# The shape of the Photon Transfer Curve of CCD sensors

## TL;DR

This paper analyzes the Photon Transfer Curve of CCD sensors, proposing an analytical model linking variance and pixel correlations to electrostatic properties, challenging previous assumptions about pixel boundary shifts.

## Contribution

It introduces an analytical expression for the PTC shape and correlations, connecting them to electrostatic quantities and questioning the proportional pixel boundary shift assumption.

## Key findings

- Variance flattens at high flux, indicating a variance deficit.
- Correlations between pixels increase with flux and decay with distance.
- Charge redistribution explains deviations from Poisson statistics.

## Abstract

The Photon Transfer Curve (PTC) of a CCD depicts the variance of uniform images as a function of their average. It is now well established that the variance is not proportional to the average, as Poisson statistics would indicate, but rather flattens out at high flux. This "variance deficit", related to the brighter-fatter effect, feeds correlations between nearby pixels, that increase with flux, and decay with distance. We propose an analytical expression for the PTC shape, and for the dependence of correlations with intensity, and relate both to some more basic quantities related to the electrostatics of the sensor, that are commonly used to correct science images for the brighter-fatter effect. We derive electrostatic constraints from a large set of flat field images acquired with a CCD e2v 250, and eventually question the generally-admitted assumption that boundaries of CCD pixels shift by amounts proportional to the source charges. Our results show that the departure of flat field statistics from Poisson law is entirely compatible with charge redistribution during the drift in the sensor.