Light Distribution in the Defocused Image of a Coherently Illuminated Edge*

Stephen H. Rowe

doi:10.1364/JOSA.59.000711

Journal of the Optical Society of America
Vol. 59,
Issue 6,
pp. 711-714
(1969)
•https://doi.org/10.1364/JOSA.59.000711

Light Distribution in the Defocused Image of a Coherently Illuminated Edge

Stephen H. Rowe

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Stephen H. Rowe, "Light Distribution in the Defocused Image of a Coherently Illuminated Edge*," J. Opt. Soc. Am. 59, 711-714 (1969)

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Abstract

Scalar diffraction theory is used to obtain an integral which expresses the irradiance in the defocused image of a coherently illuminated edge. This integral is evaluated numerically and the results are given for six values of defocusing.

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Equations (15)

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p	0.0	1.0	2.0	3.0	4.0	5.0	6.0

u′

15.0	1.030	1.014	9.792 × 10⁻¹	9.624 × 10⁻¹	9.864 × 10⁻¹	1.040	1.082
14.5	1.013	1.002	9.831 × 10⁻¹	9.811 × 10⁻¹	1.009	1.051	1.068
14.0	9.908 × 10⁻¹	9.896 × 10⁻¹	9.916 × 10⁻¹	1.007	1.033	1.052	1.037
13.5	9.698 × 10⁻¹	9.789 × 10⁻¹	1.003	1.033	1.052	1.042	9.935 × 10⁻¹
13.0	9.551 × 10⁻¹	9.731 × 10⁻¹	1.016	1.055	1.061	1.020	9.456 × 10⁻¹
12.5	9.507 × 10⁻¹	9.739 × 10⁻¹	1.026	1.065	1.055	9.903 × 10⁻¹	9.016 × 10⁻¹
12.0	9.586 × 10⁻¹	9.816 × 10⁻¹	1.030	1.060	1.033	9.558 × 10⁻¹	8.703 × 10⁻¹
11.5	9.778 × 10⁻¹	9.951 × 10⁻¹	1.029	1.039	9.993 × 10⁻¹	9.234 × 10⁻¹	8.594 × 10⁻¹
11.0	1.005	1.012	1.020	1.006	9.591 × 10⁻¹	9.007 × 10⁻¹	8.742 × 10⁻¹
10.5	1.033	1.027	1.005	9.671 × 10⁻¹	9.217 × 10⁻¹	8.948 × 10⁻¹	9.161 × 10⁻¹
10.0	1.056	1.037	9.879 × 10⁻¹	9.312 × 10⁻¹	8.967 × 10⁻¹	9.104 × 10⁻¹	9.821 × 10⁻¹
9.5	1.067	1.038	9.702 × 10⁻¹	9.064 × 10⁻¹	8.918 × 10⁻¹	9.486 × 10⁻¹	1.065
9.0	1.061	1.029	9.560 × 10⁻¹	8.998 × 10⁻¹	9.117 × 10⁻¹	1.007	1.153
8.5	1.038	1.009	9.493 × 10⁻¹	9.157 × 10⁻¹	9.573 × 10⁻¹	1.078	1.234
8.0	1.002	9.847 × 10⁻¹	9.535 × 10⁻¹	9.553 × 10⁻¹	1.025	1.155	1.298
7.5	9.621 × 10⁻¹	9.612 × 10⁻¹	9.705 × 10⁻¹	1.015	1.107	1.228	1.336
7.0	9.274 × 10⁻¹	9.455 × 10⁻¹	9.997 × 10⁻¹	1.086	1.191	1.287	1.344
6.5	9.074 × 10⁻¹	9.431 × 10⁻¹	1.037	1.157	1.263	1.321	1.321
6.0	9.092 × 10⁻¹	9.571 × 10⁻¹	1.078	1.214	1.307	1.323	1.268
5.5	9.361 × 10⁻¹	9.877 × 10⁻¹	1.114	1.245	1.313	1.287	1.189
5.0	9.868 × 10⁻¹	1.032	1.139	1.241	1.272	1.213	1.090
4.5	1.054	1.084	1.150	1.201	1.189	1.104	9.764 × 10⁻¹
4.0	1.123	1.130	1.141	1.128	1.071	9.717 × 10⁻¹	8.565 × 10⁻¹
3.5	1.174	1.157	1.109	1.031	9.328 × 10⁻¹	8.296 × 10⁻¹	7.384 × 10⁻¹
3.0	1.185	1.147	1.047	9.157 × 10⁻¹	7.889 × 10⁻¹	6.913 × 10⁻¹	6.292 × 10⁻¹
