One-frame two-dimensional deflectometry for phase retrieval by addition of orthogonal fringe patterns

Abstract

Deflectometry is a well-known method to characterize pure phase objects by measuring the deformation of fringes. In principle, the retrieved magnitude is the partial derivative of the phase along the coordinate orthogonal to the fringes. In order to recover the phase it is necessary to know the derivatives in two orthogonal directions, which is usually achieved by rotating 90° the original fringes and acquiring a new deformed pattern. This "time-multiplexed" two-dimensional deflectometry is a time-consuming operation if the goal is to characterize phase objects in real time. In the present paper we propose a kind of two-dimensional deflectometry that allows acquisition of fringe patterns in two orthogonal directions in a single frame. The proposed procedure utilizes a two-dimensional ("additive") fringe pattern that allows the application of Takeda's method to each coordinate independently. The advantage of the method (with respect to the traditional one) is that it simplifies the setup and reduces the acquisition time. Validation experiments are presented.

Wrapping-free phase retrieval with applications to interferometry, 3D-shape profiling, and deflectometry

“…In this case, the phase is related to the depth profile [1,15,24,25]. Similar and equivalent techniques are also utilized in deflectometry [6,26].…”

“…3D-shape profiling [1][2][3], strain analysis, temperature gradient measurements [4,5], testing of optical components [6,7], and surface deformation may be regarded as typical examples. Most of the established methods for phase determination, including phase-shifting interferometry [8][9][10][11], spatial interferometry [12], and Fourier-based techniques [13][14][15], evaluate the arctangent of the ratio of the intensity functions.…”

Three-Dimensional Shape Measurements of Specular Objects Using Phase-Measuring Deflectometry

“…Therefore, the proposed method was more applicable to dynamic wavefront measurements by using only one composite fringe image. Flores et al proposed a 2D PMD method that used a 2D additive fringe to extend the PMD from 1D to 2D [ 53 ]. The deformed fringe patterns in two orthogonal directions were acquired in a single-shot frame.…”

Color deflectometry for phase retrieval using phase-shifting methods

“…If we place a pure phase object in front of the fringe pattern, the phase object changes the optical path lengths traveled by light rays through it. If the phase is inhomogeneous in the x-direction, the rays will be deflected by [3,13] α % ∂ϕ x ∂x ;…”