zernike in matlab

Zernike polynomials are commonly used in optics to represent the wavefront aberrations of optical systems. MATLAB has a built-in function zernike() to generate Zernike polynomials.

To generate the first few Zernike polynomials, you can use the following code:

main.m
r = 1; % radius of the unit circle
theta = linspace(0, 2*pi, 100); % 100 points evenly spaced from 0 to 2*pi
[THETA, R] = meshgrid(theta, r);

% Generate the first few Zernike polynomials
Z1 = zernike(1, R.*exp(1i*THETA));
Z2 = zernike(2, R.*exp(1i*THETA));
Z3 = zernike(3, R.*exp(1i*THETA));
Z4 = zernike(4, R.*exp(1i*THETA));
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zernike(n, rho) generates the Zernike polynomial of order n with a radius rho. The radius rho is a matrix with elements corresponding to the position of each point in the grid.

In this example, we generate the first four Zernike polynomials: piston (Z1), tilt (Z2), defocus (Z3), and astigmatism (Z4). The resulting Zernike polynomials are complex matrices, so you can plot either the real or imaginary part to visualize the wavefront aberrations.

You can use these Zernike polynomials to study the optical properties of different wavefronts, and to design and optimize optical systems with the help of MATLAB.