 -1,4993 0,7790 0,0313 -1,5038 0,7800 0,0310 -1,5083

Tables of the Kubelka-Munk-Function 347

I. (continued)

Roo F(Roo) logF(~) ~ F(Roo) logF(~)

0,7810 0,0307 -1,5128 0,7820 0,0304 -1,5173 0,7830 0,0301 -1,5219 0,7840 0,0298 -1,5264 0,7850 0,0294 -1,5310 0,7860 0,0291 -1,5356 0,7870 0,0288 -1,5402 0,7880 0,0285 -1,5449 0,7890 0,0282 -1,5495 0,7900 0,0279 -1,5542 0,7910 0,0276 -1,5589 0,7920 0,0273 -1,5636 0,7930 0,0270 -1,5684 0,7940 0,0267 -1,5731 0,7950 0,0264 -1,5779 0,7960 0,0261 -1,5827 0,7970 0,0259 -1,5875 0,7980 0,0256 -1,5923 0,7990 0,0253 -1,5972 0,8000 0,0250 -1,6021

0,8010 0,0247 -1,6070 0,8020 0,0244 -1,6119 0,8030 0,0242 -1,6168 0,8040 0,0239 -1,6218 0,8050 0,0236 -1,6268 0,8060 0,0233 -1,6318 0,8070 0,0231 -1,6368 0,8080 0,0228 -1,6418 0,8090 0,0225 -1,6469 0,8100 0,0223 -1,6520 0,8110 0,0220 -1,6571 0,8120 0,0218 -1,6623 0,8130 0,0215 -1,6674 0,8140 0,0213 -1,6726 0,8150 0,0210 -1,6778 0,8160 0,0207 -1,6831 0,8170 0,Q205 -1,6883 0,8180 0,0202 -1,6936 0,8190 0,0200 -1,6990 0,8200 0,0198 -1,7043

0,8210 0,0195 -1,7097 0,8220 0,0193 -1,7151 0,8230 0,0190 -1,7205 0,8240 0,0188 -1,7259 0,8250 0,0186 -1,7314 0,8260 0,0183 -1,7369 0,8270 0,0181 -1,7424 0,8280 0,0179 -1,7480 0,8290 0,0176 -1,7536 0,8300 0,0174 -1,7592 0,8310 0,0172 -1,7649 0,8320 0,0170 -1,7705 0,8330 0,0167 -1,7762 0,8340 0,0165 -1,7820 0,8350 0,0163 -1,7877 0,8360 0,0161 -1,7935 0,8370 0,0159 -1,7994 0,8380 0,0157 -1,8052 0,8390 0,0154 -1,8111 0,8400 0,0152 -1,8171

0,8410 0,0150 -1,8230 0,8420 0,0148 -1,8290 0,8430 0,0146 -1,8351 0,8440 0,0144 -1,8411 0,8450 0,0142 -1,8472 0,8460 0,0140 -1,8534 0,8470 0,0138 -1,8595 0,8480 0,0136 -1,8657 0,8490 0,0134 -1,8720 0,8500 0,0132 -1,8783 0,8510 0,0130 -1,8846 0,8520 0,0129 -1,8909 0,8530 0,0127 -1,8973 0,8540 0,0125 -1,9038 0,8550 0,0123 -1,9103 0,8560 0,0121 -1,9168 0,8570 0,0119 -1,9233 0,8580 0,0118 -1,9299 0,8590 0,0116 -1,9366 0,8600 0,0114 -1,9433

348 Appendix

I. (continued)

Roo F(Roo) logF(~) ~ F(~) logF(~)

0,8610 0,0112 -1,9500 0,8620 0,0110 -1,9568 0,8630 0,0109 -1,9636 0,8640 0,0107 -1,9705 0,8650 0,Q105 -1,9774 0,8660 0,0104 -1,9843 0,8670 0,0102 -1,9913 0,8680 0,0100 -1,9984 0,8690 0,0099 -2,0055 0,8700 0,0097 -2,0127 0,8710 0,0096 -2,0199 0,8720 0,0094 -2,0271 0,8730 0,0092 -2,0344 0,8740 0,0091 -2,0418 0,8750 0,0089 -2,0492 0,8760 0,0088 -2,0567 0,8770 0,0086 -2,0642 0,8780 0,0085 -2,0718 0,8790 0,0083 -2,0794 0,8800 0,0082 -2,0872

0,8810 0,0080 -2,0949 0,8820 0,0079 -2,1027 0,8830 0,0078 -2,1106 0,8840 0,0076 -2,1186 0,8850 0,0075 -2,1266 0,8860 0,0073 -2,1347 0,8870 0,0072 -2,1428 0,8880 0,0071 -2,1510 0,8890 0,0069 -2,1593 0,8900 0,0068 -2,1676 0,8910 0,0067 -2,1761 0,8920 0,0065 -2,1845 0,8930 0,0064 -2,1931 0,8940 0,0063 -2,2018 0,8950 0,0062 -2,2105 0,8960 0,0060 -2,2193 0,8970 0,0059 -2,2281 0,8980 0,0058 -2,2371 0,8990 0,0057 -2,2461 0,9000 0,0056 -2,2553

0,9010 0,0054 -2,2645 0,9020 0,0053 -2,2738 0,9030 0,0052 -2,2832 0,9040 0,0051 -2,2927 0,9050 0,0050 -2,3022 0,9060 0,0049 -2,3119 0,9070 0,0048 -2,3217 0,9080 0,0047 -2,3315 0,9090 0,0046 -2,3415 0,9100 0,0045 -2,3516 0,9110 0,0043 -2,3618 0,9120 0,0042 -2,3721 0,9130 0,0041 -2,3825 0,9140 0,0040 -2,3930 0,9150 0,0039 -2,4036 0,9160 0,0039 -2,4144 0,9170 0,0038 -2,4252 0,9180 0,0037 -2,4362 0,9190 0,0036 -2,4474 0,9200 0,0035 -2,4586

0,9210 0,0034 -2,4700 0,9220 0,0033 -2,4816 0,9230 0,0032 -2,4933 0,9240 0,0031 -2,5051 0,9250 0,0030 -2,5170 0,9260 0,0030 -2,5292 0,9270 0,0029 -2,5415 0,9280 0,0028 -2,5539 0,9290 0,0027 -2,5665 0,9300 0,0026 -2,5793 0,9310 0,0026 -2,5923 0,9320 0,0025 -2,6054 0,9330 0,0024 -2,6188 0,9340 0,0023 -2,6323 0,9350 0,0023 -2,6460 0,9360 0,0022 -2,6599 0,9370 0,0021 -2,6741 0,9380 0,0020 -2,6884 0,9390 0,0020 -2,7030 0,9400 0,0019 -2,7179

Tables of the Kubelka-Munk-Function 349

I. (continued)

Rx, F(Rx,) logF(Rx,) Rx, F(Rx,) logF(Rx,)

0,9410 0,0018 -2,7329 0,9420 0,0018 -2,7482 0,9430 0,0017 -2,7638 0,9440 0,0017 -2,7796 0,9450 0,0016 -2,7957 0,9460 0,0015 -2,8121 0,9470 0,0015 -2,8288 0,9480 0,0014 -2,8458 0,9490 0,0014 -2,8632 0,9500 0,0013 -2,8808 0,9510 0,0013 -2,8988 0,9520 0,0012 -2,9172 0,9530 0,0012 -2,9359 0,9540 0,0011 -2,9551 0,9550 0,0011 -2,9746 0,9560 0,0010 -2,9946 0,9570 0,00097 -3,0150 0,9580 0,00092 -3,0359 0,9590 0,00088 -3,0573 0,9600 0,00083 -3,0792

