Full-field 3D shape measurement of discontinuous specular objects by direct phase measuring deflectometry

Abstract

AbstarctWith the advent of intelligent manufacturing, phase measuring deflectometry (PMD) has been widely studied for the measurement of the three-dimensional (3D) shape of specular objects. However, existing PMDs cannot measure objects having discontinuous specular surfaces. This paper presents a new direct PMD (DPMD) method that measures the full-field 3D shape of complicated specular objects. A mathematical model is derived to directly relate an absolute phase map to depth data, instead of the gradient. Two relevant parameters are calibrated using a machine vision-based method. On the basis of the derived model, a full-field 3D measuring system was developed. The accuracy of the system was evaluated using a mirror with known positions along an accurate translating stage. The 3D shape of a monolithic multi-mirror array having multiple specular surfaces was measured. Experimental results show that the proposed DPMD method can obtain the full-field 3D shape of specular objects having isolated and/or discontinuous surfaces accurately and effectively.

A Calibration Method for System Parameters in Direct Phase Measuring Deflectometry

“…The experimental results demonstrate that the proposed calibration method can reconstruct the 3D shape of specular objects with high precision and reliability. The absolute error in the distance between neighboring steps was below 22 µm, while the value is 52 µm by using the existing calibration method [37]. Figure 12.…”

“…A novel DPMD (direct PMD) method that can obtain the full-field 3D shape of specular objects with discontinuous and/or isolated surfaces has been developed to solve the problem of measuring complex specular surfaces [36][37][38]. This method builds a direct relationship between the absolute phase and the depth information.…”

Measurement of Freeform Optical Surfaces: Trade‐Off between Accuracy and Dynamic Range

“…c) Reproduced with permission. [ 154 ] Copyright 2017, Springer Nature. d) Reproduced with permission.…”

“…[ 153 ] The PMD using two LCD screens successfully measured and reconstructed multiple discontinuous surfaces sharing a monolithic substrate on the mid‐infrared spectrometer for JWST as shown in Figure 16c. [ 154 ] However, PMD has fundamental limitation of satisfying a line of sight condition, which makes it generally suitable to concave or weak convex surfaces with a large radius of curvature, e.g., grazing‐incidence X‐ray mirrors as demonstrated in the work by Huang et al. [ 147 ] The rays going through the camera pinhole reflect and diverge off the test surface in a reverse way for general convex surfaces.…”

Performance analysis and evaluation of direct phase measuring deflectometry

“…To solve the above problems and build a stable measurement system, a direct PMD (DPMD) system [19] has been developed to form a relationship between the phase and the depth directly without the need for a slope integration procedure. The proposed system consists of two LCD screens, one beam splitter (BS) plate and one charge-coupled device (CCD) camera.…”