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This paper derives the optimal fit to a pixel's count rate in the case of anideal detector read out nondestructively in the presence of both read andphoton noise. The approach is general for any readout scheme, providesclosed-form expressions for all quantities, and has a computational cost thatis linear in the number of resultants (groups of reads). I also derive the biasof the fit from estimating the covariance matrix and show how to remove it tofirst order. The ramp-fitting algorithm I describe provides the $\chi^2$ valueof the fit of a line to the accumulated counts, enabling hypothesis testing forcosmic ray hits using the entire ramp. I show that this approach can besubstantially more sensitive than one that only uses the difference betweensequential resultants, especially for long ramps and for jumps that occur inthe middle of a group of reads. It can also be implemented for a computationalcost that is linear in the number of resultants. I provide and describe a purePython implementation of these algorithms that can process a 10-resultant rampon 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 asingle core of a 2020 Macbook Air. This Python implementation, together withtests and a tutorial notebook, are available athttps://github.com/t-brandt/fitramp.

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