Small-phase retrieval with a single far-field image

A method to retrieve small-phase aberrations from a single far-field image is proposed. It is found that in a small-phase condition, the odd and even parts of a phase aberration can be obtained with a simple linear calculation method. The difference between a single measured image with aberration and a calibrated image with inherent aberration is used in the calculation process. It is proved that most of the inherent phase aberration of the imaging system must be of an even type, such as defocus, astigmatism, etc., to keep the method working. The results of numerical simulations on atmosphere-disturbed phase aberrations show that the proposed small-phase retrieval method works well when the RMS phase error is less than 1 rad. It is also shown that the method is valid in a noise condition when the SNR > 100. (c) 2008 Optical Society of America.