By Okan K. Ersoy
This booklet provides present theories of diffraction, imaging, and similar themes in line with Fourier research and synthesis concepts, that are crucial for realizing, interpreting, and synthesizing sleek imaging, optical communications and networking, in addition to micro/nano structures. purposes coated contain tomography; magnetic resonance imaging; man made aperture radar (SAR) and interferometric SAR; optical communications and networking units; computer-generated holograms and analog holograms; and instant platforms utilizing EM waves.
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Additional resources for Diffraction, fourier optics, and imaging
In this and next sections, we will discuss the 1-D transforms only. 0 p=2 f <0 ð2:6-2Þ ð2:6-3Þ The inverse RFT is given by uðtÞ ¼ 1 ð Uð f Þ cosð2p ft þ yð f ÞÞdf ð2:6-4Þ À1 It is observed that cosð2pft þ yð f ÞÞ equals cosð2pftÞ for f ¼ 0 and sinð2pj f jtÞ for f < 0. This is a ‘‘trick’’ used to cover both the cosine and sine basis functions in a single integral. Negative frequencies are used for this purpose. 3. The basis function 0 Frequency 5 10 pﬃﬃﬃ 2 cosð2pft þ yðf ÞÞ for t ¼ 0:25 and À10 < f < 10.
In order to reduce aliasing, the input and output apertures can be zero padded to a size, say, M 0 ¼ 2M. Then, N can be chosen as follows: & N even 2M 0 N¼ ð4:4-18Þ 2M 0 þ 1 N odd In addition, FFT algorithms are usually more efficient when N is a power of 2. Hence, N may actually be chosen larger than the value computed above to make it a power of 2. 4-16) can now be written as U½n1 ; n2 ; z ¼ ðÁf Þ2 N À1 X N À1 X A½m1 ; m2 ; 0e jz ! 4-19) is in the form of an inverse 2-D DFT except for a normalization factor.
Then, we get E ¼ ðEx0 ex Æ Ey0 ey Þ cosðkz þ wtÞ ð3:7-11Þ In this case, ðEx0 ex Æ Ey0 ey Þ can be considered as a vector that does not change in direction with time or propagation distance. Circular polarization is obtained when 0 ¼ Æp=2; and E0 ¼ Ex0 ¼ Ey0 . Then, we get E ¼ E0 cosðkz þ wtÞex Æ E0 sinðkz þ wtÞey ð3:7-12Þ We note that jEj ¼ E0 . For 0 ¼ Àp=2, E describes a circle rotating clockwise during propagation. For 0 ¼ þp=2, E describes a circle rotating counterclockwise during propagation.