Accuracy of Geometric Point Spread Function Estimation using the Ray-Counting Method

摘要

The geometric point spread function (PSF) is an appropriate tool for modeling image degradation of an optical system, whenever the effect of diffraction is small compared to that of aberrations. The PSF is conventionally estimated by computing the density of ray intersections with the image plane (ray-counting method). We studied the effect of two factors on the estimation: the number of rays, using an error model, and the influence of the ray sampling pattern. We measured the accuracy of the PSFs estimation in three ideal cases, where we could derive an analytical expression for the irradiance. Additionally we estimated the PSFs generated by a single rear landscape lens. We have observed a consistent improvement of 4.5 dB (Signal-to-Noise Ratio) when doubling the number of rays. This ensures that an arbitrarily high accuracy on the estimation of geometric PSFs is theoretically attainable. However, the method is not very efficient because of the slow convergence rate. As an alternative, to avoid tracing a large number of rays, we investigated the benefits of interpolating rays intersections (using cubic splines) of the ray mapping. For instance, by interpolating only 100 traced rays we may obtain a similar quality in the estimation as when using 100 million of real traced rays. Among different uniform ray pupil sampling patterns (square, jittered square, hexapolar and hexagonal) we found that the hexagonal outperformed the other ones.