52 lines
1.5 KiB
C
52 lines
1.5 KiB
C
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#pragma once
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#include <gsl/gsl_histogram.h>
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#include <gsl/gsl_vector_double.h>
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/* Intensity function parameters */
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struct param {
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double a; // aperture radius
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double k; // wavenumber
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double e; // wave amplitude
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double l; // screen distance
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};
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/* Intensity of the EM field at a large distance
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* from a circular aperture diffraction of a plane
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* wave.
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*
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* The intensity is given as a function of θ,
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* the diffraction angle. All the other physical
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* parameters are controlled by the structure `param`.
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*
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* See Fraunhöfer diffraction on "Hect - Optics" for
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* a derivation of the formula.
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*/
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double intensity(double theta, struct param p);
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/* `gaussian_kernel(bins, sigma)` generates a convolution
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* kernel for the intensity histogram with `bins` bins.
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*
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* The kernel is a gaussian PDF with μ at the central bin
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* and σ equal to `sigma`. The size is 6% of `bins` and
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* the bin width is the same of the intensity histogram:
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* π/2 / `bins`.
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*/
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gsl_histogram* gaussian_kernel(size_t bins, double sigma);
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/* `gsl_vector_convolve(a, b, res)` computes the linear
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* convolution of two vectors. The resulting vector
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* has size `a->n + b->n - 1` and is stored in `res`.
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*/
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int gsl_vector_convolve(gsl_vector *a, gsl_vector *b, gsl_vector *res);
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/* Convolves two histograms while keeping the
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* original bin edges. This is a simple wrapper
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* function around `gsl_vector_convolve`.
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*/
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gsl_histogram* histogram_convolve(gsl_histogram *a, gsl_histogram *b);
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