By David G. Voelz
Computational Fourier Optics is a textual content that indicates the reader in an academic shape the best way to enforce Fourier optical idea and analytic equipment at the computing device. a chief aim is to provide scholars of Fourier optics the potential of programming their very own simple wave optic beam propagations and imaging simulations. The e-book can also be of curiosity to expert engineers and physicists studying Fourier optics simulation techniques-either as a self-study textual content or a textual content for a quick direction. For extra complicated examine, the latter chapters and appendices offer equipment and examples for modeling beams and scholar features with extra complex constitution, aberrations, and partial coherence. For a pupil in a path on Fourier optics, this e-book is a concise, obtainable, and functional spouse to any of numerous very good textbooks on Fourier optical idea.
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Additional info for Computational Fourier Optics : a MATLAB tutorial (SPIE Tutorial Texts Vol. TT89)
The integrals on the left side can be evaluated numerically for various values of B until Eq. 10) is satisfied. With this approach the effective bandwidth is found to be B 5 . 3 illustrates the portion of the spectrum that encompasses 98% of the spectral power. Substituting Eq. 11) into Eq. 12) which says at least 10 samples across the half-width of the rect function (20 across the full width) are required to retain the effective bandwidth indicated in Eq. 11). It is important to realize that the part of the analytic spectrum that lies beyond the Nyquist frequency does not simply disappear.
3 illustrates the portion of the spectrum that encompasses 98% of the spectral power. Substituting Eq. 11) into Eq. 12) which says at least 10 samples across the half-width of the rect function (20 across the full width) are required to retain the effective bandwidth indicated in Eq. 11). It is important to realize that the part of the analytic spectrum that lies beyond the Nyquist frequency does not simply disappear. Even though small in power, it can introduce noticeable aliased frequency content that is erroneous.
Arguments are set up to graph the discrete and analytic results on the same plot, and the legends are added to the display. The resulting plots (Fig. 8) compare the FFT and analytic results. The magnitude results are nearly identical, but the FFT result has slightly higher values than the analytic curve at the edges. 5). The phase plots differ only in some transitions between and − for the digital result, which are of no consequence. 6 Convolution Example A convolution can be performed using the FFT and applying the Fourier convolution theorem.
Computational Fourier Optics : a MATLAB tutorial (SPIE Tutorial Texts Vol. TT89) by David G. Voelz