Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement

Existing phase-shifting measurement methods involve processing of three acquired images or computation of functions that require more complex processing than linear functions. This paper presents a novel two-step triangular-pattern phase-shifting method of 3-D object-shape measurement that combines advantages of earlier techniques. The method requires only two image-acquisition steps to capture two images, and involves projecting linear grayscale-intensity triangular patterns that require simpler computation of the intensity ratio than methods that use sinusoidal patterns. A triangular intensity-ratio distribution is computed from two captured phase-shifted triangular-pattern images. An intensity ratio-to-height conversion algorithm, based on traditional phase-to-height conversion in the sinusoidal-pattern phase-shifting method, is used to reconstruct the object 3-D surface geometry. A smaller pitch of the triangular pattern resulted in higher measurement accuracy; however, an optimal pitch was found, below which intensity-ratio unwrapping failure may occur. Measurement error varied cyclically with depth and may partly be due to projector gamma nonlinearity and image defocus. The use of only two linear triangular patterns in the proposed method has the advantage of less processing than current methods that process three images, or methods that process more complex functions than the intensity ratio. This would be useful for high speed or real-time 3-D object-shape measurement.