VERTECS: PSF modeling using a 3D-CNN-initialized phase diversity method

Abstract

VERTECS (Visible Extragalactic background RadiaTion Exploration by CubeSat) is a visible-light astronomical imaging satellite being developed under the JAXA-SMASH program to measure the extragalactic background light (EBL). Accurate foreground-light removal within each field requires a point-spread-function (PSF) model that varies smoothly across the field of view and remains valid under on-orbit temperature fluctuations. However, the VERTECS telescope uses a fast F/2 optical system, and the resulting PSFs are strongly undersampled at 11.08 arcsec pixel−1. Conventional Shack-Hartmann or wavefront-sensor measurements are difficult because the fast beam cannot be relayed as a sufficiently well-collimated beam without introducing alignment-dependent aberrations, while direct phase-diversity (PD) optimization is sensitive to initial values because the PSF core is concentrated into nearly one detector pixel. We therefore developed a two-stage wavefront estimation method combining a three-dimensional convolutional neural network (3D-CNN) with PD-based nonlinear optimization. Laboratory through-focus PSFs were measured at 27 defocus positions for 100 field points in four wavelength bands. The 3D-CNN was trained only on simulated through-focus PSFs generated from randomly sampled Zernike coefficients and provided initial estimates for eight low-order Zernike modes. These initial values stabilized the subsequent PD refinement, whereas zero initialization often caused divergence, stagnation, or convergence to local minima. The final defocus comparison gave an RMS error of 0.075 waves. The resulting field-dependent wavefront model reproduces laboratory PSFs and incorporates a parameterized temperature-dependent defocus term, providing a basis for in-orbit PSF prediction and foreground-light removal for VERTECS EBL measurements.