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Super-resolution imaging using super-oscillatory diffractive neural networks

Hang Chen, Sheng Gao, Zejia Zhao, Zhengyang Duan, Haiou Zhang, Gordon Wetzstein, Xing Lin

Abstract

Optical super-oscillation enables far-field super-resolution imaging beyond diffraction limits. However, the existing super-oscillatory lens for the spatial super-resolution imaging system still confronts critical limitations in performance due to the lack of a more advanced design method and the limited design degree of freedom. Here, we propose an optical super-oscillatory diffractive neural network, i.e., SODNN, that can achieve super-resolved spatial resolution for imaging beyond the diffraction limit with superior performance over existing methods. SODNN is constructed by utilizing diffractive layers to implement optical interconnections and imaging samples or biological sensors to implement nonlinearity, which modulates the incident optical field to create optical super-oscillation effects in 3D space and generate the super-resolved focal spots. By optimizing diffractive layers with 3D optical field constraints under an incident wavelength size of $λ$, we achieved a super-oscillatory spot with a full width at half maximum of 0.407$λ$ in the far field distance over 400$λ$ without side-lobes over the field of view, having a long depth of field over 10$λ$. Furthermore, the SODNN implements a multi-wavelength and multi-focus spot array that effectively avoids chromatic aberrations. Our research work will inspire the development of intelligent optical instruments to facilitate the applications of imaging, sensing, perception, etc.

Super-resolution imaging using super-oscillatory diffractive neural networks

Abstract

Optical super-oscillation enables far-field super-resolution imaging beyond diffraction limits. However, the existing super-oscillatory lens for the spatial super-resolution imaging system still confronts critical limitations in performance due to the lack of a more advanced design method and the limited design degree of freedom. Here, we propose an optical super-oscillatory diffractive neural network, i.e., SODNN, that can achieve super-resolved spatial resolution for imaging beyond the diffraction limit with superior performance over existing methods. SODNN is constructed by utilizing diffractive layers to implement optical interconnections and imaging samples or biological sensors to implement nonlinearity, which modulates the incident optical field to create optical super-oscillation effects in 3D space and generate the super-resolved focal spots. By optimizing diffractive layers with 3D optical field constraints under an incident wavelength size of , we achieved a super-oscillatory spot with a full width at half maximum of 0.407 in the far field distance over 400 without side-lobes over the field of view, having a long depth of field over 10. Furthermore, the SODNN implements a multi-wavelength and multi-focus spot array that effectively avoids chromatic aberrations. Our research work will inspire the development of intelligent optical instruments to facilitate the applications of imaging, sensing, perception, etc.
Paper Structure (11 sections, 1 equation, 8 figures)

This paper contains 11 sections, 1 equation, 8 figures.

Table of Contents

  1. 1 Introduction
  2. 2 Methods
  3. 3 Results
  4. 4 Discussion
  5. 5 Conclusion

Figures (8)

  • Figure 1: Training SODNN to optimize the diffractive elements with 3D optical field constrains. (a) Utilizing diffractive modulation layers and free-space propagation to implement the weighted optical interconnections and imaging samples or biological sensors to implement nonlinearity. SODNN can modulate the multi-wavelength incident optical field to create optical super-oscillation effects in 3D super-oscillatory regions. (b) The conventional methods optimize a 2D focus spot at a specific focusing distance to achieve optical super-oscillation with a large side lobe. (c) The enlarged 3D super-oscillatory regions show that SODNN optimizes the 3D optical field in a certain distance range to achieve super-oscillation without the side lobe.
  • Figure 2: Optical super-oscillatory spots and optical needle design of SODNN. The FWHM (a) and the output (b) of super-oscillatory spots at the designed focal length and distributions offsetting the designed focal length with the collimated input optical field. (c) The optical super-oscillatory needle within a DoF of 6 $\mu$m with uniform light intensity and consistent FWHM. (d) The 3D distributions of the output optical super-oscillatory needle. (e) The output of the slices of the optical super-oscillatory needle.
  • Figure 3: Multi-wavelength and multi-focus SODNNs. (a) The super-oscillatory spots under red, green, and blue light channels with the FWHM of 259 $nm$, 221 $nm$, and 199 $nm$, respectively. (b) The 3 × 5 super-oscillatory spot arrays under red, green, and blue light channels with the FWHM of 267 $nm$, 222 $nm$, and 199 $nm$, respectively. (c) The super-oscillatory spots of the T-H-U pattern with the FWHM of 274 $nm$ and the super-oscillatory spots of the heart-shaped pattern with the FWHM of 262 $nm$.
  • Figure 4: Characterization of SODNN. (a) Schematic of the experimental setup. (b, c) Imaging results of the resolution testing chart by commercial Olympus objective and SODNN. (d) The diffractive modulation layer of single-layer SODNNs for a single-focus (left) and 2 × 2 multi-focus (middle) with the layer profile characterized by scanning electron microscope, i.e., SEM (right). (e) The numerical analysis results (left) and experimental results (middle) of the single-focus SODNN. (f) The numerical analysis results (left) and experimental results (middle) of the 2 × 2 multi-focus SODNN.
  • Figure 5: Performance analysis of SODNN. The FWHM of the output spot with respect to the modulation element number (a), layer number (b and c), and modulation element sizes (d).
  • ...and 3 more figures