N-ary gray-level (nGL) coding strategy is an effective method for absolute phase retrieval in the fringe projection technique. However, the conventional nGL method contains many unwrapping errors at the boundaries of codewords. In addition, the number of codewords is limited in only one pattern. Consequently, this paper proposes a new gray-level coding method based on half-period coding, which can improve both these two deficiencies. Specifically, we embed every period with a 2-bit codeword, instead of a 1-bit codeword. Then, special correction and decoding methods are proposed to correct the codewords and calculate the fringe orders, respectively. The proposed method can generate n² codewords with n gray levels in one pattern. Moreover, this method is insensitive to moderate image blurring. Various experiments demonstrate the robustness and effectiveness of the proposed strategy.

The calibration of camera systems employing zoom lenses raises several challenges, as changes in lens control settings introduce various imaging conditions, especially different degrees of defocus. This article presents a Fourier-based defocus calibration method to calibrate a camera attached with an electronically focus-tunable lens (ETL). Different from the traditional method which requires changing the scale of the calibration object for sharp images, the proposed method is more concerned with the frequency characteristics of the captured images than the gray distributions. According to the invariance of the fundamental frequencies before and after defocusing the images, coordinates of feature points can be extracted accurately, even in different degrees of defocus. Therefore, one normal size target can also be qualified for zoom system calibration. Then polynomial approximation is used to account for the variation of the intrinsic and distortion parameters across the zoom range. Extensive simulations and experiments were implemented to demonstrate the proposed idea's robustness against defocus, flexibility, and accuracy.

Coaxial optical systems are typically used to measure objectswith significant height changes.