Results and Discussions After the final image is obtained by the platform, PSF is used to evaluate the quality of the final image, and the imaging results are compared with the simulation results [Fig. 7(c)] and the results of model of ideal MLAs [Fig. 10(d)]. The FWHM value of the ideal PSF curve [the dot-and-dash line in Fig. 10(d)] without considering the errors is 51.72 μm, and that of the simulated PSF curve (the solid line) with the error added is 75.35 μm. The FWHM value of the PSF curve (the dotted line) measured experimentally is 84.77 μm. Therefore, compared with the model of ideal MLAs, the model of MLAs considering the errors is more accurate, and the error of the measurement result compared to simulation result is about 12%. The reason is that the model of ideal MLAs cannot fully consider the actual imaging situation, and its interference factors are fewer. Therefore, the imaging result is better than the actual one, and the FWHM value is smaller.

To study the influencing factors of imaging quality of microlens arrays (MLAs), this paper conducts optical simulations and experiments to establish the relationship between lens errors and optical imaging quality of MLAs. The results can provide a theoretical basis and guidance for the establishment of function-driven ultra-precision machining technology for optical MLAs. The methods for preparing MLAs can be divided into direct and indirect methods considering the necessity of making masks or molds with three-dimensional concave structures. In any case, the manufacturing errors will eventually be mapped onto the lenses and have an impact on the optical performance of the lenses. Most published studies on the imaging simulation of MLAs do not consider the impact of errors on imaging performance. Meanwhile, the image obtained by MLAs, falling within indirect computational imaging, is the calculation result based on the information received from the sensor. The existing studies on the optical performance measurement of MLAs, however, mainly analyze the image information directly received from the sensor. Therefore, for the MLAs produced by the slow tool servo diamond turning and the UV light curing process, a simulation model of optical MLAs is developed in the optical software Zemax, and the lens errors are introduced into the simulation of imaging performance. In this paper, the errors include the depth error and curvature radius error of the lens unit, as well as the error of the entrance pupil diameter. Moreover, a platform for the optical performance measurement of MLAs is established to test the imaging performance of MLAs, which applies the calculated final imaging results for imaging quality evaluation. Finally, the accuracy of the simulation model is verified by the comparison of the simulation and experimental results.

Both simulation and experiments are applied in this study. Zemax is the optical design software of Zemax Development Corporation of the United States. It can calculate the point spread function (PSF) curve of the current optical system, and the imaging quality can be evaluated according to the full width at half maximum (FWHM) of the PSF curve. A smaller FWHM indicates a smaller degree of spot dispersion and better imaging quality. The construction of the simulation model of optical MLAs includes the following steps. Firstly, the test optical path should be set. A single-wavelength (0.656 μm) parallel light reaches the image sensor after passing through the MLAs. At this time, each lens unit forms an image, which is a diffuse spot that will be received by the image sensor. The image sensor is set at a predetermined focal distance, namely, the effective focal length of the ideal lens unit (30.66 mm). Secondly, according to the test optical path, the model of ideal MLAs is built by Zemax. Thirdly, the image formed by each lens unit is calculated, and the original light field image and the final image are obtained, where the latter is obtained with the pixel rearrangement method (Fig. 2). At this time, the final image is still a diffuse spot, and hence, the PSF curve of the final image and its FWHM can be generated by the light intensity distribution of the spot. Similarly, after measurement, the errors of actual MLAs are added to the model of ideal MLAs, and its PSF curve as well as the FWHM of the curve can be generated. A platform for the optical performance measurement of MLAs is established (Fig. 8) to verify the accuracy of the simulation model of optical MLAs and form a performance detection system for optical MLA elements. The test optical path of the detection platform is the same as above. The test platform can measure the focal length of each lens unit of MLAs, and the measurement results are compared with the simulation results (Table 5) to verify the model of optical MLAs upon the addition of errors. After that, the light field imaging system for MLAs is established. The position and size of the focal spot are measured, and the quality of the final image of the MLAs is evaluated by the PSF curve and its FWHM.

In this paper, a simulation method based on Zemax for MLAs is proposed. The related errors of lens units (the curvature radius error, entrance pupil diameter, lens depth error, and surface irregularity error) are measured. According to the measurement results, a simulation model of MLAs considering the errors is built. Compared with the model of ideal MLAs that does not consider lens errors, the simulation model built in this paper is more accurate. In addition, a platform for the optical performance measurement of MLAs established in this paper can be used as an evaluation and measurement tool for the imaging results of MLAs. The platform can detect the imaging quality of MLAs and evaluate the final imaging result. The focal-spot size and position errors of each lens unit are measured, and the standard deviation of focal length measurement is about 0.12 mm. The PSF curve is used to evaluate the quality of the final imaging results. Compared with the simulation, the FWHM error is about 12%. To sum up, through simulation and measurement, the relationship between the lens error of MLAs and the optical imaging quality is established, which can provide guidance and suggestions for the manufacturing of MLAs.