Improved algorithm for phase-to-height mapping in phase measuring profilometry

Abstract

An improved algorithm for phase-to-height mapping in phase-measuring profilometry (PMP) is proposed, in which the phase-to-height mapping relationship is no longer restricted to the condition that the optical axes of the imaging system must be orthogonal to the reference plane in the basic PMP. Only seven coefficients independent of the coordinate system need to be calibrated, and the system calibration can be accomplished using only two different gauge blocks, instead of more than three different standard planes. With the proposed algorithm, both the phase measurement and system calibration can be completed simultaneously, which makes the three-dimensional (3-D) measurement faster and more flexible. Experiments have verified its feasibility and validity.

Improved geometrical model of fringe projection profilometry

“…In this section, we will introduce in the order of the PTH mapping relationship proposed by Takeda, et al [1] ,an improved PTH mapping by Mao, et al [2] , the work by Xiao, et al [3] , and then problem statement. Figure 2 shows an improved geometric model proposed in [2], which allows the camera to move along z-axis direction, and hence is more flexible than the ideal one in [1].…”

“…3 is proposed in [3], where camera and projector are allowed to be different height relative to reference plane, and optical axis of camera is permitted not to be vertical to reference plane. Hence, compared to the simplified geometric model as Fig.…”

“…Fringe Projection Profilometry (FPP) has been considered as an enabling technology for noncontact 3-D shape measurement due to such advantages as simple structure and fast measurement [1][2][3][4] . A typical FPP system consists of a digital projector, a camera, a computer and a reference plane.…”

“…However, the second and third conditions are still required. Recently in 2012, further effort for solving the problem was reported in [3], where a PTH mapping was proposed to remove the first and third condition in that camera and projector are permitted to locate at different distance from the reference plane, and the optical axis of camera is not required to be vertical to the reference plane. However, the second condition remains.…”

Phase unwrapping method based on multiple fringe patterns without use of equivalent wavelengths

“…In order to reconstruct the 3D shape, various fringe pattern analysis methods have been developed, e.g., Fourier transform profilometry (FTP) [2], phase shift profilometry (PSP) [3], modulation measurement profilometry (MMP) [4], phase-measuring profilometry (PMP) [5], etc.…”