A source penumbral image reconstruction method with linear mapping principle for geometrical optics is established. The ideal binary point spread function (PSF) can be obtained using a geometrical optics model. The system PSF with certain sharpness was obtained using a Monte Carlo (MC) model. Considering other factors besides the transportation of the x (gamma)-rays or particles (fusion neutrons) in the penumbral encoding aperture in MC model, such as the scattering background and the systematic error, the PSF from MC model "source-image pair matching" experiments with a large area standard oval shape source were processed. A method for correcting and calibrating the PSF by the expectation maximization adaptive algorithm was established and the optimized PSF with 22.30 microm sharpness was achieved. This is more consistent with the real system PSF despite the increased noise level of the two-dimensional PSF and large irregularity in the PSF profile.