Detector shape in hexagonal sampling grids

Abstract

Recent improvements in CCD technology make hexagonal sampling attractive for practical applications and bring a new interest on this topic. In the following the performances of hexagonal sampling are analyzed under general assumptions and compared with the performances of conventional rectangular sampling. This analysis will take into account both the lattice form (squared, rectangular, hexagonal, and regular hexagonal), and the pixel shape. The analyzed hexagonal grid will not based a-priori on a regular hexagon tessellation, i.e., no constraints will be made on the ratio between the sampling frequencies in the two spatial directions. By assuming an elliptic support for the spectrum of the signal being sampled, sampling conditions will be expressed for a generic hexagonal sampling grid, and a comaprison with the well-known sampling conditions for a comparable rectangular lattice will be performed. Further, by considering for sake of clarity a spectrum with a circular support, the comparison will be performed under the assumption of same number of pixels for unity of surface, and the particular case of regular hexagonal sampling grid will also be considered. Regular hexagonal lattice with regular hexagonal sensitivity shape of the detector elements will result as the best trade-off between the proposed sampling requirement. Concerning the detector shape, the hexagonal is more advantageous than the rectangular. To show that a figure of merit is defined which takes into account that the MTF (modulation transfer function) of a hexagonal detector is not separable, conversely from that of a rectangular detector. As a final result, octagonal shape detectors are compared to those with rectangular and hexagonal shape in the two hypotheses of equal and ideal fill factor, respectively.