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

Abstract

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 = + ln( + ) + of a pixel for the digital response to an illuminance and shows that the FPN arises from a variation of the offset , gain , and bias 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. Index Terms-CMOS image sensors, fixed pattern noise, logarithmic pixels.

Transient Response and Fixed Pattern Noise in Logarithmic CMOS Image Sensors

“…The digital response of a logarithmic pixel depends on the light stimulus by the model (1) where , and are called the offset, gain, bias, and error, respectively [3]. While may vary randomly from sample to sample, , and are constant for a pixel.…”

“…An expression may be derived, as a function of time , for the column-bus voltage in terms of a constant pixel-drive voltage and an initial column-bus voltage , known at time when switch is closed. When the switch is closed, the column bus will charge or discharge towards the steady-state value [3], i.e.,…”

“…These can be used with (7)- (9), where the load capacitance is given by (3) and (4) , the on-resistance of and the finite output resistance of and in saturation. The settling time of the readout circuit in the BSIM3 simulation may be predicted from the Level 1 model.…”

“…The column-bus voltage is switched in turn to drive an output bus, shared by all columns, via a second-stage source follower, which mirrors the parallel source followers of Fig. 1 except with PMOS transistors instead of NMOS transistors [3]. Analysis of the transient response of the output-bus voltage for any column-drive voltage is complementary to the above analysis and, thus, is not repeated.…”

“…Nonetheless, they occupy a niche in the world of imaging because of their edge in dynamic range and bandwidth [2]. There is potential for this niche to grow, however, given the work of Joseph and Collins, who modeled the logarithmic pixel and employed calibration to achieve an image quality comparable to that of conventional linear pixels [3], [4]. Having proven the feasibility of achieving high-quality color images with these cameras, Collins et al have since been migrating the approach towards self-calibration and have been reducing the computational load [5], [6].…”