The Knox–Thompson, or cross-spectrum, method provides two
two-dimensional difference equations for the phase of the object
spectrum. We demonstrate that, in general, the object spectrum
phase can be decomposed into a regular, single-valued function
determined by the divergence of the phase gradient, as well as a
multivalued function determined by the circulation of the phase
gradient; this second function has been called the hidden
phase. The standard least-squares solution to the two-dimensional
difference equations will always miss this hidden phase. We present
a solution method that gives both the regular and the hidden parts of
the object spectrum phase. Finally, we illustrate several examples
of imaging through turbulence and postprocessing with the
Knox–Thompson method, including the hidden phase.
© 2000 Optical Society of America
Equations on this page are rendered with MathJax. Learn more.