Integrated calibration of multiview phase-measuring profilometry

Abstract

Phase-measuring profilometry (PMP) measures per-pixel height information of a surface with high accuracy. Height information captured by a camera in PMP relies on its screen coordinates. Therefore, a PMP measurement from a view cannot be integrated directly to other measurements from different views due to the intrinsic difference of the screen coordinates. In order to integrate multiple PMP scans, an auxiliary calibration of each camera’s intrinsic and extrinsic properties is required, in addition to principal PMP calibration. This is cumbersome and often requires physical constraints in the system setup, and multiview PMP is consequently rarely practiced. In this work, we present a novel multiview PMP method that yields three-dimensional global coordinates directly so that three-dimensional measurements can be integrated easily. Our PMP calibration parameterizes intrinsic and extrinsic properties of the configuration of both a camera and a projector simultaneously. It also does not require any geometric constraints on the setup. In addition, we propose a novel calibration target that can remain static without requiring any mechanical operation while conducting multiview calibrations, whereas existing calibration methods require manually changing the target’s position and orientation. Our results validate the accuracy of measurements and demonstrate the advantages on our multiview PMP.

Introduction

Phase measuring profilometry (PMP) has been widely used for professional applications of highly accurate height measurements. A projector in PMP illuminates a surface with a periodic sequence of sinusoidal patterns. A per-pixel height profile can be then driven from phase shifts of the sinusoidal patterns, captured by a camera. To obtain heights from phase shifts, PMP calibration is an essential process that defines a geometric relationship between the camera and the projector.

The traditional PMP calibration is designed to measure height per pixel from a captured image, i.e., the captured height information is valid in screen coordinates of the camera, which cannot be easily integrated to other views [1], [2], [3], [4]. In order to integrate multiple PMP measurements, an auxiliary calibration of the camera’s extrinsic properties is necessary. Xiao et al. [5] and Albers et al. [6] proposed a multiview calibration method by applying an extrinsic calibration method to determine camera properties to calculate perspective projection. These previous methods rely on the traditional Zhang method [7] to obtain the extrinsic properties of cameras. They therefore inherit the fundamental drawbacks of the Zhang method, whick requires multiple input images by mechanically changing the orientation of a checkerboard target, a process that is cumbersome and undesirable for microscale profiling systems [5], [6], [8], [9], [10], [11], [12], [13]. Alternatively, Liu et al. [14], Zhu et al. [15], Villa et al. [16] and Gdeisat et al. [17] also introduced multiview PMP methods that can provide three-dimensional global coordinates without using the Zhang method. Instead, they still require additional calibration process with changing the target positions or orientations using an expensive hardware such as a high-precision linear Z-stage. This process is therefore cumbersome and can cause unpredicted errors when mechanically operating the target.

In this work, we propose a novel PMP calibration method to address these practical issues of additional extrinsic calibration and mechanical operations in state-of-the-art calibration approaches for achieving multiview PMP [5], [6], [16], [17]. Different from other methods, our integrated PMP calibration process allows us to measure not only height but also (x, y) coordinates in the three-dimensional global coordinates system, allowing for direct integration of multiview PMP measurements without requiring any additional calibration of camera extrinsic parameters. In addition, our method captures only a single static scene without changing the target’s orientation, which minimizes any potential errors that might occur while operating the target, while conducting calibration and scanning. Finally, our calibration does not require any constraints in the setup or any additional expensive instruments, such as a high-precision Z-stage. The following section presents more details of the suggested method.