Estimating transmitted wavefronts in a broad bandwidth based on Zernike coefficients

Abstract

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.

Topology Optimization Design of an Active Deformable Mirror Based on Discrete Orthogonal Zernike Polynomials

“…Optical wave aberration, which is commonly used to assess the quality and the shape of the wave aberration, is rather complicated and in general it is difficult to use its simple function accurately, in all kinds of approximate method by Zernike polynomials in the circle domain orthogonal to each other, and the low-order model and the corresponding seidel aberration in optical design become important to describe the wave aberration of the description method [26].…”

“…Zernike polynomial after discretization loses orthogonality. Therefore, there is always a theoretical error when calculating the coefficients of the Zernike polynomial using Equation (26). To solve the above problem, the method of Nth order Legendre polynomials [28] is used in this paper to construct the discrete orthogonal Zernike polynomials.…”

Multi-wavelength laser interferometer control system design

“…The transmitted wavefront of an optical system contains a wealth of information, and detection of the wavefront is an important means of evaluating the performance of an optical system and studying the optical field. Traditional wavefront detection techniques can only detect transmitted wavefronts at a limited number of specific wavelengths [1] . The basic principle of optical system multi-wavelength wavefront detection is to detect the wavefront of the optical system at several different wavelengths, and then use these specific wavelength wavefront Zernike coefficients to obtain the Zernike coefficient-wavelength curve through a certain functional relationship, and then calculate the Zernike coefficient of any specific wavelength according to the Zernike coefficient-wavelength curve, and finally fit the calculated Zernike coefficients to other wavelengths [2,3] .…”