Traditional refractive lenses usually have a large thickness, thus limiting their application in some small optical systems. Diffraction lenses have a much smaller thickness than refractive lenses, so they are mostly employed in lightweight systems. Diffraction lenses, however, are usually designed to operate in a single band, which makes them more chromatic than refractive lenses. In fact, the chromatic difference of traditional refractive lenses is usually only determined by the material dispersion, while that of diffraction lenses is mainly caused by the change of diffraction angle on the microstructure of different positions. The angle is directly proportional to the wavelength of the incident light, and the dispersion caused by the change is much stronger than the material dispersion. At present, most achromatic diffraction lens technologies are characterized by complex structures and difficult processing. Therefore, designing an achromatic diffraction lens with simple structure and easy processing is the key to widely employing diffraction lenses.

This paper proposes a design method of multi-wavelength diffraction lens (MDL). The spectral point spread function (PSF) of a series of wavelengths is almost identical via adjusting and optimizing the distribution of diffraction microstructure on the plane substrate. This method can balance the PSF distribution of each wavelength, and reduce the color difference and complexity of the wideband imaging system. It provides a new idea for the application and development of diffraction imaging systems. The heights of diffraction lens microstructure are discretized and are assumed to be invariant over a width interval. An objective function is constructed to describe the sum of the deviations between the complex transmission function of MDL and the complex transmission function of DOE at each operating wavelength, and then the microstructure height that minimizes the objective function is found. The process is repeated on the whole surface of the lens, and the weight of each wavelength in the evaluation function is adjusted according to the simulation results. To verify the feasibility of the design method, this paper designs an MDL with three wavelengths and four steps combined with the existing processing conditions. The scalar diffraction theory is employed for simulation analysis and comparison with DOE. The design parameters are shown in Table 1.

The simulation results show that MDL has the expected achromatic performance. DOE only has a sharp crest in its designed band, while in the other two bands, it almost does not respond or is diffused. A lot of noise is generated in the whole image plane, which leads to declined overall image quality. MDL has relatively sharp wave peaks in the three bands designed by MDL, and the response of the three bands in the image plane is relatively consistent, which will not produce a lot of noise in the image plane and can effectively reduce the color difference generated during the diffraction lens imaging, indicating that MDL has a certain achromatic ability. Half-peak full width (FWHM) is the peak width at half of the normalized light intensity. Compared with that of DOE, the minimum FWHM of MDL is slightly increased, but the overall performance is more balanced, and the mean square error of FWHM is only 0.0053 (Fig. 5). The spot size of MDL is also consistent at different wavelengths and has good imaging effects when the three wavelengths are incident together (Fig. 6). MDL sacrifices the diffraction efficiency of a certain band in exchange for improving the diffraction efficiency of the other bands. MTF of MDL in small field of view has little change, which reflects that MDL has certain anti-interference ability in small field of view (Fig. 8). When the three wavelengths are incident together, the diffraction efficiency of MDL is significantly higher than that of DOE (Fig. 9). The MDL is optimized for the bandwidth of the light source, and the achromatic performance of the optimized MDL is significantly improved under a certain bandwidth (Fig. 10). In terms of processing feasibility, the designed lens meets the processing conditions of multi-mask lithography.

This paper proposes a design method of diffraction lens that can work in multiple wavelengths simultaneously and designs a four-step MDL for simulation analysis. The results show that it can balance the imaging effect at multiple wavelengths. By comparison between PSF and MTF of DOE, the essence of MDL is found to sacrifice the imaging quality of one band to exchange the imaging quality of the other bands by regulating the surface microstructure distribution. The diffraction efficiency of MDL is also calculated, and the results show that the diffraction efficiency of MDL is higher than that of DOE when multiple wavelengths are incident together. Considering that there is no single wavelength of light in practical application, the MDL is optimized to have a good achromatic effect even under the light source with a certain bandwidth. Finally, the processing feasibility of MDL is analyzed, and the results show that it meets the existing processing conditions, thereby ensuring the feasibility of MDL in practical application.