Growth of pixel density and sensor array size increases the likelihood of developing in-field pixel defects. An ongoing study on defect development in imagers has now provided us sufficient data to be able to quantify characteristics of defect growth. Preliminary investigations have shown that defects are distributed randomly and the closest distance between two defective pixels is approximately 79-340 pixels apart. Furthermore, from an observation of 98 cluster-free defects, the diameter of the defect is estimated to be less than 2.3% of a pixel size at 99% confidence level. The fact that no defect clusters were found in the study of various digital cameras allows us to conclude that defects are not likely to be related to material degradation or imperfect fabrication but are due to environmental stress such as radiation. Furthermore, as verified by a statistical study, the absence of defect clustering provides information on the size of defects and insight into the nature of the defect development.

The lifetime of solid-state image sensors is limited by the appearance of defects, particularly hot-pixels, which we have previously shown to develop continuously over the sensor lifetime. Analysis based on spatial distribution and temporal growth of defects displayed no evidence of the defects being caused by material degradation. Instead, high radiation appears to accelerate defect development in image sensors. It is important to detect these faulty pixels prior to the use of image enhancement algorithms to avoid spreading the error to neighboring pixels. The date on which a defect has first developed can be extracted from past images. Previously, an automatic defect detection algorithm using Bayesian probability accumulation was introduced and tested. We performed extensive testing of this Bayes-based algorithm by detecting defects in image datasets obtained from four cameras. Our results have indicated that the Bayes detection scheme was able to identify all defects in these cameras with less than 3% difference from visual inspected result. In this paper, we introduce an alternative technique, the Maximum Likelihood detection algorithm, and evaluate its performance using Monte Carlo simulations based on three criterias: image exposure, defect parameters and pixel estimation. Preliminary results show that the Maximum likelihood detection algorithm is able to achieve higher accuracy than the Bayes detection algorithm, with 90% perfect detection in images captured at long exposures (>0.125s).

Characterization of in-field defect growth with time in digital image sensors is important for measuring the quality of sensors as they age. While more defects were found in cameras exposed to high cosmic ray radiation environments, comparing the collective growth rate of different sensor types has shown that CCD imagers develop twice as many defects as APS imagers, indicating that CCD imagers may be more sensitive to radiation. The defect growth of individual imagers can be estimated by analyzing historical image sets captured by individual cameras. This paper presents a defect tracing algorithm, which determines the presence or absence of defects by accumulating Bayesian statistics collected over a sequence of images. Recognizing the complexity of image scenes, camera settings, and local clustering of defects in color images (due to demosaicing), refinements of the algorithm have been explored and the resulting detection accuracy has increased significantly. In-field test results from 3 imagers with a total of 26 defects have shown that 96% of the defects' dates were identified with less than 10 days difference compared to visual inspection. In addition to our continuous study of in-field defects in high-end digital SLRs, this paper presents a preliminary study of 10 cellphone cameras. Our test results address the comparison of defects types, distribution and growth found in low-end and high-end cameras with significantly different pixel sizes.

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An analytic solution to the problem of determining photon direction after successive scatterings in an infinite, homogeneous, isotropic medium, where each scattering event is in accordance with a two-term Henyey-Greenstein phase function, is presented and compared against Monte Carlo simulation results. The photon direction is described by a probability density function of the dot product of the initial direction and the direction after multiple scattering events, and it is found that such a probability density function can be represented as a weighted series of one-term Henyey-Greenstein phase functions.