Abstract—Logarithmic CMOS image sensors are appealing for their high-contrast and high-speed response but they require postprocessing to achieve high-quality images. Previously published work has explained the fixed pattern noise (FPN) in these image sensors using a steady-state analysis. This paper explains how the transient response of the readout circuit may also contribute to FPN. Thus, the performance of these CMOS cameras may be optimized with a proper understanding of the transient response, which is explained here through modeling and simulation with some experimental validation. In particular, the gain variation of a logarithmic camera is shown to be caused primarily by premature digitization. As logarithmic and linear active pixel sensors use similar circuits, some results in this paper, e.g., an analysis of readout capacitance, apply equally to the latter. Index Terms—Fixed pattern noise (FPN), logarithmic pixels, modeling and calibration, transient response. I.

Logarithmic CMOS image sensors encode a high dynamic range scene in a manner that roughly approximates human perception whereas linear sensors with equivalent quantization suffer from saturation or loss of detail. Moreover, the continuous response of logarithmic pixels permit high frame rates and random access, features that are useful in motion detection. This paper describes how to model, calibrate, and render pixel responses from a color logarithmic sensor into a standard color space. The work unifies color theory in conventional linear sensors and fixed pattern noise theory in monochromatic logarithmic sensors. Experiments with a Fuga 15RGB sensor demonstrate calibration and rendition using a Macbeth chart and neutral density filters. Color rendition of the sensor with an empirical model, tested over three decades of dynamic range, competes with conventional digital cameras, tested over 1.5 decades. Photodiode leakage currents complicate modeling and calibration and degrade rendition in dim lighting.

Hybrid image sensors combine advantages of the two leading imaging technologies (the fill factor of CCD, and the signal processing of CMOS) via vertical integration. This report derives a simple model for the photodetector of the hybrid image sensor, and the affiliated set of differential equations. This bounded-value problem is subsequently solved numerically in 1D, and a simple analytical model is derived from the numerical solution. Lastly, simulation results are presented, including an optimum photodetector length for best current signal level. model. Index Terms Hybrid image sensors, photodetectors, vertical integration, numerical solution, analytical

Abstract—This paper presents a model that is then simplified to explain the temperature dependence of fixed pattern noise (FPN) in logarithmic complementary metal–oxide semiconductor (CMOS) image sensors. The simplified model uses the average dark response of pixels, which depends only on temperature, to help predict the FPN in the light response, which depends on temperature and illuminance. To calibrate a logarithmic camera, one requires images that are taken at different temperatures and illuminances, which need not be measured, of a uniform stimulus. To correct the FPN in an arbitrary image, one uses the simplified model parameters, which are estimated once by the calibration, and the average dark response, which is infrequently determined by closing the aperture. Through simulation (using mismatch data from a real CMOS process) and experiment (using a commercial logarithmic camera), an improvement is shown in the residual error per image, after calibration, when the proposed method is compared with a related method in the literature that does not account for temperature dependence. Index Terms—Calibration, complimentary metal–oxide– semiconductor (CMOS) image sensors, fixed pattern noise (FPN), logarithmic response, modeling, temperature dependence. I.