0,9610 0,00079 -3,1016 0,9620 0,00075 -3,1246 0,9630 0,00071 -3,1483 0,9640 0,00067 -3,1725 0,9650 0,00064 -3,1974 0,9660 0,00060 -3,2230 0,9670 0,00056 -3,2494 0,9680 0,00053 -3,2766 0,9690 0,00050 -3,3046 0,9700 0,00046 -3,3336 0,9710 0,00043 -3,3635 0,9720 0,00040 -3,3944 0,9730 0,00038 -3,4264 0,9740 0,00035 -3,4596 0,9750 0,00032 -3,4942 0,9760 0,00030 -3,5301 0,9770 0,00027 -3,5675 0,9780 0,00025 -3,6065 0,9790 0,00022 -3,6474 0,9800 0,00020 -3,6902

0,9810 0,00018 -3,7352 0,9820 0,00016 -3,7826 0,9830 0,00015 -3,8327 0,9840 0,00013 -3,8858 0,9850 0,00011 -3,9423 0,9860 0,00010 -4,0027 0,9870 0,00008 -4,0675 0,9880 0,00007 -4,1374 0,9890 0,00006 -4,2134 0,9900 0,00005 -4,2967 0,9910 0,00004 -4,3886 0,9920 0,00003 -4,4914 0,9930 0,00002 -4,6078 0,9940 0,00002 -4,7421 0,9950 0,00001 -4,9009 0,9960 0,00001 -5,0952 0,9970 0,00000 -5,3455 0,9980 0,00000 -5,6981 0,9990 0,00000 -6,3006

350 Appendix

II. Tables of sinh -1 x; cosh -1 x; coth -1 x

x sinh -1 x cosh -1 x coth -1 x x sinh- 1 x cosh-1 X coth -1 x

0,00 0,0000 0,50 0,4812 0,D1 0,0100 0,51 0,4901' 0,02 0,0200 0,52 0,4990' 0,03 0,0300 0,53 Q,5079. 0,04 0,0400 0,54 0,5167

0,05 0,0500. 0,55 0,5255. 0,06 0,0600. 0,56 0,5342' 0,D7 0,0699' 0,57 0,5429' 0,08 0,0799 0,58 0,5516 0,09 0,0899. 0,59 0,5602'

0,10 0,0998' 0,60 0,5688' 0,11 0,1098. 0,61 0,5774. 0,12 0,1197 0,62 0,5859 0,13 0,1296' 0,63 0,5944. 0,14 0,1395" 0,64 0,6028'

0,15 0,1494' 0,65 0,6112' 0,16 0,1593' 0,66 0,6196 0,17 0,1692 0,67 0,6279 0,18 0,1790' 0,68 0,6362 0,19 0,1889. 0,69 0,6445.

0,20 0,1987 0,70 0,6527. 0,21 0,2085 0,71 0,6608' 0,22 0,2183. 0,72 0,6690. 0,23 0,2280' 0,73 0,6771. 0,24 0,237& 0,74 0,6851'

0,25 0,247~ 0,75 0,6931' 0,26 0,2574 0,76 0,7011' 0,27 0,2668' 0,77 0,7091 0,28 0,2765. 0,78 0,7170. 0,29 0,286l. 0,79 0,7248'

0,30 0,2957. 0,80 0,7327. 0,31 0,3052' 0,81 0,7405. 0,32 0,3148. 0,82 0,7482 0,33 0,3243 0,83 0,7559' 0,34 0,3338. 0,84 0,7636 0)5 0,3432' 0,85 0,7712' 0,36 0,3526' 0,86 0,7788' 0,37 0,3620' 0,87 0,7864 0,38 0,3714 0,88 0,7939' 0,39 0,3801' 0,89 0,8014

0,40 0,3900' 0,90 0,8089. 0,41 0,3993 0,91 0,8163. 0,42 0,4085' 0,92 0,8237. 0,43 0,4177" 0,93 0,8310 0,44 0,4269 0,94 0,8383

0,45 0,4360' 0,95 0,8456. 0,46 0,4452. 0,96 0,8528 0,47 0,4542' 0,97 0,8600 0,48 0,4633. 0,98 0,8672. 0,49 0,4722' 0,99 0,8743

0,50 0,4812 1,00 0,8814.

Tables of sinh-1 x; cosh -1 x; coth-1 x 351

II. (continued)

x sinh-1 x COSh-I x coth- ' X x sinh-I x COSh-I x coth-'x

f,OO 0,8814. 0,0000 00 f,50 1,1948. 0,9624' 0,804T 1,01 0,8884' 0,1413 2,652. 1,51 1,2003 0,9713 0,7968 1,02 0,8954' 0,1997. 2,308. 1,52 1,2058 0,9801 0,7891 1,03 0,9024' 0,2443' 2,10T 1,53 1,2113 0,9888 0,7815' 1,04 0,9094. 0,2819 1,966 1,54 1,216T 0,9974. 0,7742.

1,05 0,9163 0,3149' 1,857. 1,55 1,2222. 1,0059. 0,7670. 1,06 0,9232. 0,3447 1,768 1,56 1,2276 1,0143. 0,7599 1,07 0,9300 0,3720' 1,693' 1,57 1,2330. 1,0226. 0,7530 1,08 0,9368' 0,3974. 1,629 1,58 1,2383' 1,0308 0,7463. 1,09 0,9436 0,4211' 1,573. 1,59 1,2437. 1,0389' 0,7396'

f,fO 0,9503' 0,4436. 1,522' f,60 1,2490. 1,0470. 0,7332. 1,11 0,957l. 0,4648' 1,477 1,61 1,2543. 1,0549' 0,7268' 1,12 0,963T 0,4851' 1,436 1,62 1,2595' 1,0628' 0,7206 1,13 0,9704. 0,5045' 1,398' 1,63 1,2648. 1,0706' 0,7145 1,14 0,9770 0,5232. 1,363' 1,64 1,2700 1,0784. 0,7085'

1,15 0,9836. 0,5411 1,331' 1,65 1,2752 1,0860 0,7027. 1,16 0,9901 0,5584 1,301' 1,66 1,2804. 1,0936 0,6969' 1,17 0,9966' 0,5751' 1,273' 1,67 1,2855 1,1011 0,6913. 1,18 1,0031 0,5913' 1,247 1,68 1,2906' 1,1086. 0,685T 1,19 1,0096. 0,6071. 1,222' 1,69 1,295T 1,1159' 0,6803

f,20 1,0160. 0,6224. 1,199 f,70 1,3008' 1,1232' 0,6750. 1,21 1,0224. 0,6372' 1,177. 1,71 1,3059. 1,1305. 0,669T 1,22 1,0287 0,651T 1,156. 1,72 1,3109' 1,1376' 0,6646. 1,23 1,0350' 0,6659. 1,136 1,73 1,3159' 1,1448. 0,6595 1,24 1,0413' 0,6797. 1,117. 1,74 1,3209' 1,1518' 0,6545'

1,25 1,0476 0,6931' 1,099. 1,75 1,3259 1,1588 0,6496' 1,26 1,0538' 0,7063' 1,0.81' 1,76 1,3308' 1,165T 0,6448' 1,27 1,0600' 0,7192' 1,065. 1,77 1,3358. 1,1726' 0,6401 1,28 1,0662 0,7319 1,049. 1,78 1,3407 1,1794' 0,6355. 1,29 1,0723' 0,7443. 1,033' 1,79 1,3456. 1,1862 0,6309.

