Order-shifting temporal phase unwrapping using uneven duty gray-code for high-accurate and high-efficient 3D measurement

Higher-frequency fringe projection inherently has higher 3D measurement accuracy due to its shorter equivalent wavelength, but it also requires encoding more fringe orders. Conventional Gray-code (GC) methods can encode these fringe orders but rely on more auxiliary encoding patterns, limiting 3D reconstruction efficiency. To overcome this, we propose for the first time, to the best of our knowledge, an order-shifting temporal phase unwrapping (OSTPU) based on uneven duty cycle GC. Within the system's measurement range, OSTPU encodes the relative order shifts caused by height variations at a high frequency of 76 or more, reducing the required codewords from 76 absolute orders to just 12 order-shift codewords encoded by only 3 additional patterns. Our OSTPU relaxes the one-to-one mapping between GC word and fringe order, allowing spatial repetition and reducing complexity. Experiments verify that OSTPU achieves high-fidelity reconstruction of complex color geometry with fewer fringes (from 7 to 3), improving projection efficiency by over 57%, providing an accurate, efficient, and robust solution for high-frequency 3D measurement.