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At present, most CMOS image sensors use an array of pixels with a linear response. However, pixels with a logarithmic response are also possible and are capable of imaging high dynamic range scenes without saturating. Unfortunately, logarithmic image 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)+ε of a pixel for the digital response y to an illuminance x and shows that the FPN arises from a variation of the offset a, gain b, and bias c from pixel to pixel. Equations are derived to estimate these parameters by calibrating images of uniform stimuli, taken with varying illuminances. Experiments with a Fuga 15d image sensor, demonstrating parameter calibration and FPN correction, show that the nonlinear model outperforms previous models that assume either only offset or offset and gain variation.