The Geometrical Modulation Transfer Function (MTF) - for different pixel active area shapes

In this work we consider the effect of the pixel active area geometrical shape on the modulation transfer function (MTF) of an image sensor. When designing a CMOS Active Pixel Sensor (APS), or a CCD or CID sensor for this matter, the active area of the pixel would have a certain geometrical shape which might not cover the whole pixel area. To improve the device performance, it is important to understand the effect this has on the pixel sensitivity and on the resulting MTF. We perform a theoretical analysis of the MTF for the active area shape and derive explicit formulas for the transfer function for pixel arrays with a square, a rectangular and an L shaped active area (most commonly used), and generalize for any connected active area shape. Preliminary experimental results of subpixel scanning sensitivity maps and the corresponding MTFs have also been obtained, which confirm the theoretical derivations. Both the simulation results and the MTF calculated from the Point Spread Function (PSF) measurements of the actual pixel arrays show that the active area shape contributes significantly to the behavior of the overall MTF. The results also indicate that for any potential pixel active area shape, the effect of its diversion from the square pixel could be calculated, so that tradeoff between the conflicting requirements, such as SNR and MTF, could be compared per each pixel design for better overall sensor performance.