A least squares calibration method for fringe projection profilometry

Abstract

This paper presents a novel least squares calibration approach for fringe projection profilometry. This approach is based on a simple nonlinear function, which is deduced by analyzing the geometry of measurement system and perfectly describes the mapping relationship between the depth map and phase distribution. The calibration is implemented by translating a target plane to a sequence of given positions with known depths, and measuring its phase distributions.Based on least squares estimation, an algorithm with linear computation is deduced to retrieve the related parameters, by which the burden of computational complexity is effectively alleviated. In experiment, a plaster statue is measured to demonstrate the validity of the principle.

Parallax correction of texture image in fringe projection profilometry

“…Even so, relationship for each pixel ðu; vÞ, according to the geometric analysis in Ref. 39, can always be formulated with E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 6 3 ; 9 2Δ…”

Improved least-squares method for phase-to-height relationship in fringe projection profilometry

“…The LUT contains the related coefficients that appear in the phase-to-height relationship for each pixel. In this method, the height for each pixel is obtained as a fractional equation or a polynomial equation of the phase value [11][12][13][14]:…”

“…When the parameters were determined by the LSM, the modeling results were very good. Guo et al [12] presented a rational function instead of a polynomial function at each pixel. Because the rational function is derived from the geometry of the measurement system, it achieved higher accuracy than the polynomial function in the measurement noise produced by the inherent divergent illumination of a projector.…”

“…The third method uses a simple look-up table (LUT) containing the relationship between phase values and heights for each camera pixel [11][12][13][14]. The LUT method obtains the phase-to-height relationship for each pixel without any geometric analysis and then stores the information in the LUT, which it uses to measure the height.…”

“…A typical 3-D measurement system based on a fringe pattern projection (FPP) system [2][3][4][5][6][7][8][9][10][11][12][13][14] is constructed using a white light projector and a charge-coupled device (CCD) camera. The projector projects sinusoidal fringe patterns onto an object, and the CCD camera acquires the patterns that are deformed by the object's shape.…”