1,30 1,0785. 0,7564' 1,018' f,SO 1,3504' 1,1929 0,6264. 1,31 1,0845' 0,7684. 1,004' 1,81 1,3553 1,1996. 0,6220. 1,32 1,0906 0,7801. 0,9905 1,82 1,3601 1,2062. 0,6176 1,33 1,0966 0,7916. 0,9773. 1,83 1,3649' 1,212T 0,6133 1,34 1,1026 0,8029. 0,9645. 1,84 1,3697 1,2192' 0,6091.

1,35 1,1086. 0,8140 0,9521' 1,85 1,3745. 1,2257. 0,6049' 1,36 1,1145 0,8249' 0,9402. 1,86 1,3792 1,232l. 0,6008' 1,37 1,1204' 0,8357 0,9286. 1,87 1,3839' 1,2384' 0,5968 1,38 1,1263 0,8463 0,9173' 1,88 1,3886' 1,244T 0,5928 1,39 1,1322. 0,856T 0,9065. 1,89 1,3933' 1,2510. 0,5889

1,40 1,1380. 0,8670 0,8959. f,90 1,3980 1,2572 0,5850' 1,41 1,1438. 0,8771' 0,8856 1,91 1,4026' 1,2634. 0,5812' 1,42 1,1496. 0,8871' 0,8756' 1,92 1,4073. 1,2695 0,5775. 1,43 1,1553 0,8970 0,8659' 1,93 1,4119 1,2756. 0,5738 1,44 1,1610 0,9067 0,8565 1,94 1,4165. 1,2816 0,5701'

1,45 1,1667 0,9163 0,8473 1,95 1,4210' 1,2876 0,5665' 1,46 1,1724. 0,9258. 0,8383' 1,96 1,4256 1,2935' 0,5630 1,47 1,1780 0,9351 0,8296' 1,97 1,4301' 1,2995. 0,5595 1,48 1,1836' 0,9443 0,8211 1,98 1,4347. 1,3053' 0,556l. 1,49 1,1892 0,9534' 0,8128 1,99 1,4392. 1,3112. 0,5527.

1,50 1,1948. 0,9624' 0,804T 2,00 1,4436' 1,3170. 0,5493

352 Appendix

II. (continued)

x sinh-I x cosh -I x coth-I X x sinh- 1 x cosh- 1 x coth-I X

2,00 1,4436' 1,3170. 0,5493 2,50 1,6472' 1,5668 0,4236' 2,01 1,4481 1,3227 0,5460 2,51 1,6509' 1,5712. 0,4218_ 2,02 1,4525' 1,3284- 0,5421' 2,52 1,6546- 1,5755 0,4199_ 2,03 1,4570. 1,3341 0,5395 2,53 1,6583 1,5798 0,4180 2,04 1,4614. 1,3391' 0,5363' 2,54 1,6620 1,5841 0,4162.

2,05 1,4658_ 1,3454_ 0,5332. 2,55 1,6656- 1,5884_ 0,4143-2,06 1,4702_ 1,3509- 0,530l. 2,56 1,6693 1,5926- 0,412S" 2,07 1,4745 1,3565. 0,5270 2,57 1,6729- 1,5969_ 0,4101' 2,08 1,4789_ 1,3620_ 0,5240 2,58 1,6765' 1,601l. 0,4090_ 2,09 1,4832_ 1,3674' 0,5210 2,59 1,6801- 1,6053. 0,4072

2,10 1,4875. 1,3729_ 0,5180' 2,60 1,6831' 1,6094- 0,4055_ 2,11 1,4918. 1,3783_ 0,5151- 2,61 1,6873- 1,6136 0,4031' 2,12 1,4960- 1,3836' 0,5123_ 2,62 1,6909 1,6171' 0,4020' 2,13 1,5003 1,3890_ 0,5094 2,63 1,6945_ 1,6219_ 0,4003-2,14 1,504s" 1,3943_ 0,5066 2,64 1,6980 1,6260_ 0,3986'

2,15 1,5088_ 1,3995- 0,5038' 2,65 1,701s" 1,6300- 0,3970_ 2,16 1,5130_ 1,4048_ 0,501l. 2,66 1,705l. 1,6341 0,3953-2,17 1,5172_ 1,4100- 0,4984- 2,67 1,7086_ 1,6382_ 0,3937 2,18 1,5214_ 1,4152_ 0,4957 2,68 1,712l. 1,6422 0,392l. 2,19 1,5255 1,4203 0,4930' 2,69 1,7156_ 1,6462 0,3904-

2,20 1,5297_ 1,4254- 0,4904 2,70 1,7191. 1,6502 0,3889_ 2,21 1,5338 1,4305 0,4878- 2,71 1,7225- 1,6542_ 0,3873_ 2,22 1,5379 1,4356_ 0,4853_ 2,72 1,7260. 1,6581- 0,3857 2,23 1,5420 1,4406 0,4821' 2,73 1,7294- 1,662l. 0,3841-2,24 1,5461 1,4456 0,4802' 2,74 1,7329_ 1,6660 0,3826

2,25 1,5502_ 1,4506_ 0,4778_ 2,75 1,7363_ 1,6699- 0,3811. 2,26 1,5542 _1,4555- 0,4753 2,76 1,7397 1,6738 0,3796_ 2,27 1,5583_ 1,4604- 0,4729 2,77 1,7431 1,6777 0,3780-2,28 1,5623_ 1,4653- 0,4705 2,78 1,7465_ 1,6816. 0,3766_ 2,29 1,5663 1,4702 0,4681' 2,79 1,7499_ 1,6854 0,375l.

2,30 1,5703_ 1,4750' 0,4658_ 2,80 1,7532- 1,6892- 0,3736 2,31 1,5743_ 1,4799_ 0,4635. 2,81 1,7566 1,693l. 0,3722_ 2,32 1,5782' 1,4846- 0,4612. 2,82 1,7599- 1,6969_ 0,3707 2,33 1,5822_ 1,4894 0,4589 2,83 1,7633_ 1,7006- 0,3693_ 2,34 1,5861 1,4942_ 0,4567. 2,84 1,7666 1,7044 0,3679_

2,35 1,5900- 1,4989_ 0,4544- 2,85 1,7699 1,7082_ 0,3664-2,36 1,5939' 1,5036_ 0,4522' 2,86 1,7732- 1,7119 0,3650' 2,37 1,5978- 1,5082' 0,450l. 2,87 1,7765 1,7156- 0,3637_ 2,38 1,6011' 1,5129_ 0,4479 2,88 1,7798 1,7193' 0,3623_ 2,39 1,6056 1,5175 0,4458. 2,89 1,7831. 1,7230- 0,3609

2,40 1,6094' 1,5221. 0,4437_ 2,90 1,7863" 1,7267 0,3596. 2,41 1,6133_ 1,5267_ 0,4416. 2,91 1,7896 1,7304_ 0,3582-2,42 1,6171 1,5312 0,4395 2,92 1,7928' 1,7340- 0,3569. 2,43 1,6209 1,5351' 0,4374' 2,93 1,796l. 1,7377. 0,3556_ 2,44 1,6247 1,5402- 0,4354 2,94 1,7993 1,7413 0,3542-

2,45 1,6285 1,5447 0,4334 2,95 1,8025 1,7449 0,3529' 2,46 1,6323_ 1,5492. 0,4314 2,96 1,8051' 1,7485 0,3516-2,47 1,6360' 1,5536 0,4294' 2,97 1,8089- 1,752l. 0,3504. 2,48 1,6398_ 1,5580- 0,4275 2,98 1,8121 1,7556- 0,3491 2,49 1,6435 1,5624- 0,4256_ 2,99 1,8153_ 1,7592 0,3478-

2,50 1,6472" 1,5668 0,4236- 3,00 1,8184- 1,7621' 0,3466_

Tables of sinh -1 x; cosh -1 x; coth -1 x 353

II. (continued)

x sinh-I x COSh-I x coth -I x x sinh-I x COSh-I x coth- I X

3,00 1,8184' 1,7621' 0,3466. 3,50 1,9651' 1,9248' 0,2939 3,01 1,8216 1,7663. 0,3453' 3,51 1,9685. 1,9278' 0,2930 3,02 1,8248. 1,7698 0,3441 3,52 1,9712 1,9308 0,2921' 3,03 1,8279 1,7733 0,3429. 3,53 1,9739' 1,9338. 0,2913. 3,04 1,8310' 1,7768 0,3416' 3,54 1,9767. 1,9367 0,2904.

