Simulation of inverse Fredholm reconstruction in a vignetting zone: application to ASPIICS

Abstract

Aims. This work deals with image reconstruction in a vignetting zone where the point spread function becomes evanescent and the image undergoes a Fredholm transformation. The application of this method is aimed at the reconstruction of the solar corona in the vignetting zone of the ASPIICS coronagraph. It extends on a previous paper in several aspects. Methods. We used a matrix formalism for the exact inversion of the Fredholm integral. The stray light appears there as a bias. We performed two procedures: either the direct processing of the biased data or their processing following the subtraction of the bias. In the first case, the statistics follow a Poisson distribution and a Kullback-Leibler divergence was used; in the second case, we were led to use a simplifying Gaussian statistic. In both cases, a physical regularization using a Strehl criterion was implemented and this improved the results. Image reconstruction in the vignetting area is done in the case of a perfect coronagraph for two diameters of the internal occulter, but also in the case of formation flight errors and optical defects that are present but ignored by the inversion procedure. Results. Poisson and Gauss models both give much better results than simple flux compensation. For the Poisson model, unexpected pseudo-fringes are present in the reconstructed raw image but are greatly reduced using regularization. The Gaussian model (using de-biased data) is found to give better results, no matter whether it is the regularized or non-regularized version of the algorithm that is used. Despite a high level of stray light, the internal occulter of a smaller dimension allows us to approach much closer to the solar edge without too great a loss in terms of quality in the outer regions. This conclusion remains true in the case of optical micro-defects leading to speckles in the PSF because that has only a slight impact on the images in the vignetting area. In the case of formation flying errors, the Fredholm inversion is more affected by these for the small internal occulter than for the larger one. Conclusions. The method proposed for the Fredholm inversion is general and can be transposed to other systems using external occulters. An application of this method to the imaging of exoplanets is generally envisaged.