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 tools at the laptop. a major target is to provide scholars of Fourier optics the aptitude of programming their very own easy wave optic beam propagations and imaging simulations. The ebook can 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 learn, the latter chapters and appendices supply equipment and examples for modeling beams and student features with extra advanced constitution, aberrations, and partial coherence. For a pupil in a direction on Fourier optics, this e-book is a concise, obtainable, and useful significant other to any of a number of first-class textbooks on Fourier optical concept.
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Additional resources for Computational Fourier Optics : a MATLAB tutorial (SPIE Tutorial Texts Vol. TT89)
Example text
A confusing detail for 2D array data is that MATLAB uses a row–column indexing scheme, where (i, j) indicates the ith row and the jth column. This is, in a sense, a reverse of standard Cartesian coordinate notation, where x (horizontal axis or “column”) is listed first and y (vertical axis or “row”) is listed second. Thus, the j-indices correspond to x-coordinates and i-indices correspond to ycoordinates. This explains the (j, i) listing (N/2+1, M/2+1) paired with [x,y] values in Fig. 5. Fortunately, MATLAB’s vector operation notation is developed for the Cartesian coordinate system; so, this issue is mostly transparent as far programming is concerned.
In order for the periodic convolution to match the analytic convolution, the combined support of the two functions being convolved needs to be less than the array side length, or D1 D2 L . 27) For the example in Fig. 7, D1 = 9 and D2 = 15, but L = 20; so, Eq. 27) is violated, and the FFT-derived result does not match the analytic result. 1 For a sample interval of x = 10 m and side length L = 5 mm, what is the sample number M? What is the Nyquist frequency? What is the frequency sample interval?
However, software applications use positive integer values for vector or array (matrix) indexing. In the case of MATLAB, indexing for a one-dimensional (1D) vector begins at (1). For display purposes it is convenient to “center” the function of interest in the vector, which means the zero coordinate will correspond to the (M/2+1) index. However, the convention for the 1D FFT algorithms is that the data value placed in the first index position corresponds to the zero coordinate. Thus, a “shift” of the centered vector values is needed before an FFT operation.