Optical correlation algorithm for reconstructing phase skeleton of complex optical fields for solving the phase problem

O V Angelsky,S G Hanson,P V Polyanskii,V P Lukin,M P Gorsky,I I Mokhun,P A Ryabiy

doi:10.1364/oe.22.006186

Abstract

We propose an optical correlation algorithm illustrating a new general method for reconstructing the phase skeleton of complex optical fields from the measured two-dimensional intensity distribution. The core of the algorithm consists in locating the saddle points of the intensity distribution and connecting such points into nets by the lines of intensity gradient that are closely associated with the equi-phase lines of the field. This algorithm provides a new partial solution to the inverse problem in optics commonly referred to as the phase problem.

Highlights

Solving the phase problem in optics has attracted much attention, primarily in problems of diagnostics of an object structure within microscopy, pattern recognition, terrestrial telescopy, and biomedical optics [1, 2]
We propose an optical correlation algorithm illustrating a new general method for reconstructing the phase skeleton of complex optical fields from the measured two-dimensional intensity distribution
Generalization of the proposed approach with experimental verification will soon be reported elsewhere

Summary

1.Introduction

Solving the phase problem in optics has attracted much attention, primarily in problems of diagnostics of an object structure within microscopy, pattern recognition, terrestrial telescopy, and biomedical optics [1, 2]. Knowing the locations and signs of amplitude zeroes, one can predict, at least in a qualitative manner, the behavior of a field (including spatial phase distribution, with accuracy not exceeding π 2 ) in all regions between the amplitude zeroes Within this approach, solving the phase problem for scalar, viz. In contrast to the standard singular optical approach dealing with amplitude zeroes, we consider just the saddle points of a spatial intensity distribution as the structure-forming elements, as these points are interconnected by the lines of intensity gradient and really constitute (together with these lines) the phase skeleton of a field. The proposed algorithm includes the following three actions: (i) bicubic spline interpolation [22]; (ii) location of the saddle points of intensity; (iii) connecting the saddle points of intensity by the gradient lines

Location of the saddle points of intensity

Connecting saddle points by intensity gradient lines

Conclusions