3,05 1,8341' 1,7803. 0,3404' 3,55 1,9794. 1,9396' 0,2895' 3,06 1,8373. 1,7831' 0,3392' 3,56 1,9821. 1,9426. 0,2887. 3,07 1,8404. 1,7872. 0,3380' 3,57 1,9848. 1,9455 0,2878 3,08 1,8434' 1,7906 0,3369. 3,58 1,9875. 1,9484 0,2870. 3,09 1,8465' 1,7940' 0,3357 3,59 1,9902. 1,9513 0,2861

3,iO 1,8496 1,7975. 0,334Y 3,60 1,9928' 1,9542 0,2853. 3,11 1,8527. 1,8009. 0,3334. 3,61 1,9955 1,9571 0,2844' 3,12 1,8551' 1,8042' 0,3322' 3,62 1,9982. 1,9600. 0,2836 3,13 1,8588. 1,8076' 0,3311. 3,63 2,0008' 1,9628' 0,2828 3,14 1,8618 1,8110 0,3299' 3,64 2,0035 1,9657 0,2820.

3,15 1,8648' 1,8143' 0,3288' 3,65 2,0061' 1,9686. 0,2812. 3,16 1,8679. 1,8177 0,3277 3,66 2,0088. 1,9714 0,2803' 3,17 1,8709. 1,8210' 0,3266 3,67 2,0114 1,9742' 0,2795' 3,18 1,8739. 1,8243' 0,3255 3,68 2,0140' 1,977l. 0,2781' 3,19 1,8769. 1,8276' 0,3244 3,69 2,0166' 1,9799 0,2779'

3,20 1,8799. 1,8309' 0,3233 3,70 2,0193. 1,9827 0,2772. 3,21 1,8828' 1,8342' 0,3222' 3,71 2,0219. 1,9855 0,2764. 3,22 1,8858 1,8375 0,3212. 3,72 2,0245. 1,9883 0,2756 3,23 1,8888. 1,8408. 0,3201 3,73 2,0271. 1,9911. 0,2748 3,24 1,8911' 1,8440 0,3190' 3,74 2,0296' 1,9939. 0,2740'

3,25 1,8947. 1,8472' 0,3180 3,75 2,0322' 1,9966' 0,2733. 3,26 1,8976 1,8505. 0,3170. 3,76 2,0348 1,9994 0,2725 3,27 1,9005' 1,8537 0,3159' 3,77 2,0374. 2,0021' 0,2711' 3,28 1,9035. 1,8569 0,3149 3,78 2,0399' 2,0049 0,2710 3,29 1,9064. 1,8601 0,3139. 3,79 2,0425. 2,0076' 0,2702'

3,30 1,9093. 1,8633. 0,3129. 3,80 2,0450' 2,0104. 0,2695 3,31 1,9122. 1,8665. 0,3118' 3,81 2,0476. 2,0131 0,2688. 3,32 1,9151. 1,8696' 0,3108' 3,82 2,0501 2,0158 0,2680' 3,33 1,9179' 1,8728. 0,3098' 3,83 2,0526' 2,0185 0,2673 3,34 1,9208 1,8759 0,3089. 3,84 2,0552. 2,0212' 0,2666.

3,35 1,9237. 1,8790' 0,3079. 3,85 2,0577. 2,0239 0,2658' 3,36 1,926Y 1,8822. 0,3069 3,86 2,0602 2,0266 0,2651 3,37 1,9294. 1,8853. 0,3059' 3,87 2,0627 2,0293. 0,2644 3,38 1,9322' 1,8884 0,3050. 3,88 2,0652 2,0319' 0,2637. 3,39 1,9351. 1,8915. 0,3040' 3,89 2,0677. 2,0346 0,2630.

3,40 1,9379. 1,8946. 0,303l. 3,90 2,0702. 2,0373. 0,2623. 3,41 1,9407 1,8976' 0,3021' 3,91 2,0727. 2,0399 0,2616. 3,42 1,9435 1,9007 0,3012 3,92 2,0751' 2,0426. 0,2609. 3,43 1,9463 1,9031' 0,3003. 3,93 2,0776 2,0452 0,2602. 3,44 1,9491 1,9068 0,2993' 3,94 2,0801. 2,0478' 0,2595.

3,45 1,9519 1,9098' 0,2984 3,95 2,0825 2,0504' 0,2588 3,46 1,9547. 1,9128' 0,2975 3,96 2,0850. 2,053l. 0,2581 3,47 1,9574' 1,9159. 0,2966 3,97 2,0874 2,0557. 0,2574' 3,48 1,9602 1,9189. 0,2957. 3,98 2,0899. 2,0583. 0,2568. 3,49 1,9630. 1,9219. 0,2948 3,99 2,0923 2,0609. 0,2561.

3,50 1,9651' 1,9248' 0,2939 4,00 2,0947 2,0634' 0,2554

23 Kortum, Reflectance Spectroscopy

354 Appendix

II. (continued)

x sinh-I x cosh -I x coth -I x x sinh-I x cosh -I x coth -I x

4,00 2,0947 2,0634' 0,2554 4,50 2,2093' 2,1&46' 0,2260 4,01 2,0971' 2,0660 0,2541' 4,51 2,2115 2,1869' 0,2255. 4,02 2,0996. 2,0686 0,2541 4,52 2,2137. 2,1892 0,2250. 4,03 2,1020. 2,0712. 0,2534' 4,53 2,2158' 2,1915. 0,2244' 4,04 2,1044. 2,0737 0,2528. 4,54 2,2180 2,1931' 0,2239'

4,05 2,1068. 2,0763. 0,2521' 4,55 2,2201' 2,1960. 0,2234' 4,06 2,1092. 2,0788 0,2515. 4,56 2,2223. 2,1982' 0,2229' 4,07 2,1116. 2,0813' 0,2508' 4,57 2,2244' 2,2005. 0,2224 4,08 2,1139' 2,0839. 0,2502 4,58 2,2266. 2,2027 0,2219 4,09 2,1163 2,0864 0,2496. 4,59 2,2287 2,2049' 0,2214

4,10 2,1187 2,0889' 0,2489' 4,60 2,2308 2,2072. 0,2209 4,11 2,1211. 2,0914' 0,2483 4,61 2,2329' 2,2094 0,2204' 4,12 2,1234 2,0939' 0,2477. 4,62 2,235l. 2,2116' 0,2199' 4,13 2,1258. 2,0964' 0,2470' 4,63 2,2372. 2,2138' 0,2194' 4,14 2,1281' 2,0989' 0,2464 4,64 2,2393. 2,2160' 0,2190.

