Estimating transmitted wavefronts in a broad bandwidth based on Zernike coefficients

Existing technologies and methods for measuring transmitted wavefronts typically operate at only a few specific wavelengths. In this paper, we propose a new method for estimating the wavefront distortion of an optical transmission system in a broad bandwidth. We establish the relationship between the transmitted wavefront and wavelength, using Zernike fringe coefficients to represent the wavefront. From simulations of several different types of optical systems, we found that two formulas can be used to express Zernike-wavelength curves: the Conrady dispersion formula and a new formula that we have named the apochromatic characteristic formula. To reduce the influence of measurement errors on predictions, fitting method is biased in favor of simulation rather than experimental data. We illustrate the validity of this technique by reconstructing a wavefront transmitted at 671 nm using Zernike polynomials, demonstrating that the predicted wavefront is very similar to the wavefront measured experimentally. Using the Conrady formula, we illustrate that the wavefront of a monochromatic system can be predicted for any wavelength in a broad range, using data from three standard wavelengths. As Seidel coefficients correspond to Zernike coefficients, the relationship between optical aberration and wavelength detailed here can also be applied to areas such as optical design, optical computing and adaptive optics.

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