By David G. Voelz
Computational Fourier Optics is a textual content that exhibits the reader in an instructional shape find out how to enforce Fourier optical concept and analytic equipment at the laptop. a major target is to provide scholars of Fourier optics the potential of programming their very own uncomplicated wave optic beam propagations and imaging simulations. The booklet can also be of curiosity to specialist engineers and physicists studying Fourier optics simulation techniques-either as a self-study textual content or a textual content for a quick path. For extra complex examine, the latter chapters and appendices supply tools and examples for modeling beams and scholar features with extra advanced constitution, aberrations, and partial coherence. For a scholar in a direction on Fourier optics, this e-book is a concise, obtainable, and functional spouse to any of a number of first-class textbooks on Fourier optical conception.
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In our example M = 200 and the definition of the x vector causes the rectangle function to be centered at the M/2+1 position (101). More care needs to be taken when shifting vectors that contain an odd number of samples. For example, if the fftshift function is used with an odd number of samples, then the ifftshift function should be used to undo the shift. For an even number of samples, the fftshift function works both forward and backward. ). 4 Computing the FFT and Displaying Results To compute the FFT of the vector “f0,” add the following below the last piece of code: 24 25 26 27 28 29 30 31 32 33 F0=fft(f0)*dx; %FFT and scale figure(5) plot(abs(F0)); %plot magnitude title('magnitude'); xlabel('index'); figure(6) plot(angle(F0)); title('phase'); xlabel('index'); %plot phase Here, the 1D FFT algorithm in MATLAB is used.
Thus, the valleys shown in the curve do not necessarily appear to reach zero. The phase plot may look curious, but there are essentially three phase values in the plot: 0, −, and . However, − and represent the same value in a modulo 2 format, so the sharp transitions in the plot between − and are not particularly important, and the phase is effectively constant in these places. These sharp 2 transitions occur because of slight numerical differences between samples. With this interpretation, you should understand that the important phase transition is from 0 to (or −), which occurs about every 18 points.
It is optimized for vector and matrix operations and, therefore, is a good tool for Fourier optics simulations, which generally involve at least two dimensions. The examples in this chapter and throughout the book use a basic set of MATLAB features, in part to keep the material at a tutorial level but also because the details of the programming steps are more obvious. As you become familiar with the software, you may find more convenient and efficient ways to implement the programming. 1 is used in this book.