Microlens array is one of the most important components in micro-optics, and it has been widely used in many fields. It is becoming more and more important to achieve higher measurement accuracy and faster measurement speed of the microlens array focal length. Traditional measurement methods such as interferometer measurement, microscope measurement, light intensity measurement, etc., are difficult to meet the requirements of high precision and rapid measurement simultaneously. Because the traditional scanning angle method needs to rotate the light tube or lenses, and the movement of the light spot cannot be determined in a single measurement, the measurement result is easy to be affected by the measuring device. Therefore, the scanning angle method based on multi-slit diffraction grating uses the multi-slit diffraction principle to determine the focal length by calculating the distance between adjacent orders, which improves the measurement efficiency. However, a single measurement can only obtain a single focal length value in this scheme, and it is still necessary to implement multiple measurements to eliminate various random errors. In addition, the non-negligible high diffraction orders of the traditional grating will introduce additional measurement noise, which will deteriorate the positioning accuracy of the centroids of those desired spots, resulting in the deterioration of the final accuracy. So, in order to eliminate random errors, multiple measurements have to be implemented in practice. To address the above problems, a fast focal length measurement scheme based on high-order-suppression Dammann gratings (HOSDGs) rather than traditional gratings is proposed in this paper.

In this study, a specially designed HOSDG is used to measure the focal length of the microlens. After the beam passes through the HOSDG, the diffractive light transmits through the microlens, and finally the camera receives the focused spot of each sublens on its focal plane. The distribution of the focus spots of each sublens is related to the focal length and the diffraction angle of the grating. After data processing, multiple distances among several desired orders are obtained, and then several values of the focal length for each sublens are calculated. In order to suppress the influence of high-order diffraction, the complex amplitude modulation combined with simulated annealing algorithm is used to optimize HOSDGs. In the experiment, this grating is fabricated by multistep overlapped lithography and wet etching technologies.

The simulation results show that the high order sidelobe ratio is reduced from 11.13% to 5.3% (Fig. 4), and the experiment results indicate that the sidelobe ratio is reduced from 19.66% to 9.88%, which suggests that the high-order diffraction is effectively suppressed by this specially designed HOSDG. Due to its multiple equal-intensity orders (Fig. 5), HOSDG makes it possible to obtain multiple values of focal length through a single measurement after late-stage data processing (Fig. 7). It is shown that the single measurement error of the focal length of 11×7 microlenses is 3.5%, and the errors of the 15 repeated measurements are all within 4.5%.

In this paper, a two-dimensional Dammann grating based on high-order diffraction suppression is proposed to measure the focal length of microlens array, which can effectively suppress the high-order diffraction energy and improve the measurement signal-to-noise ratio. In the proof-of-principle experiment, the designed five-beam HOSDG generates multiple focused light spots within each microlens aperture. The combination of multiple light spots to achieve a single acquisition is equivalent to 10 times of ordinary grating experiments, which effectively reduces the measurement random error, making the single measurement error less than 3.5% and repeated measurement error less than 4.5%. Therefore, this scheme can improve the measurement efficiency and reduce the measurement error in the high-precision measurement of the focal length of large-scale microlens array. This work will promote the fabrication, measurement and application of various microlenses.