Calibration method for projector-camera-based telecentric fringe projection profilometry system

Abstract

By combining a fringe projection setup with a telecentric lens, a fringe pattern could be projected and imaged within a small area, making it possible to measure the three-dimensional (3D) surfaces of micro-components. This paper focuses on the flexible calibration of the fringe projection profilometry (FPP) system using a telecentric lens. An analytical telecentric projector-camera calibration model is introduced, in which the rig structure parameters remain invariant for all views, and the 3D calibration target can be located on the projector image plane with sub-pixel precision. Based on the presented calibration model, a two-step calibration procedure is proposed. First, the initial parameters, e.g., the projector-camera rig, projector intrinsic matrix, and coordinates of the control points of a 3D calibration target, are estimated using the affine camera factorization calibration method. Second, a bundle adjustment algorithm with various simultaneous views is applied to refine the calibrated parameters, especially the rig structure parameters and coordinates of the control points forth 3D target. Because the control points are determined during the calibration, there is no need for an accurate 3D reference target, whose is costly and extremely difficult to fabricate, particularly for tiny objects used to calibrate the telecentric FPP system. Real experiments were performed to validate the performance of the proposed calibration method. The test results showed that the proposed approach is very accurate and reliable.

Calibration routine for a telecentric stereo vision system considering affine mirror ambiguity

“…Liu et al 12 combined the Tomasi-Kanade factorization algorithm with a 3-D calibration target in order to retrieve the parameters of a fringe projection system with telecentric camera and projector. The authors use a 3-D calibration target with randomly distributed markers.…”

“…In the first step, the initial parameter values for the affine camera matrices, the truncated rigid body transformation, and the transformation from the first to the second 2-D calibration plane are estimated. To this end, according to the approach introduced by Liu et al, 12 the Tomasi-Kanade factorization algorithm 26 is used in order to reconstruct the 3-D data of the calibration target coordinates. In contrast to the approach by Liu et al, two equidistant marker grids with defined distances are used, instead of randomly distributed markers.…”

“…Fringe projection profilometry is a state-of-the-art method in order to characterize the geometry information of three-dimensional (3-D) objects, as it allows a noncontact, fast, and areal data acquisition in the micrometer range. [1][2][3] If a measurement setup with a small field-of-view (FOV) is required, telecentric lenses can be employed either in stereo vision (with 4,5 or without additional projector 6,7 ) or in single camera-projector configurations (with entocentric [8][9][10] or telecentric projector 11,12 ) or telecentric Scheimpflug approaches. 13,14 The calibration of a telecentric structured light sensor is not as straightforward as in the entocentric case, as a telecentric camera cannot be modeled by the pinhole camera but requires the introduction of the so-called affine camera model instead.…”

Quantitative 3D Reconstruction from Scanning Electron Microscope Images Based on Affine Camera Models

“…The theory of these effects was deeply studied in the early works of computer vision. Nowadays, it finds its application in several disciplines like modelling imaging systems that use telecentric lenses [ 22 ], pushbroom cameras that provide satellite images [ 23 ] or in this scenario the SEM’s imaging system. Although all these systems do not fully comply with an ideal affine projection, its application is especially suitable when the depth relief of the scene is small compared to its average depth and when the distance of a considered point to the optical axis is small.…”

Microscopic Three-Dimensional Measurement Based on Telecentric Stereo and Speckle Projection Methods

“…The microscopic fringe projection method, on the contrary, is studied widely and suitable for measuring microstructures whose dimensions are in the order of millimeters and above with the measurement accuracy from a few to tens of microns [ 9 , 10 , 11 ]. It can realize well 3D measurement of microstructures with different surfaces such as a gauge block [ 12 ], ball grid arrays (BGA) [ 13 , 14 ], coins [ 15 , 16 ], a wafer [ 17 ], an earphone diaphragm [ 18 ], and a step master [ 19 ], and can also perform dynamic measurements [ 20 , 21 ]. Due to a lack of suitable methods for system calibration and removing carrier-phase components from the measurement phases [ 22 ], it is difficult for its measurement accuracy to reach two or three microns and below.…”