Defocus impact analysis on telescope wavefront reconstruction by scattering spot with parametric optimization technique

Subject of Research. Wavefront reconstruction by the known scattering spot intensity with parametric optimization is presented. The Zernike polynomial coefficients of the wave function expansion as optimization parameters are used. The known defocus impact is performed on the method convergence. Methods. For method verification we used simulated scattering spot with four known Zernike coefficients (coma c31, s31 and astigmatism с22, s22) as input data. Then parametric optimization was applied to simulated scattering spot. The cost function was the standard deviation of the reference scattering spot from the one calculated at each optimization step. As a result, we got Zernike reconstructed coefficient values that can be compared with initial ones. If result coefficient values differed from initial ones less than 10–5λ, the restoration was successful. For better method conjugation various defocus values were used related to the best focus position. Main Results. The presented parametric optimization method gives the possibility to restore Zernike coefficients, describes coma and astigmatism in wavefront description by the known scattering spot intensity. Focused scattering spot intensity is not enough to restore aberration coefficients, but with the known defocus method it becomes more stable. It is shown that for successful restoration the use of defocus Zernike coefficient from the best focus position in the range of 0.1–0.5λ is enough. Practical Relevance. Wavefront reconstruction by the known defocused scattering spot intensity with parametric optimization technique can be used for telescope alignment during operation. By tolerance data, calculated for all optical systems in optical system design software, it is possible to define tilt and decenter of optical details direction by Zernike coefficient values. It is an especially important task for telescopes without axial symmetry.