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

Abstract – The quality of the output images from high dynamic range logarithmic sensors is limited by fixed pattern noise (FPN) which is caused by device mismatches within pixels in an array. It leads to inferior image quality in comparison to images from other sensors of similar resolution. Previous design and post-chip attempts to correct this type of noise, have been either impractical or resulted in other complexities. However, FPN correction can be attempted using an accurate model approach for the response of this type of pixel. A three parameter model, previously suggested for logarithmic pixels, has been tried for this purpose. In this paper a simple parameter extraction procedure is proposed using this model to calibrate and correct FPN. The result is a model that works well over six decades of illumination but fails at high photocurrents. It is shown that this is caused by a breakdown in an assumption used to create the three parameter model. Consequently, a new four parameter model is developed that fits the data over six decades, and is usable in FPN correction for many wide current range applications that require complete and accurate characterisation.

At present, most CMOS image sensors use an array of pixels with a linear response. However, logarithmic CMOS sensors are also possible, which are capable of imaging high dynamic range scenes without saturating. Unfortunately, logarithmic sensors suffer from fixed pattern noise (FPN). Work reported in the literature generally assumes the FPN is independent of illumination. This paper develops a nonlinear model y = a + bln(c +x) of the pixel response y to an illuminance x showing that FPN arises from variation of the offset a, gain b and bias c. Equations are derived, which can be used to extract these parameters by calibration against a uniform illuminance of varying intensity. Experimental results, demonstrating parameter calibration and FPN correction, show that the nonlinear model outperforms previous models that assume either only offset or offset and gain variation. Keywords -- CMOS image sensors, logarithmic pixels, fixed pattern noise.