Phase measuring deflectometry for obtaining 3D shape of specular surface: a review of the state-of-the-art

Abstract

Phase measuring deflectometry (PMD) is a superior technique to obtain three-dimensional (3D) shape information of specular surfaces because of its advantages of large dynamic range, noncontact operation, full-field measurement, fast acquisition, high precision, and automatic data processing. We review the recent advances on PMD. The basic principle of PMD is introduced following several PMD methods based on fringe reflection. First, a direct PMD (DPMD) method is reviewed for measuring 3D shape of specular objects having discontinuous surfaces. The DPMD method builds the direct relationship between phase and depth data, without gradient integration procedure. Second, an infrared PMD (IR-PMD) method is reviewed to measure specular objects. Because IR light is used as a light source, the IR-PMD method is insensitive to the effect of ambient light on the measured results and has high measurement accuracy. Third, a proposed method is reviewed to measure the 3D shape of partial reflective objects having discontinuous surfaces by combining fringe projection profilometry and DPMD. Then, the effects of error sources that mainly include phase error and geometric calibration error on the measurement results are analyzed, and the performance of the 3D shape measurement system is also evaluated. Finally, the future research directions of PMD are discussed.

Surface Shape Distortion Online Measurement Method for Compact Laser Cavities Based on Phase Measuring Deflectometry

“…Based on the reference wavefront, the surface shape distortion will be accurately measured. Similar to the PMD method [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], the COPMD method is also based on sinusoidal fringe pattern projection and detection to acquire the wavefront slope through a phase-shift algorithm and then numerical integration to reconstruct the wavefront distortion. In the measurement process of the COPMD, the surface shape of the mirror before laser operation is measured first and taken as the reference.…”

“…As a low-cost, full-field three-dimensional shape measurement technique with a high dynamic range, the phase measuring deflectometry (PMD) method was first introduced in 2004 and improved to be a flexible and effective approach to inspect specular reflecting surfaces [12]. It could be used to accurately measure the surface shape of a single optical element with the unique advantages of a high dynamic range, full field of view, and non-null measurement [13] on the basis of the triangulation law [14], Scheimpflug principle [15], and diffuse-versus-specular reflections principle [16]. Based on the synergy between deflectometry and ray-tracing, the PMD method was employed for the on-site evaluation of the free-form mirrors with a high speed, high accuracy, and cost reduction [17][18][19].…”

“…In 2018, the phase measuring deflectometry system combined with a laser resonator was designed to achieve a high-precision online thermal distortion measurement of crystals in the high-power laser [27]. However, limited by the wavefront reconstruction principle and algorithm, the screen of the liquid crystal display (LCD) has to be placed in parallel with the surface of the mirror under test, which takes up a large measurement space [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Thus, these mentioned methods are primarily constrained in offline tests and not applicable for real-time measurement in the enclosed laser facility.…”

The effects of pattern screen surface deformation on deflectometric measurements: a simulation study

“…In phase-measuring deflectometry (PMD), horizontal and vertical sinusoidal fringe patterns that are shifted in several discrete steps serve this purpose; the phase information effectively encodes the pattern coordinates. [6][7][8][9] Being able to associate a pattern coordinate to every camera pixel allows the inference of potential light paths from the points of origin of the light on the pattern to the corresponding camera pixels. The information of potential light paths is equivalent to a field of potential normal vectors of the surface in the measurement space.…”

“…6,[12][13][14][15][16] The majority of PMD measurement setups described in the scientific literature use a computer screen to present the patterns. 7,9,14,15,17,18 For the purpose of determining the origin of the signal measured in a camera pixel, they are usually modeled in the PMD evaluation algorithms as a planar light source with a very regular grid of light emitting square pixels. However, the assumption of a planar screen surface may not always be appropriate, particularly when considering measurement setups with the screen mounted at an inclined orientation.…”