Field-of-View Distortion Calibration and Compensation for Ultra-high Accuracy Video-Based Metrology Systems

Field-of-View (FOV) distortion affects measurement accuracy by generating location-dependent results in video-based metrology systems. For ultra-high accuracy systems equipped with high-quality lenses, this error can be as small as the uncertainty of obtainable dimensional references. In this research, we develop a method that calibrates the distortion using an uncertified planar artifact. Since the measurement is performed on a plane with a (nominal) constant magnification, we can decouple the calibration for distortion and the calibration for pixel scaling factors, eliminating the need for high-accuracy dimensional references. We first establish a distortion model, and then we solve the model parameters by nonlinear least squares fitting. Furthermore, we find the significant distortion terms by adding them one by one to the model and comparing the fitting residual and convergence. Experimental results of the method on five system configurations show reduced measurement variation across the FOV by up to 80%. INTRODUCTION A constant magnification across the Field-OfView (FOV) is desirable in ultra-high accuracy (UHA) dimensional metrology systems equipped with video-probes and high-quality lenses. Such a system would ideally render true-to-scale images of the 2D object in the object plane, enabling one to apply constant scaling factors in converting pixel dimensions to physical dimensions. Customers, however, often obtain slightly different measurement results when measuring the same feature in different regions of the FOV. This discrepancy arises from distortion caused by system imperfections such as optical aberrations and non-square sensor elements. In FIGURE 1, for example, the image of an equally spaced grid is no longer true-to-scale because of imaging system distortion. The distortion is nonlinear, which invalidates the assumption of constant magnification, resulting in FOV location-dependent measurement errors. To maintain a constant scaling factor, we therefore need to calibrate and compensate the nonlinear distortion in order to recover the distortion-free, true-to-scale image of the object. This is a challenging task mainly due to the small magnitude of distortion in UHA systems (often in the sub-micrometer range). Relation to previous work Distortion calibration is normally performed as part of camera geometric calibration, where both intrinsic and extrinsic parameters are estimated by measuring features of known physical dimensions ([1,2]). Most artifacts, however, are only accurate to 1μm or 0. 1μm, which is not sufficient for calibrating the submicron distortions for UHA systems. The motivation of this research is to develop a calibration method that does not rely on the knowledge of physical dimensions of the artifact. Contribution of this paper We exploit the fact that non-linear distortion can be decoupled from scaling factor and develop a method to calibrate the nonlinear FOV distortion using an uncertified planar Chrome-On-Glass (COG) artifact with features whose pixel locations can be measured accurately. Since the artifact does not need to be certified, its cost is greatly reduced. Furthermore, our method does not need a high-accuracy positioning system and is practical for on-site calibration. The 2D equally spaced grid Distortion-free image Distorted (observed) image Captured image Distortion FIGURE 1. FOV distortion. DISTORTION CALIBRATION Distortion model The distortion model for UHA systems can be derived from the general pinhole camera model by assuming a constant nominal magnification. A general pinhole model consists of four steps ([1,2]): Step 1: 3D rigid body transformation from the World Coordinate System WCS [xw, yw, zw] to the Camera Coordinate System CCS [xc, yc, zc]