Reference-plane-based fast pixel-by-pixel absolute phase retrieval for height measurement

Absolute phase retrieval is essential for height measurement in digital fringe projection. However, projections of additional structured patterns that are normally required for phase unwrapping increase the measurement complexity. In this paper, we propose two reference-plane-based pixel-by-pixel absolute phase retrieval techniques with as few projections as possible, suitable for different object depth ranges. The wrapped phase on the object is absolutely unwrapped by referring just to the absolute phase map on the reference plane. Single-frequency absolute phase retrieval with one-reference-plane-based calibration is first proposed for objects within a height limit that equals a calibrated system constant. To extend the measurement depth range, dual-frequency absolute phase retrieval with two parallel reference planes is further proposed. The additional low frequency is used to choose the unwrapping reference from the two reference plane phases for unwrapping the high-frequency phase. Moreover, the proposed techniques are capable of high-frequency absolute phase unwrapping for objects with step-height surface discontinuities. Experiments have been conducted to demonstrate the efficiency of the proposed two techniques.