Infrared optical systems have unique advantages in infrared guidance, target identification and tracking, battlefield reconnaissance, anti-stealth, and other fields. However, the optical materials used in such systems are rare, which causes the disadvantages of complex systems, time-consuming calculations, and so on. Multi-layer diffractive optical elements (MLDOEs) can achieve high diffraction efficiency over a wide waveband. Hybrid imaging optical systems composed of diffractive optical elements (DOEs) with special imaging characteristics and refractive lenses can not only meet the requirements of high-quality imaging but also reduce the number of lenses, system weight, and system cost. Especially, the MLDOEs applied in infrared optical systems can correct both color and thermal aberrations, thereby effectively reducing the system's complexity and dependence on optical materials. However, the ambient temperature affects diffraction efficiency and further influences the modulation transfer function (MTF) of the hybrid imaging optical system. So, it is an important research topic in the field of infrared optics, and research should be conducted on investigating the effect of temperature change on a hybrid imaging optical system, proposing a suitable athermalization design, reducing the effect of temperature on imaging quality, and enhancing the temperature adaptability of the hybrid infrared optical system.

This paper selects the commonly used separated double-layer DOE as an example to illustrate the microstructure changes caused by the changes in the ambient temperature (Fig. 1). A concept and a model of temperature-bandwidth integral average diffraction efficiency (TBIADE) are proposed to represent the comprehensive diffraction characteristics of a DOE in a certain temperature range and working waveband, and the optimal design of a double-layer DOE is achieved by selecting the design wavelength pair. Then, a cooled hybrid imaging optical system in the mid-infrared waveband is optimally designed with ZnSe-Ge as the substrate material of the double-layer DOE. Finally, the MTF of the hybrid imaging optical system with the traditional design is compared with that of the system with the optimal design presented in this paper to verify the correctness of the proposed design.

The MATLAB software is used to calculate the effects of the temperature range and the mid-infrared waveband on diffraction efficiency under the TBIADE-based optimal design (Fig. 3 and Table 2). The diffraction efficiency of the double-layer DOE with ZnSe-Ge as its substrate material is calculated with due consideration given to both the working waveband and ambient temperature (Fig. 4). Compared with the traditional design, the optimized design can more effectively improve the diffraction efficiency and TBIADE of the DOE in the ambient temperature range, which also proves that the design of the hybrid imaging optical system is reliable. Then, a cooled infrared detector with a pixel size of 30 μm and an area array size of 320×256 is employed to optimally design a hybrid imaging system in the mid-infrared waveband composed of 6 lenses. The back and front surfaces of the 3rd and 4th lenses are the 1st and 2nd surfaces of the double-layer DOE, and the middle is a thin air gap (Fig. 5). The specific design parameters of the optimized hybrid imaging optical system are calculated (Table 4). After optimization, the real MTF of the system under different ambient temperatures also fully meets the design requirements at the cutoff frequency of 17 lp/mm when the effect of the TBIADE of the double-layer DOE on the real MTF is considered (Fig. 6).

The ambient temperature affects the structure and properties of optical elements, including traditional refractive lenses and DOEs. In particular, it can lower diffraction efficiency and ultimately reduce the imaging quality of hybrid imaging optical systems. However, the traditional design ignores the effect of temperature change on diffraction efficiency, resulting in inaccurate evaluations of the actual image quality. To enable such optical systems to achieve the optimal image quality over a wide ambient temperature range, this paper proposes the concept and design of TBIADE and selects the optimal design wavelength pair on the basis of the given substrate material combination and working ambient temperature range. Then, the paper calculates the corresponding microstructure parameters to ensure the optimal MTF of the hybrid imaging optical system. Finally, it designs a hybrid imaging optical system in the mid-infrared waveband based on a double-layer DOE and presents the thermal aberration correction of the system. The result shows that this design can effectively improve the diffraction efficiency of the double-layer DOE under the comprehensive influence of wide waveband and temperature range, and the results of the microstructure parameters are better than their counterparts in the traditional design. Better results can then be achieved in both design and processing, and more accurate image quality evaluation is ensured. The proposed method helps promote the design theory of diffractive optics and extend it to the design and image quality evaluation of common types of DOEs.