4,15 2,1305. 2,1014 0,2458 4,65 2,2414. 2,2182' 0,2185. 4,16 2,1328 2,1039 0,2452. 4,66 2,2435. 2,2204' 0,2180. 4,17 2,1351' 2,1064. 0,2446. 4,67 2,2456. 2,2226' 0,2175 4,18 2,1375. 2,1088' 0,2440. 4,68 2,2477. 2,2248' 0,2170' 4,19 2,1398 2,1113 0,2434. 4,69 2,2498. 2,2270 0,2165'

4,20 2,1421 2,1131' 0,2428. 4,70 2,2518' 2,2292 0,2161. 4,21 2,1444' 2,1162 0,2422. 4,71 2,2539' 2,2314. 0,2156 4,22 2,1461' 2,1186' 0,2416. 4,72 2,2560 2,2335' 0,2151' 4,23 2,1490' 2,121l. 0,2410. 4,73 2,258l. 2,2357 0,2147. 4,24 2,1513' 2,1235 0,2404. 4,74 2,2601' 2,2379. 0,2142

4,25 2,1536' 2,1259' 0,2398 4,75 2,2622 2,2400' 0,2131' 4,26 2,1559 2,1283" 0,2392 4,76 2,2643. 2,2422. 0,2133. 4,27 2,1582 2,1308. 0,2386' 4,77 2,2663 2,2443' 0,2128 4,28 2,1605. 2,1332. 0,2380' 4,78 2,2684. 2,2465. 0,2123' 4,29 2,1621' 2,1356. 0,2375. 4,79 2,2704 2,2486 0,2119.

4,30 2,1650' 2,1380. 0,2369 4,80 2,2724' 2,2501' 0,2114' 4,31 2,1673. 2,1403' 0,2363' 4,81 2,2745. 2,2529. 0,2110. 4,32 2,1695' 2,1421' 0,2358. 4,82 2,2765 2,2550. 0,21OS' 4,33 2,1718 2,1451 0,2352 4,83 2,278S' 2,2571 0,2101. 4,34 2,1740' 2,1475. 0,2346' 4,84 2,2806. 2,2592 0,2096'

4,35 2,1763. 2,1498' 0,2341. 4,85 2,2826 2,2613' 0,2092 4,36 2,1785' 2,1522 0,2335 4,86 2,2846 2,2634' 0,2081' 4,37 2,1808. 2,1546. 0,2330. 4,87 2,2866' 2,265S' 0,2083 4,38 2,1830. 2,1569 0,2324 4,88 2,2886' 2,2676' 0,2079. 4,39 2.1852 2,1592' 0,2319. 4,89 2,2906' 2,2697 0,2074'

4,40 2,1874' 2,1616. 0,2313 4,90 2,2926' 2,2718 0,2070 4,41 2,1896' 2,1639 0,2308. 4,91 2,2946' 2,2739 0,2066. 4,42 2,1918' 2,1662' 0,2302' 4,92 2,2966' 2,2760. 0,2061' 4,43 2,1940' 2,1686. 0,2297 4,93 2,2986' 2,2780' 0,2057 4,44 2,1962' 2,1709. 0,2292. 4,94 2,3006 2,2801 0,2053.

4,45 2,1984' 2,1732. 0,2286' 4,95 2,3026 2,2822. 0,2048' 4,46 2,2006' 2,1755 0,2281 4,96 2,3046. 2,2842' 0,2044 4,47 2,2028' 2,1778. 0,2276. 4,97 2,3065' 2,2863 0,2040 4,48 2,2050 2,1801. 0,2270' 4,98 2,3085 2,2883' 0,2036. 4,49 2,2072. 2,1824. 0,2265 4,99 2,3105. 2,2904 0,2032.

4,50 2,2093' 2,1846' 0,2260 5,00 2,3124' 2,2924' 0,2021'

Tables of sinh -1 x; cosh -1 x; coth -1 x 355

II. (continued)

x sinh-I x COSh-I x coth- I X x sinh-I x COSh-I x coth -I x

5,0 2,3124' 2,2924' 0,2021' 7,5 2,7125. 2,7036. 0,1341' 5,1 2,3319. 2,3126' 0,1987. 7,6 2,7256 2,7169' 0,1323' 5,2 2,3509' 2,3324' 0,1941' 7,7 2,7386. 2,7301' 0,1306 5,3 2,3696' 2,3518' 0,1910. 7,8 2,7514. 2,7431' 0,1289 5,4 2,3880 2,3709. 0,1873' 7,9 2,7640 2,7560. 0,1273.

5,5 2,4061. 2,3895" 0,1839. 8,0 2,7765. 2,7687. 0,1257. 5,6 2,4238 2,4078' 0,1805 8,1 2,7888 2,7812. 0,1241 5,7 2,4412' 2,4258' 0,1773. 8,2 2,8010. 2,7935" 0,1226. 5,8 2,4584. 2,4435 0,1742. 8,3 2,8130 2,8058. 0,1211. 5,9 2,4752 2,4608' 0,1711' 8,4 2,8249 2,8178' 0,1196

6,0 2,4918. 2,4779 0,1682' 8,5 2,8367. 2,8291' 0,1182 6,1 2,5081 2,4946' 0,1654' 8,6 2,8483. 2,8415 0,1168 6,2 2,5241' 2,5111' 0,1627 8,7 2,8598. 2,8532. 0,1155. 6,3 2,5399' 2,5273' 0,1601 8,8 2,8711 2,8647. 0,1141' 6,4 2,5555 2,5433 0,1575' 8,9 2,8823' 2,8760' 0,1128'

6,5 2,5708 2,5590. 0,1551. 9,0 2,8934' 2,8873. 0,1116. 6,6 2,5859 2,5744' 0,1527 9,1 2,9044' 2,8984 0,1103' 6,7 2,6008. 2,5896' 0,1504. 9,2 2,9153 2,9094 0,1091' 6,8 2,6154' 2,6046' 0,1481' 9,3 2,9260' 2,9203. 0,1079' 6,9 2,6299. 2,6194. 0,1460. 9,4 2,9367. 2,9310 0,1068

7,0 2,6441' 2,6339 0,1438' 9,5 2,9472 2,9417. 0,1057. 7,1 2,6582. 2,6482' 0,1418 9,6 2,9576 2,9522 0,1045' 7,2 2,6720 2,6624. 0,1398 9,7 2,9679' 2,9626 0,1035. 7,3 2,6857. 2,6763 0,1379. 9,8 2,9781' 2,9729 0,1024 7,4 2,6992. 2,6900' 0,1360. 9,9 2,9882' 2,9831' 0,1014.

7,5 2,7125. 2,7036. 0,1341' to,o 2,9982' 2,9932' 0,1003'

23*

Subject Index absolute and relative measurements

137 ff. - - - reflectance values 274 - diffuse reflectance of magnesium

oxide 138 - reflectance according to Melamed

167 - -, according to Shibata 143 - - for quantitative measurements

183 - - from transmittance values 142 - - of a series of white standards

148 - - - freshly prepared magnesium

oxide 137 - - - - prepared MgO according

to various authors 146 - - - - prepared MgO, table 147 - - - magnesium oxide in the infra-

red 145 absorption coefficient according to

Kubelka-Munk 112 - - as a function of particle size 59 - - definition 21, 108 - coefficients of a colored glass III

transmittance and reflectance 195 - - of aerosils 207 - - of glass powder 208 - - of graphite from reflection

measurements on aerosil-graphite mixtures 210

- cross section according to M ie 256 - index, definition 21 - maximum of chlorophyll in living

cells 307 - - relative shift as function of the

half width and of the wave number dependence of S 212

- parameter, definition 315 - spectra of K(Mn, Cl)04 mixed

crystals 187

absorption sprectrum of monocellular algae in aqueous suspension 307

acid-base reaction between the adsorbed substance and the adsorbent 257

activation energies, calculation from the rate constants 283

adsorption from solution 243 - from the gas phase 242 - isotherm of p-dimethylamino-

azobenzene on BaS04 259 - isotherms of the chemisorption on

NaCl of different grain sizes 272 - of 12 of Br2 on highly dried oxides

263 aerosil, diffuse reflectance 149 - goniophotometriccurves 52 -, grain size dependence of scattering

coefficients 203 ageing standards 149 albedo, definition 28 analytical photometric measurements

in reflexion 290ff. - procedure according Ringbom and

Giovanelli 292 angle of polarization, definition 8 angular distribution, isotropic at

multiple scattering 99 - - of Rayleigh scattering 78 - - of the scattered intensity after

single and twofold scattering on dielectric spheres 99

- - of the scattered radiation at a homogeneous sphere 84

anthraquinone oxidation on surfaces 278

anisotropic materials, investigation by ATR 330

apparent absorbance of powders 59 applications of A TR 329 ff. approximate equations of the Kubelka-

