Файл: Ersoy O.K. Diffraction, Fourier optics, and imaging (Wiley, 2006)(ISBN 0471238163)(427s) PEo .pdf
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100
Table 7.1. Output plane position coordinates in mm with FFT and the Fresnel approximation.
8.0998 – 8.0998i |
8.0682 – 8.0998i |
8.0366 – 8.0998i |
8.0049 – 8.0998i |
7.9733 – 8.0998i |
7.9416 – 8.0998i |
7.9100 – 8.0998i |
7.8784 |
8.0998 – 8.0682i |
8.0682 – 8.0682i |
8.0366 – 8.0682i |
8.0049 – 8.0682i |
7.9733 – 8.0682i |
7.9416 – 8.0682i |
7.9100 – 8.0682i |
7.8784 |
8.0998 – 8.0366i |
8.0682 – 8.0366i |
8.0366 – 8.0366i |
8.0049 – 8.0366i |
7.9733 – 8.0366i |
7.9416 – 8.0366i |
7.9100 – 8.0366i |
7.8784 |
8.0998 – 8.0049i |
8.0682 – 8.0049i |
8.0366 – 8.0049i |
8.0049 – 8.0049i |
7.9733 – 8.0049i |
7.9416 – 8.0049i |
7.9100 – 8.0049i |
7.8784 |
8.0998 – 7.9733i |
8.0682 – 7.9733i |
8.0366 – 7.9733i |
8.0049 – 7.9733i |
7.9733 – 7.9733i |
7.9416 – 7.9733i |
7.9100 – 7.9733i |
7.8784 |
8.0998 – 7.9416i |
8.0682 – 7.9416i |
8.0366 – 7.9416i |
8.0049 – 7.9416i |
7.9733 – 7.9416i |
7.9416 – 7.9416i |
7.9100 – 7.9416i |
7.8784 |
8.0998 – 7.9100i |
8.0682 – 7.9100i |
8.0366 – 7.9100i |
8.0049 – 7.9100i |
7.9733 – 7.9100i |
7.9416 – 7.9100i |
7.9100 – 7.9100i |
7.8784 |
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Table 7.2. Output plane position coordinates in mm with FFT and the NFFA.
8.1535 – 8.1535i |
8.1214 – 8.1533i |
8.0894 – 8.1531i |
8.0573 – 8.1529i |
8.0253 – 8.1527i |
7.9932 – 8.1525i |
7.9612 – 8.1523i |
8.1533 – 8.1214i |
8.1212 – 8.1212i |
8.0892 – 8.1210i |
8.0571 – 8.1208i |
8.0251 – 8.1206i |
7.9930 – 8.1204i |
7.9610 – 8.1202i |
8.1531 – 8.0894i |
8.1210 – 8.0892i |
8.0890 – 8.0890i |
8.0569 – 8.0888i |
8.0249 – 8.0886i |
7.9928 – 8.0884i |
7.9608 – 8.0881i |
8.1529 – 8.0573i |
8.1208 – 8.0571i |
8.0888 – 8.0569i |
8.0567 – 8.0567i |
8.0247 – 8.0565i |
7.9926 – 8.0563i |
7.9606 – 8.0561i |
8.1527 – 8.0253i |
8.1206 – 8.0251i |
8.0886 – 8.0249i |
8.0565 – 8.0247i |
8.0245 – 8.0245i |
7.9924 – 8.0243i |
7.9604 – 8.0240i |
8.1525 – 7.9932i |
8.1204 – 7.9930i |
8.0884 – 7.9928i |
8.0563 – 7.9926i |
8.0243 – 7.9924i |
7.9922 – 7.9922i |
7.9602 – 7.9920i |
8.1523 – 7.9612i |
8.1202 – 7.9610i |
8.0881 – 7.9608i |
8.0561 – 7.9606i |
8.0240 – 7.9604i |
7.9920 – 7.9602i |
7.9600 – 7.9600i |
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101
102
Table 7.3. Error in output position in mm (difference between Tables 7.1 and 7.2).
0.0537 – 0.0537i |
0.0532 – 0.0535i |
0.0528 – 0.0532i |
0.0524 – 0.0530i |
0.0520 – 0.0528i |
0.0516 – 0.0526i |
0.0512 – 0.0524i |
0.0535 – 0.0532i |
0.0530 – 0.0530i |
0.0526 – 0.0528i |
0.0522 – 0.0526i |
0.0518 – 0.0524i |
0.0514 – 0.0522i |
0.0510 – 0.0520i |
0.0532 – 0.0528i |
0.0528 – 0.0526i |
0.0524 – 0.0524i |
0.0520 – 0.0522i |
0.0516 – 0.0520i |
0.0512 – 0.0518i |
0.0508 – 0.0516i |
0.0530 – 0.0524i |
0.0526 – 0.0522i |
0.0522 – 0.0520i |
0.0518 – 0.0518i |
0.0514 – 0.0516i |
0.0510 – 0.0514i |
0.0506 – 0.0512i |
0.0528 – 0.0520i |
0.0524 – 0.0518i |
0.0520 – 0.0516i |
0.0516 – 0.0514i |
0.0512 – 0.0512i |
0.0508 – 0.0510i |
0.0504 – 0.0508i |
0.0526 – 0.0516i |
0.0522 – 0.0514i |
0.0518 – 0.0512i |
0.0514 – 0.0510i |
0.0510 – 0.0508i |
0.0506 – 0.0506i |
0.0502 – 0.0504i |
0.0524 – 0.0512i |
0.0520 – 0.0510i |
0.0516 – 0.0508i |
0.0512 – 0.0506i |
0.0508 – 0.0504i |
0.0504 – 0.0502i |
0.0500 – 0.0500i |
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NUMERICAL EXAMPLES |
103 |
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Figure 7.4. The output intensity from an aperture with the exactly computed and NFFA approximated diffraction integral.
Figure 7.4 shows the output diffraction pattern intensities for both the exact method and the NFFA method almost perfectly overlapping each other. Figure 7.5 shows the normalized intensity error defined by
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Error |
¼ |
IExact INFFA |
ð |
7:6-2 |
Þ |
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IExact |
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Figure 7.5. The output intensity error between the exactly computed and NFFA approximated diffraction integrals.
104 |
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WIDE-ANGLE NEAR AND FAR FIELD APPROXIMATIONS |
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Figure 7.6. The output phase angle with the exactly computed and NFFA approximated diffraction integral.
where IExact and INFFA are the exact and NFFA intensities. Figure 7.6 shows the output phase angles for the exact method and the NFFA method almost perfectly overlapping each other.
Figure 7.7 shows the output diffraction pattern intensity computed with the Fresnel approximation in comparison with the exact method. Figure 7.8 shows the
Figure 7.7. The output intensity with the Fresnel approximation in comparison with the exactly computed diffraction integral.
NUMERICAL EXAMPLES |
105 |
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Figure 7.8. The output phase angle with the Fresnel approximation in comparison with the output phase angle with the exactly computed diffraction integral.
output phase angle computed with the Fresnel approximation in comparison with the exact method. It is observed that the errors with the Fresnel approximation in the geometry considered are nonnegligible.
In the next set of experiments, 3-D results are discussed. Figure 7.9 shows the input square aperture used in the simulations. Two sets of parameters were used. In the first set, the parameters are as follows:
Z ¼ 50 mm; DI ðinput square aperture sideÞ¼ 0:2 mm; N ¼ 512; l ¼ 0:6328 m
Figure 7.9. The input square aperture used in simulations.