Due to the ‘invisible’ property of the specular surface, it is difficult for the stitching deflectometry to identify the overlapping area. Previously, markers were used on the unit under test with a roughly known shape to find the overlapping area. We propose a marker-free stitching deflectometry that utilizes the stereo-iterative algorithm to calculate the sub-aperture point cloud without height-slope ambiguity, and the overlapping area is identified with the point cloud datum. The measured area is significantly enlarged. The simulation and experiments are conducted to verify the proposal and evaluate the accuracy. We test a high-quality flat with 190mm diameter, the measurement error is below 100nm RMS with comparison to the interferometer.

As a highly accurate metrology, phase measuring deflectometry (PMD) can be used for in-situ surface shape measurement. However, due to the reflection off the back surface, PMD cannot measure both the front and back surfaces of the transparent planar element simultaneously. Therefore, this paper proposes a method for measuring the front and back surfaces of the transparent planar element. The phase distribution corresponding to the front and back surfaces can be firstly acquired by multi-frequency fringe deflectometry. Then, the front and back surface shapes can be obtained by inverse ray-tracing and nonlinear optimization. Numerical simulation and experiment verify the proposed method. The surface shape of window glass with a thickness of 10 mm is measured in the experiment. The surface shape error is around 50 nm in the root mean square with a diameter of 51 mm.

A camera calibration method for phase measuring deflectometry (PMD) based on the entrance pupil center (EPC) of the camera lens is proposed. In our method, the position of the entrance pupil of the camera lens is first measured; next the absolute coordinates of the EPC are calibrated by using a reference flat and an external stop that is mounted in front of the camera lens; then the EPC as the camera coordinates is used for PMD. The feasibility of the proposed method is verified by simulation. The surface shapes of a planar optical element and a planar window glass are separately measured in our experiments, and a subwavelength accuracy level is achieved. Meanwhile, the effects of the camera lens with different aperture settings on captured images are investigated (including exposure time, image contrast, and measurement accuracy). The experimental results show that the exposure time required declines with the decrease in the f-number, and the measurement accuracy is higher than others when the f-numbers are changed from f/5.6 to f/11.

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Purpose This study aimed to explore the relationship between obesity- and lipid-related indices and insulin resistance (IR) and construct a personalized IR risk model for Xinjiang Kazakhs based on representative indices. Methods This cross-sectional study was performed from 2010 to 2012. A total of 2170 Kazakhs from Xinyuan County were selected as research subjects. IR was estimated using the homeostasis model assessment of insulin resistance. Multivariable logistic regression analysis, least absolute shrinkage and selection operator penalized regression analysis, and restricted cubic spline were applied to evaluate the association between lipid- and obesity-related indices and IR. The risk model was developed based on selected representative variables and presented using a nomogram. The model performance was assessed using the area under the ROC curve (AUC), the Hosmer–Lemeshow goodness-of-fit test, and decision curve analysis (DCA). Results After screening out 25 of the variables, the final risk model included four independent risk factors: smoking, sex, triglyceride-glucose (TyG) index, and body mass index (BMI). A linear dose–response relationship was observed for the BMI and TyG indices against IR risk. The AUC of the risk model was 0.720 based on an independent test and 0.716 based on a 10-fold cross-validation. Calibration curves showed good consistency between actual and predicted IR risks. The DCA demonstrated that the risk model was clinically effective. Conclusion The TyG index and BMI had the strongest association with IR among all obesity- and lipid-related indices, and the developed model was useful for predicting IR risk among Kazakh individuals.