A method for simplifying phase-height mapping in phase measurement profilometry

Abstract

Phase-height mapping algorithm is the key technology of phase measurement profilometry (PMP). Because of lens distortion of the projector, phase-height mapping is not simple linear transform and the mapping procedure become complex. A method is introduced to simplify phase-height mapping. The detail of this method is expressed as following: (1) Two suits of sinusoidal gratings which are perpendicular to each other are projected to the calibration target respectively. (2) The position of each target mark in calibration target is estimated using standard image processing technique. (3) Distortion coefficients of projector are estimated from the phase of target marks and their positions, according to the camera model. (4) Ideal phase distribution for projecting is designed. (5) According to the camera distortion model, distorting and transforming the ideal phase distribution, distorted phase distribution in the image plane is acquired. Then the phase-shifting sinusoidal fringes with distorted phase are generated. The anamorphic sinusoidal fringes are distorted inversely during projecting because projecting process is the reverse process of imaging. Therefore, the ideal sinusoidal fringes are projected. The phase-height mapping of PMP system can be ideally expressed and the mapping procedure is simplified. A practical PMP measurement system was constructed and the distortion coefficients are estimated by calibrating the system. They are <i>k</i>1=-6.989&times;10^-2 and <i>p</i>₁=5.957&times;10^-3. Then the distorted sinusoidal fringes are generated and projected for calibrating. Distortion coefficients are estimated again. They are <i>k</i>₁=-7.882&times;10^-3 and <i>p</i>₁=-3.777&times;10^-3. It is found from the experimental results that the distortion of projector is reduced a lot after grating correction.