Abstract

We develop a method for subaperture piston phase retrieval in a telescope using a segmented primary mirror. We assume that the mirror subapertures are arranged on a two-dimensional lattice, and in addition, the separate subaperture point-spread functions are focused and overlapped on the focal plane. Therefore, the residual errors are the subaperture piston phase errors, represented as a phasor, a unit modulus complex number, for each subaperture. Under these conditions, we find considerable simplicity in the calculated optical transfer function (OTF) at special subaperture lattice spatial frequencies. We then construct a phasor-based error function based on the modulus squared of the difference between the measured OTF and the calculated OTF. The remaining steps in our piston phase retrieval algorithms are developed by calculating the error-function variation, with respect to each phasor element. The resulting equations for the error gradient are then used iteratively, in a phasor-based algorithm, to find the minimum of the error function. In the applications, we simulate photon-noise-limited piston retrieval for a segmented primary with 18 hexagonal subapertures. When we invoke phase diversity, the piston retrievals prove unique and accurate.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (4)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Tables (2)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (18)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription