Optimum plane selection criteria for single-beam phase retrieval techniques based on the contrast transfer function

In this work, an optimum plane selection methodology is reported that can be applied to a wide range of single-beam phase retrieval techniques, based on the contrast transfer function. It is shown that the optimum measurement distances obtained by this method form a geometric series that maximizes the range of spatial frequencies to be recovered using a minimum number of planes. This allows a noise-robust phase reconstruction that does not rely on regularization techniques, i.e., an extensive search for a regularization parameter is avoided. Measurement systems that employ this optimization criteria give an instant deterministic noise-robust phase reconstruction with higher accuracy, and enable the phase retrieval of the entire object spectrum, including lower frequency components.