Munk-theory 120

358 Subject Index

aromatic hydrocarbons adsorbed on cracking catalysts 265

ATR spectra of aqueous Eosin-Y solu-tions 334

attachment for attenuated total reflec-tion according to Fahrenfort 326

- for commercial spectrophotometers for measuring internal reflection spectra 327

attenuated total reflection 309 ff. - - - in the visible and UV spectral

regions 332 - - - on a phase boundary as

function of the angle of incidence with different absorption index of the rarer medium 311

- - -, sensitivity to changes inx 311 average path length of radiation in a

scattering medium 107

Babinet compensator 18 ball mills 237 biological materials, reflectance

measurements 306 Bouguer-BeerLaw inATR-spectra 333 Bouguer elementary mirror hypothesis

52 - hypothesis of elementary mirrors

29 ff. Brewster Law 8,58 bulk dyes in the textile, laquers, pig-

ments and plastics industries 301

calibration curves for determination of concentrations 290

characteristic absorption of ads or bents 297

- function 158 -, linear of amplifier and detector 226 characteristics of the rotation ellipsoid

247 charge-transfer-band of the complex

pyrene-s-trinitrobenzene 275 charge transfer complexes on surfaces

262 ff. chemisorption and physical adsorption

272 -, spectral changes 257

chromatogram-spectrophotometer 225

circularly diffuse reflection 29 cleavage reactions, reversible on

surfaces 266 color curve, typical 186 - matching 303 - measurement 301 - measuring instruments 231 complexes, formation on surfaces 261 - OH- 12 and OH- Br2 203 complex refractive index 21,310 continuum theory of absorption and

scattering of tightly packed particles 103

contrast ratio, ideal 112 covering glasses, effect on scattering

and transmission of a sample 135 - -, influence on reflectance spectra

189 cracking catalysts, adsorption 265 critical angle of total reflection 13 crystal spectra and solution spectra of

complexes 285

deformation and shift of bands at inter-nal reflection 319

dehydration of phenylbenzyl carbinol to stilbene on Al20 3 as catalyst 283

depolarization of linear polarized light at diffuse reflection 37

depth of penetration in the rarer medium at toal reflection 316

- - of radiation in powders 59 - -, relative and effective layer

thickness at ATR-measurements 318

deviations between Kubelka-Munk theory and rigorous theory 162

- from the Lambert Cosine Law 38ff., 173

- from the Lambert Law in the region of selective absorption 55

dielectric polarization 80 differential equations, simultaneous of

isotropic scattering 104, 109

Subject Index 359

differential equations, substitution for the radiation transfer equation 157

diffraction .phenomena at total reflec-tion 20

diffuse reflectance at absorbing materials 55

- - on aerosil 44 - reflection, definition 26 dilution method 175 ff. - - in measuring reflectance spectra

215 - series with the same standard 180 dimethylaminoazobenzene, reflection

spectrum in adsorbed state 257 dipole moment, definition 75 discontinuum theories 163ff. - theory according to Melamed 166 - - - to Melamed, experimental

test 216 discussion of errors 250 dispersion of the optically rarer medium

at ATR measurements 319 - of the refractive index, influence on

scattering coefficients 206 dissociation equilibrium of molecular

complexes on surfaces 276. distribution function for the grain sizes

of ground glas 192 - - for the Bouguer elementary mirrors 32, 45 double-beam spectrophotometer,

attachments for reflection measure-ments 226

- spectrophotometer for determina-tion of reflection spectra 328

double-pass elements for internal reflection 322

dyeing recipes 304 dynamic reflectance spectroscopy 288

effective layer thickness at films 318 - - -, defination 316 efficiency factor according to M ie for

spherical particles 90 - -, definition 89 - factors of gold sols according to

Mie 93

electric vector of the radiation 6 elementary mirror hypothesis according

to Bouguer 32 elements for internal reflection 324 elliptical polarization at total reflection

18 Elrepho of Zeiss 222 equilibria at surfaces 273 errors, relative of Kubelka-Munk

function 250 external and internal field 80 extinction E.l and Ell of an aqueous

solution of Eosin B as a function of concentration 335

fading reaction of the tautomeric 2-(2'.4' -dinitrobenzyl)-pyridine, adsorbed on Si02 282

Fahrenfort method for determination of nand K 309ff.

forward and backward scattering 88,95

Fresnel equations 8 - - for complex refractive index

310 - - for the reflection of absorbing

materials 21 - - for total reflection 18 - formulas, development in series

332 - reflectance of Ti02 (rutile) MgO,

BaS04 and Si0 2 46 Freundlich isotherm 263

gas chromatograph fraction, spectra by ATR 331

geophysical problems, investgation with reflectance measurements 307

germanium detector 248 glass powder, scattering coefficients as

function of wavenumber 206 - powders, absorption coefficients

207 - -, reflectance as function of wave-

length 62 gloss, definition 173 glossy peaks as a Fresnel effect 38, 44

360 Subject Index

glove boxes 236 goniophotometer for testing Lamberts

cosine law 217 - of Carl Zeiss 218 -, recording 219 goniophotometric curves 35 - - of BaSO 4' Rutil, MgO, Aerosil

43 - measurements on K2Cr04 powder

at different wavelengths 56 - - testing the Lambert Cosine Law

38 grain size dependence of F(Roo) 214 - - - of the scattering coefficients

of aerosil 203 - - distribution of ground Didym

filter glass 192 grinding time influence on the reflec-

tion spectra 238

half cylinder for 5-fold reflection according to F ahre1ifort 321

- - for measurements of the attenuated total reflection 320

Hardy spectrophotometer for reflectance measurements 228

heavy metal complexes, analytical determination 293

Helmholtz Reciprocity Law 10, 39, 172

hiding power 112 H-integrals 158 hohlraum reflectance spectrophoto-

meter for the infrared 246 hyperbolic functions 116 - -, expressed in series 121

ideal diffuse reflector 28 indicatrix, definition 29 - for the reflection of infrared radiation

of germanium powder 36 - - on drawing paper 37 - of a Lambert radiator 30 - of a Seeliger radiator 30 infinite layer thickness 213

influence of regular reflection on F(Roo) 174

influence of various parameters on the validity of the Lambert Law 38

infrared reflectance spectrometers 247 - - spectrometer with rotation

ellipsoid 248, 249 - spectra ofliquid dibutyl phthalate in

transmission, normal reflection and in attenuated total reflection 314

inhomogeneous layers, reflectance and transmittance according to Kubelka 123

- media, treated by Giovanelli 163 inhomogenieties in chromatogram

spots 300 integrating sphere according to Taylor

139, 219ff. - - for the vacuum UV 220 - -, radiation flux 219 - -, sphere error (table) 221 interference method for the measure-

ment of phase difference 24 - of scattered waves 83 - spectroscopy 323 "internal" regular reflection according

to Ryde 131 - - - of diffuse radiation 132 - reflectance at phase boundaries 15 - -, dependence on the extinction

modulus of the optically rarer medium 315

- - of a phase boundary as function of the angle of incidence 310

- reflection coefficient 168 - -, definition 14 - - spectroscopy 313ff. intrinsic absorption of reference

standards 183 iodides of heavy metals adsorbed on

alkali or alkaline earth halides 260 ion-exchange resins 293 iron oxide pigments 253 isomeric matched coloration 305 isotropic diffuse reflection 32 - distribution of multiple scattering

