On the optimal measurement of conversion gain in the presence of dark noise

Working from a model of Gaussian pixel noise, we present and unify over twenty-five years of developments in the statistical analysis of the photon transfer conversion gain measurement. We then study a two-sample estimator of the conversion gain that accounts for the general case of non-negligible dark noise. The moments of this estimator are ill-defined (their integral representations diverge) and so we propose a method for assigning pseudomoments, which are shown to agree with actual sample moments under mild conditions. A definition of optimal sample size pairs for this two-sample estimator is proposed and used to find approximate optimal sample size pairs that allow experimenters to achieve a predetermined measurement uncertainty with as little data as possible. The conditions under which these approximations hold are also discussed. Design and control of experiment procedures are developed and used to optimally estimate a per-pixel conversion gain map of a real image sensor. Experimental results show excellent agreement with theoretical predictions and are backed up with Monte Carlo simulation. The per-pixel conversion gain estimates are then applied in a demonstration of per-pixel read noise estimation of the same image sensor. The results of this work open the door to a comprehensive pixel-level adaptation of the photon transfer method.

A novel approach to photon transfer conversion gain estimation

Nonuniformities in the imaging characteristics of modern image sensors are a primary factor in the push to develop a pixel-level generalization of the photon transfer characterization method. In this paper, we seek to develop a body of theoretical results leading toward a comprehensive approach for tackling the biggest obstacle in the way of this goal: a means of pixel-level conversion gain estimation. This is accomplished by developing an estimator for the reciprocal-difference of normal variances and then using this to construct a novel estimator of the conversion gain. The first two moments of this estimator are derived and used to construct exact and approximate confidence intervals for its absolute relative bias and absolute coefficient of variation, respectively. A means of approximating and computing optimal sample sizes are also discussed and used to demonstrate the process of pixel-level conversion gain estimation for a real image sensor.