Application of transport-of-intensity equation in fringe analysis

Abstract

The transport-of-intensity equation (TIE) is applied in the reconstruction of two interfering wavefronts by analyzing the interference patterns and their derivatives along their common propagation directions. The TIE is extended from one wave to two waves and is then applied to calculate the phase of the interference field. Finally, the phase shift concept is applied to reconstruct the phase distribution of two waves. The consistency of the method is verified by simulation.

Experimental verification of reconstruction of two interfering wavefronts using the transport of intensity equation

“…Empirical results of this research suggests that the method suggested in reference [9] has provided acceptable results on real experimental data in which the RMS error of the difference of ΔΦ and Φ′ Δ is 0.5 rad. We believe that the systematic errors are due to: (a) proper amount of dz is not really well-defined, (b) accuracy of the method for solving the TIE equation for non-uniform intensity, (c) there is a source of error due to transverse movement of the camera whenever camera is moved in z direction.…”

“…In this case, there is no need to have a known reference wavefront or it may be used to test validity of the reference wavefront. For reconstructing two unknown interfering wavefronts, four methods have already been proposed [6][7][8][9].…”

“…In this paper, we present the experimental verification of interferometric TIE method [9]. A Fizeau interferometer is used to test a flat surface.…”

“…Figure.1 shows the experimental setup that is used for evaluating the method presented in Ref. [9]. (c) A phase shift of π is introduced by PZT and sequence of step (a) is repeated for recording data set 3.…”

A guide to properly select the defocusing distance for accurate solution of transport of intensity equation while testing aspheric surfaces

“…For solving the TIE, many effective numerical methods such as the method based on Green's function [19], multigrid (MG) [20,21], and the Zernike polynomial expansion method [22,23] were presented. Currently, TIE technique is used in different fields of physics such as adaptive optics [24,25], microscopy [26,27], optical measuring [28][29][30], and optical tomography [31][32][33], just to name a few.…”