100

Subject Index 361

KBr-method in the infrared 2 kinetic measurements on surfaces 281 KR/KT ratio 195 Kubelka-Munk coefficients Roo, R o,

K, S, a, b (table) 119 - function 111 - - and absorbance as function of

Roo and T respectively 179 - -, concentration dependence 178,

181 - -, additivity in mixtures 303 - - of a rutile-anatase mixture,

measured against pure anatase as standard 291

- - of stilbene, adsorbed on active A1 20 3 , concentration dependence 284

- -, particle-size dependence 213 - -, relativ errors 250 - -, testing by means oftransmittance

and reflectance measurements on the same mixed crystals 188

-, limiting straight line of pyrene, adsorbed on NaCI 182

:- theory, application on papers 126 - -, applicability on papers . 199

- - at directed irradiation 127 - -, comparison with rigorous theory

160

- -, exponential solution 107

- -, hyperbolic solution 116

lactone of malachite-green-o-carboxylic acid, cleavage reaction 266

Lambert Cosine Law 28 - - -, experimental test 34, 217 - Law and Bouguer hypothesis 50 - -, deviations according to

Pokrowski 31 - -, influence of the azimuth 35 Langmuir adsorption isotherm 260,

271 layer thickness for the measurement of

Roo 239 - - for measurments of Ro 240

Legendre polynomials 157 low temperature cells 230 luminescence of scattering samples 150 - reabsorption in scattering media 154 -, true in scattering media 156 luminescent radiation flux in scattering

media 153 lyophilisation 238

magnesium oxide as reflectance standard 137

- - primary standard according to Zeiss 147

major angle of incidence, definition 22 - azimuth, definition 22 mean path length of diffuse irradiation

108 measurement of the regular reflectance

of plane surfaces 228 measurements in the infrared 245 - with linearly polarized radiation 231 Melamed, discontinuum theory 166 - statistical theory of diffuse

reflectance, experimental test 216 metameric colorations 304 methods, ATR-measurements ff. 319 - for determination of nand )( 22 Mie functions 89 - scattered radiation, variation of the

wavelength exponents 92 Mie-theory 84, 85 - for absorbing spheres 93 mirror reflection 5 mixture of colored pigments, quantita-

tive analysis 302 moisture, influence on reflectance spectra 234 molecular complex hexamethylbenzene-

s-trinitrobenzene, adsorbed on si-licagel 275

multiple reflection of a plate bounded by parallel planes 10

- scattering 94

natural extinction modulus, definition 21

normal spectral values for the equal-energy spectrum 304

362 Subject Index

numerical quadrature according to Gauss 157

opacity 112 optical clearing agents 233 - constants nand" 309ff. - contact between sample and reflec-

tion element 325 - geometry of reflectometers 227 - - of the measuring arrange-

ments 170ff. - projection of a surface LlF onto a

smaller surface LlF' 245 - - of the sample onto the detector

by means of a rotation ellipsoid 248

- thickness 163 - -, definition 101 orientation of adsorbed molecules on

surfaces 277 - of elementary mirrors to the

macroscopic surface 46

packing density 201,239 paper chromatograms, consideration of

the spot size 298 - -, dependence of F(Rads)/n on the

amount of material present 300 - -, quantitative evaluation 298 papers, applicability of Kubelka-Munk

function 197 particle size dependence of absorption

at reflectance measurements 214 - - - of light absorption in

heterogeneous systems 61 - - - of the absorption at adsorbed

substances 216 Perkin-Elmer 12 C spectrometer, con-

verted to a reflection spectrometer with rotation ellipsoid 249

phase difference in case of scattering at two centers with a given distance 82

- function, definition 101 - functions, different 102

shift at reflection on metals 24 - - at total reflection 17 phenomenological theories of

absorption and scattering 103

photochemical reaction of anthra-quinone, adsorbed on Alz0 3 278

- reactions on surfaces 278 photography in the IR 256 photometric determination of heavy

metal ions 293 piezochromism and thermochromism of

bianthrone and bixanthylene 284 pigments 253 plates for multiple internal reflection

322 polar diagram of the dipole scattering

of non-polari7ed light 79 polarizability of dissolved molecules 80 - of molecules. definition 74 polarization of natural radiation on

diffuse reflection at absorbing materials 58

polarized radiation for determination of optical constants 325

powders, surface area determination 270

preparation of samples for measurement 237

primary standard according to Zeiss 147

quantitative analysis of mixed powders 290

- determination of water by reflectance in the infrared 293

quantum efficiency of luminescence from reflectance measurements 152

radiation characteristic of a dipole 75, 77

- densities, normalized according to v.Seeliger 53

- -, - of powders of different refractive index 51

- density according to Lambert and to v. Seeliger 28

- -, definition 27 - -, methods of measurement 29 - - of white standards, A-dependence

52

Subject Index 363

radiation flux of dipole scattering 76 - - perunitarea,definition 5 - intensities of different scattering

order in case of multiple scattering 98

- loss due to scattering 2 radiation-transfer equation 100 - -, attempts for a rigorous solution

156 - -, general form 101 radical ions of aromatic hydrocarbons

265 rate constants, calculation from

reflectance measurements 281 Rayleigh scattering 73 - - a limiting case of the Mie theory

88 - - formula for the dilute gas 78 reactions in mixed solid phases 282 reactivity of powdered pharmaceutical

preparations 307 reciprocity law 224 redox reactions on surfaces 265 red-shift of bandmaxima of typical

color curves 211 ~ of bandmaxima by wavenumber

dependence of S 211 reflectance according to Giovanelli for

semi-infinite media 160

- and dyestuff concentration 301 - and transmittance of filter papers

198 - - of opal glass plates 131 - - of samples with covering glasses

136 - - of several layers 123 - - - layers one behind the other

197 -, concentration dependence 178 - dependent on the refractive index

of the reflecting medium 45 -, diffuse, definition 110 -, - of a layer with black background

111 - for diffuse incident radiation 11 - function for isotropic scattering 105

reflectance of a semi-infinite medium in a matrix 301

- - - with non-isotropic scattering 158

- - scattering medium embedded in an matrix according to Fresnel equations 134

- of magnesium oxide, dependence on different parameters 142

- of non-homogeneous scattering layers 123

- of transparent papers from trans-mittance measurements 144

- oximetry 306 - Roo, calculated according to Giova-

nelli and Kubelka-Munk 161 -, relative of a mixture of CrZ0 3 with

impure CaF z in excess 184 - spectra at extremely high or low

temperatures 229 - - obtained by attenuated total

reflection 309ff. - - of allotropes 289 - - of heavy metal complexes on

ion-exchange resins 293 - standards, different 146 - -, intrinsie absorption 149 reflection coefficients, definition 8 - - in the case of reflection at the

rarer medium 14 - cuvette for measurements at low

temperatures 230 -, diffuse of a layer of finite thickness

with black background 113 - losses at phase boundaries 1 - measurements as a function of the

optical geometry 170 - of infrared radiation at powdered

germanium 35 - of linearly-polarized radiation at

powders of various particle sizes 66 - spectra of adsorbed substances 256

- - of anthracene on silica gel, influence of drieing 241

- - of anthraquinone, undiluted or adsorbed on NaCI 177

364 Subject Index

reflection spectra of Cr 203 + excess of CaF2 in dependence on water vapor pressure 235

