By Jason D. Schmidt

Wave-optics simulation is an immensely great tool for lots of functions. The simulation options during this booklet are at once acceptable to atmospheric imaging, astronomy, adaptive optics, free-space optical communications, and LADAR. furthermore, a few of the simple options are appropriate to built-in optics and nonlinear, anisotropic, and optically energetic media. Numerical Simulation of Optical Wave Propagation is simply devoted to wave-optics simulations. The publication discusses electronic Fourier transforms (FT), FT-based operations, a number of tools of wave-optics simulations, sampling requisites, and simulations in atmospheric turbulence. This booklet will profit optical scientists and engineers in any respect degrees as a consultant for FT-based info research, imaging process research, and wave-optics simulations. Professors can use this ebook to reinforce their Fourier optics classes and for self sustaining reviews with scholars. challenge units are given on the finish of every bankruptcy. scholars will examine ideas and methods from this ebook that may be applied all through their careers in optics. All readers also will enjoy the use of the MATLAB® scripting language and the supplied CD that includes code for the elemental instruments and examples used through the ebook. Contents - Foundations of Scalar Diffraction concept - electronic Fourier Transforms - basic Computations utilizing Fourier Transforms - Fraunhofer Diffraction and Lenses - Imaging structures and Aberrations - Fresnel Diffraction in Vacuum - Sampling requisites for Fresnel Diffraction - cozy Sampling Constraints with Partial Propagations - Propagation via Atmospheric Turbulence - Appendix A: functionality Definitions - Appendix B: MATLAB Code Listings - References - Index

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14) can be generalized to handle cross correlations between two fields u1 (r) and u2 (r). M ATLAB code for computing this cross correlation using a generalized version of Eq. 5. 6 gives an example of a two-dimensional auto-correlation. In the example, the function A (x, y) = rect (x/w) rect (y/w) is correlated with itself. 0 m, the grid size is 16 m, and there are 256 grid points per side. The mask value is one over the entire grid because there is no aperture. Because the function is symmetric about the x and y axes, the result is the same as the convolution example above.

These three properties result in three distortions to continuous FT pairs when they are computed discretely: • aliasing in the spatial-frequency domain, • rippling and smearing in the spatial-frequency domain, • and virtual periodic replication in the spatial domain. 12) g (x) ⇔ G (fx ) , respectively. The next few equations develop the sampled FT pair. 6 shows the graphical development. 14) as the example FT pair to illustrate the effects of discretization. This is for illustration purposes; the effects would be the same for any other FT pair.

10 shows example usage of the derivative_ft function. In this example, g (x) = x5 . The first two derivatives of this function are computed, and the results are shown in Fig. 5 along with the analytic results for comparison. 5 Plot of the function g (x) = x5 and its first two derivatives computed numerically with the analytic expressions included for comparison. 11 M ATLAB code for computing the discrete gradient of a function using FTs. * ft2(g, delta), F); Note that a window function is used to limit the extent of the signal and mitigate aliasing of the computed spectrum because g (x) and its first few derivatives are not bandlimited functions.

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Numerical Simulation of Optical Wave Propagation With by Jason D. Schmidt
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