Absolute phase retrieval based on phase-intensity hybrid encoding without any additional pattern

• An absolute phase retrieval method without any additional encoding pattern based on phase-intensity hybrid encoding is proposed. • By using the complementary feature in the four-step PSP, the codeword is ingeniously implanted into the sinusoidal fringes to fulfil phase-intensity hybrid encoding. • Three-level four-bit codewords instead of traditional binary codewords can encode 81 fringe orders to satisfy most scenarios. • A fringe order segmentation algorithm is proposed to decode complete codewords and complete sinusoidal deformed patterns as well as to correct codewords. • The encoding method can locate the beginning bit of codeword easily, reduce the codeword proximity effects and resist noise interference. An absolute phase retrieval method based on phase-intensity hybrid encoding is proposed. It can robustly retrieve the absolute phase without adding any additional pattern. At first, four-step phase-shifting profilometry is applied to resolve the phase, and the first and the third sinusoidal fringe patterns just complementary to each other are used for both phase resolving and implantation of codewords. Then three-level four-bit codewords are designed to encode all the fringe orders and are separated into two halves. The first half codeword covers the first half sinusoidal pattern in the corresponding period of the first phase-shifting pattern, while the second half codeword covers the second half sinusoidal pattern on the corresponding period of the complementary pattern. So, this pair of complementary sinusoidal patterns are compound of the phase-intensity hybrid encoding patterns. When this pair of patterns and the remaining phase-shifting patterns are projected onto the measured object, the corresponding deformed patterns are captured with camera. And a fringe order segmentation algorithm is also proposed to achieve codeword correction and to extract both the complete codewords and the complete sinusoidal deformed patterns successfully. So, the wrapped phase caused by the height of the measured object can be resolved and the codewords can be decoded to be the correct fringe order from the lookup table so as to retrieve the absolute phase. The experimental results show the feasibility and validity of the proposed method. It reveals the codewords are more robust and the reconstruction accuracy is improved effectively without adding any additional pattern. The number of projected patterns can be reduced when there are more fringe orders available. It is also easier to locate the beginning bit of codeword and efficiently reduce codeword proximity effects.