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Zhao X J, Fan B, Liao J. Theoretical and experimental study on end-to-end hybrid multi-order diffractive lens design[J]. Opto-Electron Eng, 2025, 52(5): 250023. doi: 10.12086/oee.2025.250023
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Theoretical and experimental study on end-to-end hybrid multi-order diffractive lens design
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Abstract
This paper presents a hybrid multi-order diffractive lens that supports dual-band computational imaging in both visible and mid-wave infrared (MWIR) bands. By applying diffraction structures of varying depths on both sides of the same substrate and optimizing these structural parameters using the end-to-end optimization framework, we successfully developed a diffractive element capable of efficient focusing in the visible light band (640~800 nm) and the MWIR band (3700~4700 nm). Coupled with a specially designed image reconstruction network, this approach realizes a monolithic dual-band computational imaging system with simplicity, lightweight construction, and low cost. Experimental results show that the prototype with a diameter of 40 mm achieves static modulation transfer functions of 50.0% in the visible light band and 4.4% in the MWIR band. Under room temperature conditions, the noise equivalent temperature difference in the infrared band does not exceed 80 mK, confirming the effectiveness and practicality of the proposed design. -
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References
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Overview
High-speed maneuvering platforms increasingly demand multi-band detection and lightweight electro-optical payloads. Addressing these needs, this paper introduces a novel hybrid multi-order diffractive lens (HMODL) design coupled with an advanced image reconstruction network. To the best of our knowledge, this is the first demonstration of achieving dual-band imaging (640-800 nm visible spectrum and 3700-4700 nm mid-wave infrared spectrum) using a single diffractive element. This breakthrough significantly reduces the size, weight, and complexity of optical systems required for such applications.
The HMODL design utilizes a dual-layer diffraction structure formed by the front and rear surfaces, where different diffraction orders are employed to focus light waves in each layer. This innovative approach provides high operability and flexibility, making it especially suitable for operation over a wide wavelength range. The dual-layer configuration enables efficient and simultaneous focusing of light across both visible and infrared bands, overcoming previous limitations associated with single-band or bulky multi-element designs.
A key aspect of this work is the development of a Ray-Wave imaging model specifically tailored for analyzing non-thin or multi-layer diffractive elements. Under reasonable approximations, this model offers a fast and accurate analytical method for deal with complex diffraction phenomena. It also facilitates the calculation of the point spread function (PSF), which is crucial for evaluating imaging performance. For rotationally symmetric models, the Kirchhoff diffraction integral can be efficiently computed through the optical path and intensity interpolation, enabling gradient calculations essential for end-to-end optimization frameworks.
Furthermore, we proposed a differentiable Ray-Wave model that enhances the accuracy and speed of simulations for multi-order diffractive lenses (MODLs). This model supports the optimization process by enabling precise gradient calculations, thereby improving the overall efficiency of the design and validation phases. By integrating this model into an end-to-end learning framework, the system autonomously learns optimal optical parameters without the need for extensive human expert guidance.
To validate our approach, we fabricated a prototype HMODL with a 40 mm aperture, demonstrating impressive spatial resolutions of 124 lp/mm in the visible band and 12 lp/mm in the infrared band. Additionally, the prototype achieved an infrared noise equivalent temperature difference (NETD) ≤80 mK at room temperature, confirming its practical utility in real-world scenarios. These results highlight the potential of HMODLs for enhancing the capabilities of electro-optical systems in various applications, including surveillance, navigation, and scientific research.
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Zhao X J, Fan B, Liao J. Theoretical and experimental study on end-to-end hybrid multi-order diffractive lens design[J]. Opto-Electron Eng, 2025, 52(5): 250023. doi: 10.12086/oee.2025.250023
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Figure 1.
Dispersion characteristics of MODL
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Figure 2.
Schematic diagram of interpolation calculation for optical path in light wave field
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Figure 3.
Examples of calculating aspheric and diffractive surface combinations using various models. (a) Lens structure combining aspheric and diffractive surfaces; (b) Calculation results using TEA, Zemax, and the proposed ray-wave model, respectively
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Figure 4.
Influence of HMOLD processing errors on PSF
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Figure 5.
Impact of HMOLD processing errors on its imaging quality. (a) Ground truth image; (b) Simulated image of HMOLD without processing errors; (c) Simulated image of HMOLD with processing errors
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Figure 6.
Structure of NAFNet image reconstruction network
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Figure 7.
Variation of Strehl ratio with spectrum and focal length under initial structure of HMOLD
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Figure 8.
End-to-end optimization framework for HMOLD dual-band computational imaging
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Figure 9.
PSF, degraded images, and reconstructed images in visible band during training process
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Figure 10.
PSF, degraded images, and reconstructed images in MWIR band during training process
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Figure 11.
Simulation imaging results with optimal parameters
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Figure 12.
Changes in Strehl ratio of optimized HMODL with wavelength and focal length
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Figure 13.
Height profile of optimized HMODL. (a) Optimized profile of multi-order diffractive surface for HMODL; (b) Optimized and fitted profile of diffractive surface for HMODL
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Figure 14.
Prototype of HMODL. (a) Fabricated HMODL; (b) Dual-band imaging system of HMODL
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Figure 15.
Test optical path of HMODL prototype and PSF calibration results
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Figure 16.
Imaging results of outdoor scenes
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Figure 17.
Dual-band imaging results of prototype on specific frequency targets
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Figure 18.
Imaging results of prototype on A1 resolution plate in visible band
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Figure 19.
MTF of prototype under indoor conditions in both visible and infrared bands. (a) MTF curves of HMODL before and after reconstruction in visible band; (b) MTF curves of HMODL before and after reconstruction in MWIR band
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Figure 20.
MTF tests of prototype at different fields of view outdoors. (a) Visible band checkerboard images taken by prototype outdoors and MTF curves before and after restoration at different fields of view; (b) MWIR band checkerboard images taken by prototype outdoors and MTF curves before and after restoration at different fields of view
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Figure 21.
NETD of HMODL prototype
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