Two-zone pupil filters

The performance of pupil filters consisting of two zones each of constant complex amplitude transmittance is investigated. For filters where the transmittance is real, different classes of potentially useful filter are identified and optimized. These include leaky filters with an inner zone of low amplitude transmittance, pure phase filters with phase change of π, and equal area filters. The first of these minimizes the relative power in the outer rings for a given axial resolution, the second maximizes the Strehl ratio for a given transverse resolution, and the third minimizes the relative power in the outer rings for a given transverse resolution. Complex filters can give an axially shifted maximum in intensity: the performance parameters calculated relative to the true focus are investigated for some different classes of filter, but filters with phase change not equal to π are found to give inferior performance to the real value filters.