Spherical lens plays an important role in the optical system, and spherical lens cannot be manufactured without optical testing. The existing apparatus for measuring the structural parameters of spherical lens include: noncontact spherometer, coordinate measurement machine, and Abbey refractometers. However, these low-efficiency measuring apparatus can only measure one specific parameter at a time. Although the laser differential confocal interferometer can realize high-precision measurement for the full parameters of a lens, it is very expensive, and the complicated measurement optical path makes the installation and adjustment time-consuming. Phase measuring deflectometry (PMD) requires a simple device, is economical, and has a high dynamic range, which makes it popular. However, there is ambiguity among the structural parameters, refractive index, and thickness in the PMD measurement process. In this study, a method for measuring the structural parameters of a single lens by transmission deflectometry is proposed. This method can be used to measure the structural and postural parameters of lenses simultaneously. The measurement system is simple and does not require accurate alignment. We believe that the proposed method provides a novel way for the full-parameter measurement of spherical lenses. Moreover, it is also feasible for aspheric lenses.

Based on the principle of PMD, a structural parameter measuring method of a single lens by transmission deflectometry was proposed. First, the single lens model was built in the coordinate system in the form of a polynomial, which was derived in detail in this study. Then, the models of the measurement system and lens were established in the software based on the calibration data from the experiment. From the reverse Hartman test perspective, rays were considered to emit from the pinhole of the camera and intersect the screen after being refracted by the lens. The difference between the intersection coordinates measured in the experiment and that traced in the software was used to construct the objective function. Furthermore, as the deflection magnitude of the emitted light was caused by the front and back surfaces of the lens being tested, it was difficult to obtain the correct results with only one camera. Therefore, a dual-camera device was employed to address this issue. Finally, by optimizing the structural and postural parameters of the lens in the model using the least squares algorithm, the real value could be obtained.

In this study, a double-convex lens was simulated and experimentally tested. In the numerical simulation, the parameters of the lens were preset (Table 1), and the method proposed in this study was used for measurement. The simulation results show that the fitted values are basically the same as the preset values, and the relative errors are smaller than 4×10^-4%. The effect of the calibration errors is shown in the simulation, and the results (Table 2) show that the relative errors are smaller than 0.3% and 2% for the structural and postural parameters, respectively. In the experiment, the results (Table 3) show that the relative error of the lens structural parameter is smaller than 1%. As the lens postural parameters in the global coordinates are difficult to calibrate accurately, we verify the sensitivity of the proposed method by measuring the variation of the lens postural parameters. The results (Fig. 8) show that the proposed method has good measurement accuracy for pose parameters.

In this study, the structural parameter measuring method of a single lens by transmission deflectometry is proposed. The numerical simulation results verify the feasibility of this method. The measurement accuracy of the proposed method is evaluated by measuring a double-convex lens in the experiment. The proposed method can measure multiple parameters simultaneously without requiring accurate adjustment. Moreover, the measurement cost is considerably lower compared with other existing methods. This new method facilitates full-parameter measurement for a single lens. Moreover, as the proposed method uses mathematical polynomials to construct the lens model and completes the lens parameter measurement by optimizing the polynomial coefficients, it is theoretically feasible for measuring other surfaces with higher degrees of freedom, such as aspheric surfaces.