Based on the special imaging properties of diffractive optical elements (DOEs), the design of refractive-diffractive hybrid imaging optical systems has become a hotspot. Since infrared optical materials are rare, especially in dual bands or even multiple bands, available infrared materials are even rarer. Then, DOEs in these systems are necessary for color and thermal aberration correction among their special imaging properties, which can improve image quality, optimize the structure, and reduce the cost of infrared optical systems. Compared with the single-layer DOE, the double-layer DOE can greatly improve the diffractive efficiency of the wide waveband, which promotes the development and application of refractive-diffractive hybrid optical systems. In addition, most infrared optical systems designed in the existing references are uncooled. However, the uncooled infrared optical system has low cold stop efficiency, and its imaging can be easily disturbed by the background noise. In contrast, the cooled infrared optical system is matched with the cooled detector and has high detection sensitivity, which can guarantee a cold stop efficiency of 100%. Therefore, it is necessary to design a cooled dual-band infrared imaging optical system. We hope that our design and results can be helpful for dual- or multi-band infrared imaging optical systems, especially for their application in a wide ambient temperature range.

In order to ensure the high diffraction efficiency of a double-layer DOE caused by ambient temperature change, the optical thermal expansion coefficient of substrate materials should be reasonably selected. After comparing different infrared optical materials, we select chalcogenide glass (IRG24) and zinc sulfide (ZnS) as double-layer DOE substrate materials based on the bandwidth integral average diffraction efficiency (BIADE) maximization design and Matlab software simulation. Then, optimal design wavelengths are selected, and the corresponding micro-structure heights and diffraction orders are calculated. Finally, based on the Zemax OpticStudio software, a cooled refractive-diffractive hybrid dual-band infrared optical imaging system with a double-layer DOE is designed, and the thermal and color aberrations corrected in dual-band infrared range and wide ambient temperature range are realized. The optimal optical system consists of three refractive lenses and a double-layer DOE on two surfaces, which can be achieved in both mid- and long-band infrared range and the ambient temperature range of -40-60 ℃.

First, we select IRG24 and ZnS as the substrate materials of the double-layer DOE and calculate its diffraction efficiency by Matlab software (Fig. 5 and Fig. 6), where the comprehensive BIADE is 99.04% for the dual-band, and the diffraction efficiency is almost unchanged when the temperature varies within the wide ambient temperature range. Then, Zemax OpticStudio software is applied to optimize this cooled dual-band infrared optical system. The optical system consists of three lenses. The material of the first and third lenses from left to right is IRG24, and that of the second lens is ZnS. The double-layer DOE is on the back surface of the first lens and the front surface of the second lens (Fig. 6), respectively. Finally, the image quality is evaluated. The modulation transfer functions (MTFs) for mid- and long-band infrared are greater than 0.78 and 0.59 respectively at different temperatures (Fig. 9). The field curvature is less than 0.1 mm, and the distortion is less than 0.12% in different temperatures and bands (Fig. 10). The square encirclement energy of mid- and long-infrared bands in each field of view is greater than 90.7% and 81.1% respectively (Fig. 11).

In this study, based on the BIADE maximization method with average weight distribution in dual bands, a cooled refractive-diffractive hybrid dual-band infrared optical system is designed by using IRG24 and ZnS as the substrate materials of the double-layer DOE. The optimal design wavelengths for the double-layer DOE are 4.23 μm and 10.315 μm, and the diffraction efficiency is 99.35% and 98.73% respectively for BIADE. The comprehensive BIADE is 99.04% in infrared dual bands (3.7-4.8 μm and 8.0-12.0 μm). The MTFs, field curvature, distortion, and square encirclement energy all meet the design requirements of the dual bands and wide ambient temperature range. The optical system has the advantages of a simple structure, fewer material types, low cost, high efficiency of cold stop, high diffraction efficiency, and no thermal aberration in the ambient temperature range of -40-60 ℃. A double-layer DOE is used to design the cooled dual-band infrared optical system, which shows that the method of using only two optical materials and three lenses can simplify the design conditions and has certain advantages in military and commercial applications. Therefore, our design can further promote the development and application of refractive-diffractive hybrid imaging optical systems.