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 across the array. Chapter 4 develops a steady state model for the digital response of a logarithmic pixel to light stimulus and uses it to characterise and correct FPN, which proves to depend nonlinearly on illuminance, by calibration of simulated and experimental data. Chapter 5 models the transient response of logarithmic imagers, for typical source follower readout circuits, and shows with simulation and experiment how transient operation and design may cause FPN, which may partially be corrected by a steady state calibration. Chapter 6 extends the steady state model of the image sensor to examine and reduce the dependence of FPN on temperature, comparing in simulation and experiment methods of calibration that use pixel responses under both dark and light conditions. Chapter 7 describes the calibration of pixel responses in terms of a standard colour space, extending previous models suitable for FPN correction but unsuitable for colour rendition, and shows that colour rendition of a Fuga 15RGB logarithmic camera competes with that of conventional digital cameras. Finally, Chapter 8 discusses and summarises the main results of this thesis and outlines future theoretical, simulation and experimental work.