Abstract
This paper presents an advanced phase measuring deflectometry (PMD) method based on a novel mathematical model to obtain three dimensional (3D) shape of discontinuous specular object using a bi-telecentric lens. The proposed method uses an LCD screen, a flat beam splitter, a camera with a bi-telecentric lens, and a translating stage. The LCD screen is used to display sinusoidal fringe patterns and can be moved by the stage to two different positions along the normal direction of a reference plane. The camera captures the deformed fringe patterns reflected by the measured specular surface. The splitter realizes the fringe patterns displaying and imaging from the same direction. Using the proposed advanced PMD method, the depth data can be directly calculated from absolute phase, instead of integrating gradient data. In order to calibrate the relative orientation of the LCD screen and the camera, an auxiliary plane mirror is used to reflect the pattern on the LCD screen three times. After the geometric calibration, 3D shape data of the measured specular objects are calculated from the phase differences between the reference plane and the reflected surface. The experimental results show that 3D shape of discontinuous specular object can be effectively and accurately measured from absolute phase data by the proposed advanced PMD method.
Highlights
Specular free-form surfaces are recently widely used in many fields, such as optics, car industry, aerospace, and micro-electro mechanical systems (MEMS)
This paper presents a novel full-field 3D shape measurement method based on a bi-telecentric system for measuring discontinuous specular surfaces by building the direct relationship between absolute phase and depth data
Fringe pattern sets are generated by software and displayed on the LCD screen
Summary
Specular free-form surfaces are recently widely used in many fields, such as optics, car industry, aerospace, and micro-electro mechanical systems (MEMS). The camera captures the deformed fringe patterns reflected by the measured specular surface from the same viewpoint of the displayed LCD screens. 2. Principle The proposed measurement method displays sinusoidal fringe patterns onto an LCD screen, which is moved to two different positions along normal direction of a reference plane. It consists of an LCD screen, a camera with a bi-telecentric lens, a flat beam splitter, and a reference specular plane. Two light rays are displayed from LCD screens and reflected into the camera by the measured specular object surface and the reference specular plane. It clearly shows that depth H can be directly calculated from the captured fringe patterns only if the parameter ∆d and phase information on the reference plane mirror are determined beforehand. Denominator of Eq (3) is zero, so that the points whose normal is vertical to the LCD screen on specular objects cannot be measured effectively
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