Modelling, calibration and correction of nonlinear illumination dependent fixed pattern noise in logarithmic CMOS image sensors

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 z 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 outputs previous models that assume either only offset or offset and gain variation.