Empirical formula for rates of hot pixel defects based on pixel size, sensor area, and ISO

Abstract

Experimentally, image sensors measurements show a continuous development of in-field permanent hot pixel defects increasing in numbers over time. In our tests we accumulated data on defects in cameras ranging from large area (<300 sq mm) DSLR’s, medium sized (~40 sq mm) point and shoot, and small (20 sq mm) cell phone cameras. The results show that the rate of defects depends on the technology (APS or CCD), and on design parameters like imager area, pixel size (from 1.5 to 7 um), and gain (from ISO100 to 1600). Comparing different sensor sizes with similar pixel sizes has shown that defect rates scale linearly with sensor area, suggesting the metric of defects/year/sq mm, which we call defect density. A search was made to model this defect density as a function of the two parameters pixel size and ISO. The best empirical fit was obtained by a power law curve. For CCD imagers, the defect densities are proportional to the pixel size to the power of -2.25 times the ISO to the power of 0.69. For APS (CMOS) sensors the power law had the defect densities proportional to the pixel size to the power of -3.07 times the ISO raised to the power of 0.5. Extending our empirical formula to include ISO allows us to predict the expected defect development rate for a wide set of sensor parameters.