As optical systems become increasingly complex, miniaturized, and integrated, complex surface micro-lenses have been widely used in lighting, imaging, and other fields. Freeform micro-lens measurement is beneficial to the evaluation and processing of high-precision micro-lenses. However, the micro-lens has front and rear surfaces, and the large dynamic range characteristics of the surfaces and the requirement for high-precision inspection limit the versatility and efficiency of the existing micro-lens measurement techniques. Since the two surfaces of the micro-lens on freeform surfaces fail to be simultaneously measured with high accuracy during the detection, we propose a method based on deflectometry to solve the above problem.

In order to address the problem that the front and rear surfaces of the micro-lens cannot be measured simultaneously with high accuracy, a numerical iterative optimization algorithm for the simultaneous double-surface reconstruction of the micro-lens based on the high-precision transmission wavefront by deflectometry has been proposed. First, it is necessary to obtain the high-precision transmission wavefront aberration of the micro-lens to get the correspondence between the transmission aberration and the front and rear surfaces of the micro-lens under test. Then, wavefront aberrations with micro-lens surface information are obtained by tracing the ideal model of the measurement system through ray. After that, with the minimum wavefront aberration as the objective function, the numerical iterative optimization is performed with the two surfaces to be measured as the optimization variables to achieve the high-precision simultaneous reconstruction of the front and rear surfaces of the micro-lens. In addition, in order to solve the problem that the front and rear surfaces affect each other during the solution process, the error of each surface of the micro-lens under test is measured by changing the position of the tested element in the experiment and measuring the same tested element several times, so as to increase the number of effective equations in the optimization process. The flow chart of the surfaces of the micro-lens testing is given in Fig. 2.

In this paper, the proposed surface measurement method is simulated and experimentally verified. Experimental validation is carried out by testing a convex lens with an aperture of 6 mm through the Zygo interferometer, and the results are similar to the root-mean-square (RMS) errors of less than dozens of nanometers. In the simulation validation section, we design a freeform micro-lens with a diameter of 1 mm as the element to be tested, and the freeform surface is characterized by 37 coefficients of Zernike polynomial. According to the structure of the freeform micro-lens measurement system shown in Fig. 1, the corresponding ray tracing model of the inverse optical path is established in the ray tracing software. The ideal point light source is replaced by the pinhole CCD camera, and the imaging plane is replaced by the projection screen as shown in Fig. 3. The peak-to-valley (PV) values are 92.646 μm and 90.834 μm, respectively, as shown in Fig. 4(e) and Fig. 4(f) of the surfaces set on the front and rear surfaces. The measured freeform micro-lens is placed in four different positions, including the initial position [Fig. 4(a)], position after rotation of 10° around the x-axis [Fig. 4(b)] and y-axis [Fig. 4(c)] (denoted as Tx10° and Ty10°), and flip [Fig. 4(d)]. The wavefront reconstruction is performed for the micro-lens in the four positions to obtain the wavefront information of the four simulations. The PV values of the reconstruction of the front and rear surfaces shown in Fig. 4(g) and Fig. 4(h) are 92.072 μm and 91.241 μm, respectively. The nominal surface and the reconstructed surface have great consistency, and the RMS values are within a few tens of nanometers of error, which achieves sub-micron accuracy. In the experimental section, Fig. 5 shows the photo of the experiment system and micro-lens. The obtained wavefront information of the four positions of the micro-lens with calibrated structural errors is used to reconstruct the front and rear surfaces simultaneously by using the numerical iterative optimization algorithm of the freeform micro-lens, and the reconstructed front and rear surfaces are shown in Fig. 6(i) and Fig. 6(j). The reconstructed PV values of the front and rear surfaces are 0.308 μm and 0.096 μm, respectively. The RMS deviations from the results measured by the Zygo interferometer are 17 nm and 7 nm, respectively. Table 1 shows that most of the Zernike coefficients (Z₅-Z₁₅) are within an error of 5% and have great consistency.

In this paper, in order to realize high-precision and simultaneous inspection of the front and rear surfaces of the micro-lens, a numerical iterative optimal simultaneous reconstruction method of the surfaces of the freeform micro-lens based on deflectometry is proposed. The experimental results show that the numerical iterative simultaneous reconstruction method of the two surfaces of the micro-lens can achieve sub-micron measurement accuracy and realize the high-precision measurement of the front and rear surfaces of the micro-lens at the same time. The measurement method is characterized by a simple system structure, large measurement dynamic range, and high accuracy, and it can achieve simultaneous high-precision detection of various complex optical and industrial double-surfaces of micro-lenses.