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Modelling and calibration of logarithmic CMOS image sensors
 in 1982 and the Ph.D. degree from the University of
, 2002
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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 multiindex 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
al.,”An ElectronicCalibration Scheme for Logarithmic CMOS Pixels
 IEEE Sensors Journal
, 2006
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Temperature Dependence of Fixed Pattern Noise in Logarithmic CMOS Image Sensors
"... Abstract – This paper presents a model that explains the contribution of temperature to the fixed pattern noise (FPN) in a logarithmic CMOS image sensor. Based on this model, a simpler model is proposed to facilitate the calibration and correction of FPN. To avoid nonlinear optimization, the variati ..."
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Abstract – This paper presents a model that explains the contribution of temperature to the fixed pattern noise (FPN) in a logarithmic CMOS image sensor. Based on this model, a simpler model is proposed to facilitate the calibration and correction of FPN. To avoid nonlinear optimization, the variation of photodiode leakage current from one pixel to another is neglected. The simplified model uses the dark response of pixels, which depends only on temperature, to help predict FPN in the light response, which depends on temperature and illuminance. Calibration requires images of a uniform stimulus taken at different temperatures and illuminances, which need not be measured. After calibration, FPN is corrected in an arbitrary image using a dark image at the same temperature, which is taken infrequently. Through simulation, using mismatch data from a real CMOS process, an improvement is shown in the residual error per image after calibration, when the proposed method is compared to an established method that does not account for temperature dependence. I.
Temperature Dependence of Fixed Pattern Noise in Logarithmic CMOS Image Sensors
"... 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 temperatur ..."
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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.
(c) (d)
"... Fig. 6. Depletion capacitance [plots (a) and (b)] and the total terminal capacitance [plots (c) and (d)] at forward bias equal to E g =e as a function of the halflength of the diode [plots (b) and (d)] and as a function of the lifetime of the carriers in the laser active region [plots (a) and (c)]. ..."
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Fig. 6. Depletion capacitance [plots (a) and (b)] and the total terminal capacitance [plots (c) and (d)] at forward bias equal to E g =e as a function of the halflength of the diode [plots (b) and (d)] and as a function of the lifetime of the carriers in the laser active region [plots (a) and (c)]. We see that the depletion capacitance does not change much with the variation of L and and the variations in the terminal capacitance are due to the diffusion capacitance for the corresponding (L; ) combinations. physically very long and that have extremely low . These laser diodes have a minimal diffusion capacitance, and the depletion capacitance is dominant. To obtain a more quantitative understanding of these limits, we plot the depletion capacitance and the terminal capacitance (sum of the diffusion and depletion capacitances) for a typical bias of laser diodes as a function ofL and (Fig. 6).4 We note that the depletion capacitance is not influenced too much by L and , and by varying these variables, we affect mainly the diffusion capacitance. By comparing Figs. 3 and 4 with Fig. 6, we conclude that the diffusion capacitance affects the terminal capacitance and speed of the diode for > 1011 s ifL = 1mm and for > 1014 s ifL = 0:02m. Outside this region, manipulating theL and forminimizing the diffusion capacitance does not further affect the bandwidth of the diode, as the diffusion capacitance is already very low. III. CONCLUSION It is traditionally assumed that the bandwidth of diodes is determined mainly by the minority carrier lifetime. We have shown here by numerical simulation that there is a complex interplay between the physical length and the lifetime, and only both quantities together determine the diffusion capacitance and diode bandwidth. We have simulated a generic diode with lower lifetime of the charge carriers in a short central region (5 nm around the junction) corresponding to the active region of a laser diode. At a typical forward bias of (E g =e) the diffusion capacitance of the diode is typically larger 4We plot the depletion capacitance for L> 0:1 m, as the diodes are depleted for lower L. than the depletion capacitance, with the exception of very low , where the diffusion capacitance is extremely small. It is shown that for short L,C di