Error compensation in two-step triangular-pattern phase-shifting profilometry

This paper presents an analysis of error compensation using a newly modified two-step triangular-pattern phase-shifting measurement method, developed to reduce periodic measurement errors due to gamma nonlinearity and defocus of the projector and camera. Experimental analysis revealed that a trade-off is necessary in choosing a higher minimum projector input intensity to use the more linear region of input-to-output intensity mapping, and a lower minimum input intensity for greater dynamic range of input intensity. The modified two-step triangular-pattern phase-shifting method performs two-step triangular-pattern phase-shifting twice, the second time with an initial phase offset of one-eighth of the pitch, and generates the three-dimensional object height distribution by averaging the two obtained object-height distributions. The modified two-step triangular-pattern phase-shifting method consistently had higher measurement accuracy than the unmodified method. Errors were reduced by 23.4% at the midrange of depth using an input intensity value of 40, which yielded the highest measurement accuracy and up to 64% and 54% at small and large depths, respectively.