2.5	1.137	1.085	9.529 × 10⁻¹	7.907 × 10⁻¹	6.523 × 10⁻¹	5.677 × 10⁻¹	5.335 × 10⁻¹
2.0	1.022	9.673 × 10⁻¹	8.275 × 10⁻¹	6.623 × 10⁻¹	5.316 × 10⁻¹	4.651 × 10⁻¹	4.530 × 10⁻¹
1.5	8.494 × 10⁻¹	8.010 × 10⁻¹	6.786 × 10⁻¹	5.373 × 10⁻¹	4.312 × 10⁻¹	3.853 × 10⁻¹	3.871 × 10⁻¹
1.0	6.418 × 10⁻¹	6.074 × 10⁻¹	5.210 × 10⁻¹	4.223 × 10⁻¹	3.523 × 10⁻¹	3.260 × 10⁻¹	3.333 × 10⁻¹
0.5	4.316 × 10⁻¹	4.147 × 10⁻¹	3.727 × 10⁻¹	3.257 × 10⁻¹	2.931 × 10⁻¹	2.827 × 10⁻¹	2.885 × 10⁻¹
0.0	2.500 × 10⁻¹	2.500 × 10⁻¹	2.500 × 10⁻¹	2.500 × 10⁻¹	2.500 × 10⁻¹	2.500 × 10⁻¹	2.500 × 10⁻¹
− 0.5	1.177 × 10⁻¹	1.304 × 10⁻¹	1.616 × 10⁻¹	1.957 × 10⁻¹	2.177 × 10⁻¹	2.225 × 10⁻¹	2.158 × 10⁻¹
− 1.0	3.956 × 10⁻²	5.899 × 10⁻²	1.068 × 10⁻¹	1.583 × 10⁻¹	1.907 × 10⁻¹	1.963 × 10⁻¹	1.849 × 10⁻¹
− 1.5	6.143 × 10⁻³	2.665 × 10⁻²	7.696 × 10⁻²	1.309 × 10⁻¹	1.642 × 10⁻¹	1.694 × 10⁻¹	1.572 × 10⁻¹
− 2.0	1.206 × 10⁻⁴	1.762 × 10⁻²	6.061 × 10⁻²	1.069 × 10⁻¹	1.361 × 10⁻¹	1.419 × 10⁻¹	1.334 × 10⁻¹
− 2.5	4.368 × 10⁻³	1.694 × 10⁻²	4.823 × 10⁻²	8.309 × 10⁻²	1.073 × 10⁻¹	1.159 × 10⁻¹	1.142 × 10⁻¹
− 3.0	7.817 × 10⁻³	1.551 × 10⁻²	3.540 × 10⁻²	5.978 × 10⁻²	8.068 × 10⁻²	9.383 × 10⁻²	9.997 × 10⁻²
− 3.5	6.968 × 10⁻³	1.099 × 10⁻²	2.252 × 10⁻²	3.975 × 10⁻²	5.940 × 10⁻²	7.730 × 10⁻²	8.993 × 10⁻²
− 4.0	3.556 × 10⁻³	5.450 × 10⁻³	1.221 × 10⁻²	2.558 × 10⁻²	4.499 × 10⁻²	6.602 × 10⁻²	8.229 × 10⁻²
− 4.5	7.038 × 10⁻⁴	1.695 × 10⁻³	6.370 × 10⁻³	1.784 × 10⁻²	3.656 × 10⁻²	5.804 × 10⁻²	7.486 × 10⁻²
− 5.0	4.406 × 10⁻⁵	8.037 × 10⁻⁴	4.703 × 10⁻³	1.474 × 10⁻²	3.146 × 10⁻²	5.082 × 10⁻²	6.605 × 10⁻²
− 5.5	1.055 × 10⁻³	1.774 × 10⁻³	5.138 × 10⁻³	1.338 × 10⁻²	2.691 × 10⁻²	4.270 × 10⁻²	5.564 × 10⁻²
− 6.0	2.162 × 10⁻³	2.786 × 10⁻³	5.415 × 10⁻³	1.150 × 10⁻²	2.145 × 10⁻²	3.361 × 10⁻²	4.478 × 10⁻²
− 6.5	2.249 × 10⁻³	2.695 × 10⁻³	4.462 × 10⁻³	8.486 × 10⁻³	1.541 × 10⁻²	2.486 × 10⁻²	3.527 × 10⁻²
− 7.0	1.368 × 10⁻³	1.631 × 10⁻³	2.670 × 10⁻³	5.197 × 10⁻³	1.014 × 10⁻²	1.806 × 10⁻²	2.841 × 10⁻²
− 7.5	3.660 × 10⁻⁴	5.105 × 10⁻⁴	1.127 × 10⁻³	2.860 × 10⁻³	6.808 × 10⁻³	1.398 × 10⁻²	2.425 × 10⁻²
− 8.0	1.153 × 10⁻⁶	1.063 × 10⁻⁴	5.837 × 10⁻⁴	2.030 × 10⁻³	5.521 × 10⁻³	1.209 × 10⁻²	2.171 × 10⁻²
− 8.5	3.499 × 10⁻⁴	4.605 × 10⁻⁴	9.335 × 10⁻⁴	2.275 × 10⁻³	5.376 × 10⁻³	1.108× 10⁻²	1.935 × 10⁻²
− 9.0	8.991 × 10⁻⁴	1.016 × 10⁻³	1.474 × 10⁻³	2.652 × 10⁻³	5.194 × 10⁻³	9.724 × 10⁻³	1.627 × 10⁻²
− 9.5	1.088 × 10⁻³	1.189 × 10⁻³	1.565 × 10⁻³	2.465 × 10⁻³	4.326 × 10⁻³	7.629 × 10⁻³	1.258 × 10⁻²
− 10.0	7.760 × 10⁻⁴	8.456 × 10⁻⁴	1.099 × 10⁻³	1.695 × 10⁻³	2.942 × 10⁻³	5.280 × 10⁻³	9.119 × 10⁻³

Abstract

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Figures (3)

Tables (1)

Equations (15)

Journal of the Optical Society of America