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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 image 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 models. 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.