MTF for Bayer pattern color detector

Abstract

We present a model for calculating the Spatial Frequency Response (SFR) for Bayer pattern color detectors. The model is based on the color detector response to B/W scenes. When a Bayer color detector is compared to a B/W detector, SFR difference results from the interpolation process. This process exists only in the Bayer pattern detectors. In this work we ascribe the MTF and the spurious response to the interpolation process. The model may be applied to any linear interpolation. Although the interpolation is linear, it is not Shift Invariant (SI). Therefore, calculating the interpolation MTF is not a trivial task. Furthermore, the interpolation creates a spurious response. In order to calculate the interpolation SFR, we introduce a separable constraint (for x and y directions) by using a scene that varies only on one axis and is fixed on the other. We further assume integration in the direction of the fixed axis. By using these two assumptions, we have been able to separate the response into two axes and calculate the SFR. For distant scenes, colors saturation decreases, the colors are less visible and mostly grey colors are sensed. In these cases the Johnson Criterion can be roughly applied. In order to apply the Johnson Criterion it is required to know the MTF of the sensing system. The sensing system MTF includes the interpolation MTF. We show that the interpolation process degrades the system performance compared to B/W sensor. Another application of the model is in comparing different interpolation algorithms.