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The Zernike polynomials are a basis set for representing aberrations in optical systems. They are named after the physicist Frits Zernike, who developed them in the 1930s. In Matlab, the Zernike polynomials can be implemented using the "zernfun" function. This function takes a vector of Zernike coefficients and returns a matrix of Zernike polynomials evaluated at a set of points in the unit circle. The resulting matrix can be used to represent the wavefront aberration of an optical system. It is a powerful tool for characterizing the performance of lenses, mirrors, and other optical components. By analyzing the Zernike coefficients, one can gain insights into the sources of aberrations and develop strategies for improving the optical system.