Comparison of linear and nonlinear calibration methods for phase-measuring profilometry

Abstract

In phase-shifting-based fringe-projection surface-geometry measurement, phase unwrapping techniques produce a continuous phase distribution that contains the height information of the 3-D object surface. Mapping of the phase distribution to the height of the object has often involved complex derivations of the nonlinear relationship. In this paper, the phase-to-height mapping is formulated using both linear and nonlinear equations, the latter through a simple geometrical derivation. Furthermore, the measurement accuracies of the linear and nonlinear calibrations are compared using measurement simulations where noise is included at the calibration stage only, and where noise is introduced at both the calibration and measurement stages. Measurement accuracies for the linear and nonlinear calibration methods are also compared, based on real-system measurements. From the real-system measurements, the accuracy of the linear calibration was similar to the nonlinear calibration method at the lower range of depth. At the higher range of depth, however, the nonlinear calibration method had considerably higher accuracy. It seems that as the object approaches the projector and camera for the higher range of depth, the assumption of linearity based on small divergence of light from the projector becomes less valid.

Mínimos Cuadrados para la Calibración en Reconstrucción 3D mediante Proyección de Franjas

“…Cabe resaltar que el modelo de calibración lineal tiene una exactitud similar a esquemas de calibración no-lineales para un rango de medición moderado (0 − z máx /2). Conforme el rango de medición crece, la exactitud del modelo lineal decrece hasta en un 30 % de error en promedio [15]. A pesar de esta inexactitud del método, el modelo de calibración lineal es aplicable cuando el objeto de medición tiene dimensiones moderadas.…”

“…Partiendo del área de visión computacional, se tiene otro grupo de métodos que utilizan diferentes herramientas de calibración como cuadrículas, un plano de nube de puntos y otros objetos con profundidades conocidas [11][12][13]. Otras aproximaciones para calibrar y obtener la relación entre la fase-altura se basa en modelos matemáticos [14][15][16]. En particular, estas técnicas tienen en común el uso de un plano de referencia móvil, se coloca en diferentes posiciones equidistantes y nos permite obtener información redundante para poder estimar los parámetros del modelo matemático empleando mínimos cuadrados.…”

Object Shape Measurement Based on Brox Optical Flow Estimation and Its Correction Method

“…Substitute Equations ( 13)-( 15) into Equation (17); the expression of the height h of point D can be obtained:…”

“…In order to make the effect of the correction method obvious, we set the projection distance and observation distance with large distance. Different from the optical setup parameter estimation method [17], the optical center positions of the projector and camera are calibrated by using Zhang's calibration method [18,19]. After calibration, the distance from the projector to the reference plane is 1975.40 mm and that of the CCD sensor is 1922.80 mm.…”

An inverse error compensation method for color-fringe pattern profilometry

“…According to the heterodyne phase unwrapping algorithms [39,40], an absolute phase map is demodulated from the wrapped phase, and finally the 3D shape of the object can be recovered from the absolute phase with the pre-calibrated system parameters [41][42][43].…”