Optimal Fitting, Debiasing, and Cosmic Ray Rejection for Detectors Read Out Up-the-Ramp

Abstract

This paper derives the optimal fit to a pixel's count rate in the case of an ideal detector read out nondestructively in the presence of both read and photon noise. The approach is general for any readout scheme, provides closed-form expressions for all quantities, and has a computational cost that is linear in the number of resultants (groups of reads). I also derive the bias of the fit from estimating the covariance matrix and show how to remove it to first order. The ramp-fitting algorithm I describe provides the $\chi^2$ value of the fit of a line to the accumulated counts, enabling hypothesis testing for cosmic ray hits using the entire ramp. I show that this approach can be substantially more sensitive than one that only uses the difference between sequential resultants, especially for long ramps and for jumps that occur in the middle of a group of reads. It can also be implemented for a computational cost that is linear in the number of resultants. I provide and describe a pure Python implementation of these algorithms that can process a 10-resultant ramp on a $4096 \times 4096$ detector in $\approx$8 seconds with bias removal, or in $\approx$20 seconds including iterative cosmic ray detection and removal, on a single core of a 2020 Macbook Air. This Python implementation, together with tests and a tutorial notebook, are available at https://github.com/t-brandt/fitramp.Comment: 30 pages, 9 figures. Python implementation available at https://github.com/t-brandt/fitram