- - ferricoxidepigments 255 - - of green MnS and of red MnS

288 - - ofHgI2 260 - - of iodine adsorbed on dry NaI

262 - - - vapor on undried MgO 264 - - ofMnCI2 . 4H20 287 - - of p-dimethylamino-azobenzene.

adsorbed at different concentrations 259

- - of rutile and anatase 291 - - of substances which have been

adsorbed from solution 244 - - - which have been adsorbed

from the gaseous phase 242 - - of the molecular compound

pyrene-s-trinitrobenzene 274 - spectrometer, model 13/205 from

Perkin-EImer 247 - spectrum and transmission spectrum

of a Didym filter glass 189 - - of a naphtospirane adsorbed on

NaCI 271 - - of BiI3 adsorbed on dry KI 262 - - ofCr203/MgOwithoutand with

quartz cover plate 190 - - of perylene, adsorbed on a Si02-

AI 20 3 cracking catalysts 266 reflectometers 221 ff. regular reflectance at strongly absorbing

media 21 - - for diffuse and perpendicular

incidence, table 12 - - of absorbing materials 23 - - ofaplaneparallelplate 10 - - - parallel plate for diffuse inci-

dence 13 - - of metals (table) 25 - - of non-absorbing media 9 - reflection at phase-boundaries 130 - - of linearly polarized radiation,

method 67

relations between the coefficients of the Kubelka-Munk theory 120

relative error AF(R:"')/F(R:"') with Roo standard as parameter 185

- - in K, ratio to the relative error inRoo 251

- - in S, ratio to the relative error in Reo 251

- - of the Kubelka-Munk function in dependence on Reo 251

remission attachment for measurements between crossed polarization prisms 233

- - for the evaluation of thin layer chromatograms 224

- - RA 2 and RA 3 for the Zeiss PMQ II 223,224

- curves dependence on particle size 58

- - of glass powder of different grain sizes 62

- - of mixed crystals consisting of KMn04 and KCI04 63

- measurements of fluorescent samples 232

- spectra of pure CuS04 -5H20 with polarized radiation or with natural radiation 68

- spectrumofpureKMn04 64,70 - - - K3[Fe(CN)6J as a function

of particle size 66 residual radiation method in the infrared

23 Richter "Gloss Number" 39 ring cleavage, influence of drying of the

adsorbent 269 - - oflactones 267 - -, reversibility 268 Ryde-theory of non-isotropic

scattering 127

sample preparation 237 - surface, distance from the image-

forming lens 239 - -, effect on the measured reflectance

spectrum 239 scattering angle, definition 77

Subject Index 365

scattering coefficient according to Kubelka-Munk 112

- -, definition 73 - ~,effective 162

- - ofthe Kubelka-Munk-theory 109

- -, specific of papers 198

- coefficients and absorption coeffi-cients of the Kubelka-Munk-theory 191

- -, dependence on wavenumber and grain size 196

- -, derived from Roo and T 197 - - from measurements of Ro and

Roo or of T and Roo 239 - - from transmittance spectra 192

- - in the forward and reverse directions for parallel and per-pendicular irradiation 128

- -, linear dependence on wave-number 204

- - of aerosil, dependent on the packing density 202

- - of aerosils of different specific surface 202 .

- - of glass filter powder, dependence on grain size and wavenumber 193

- - ofMgO 204 - - of NaCI, influence of dispeJ;sion

ofrefraction index 203 - - of pure aerosil and of aerosil

+ graphite 209 - - of quartz powder 206 - - of the Kubelka-Munk theory

(Table) 200 - - of white standards as function of

wavenumber, grain size, and re-fractive index 199

- - of strongly absorbing substances 240

- diagram according to Mie for dielectric spheres 89

- intensity for spherical particles 86 - of a light wave on a dipole 74

scattering of large isotropic spherical particles 81

- power according to Kubelka-Munk 111

- - as function of Ro and Roo 195 - - - of the reflection in front of a

black background 115 - - at variable packing density 122 - -, derived from Roo and T 197 Schuster equation for isotropic

scattering 103 scintillation method 228 selecting of standards 241 self-absorption of standards, elimination

149 semi-infinite medium, definition 102 separation of scattering from absorp-

tion 3 shadowing effects in rough surfaces 52 - - of loose powder surfaces 54 single scattering, definition 72 Snell Law of Refraction 6 source function, definition 101 sources of error at reflectance

measurements 224 spectra of adsorbed materials 176 - of crystalline powders 285 - of powered materials by ATR 329 - of slightly soluble substances 253 spectrophotometers for color measure-

ments 231 spectrum from attenuated total re-

flection of the 1035 em -1 band of benzene and the optical constants nand" 312

specular reflection 7 - - of small crystals 228 sphere error of the integrating sphere

220 - factor of the integrating sphere 220 spiropyranes, adsorption as cation or

zwitterion 270 -, ring cleavage on surfaces 269 spreading on surfaces 176,261 standardizing of industrial products 3 state of polarization of "diffusely"

reflected radiation 37

366 Subject Index

surface area determination of powders 270

- brightness, definition 27 - -, normalized of powders of

different refraction index 49 - spectrum by means of in ternal

reflection 331

v. Seeliger law for diffuse reflection 28, 53

V-form element for internal reflection 323

vibrator 238 vulcanicdust, influence on the reflectance

of snow in Antarctica 308

Tappi-opacity 112 tautomeric complexes 277 - transformation of 2-(2' ,4' -dinitro-

benzyl}pyridine 279 Taylor sphere 138 temperature induced emission of a

scattering and absorbing medium 150 thermal transformation and decomposi-

tion reactions, investigation by re-flectance measurements 289

thin films, total reflection 317 thin-layer chromatography 295 total reflection 13 totally reflecting phase boundary 16 transfer complexes of aromatic hydro-

carbons 265 transmission coefficients, definition 8 - - in case of transition to an rarer

medium 15 - of a plane parallel plate 11 - ofathinlayerfordiffuseradiation 227 - spectrum according to the KBr

method and reflection derived from measurements oftheattenuated total reflection 330

transmittance, definition - of a non-homogeneous layer from

reflectance measurements 125 - of a scattering layer according to

Kubelka-Munk 118 -, true or internal 1 triphenylmethyl cation on surfaces 266 tristimulus values, normalized 304 turbidity as measure of the total

scattering power of gases 79 - as "scattering surface" 91 -, definition 73 - of solutions 81 two-constant theories 3 - - of scattering 100 - theory of Kubelka and Munk 106 typical color curve, additivity for

mixtures 256 - - -, definition 188 - - curves, distortion by the wave-

number dependence of the scattering coefficients 210

- - - of chromatogram spots 297 - - - of Cu(H20}1+-ions, enriched

on air-dried Dowex 294 - - - of iron oxide pigments 254 - - - of powders 199 - - -, relative intensities of the

individual bands 210

water content of solids, quantitative determination in the infrared 295

Wright's measurements on validity of Lambert Law 34

Zeiss chromatogram spectrophoto-meter 225

- color measuring instrument 231 - Elrepho 232 - remission attachment RA2 with

built-in polarization foils 232