“Hot Pixels” defects in digital imaging sensors accumulate as the camera ages over time at a rate that is highly dependent on pixel size. Previously we developed an empirical formula that projects hot pixel defect growth rates in terms of defect density (defects/year/mm2) via a power law, with the inverse of the pixel size raised to the power of ˜3, multiplied by the square root of the ISO (gain) We show in this paper that this increasing defect rate results in a higher probability that two defects will occur within a 5x5 pixel box. The demosaicing and JPEG image compression algorithms may greatly amplify the impact of two defective pixels within a 5x5 pixel box, spreading it into a 16x16 pixel box thus resulting in a very noticeable image degradation. We develop both analytical (generalized birthday problem formula) and Monte Carlo simulations to estimate the number of hot pixels required to achieve a given probability of having two defective pixels occur within a 5x5 square. For a 20 Mpix DSLR camera (360 mm2) only 128 hot pixels generate a 4% probability of two such defective pixels, which for pixels of size 4 μm may occur in 1.4 years at ISO 6400, and in 3.2 years at ISO 3200.
The rising demand for digital imagers has resulted in the push to reduce pixel size while increasing imager sensitivity, which in turn, results in an increasing rate of defects that develop in the field. Research has shown that “Hot Pixels” are the most common type of defects in modern digital imagers, with their number in a given imager increasing over time. In our previous studies we had developed an empirical formula to project the growth rate of hot pixel defects in terms of defects/year/mm2. We discovered that hot pixel densities tend to grow via a power law of the inverse of the pixel size raised to the power of about 3. This paper explores the effects on defect growth rate, of reducing pixel sizes even more, specifically in cell phone imagers. Due to lack of noise suppression algorithms in these imagers, we have developed specialized procedures for analyzing the collected dark frame data. We also ensure that hot pixel detections in cell phone cameras are statistically significant within the error margins. Our current results confirm the accelerated growth rate for this small pixel range, emphasizing the need for caution by designers and further study in this area of defect development.