Refractive index measurement deflectometry for measuring gradient refractive index lens.

A method based on deflectometry to measure the refractive index distribution of radial gradient refractive index (GRIN) lens is proposed in this paper. The method establishes the relationship between the refractive index distribution and the direction of light ray by deriving the propagation equation of light in a non-uniform medium. By measuring the deflection angle using the principle of deflectometry and the assumption of central refraction, the refractive index distribution of the radial GRIN lens is determined. The specific principle of refractive index measurement deflectometry (RIMD) is described in detail, and the correctness and accuracy of the method are verified through numerical simulations. Furthermore, the effects of calibration error, lens surface shape on the accuracy of the measurement results are analyzed. In the experimental section, the proposed method is applied to measure a radial GRIN lens, and the results are compared with the nominal parameters in terms of shape distribution and numerical values, demonstrating good consistency. The measurement error is controlled within the order of 10-3. This method enables rapid and convenient acquisition of full-field information of GRIN lens and holds promising potential for playing an important role in lens manufacturing and production.

Frequency-domain searching algorithm in deflectometry for measuring the surface of a transparent planar element.

This Letter presents the frequency-domain searching algorithm in deflectometry (FSAD). By encoding specialized multi-frequency fringe patterns and employing a correlation searching algorithm, the limitations of existing frequency-domain methods can be overcome to some extent, thereby separating front and back surface reflections to obtain complete measurement data. The principles of FSAD are described in detail. In the experiment, a piece of window glass with thickness of 10 mm and a square area of 96 × 96 mm is measured to verify the proposed method.

Phase measuring deflectometry for convex aspheric surface measurement.

This paper introduces what we believe to be a novel approach to accurately measure the shape of convex aspherical surfaces with large slope gradients. This approach employs a pre-distortion system to enhance the visibility of the structured light pattern that is captured by camera. The data processing involves iterative methods to obtain surface shape data. The initial step in the experimental calibration involves establishing a reference plane, which serves as the starting point for the iterative process. The calculation for slope is subsequently utilized to determine the initial slope of the surface under test, and the height of the tested element is derived by integrating these slopes. Through multiple iterations and continuous updating of the surface height, the precise and authentic true surface height is ultimately achieved. The method's accuracy is assessed through the measurement of a highly steep convex aspherical area with a diameter of 5.2 mm and a radius of curvature of approximately 7.7 mm. The proposed method demonstrates root mean square accuracy that can reach half a wavelength when compared to the measurement results obtained from high-precision profilers.

Front and back surface measurement of the transparent planar element based on multi-frequency fringe deflectometry.

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.

Phase measuring deflectometry based on calibration of the entrance pupil center of the camera lens.

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.