Overview
This paper examines the problem of Fourier phase retrieval from differential intensity measurements. The core objective is to ascertain the phase of a complex-valued function using a sequence of intensity measurements. These measurements are characterized by slight modulations within the Fourier domain.
Research Context
The modulations in the Fourier domain, which differentiate the intensity measurements, can originate from various optical elements. These include components such as prisms or phase plates. Alternatively, they may be induced through the use of spatial-light modulators. The research draws upon and generalizes principles established by the transport of intensity equation.
Approach
The methodology involves demonstrating that, given differential intensity measurements, the phase can be precisely determined. This determination is achieved by finding the solution to specific partial differential or integro-differential equations. This finding then serves as the foundation for developing reconstruction algorithms.
Findings
- The phase of a complex-valued function can be determined from differential intensity measurements.
- This determination is achieved by solving certain partial differential or integro-differential equations.
- The derived principles enable the design of efficient reconstruction algorithms.
Potential Applications
The derived approach is applied to a class of Fourier-type wavefront sensors. These include, for example, the pyramid wavefront sensor. Such sensors are frequently employed in adaptive optics systems. Numerical experiments conducted as part of this research illustrate the utility of the proposed methodology.