Optimization design method of DOE diffraction efficiency and its application in a zoom lens

Conventional single-layer diffractive optical elements (SLDOEs) frequently overlook the impact of incident angle and environmental temperature, leading to reduced diffraction efficiency, stray light, and compromised imaging quality. This study addresses these limitations by deriving the phase delay increment caused by temperature-induced changes in the refractive index and thermal expansion coefficients of the SLDOE substrate and propagation material. We propose the temperature angle bandwidth integrated average diffraction efficiency (TABIADE) concept and establish its mathematical model. An algorithm targeting the maximum TABIADE value is used to optimize the microstructure height, enabling the design of high-diffraction-efficiency SLDOEs. Our TABIADE-based design demonstrates superior performance in adapting to complex temperature variations compared to conventional designs optimized for maximum angle bandwidth integrated average diffraction efficiency (ABIADE). We designed a cooled infrared continuous zoom system incorporating multiple SLDOEs and analyzed the impact of SLDOEs' diffraction efficiency on the system modulation transfer function (MTF). Compared with the approximate maximum ABIADE method, the DOE designed by our proposed method causes less degradation in imaging quality when used in optical systems. The final system incorporates three SLDOEs, achieving an <i>M</i><i>T</i><i>F</i>>1 at 33 lp/mm across a 3.7-5 µm wavelength range. With an F-number of 4, a zoom range of 40-900 mm, and a total length of 337 mm, an innovative balance between high zoom ratio, long focal length, and lightweight design has been demonstrated. This method addresses the challenge in infrared continuous zoom system design, where ensuring imaging quality typically limits the number of SLDOEs, making it difficult to balance high zoom ratios, long focal lengths, and lightweight structures. Additionally, it provides technical support for the use of SLDOEs in various refractive-diffractive hybrid system designs.