Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the author. Logarithmic CMOS image sensors capture high dynamic range scenes without saturation or loss of perceptible detail but problems exist with image quality. This thesis develops and applies methods of modelling and calibration to understand and improve the fixed pattern noise (FPN) and colour rendition of logarithmic imagers. Chapter 1 compares CCD and CMOS image sensors and, within the latter category, compares linear and logarithmic pixel designs. Chapter 2 reviews the literature on multilinear algebra, unifying and extending approaches for analytic and numeric manipulation of multi-index arrays, which are the generalisation of scalars, vectors and matrices. Chapter 3 defines and solves the problem of multilinear regression with linear constraints for the calibration of a sensor array, permitting models with linear relationships of parameters

Logarithmic CMOS image sensors encode a high dynamic range scene in a manner that roughly approximates human perception whereas linear sensors with equivalent quantisation suffer from saturation or loss of detail. Moreover, the continuous response of logarithmic pixels permit high frame rates and random access, features that are useful in motion detection. This paper describes how to model, calibrate and render pixel responses from a colour logarithmic sensor into a standard colour space. The work unifies colour theory in conventional linear sensors and fixed pattern noise theory in monochromatic logarithmic sensors. Experiments with a Fuga 15RGB sensor demonstrate calibration and rendition using a Macbeth chart and neutral density filters. Colour rendition of the sensor with an empirical model, tested over three decades of dynamic range, competes with conventional digital cameras, tested over 1.5 decades. Photodiode leakage currents complicate modelling and calibration and degrade rendition in dim lighting. Keywords -- Logarithmic pixels, colour rendition, fixed pattern noise.