Mathematical models and imaging models that show the relationship between the transition points mismatch of analog-to-digital converters (ADCs) and the bit error rate (BER) in single-bit and multi-bit quanta image sensors (QISs) are established. The mathematical models suggest that when the root-mean-square (r.m.s.) of the read noise in jots is 0.15e-, the standard deviation of the transition points should be less than 0.15e- to ensure that the BER is lower than 1% in the single-bit QIS, and 0.21e- to ensure that the BER is lower than 5% in the multi-bit QIS. Based on the mathematical models, the imaging models prove that the fixed-pattern noise (FPN) increases with a stronger transition point mismatch. The imaging models also compare the imaging quality in the case of different spatial oversampling factors and bit depths. The grayscale similarity index (GSI) is 3.31 LSB and 1.74 LSB when the spatial oversampling factors are 256 and 4096, respectively, in the single-bit QIS. The GSI is 1.93 LSB and 1.13 LSB when the bit depth is 3 and 4, respectively, in the multi-bit QIS. It indicates that a higher bit depth and a larger spatial oversampling factor could reduce the effect of the transition points mismatch of1-bit or n-bit ADCs.
Keywords: ADC; bit error rate; imaging model; quanta image sensor; transition point.