Spectral Hadamard microscopy with metasurface-based patterned illumination

Abstract

Hadamard matrices, composed of mutually orthogonal vectors, are widely used in various applications due to their orthogonality. In optical imaging, Hadamard microscopy has been applied to achieve optical sectioning by separating scattering and background noise from desired signals. This method involves sequential illumination using Hadamard patterns and subsequent image processing. However, it typically requires costly light modulation devices, such as digital micromirror devices (DMDs) or spatial light modulators (SLMs), to generate multiple illumination patterns. In this study, we present spectral Hadamard microscopy based on a holographic matasurface. We noticed that certain patterns repeat within other Hadamard patterns under specific condition, allowing the entire set to be reproduced from a single pattern. This finding suggests that generating a single pattern is sufficient to implement Hadamard microscopy. To demonstrate this, we designed a metasurface to generate an illumination pattern and conducted imaging simulations. Results showed that holographic metasurface-based Hadamard microscopy effectively suppressed scattering signals, resulting in clear fluorescent images. Furthermore, we demonstrated that hyperspectral imaging can be achieved with Hadamard microscopy using dispersive optical elements, as the orthogonality of the Hadamard pattern enables to resolve spectral information. The reconstructed hyperspectral images displayed a color distribution closely matching the synthetic hyperspectral images used as ground truth. Our findings suggest that optical sectioning and hyperspectral imaging can be accomplished without light modulation devices, a capability typically unattainable with standard wide-field microscopes. We showed that sophisticated metasurfaces have the potential to replace and enhance conventional optical components, and we anticipate that this study will contribute to advancements in metasurface-based optical microscopy.

Keywords: Hadamard microscopy; hyperspectral imaging; metasurface; optical sectioning; patterned illumination.

Figure 1:

Concept of Hadamard patterns and their self-similarity. (a) Schematic representation of the Hadamard matrix, H, and the modified Hadamard matrix, P. (b) Arrangement of the Hadamard vector, p, for patterned illumination. The number of patterns is determined by the length of the Hadamard vector. We used the parameters $\left(n,q\right)=\left(\mathrm{19,5}\right)$ for generating illumination patterns. (c) Decoding process in Hadamard microscopy, which involves the dot products P ^T . (d) Self-similarity of the Hadamard matrix, illustrating how the entire set of illumination patterns can be reproduced by shifting a single pattern based on its self-similarity. (e) The average of all Hadamard pattern results in uniform illumination. Wide-field microscopy imaging modality can be achieved by averaging images illuminated by Hadamard patterns.

Figure 2:

Metasurface design for hologram generation. (a) The metasurface phase map was designed using the GS algorithm with a target Hadamard pattern. A hologram of the Hadamard pattern was obtained through wave propagation simulations. The remaining patterns can be derived by shifting the hologram. To suppress speckle patterns, we averaged 4 shifted images that maintained the same pattern as the original due to self-similarity. This process can be easily reproduced using a motorized stage in a real setup. (b) Structure and parameters of cylindrical meta-atom. D, diameter; H, height; P, period. (c) and (d) Optimization of phase delay (c) and transmission (d) with respect to the diameter and height of the meta-atom. (e) Transmission and phase delay with respect to the diameter at a height of 746 nm. At this height, the meta-atom covers the entire 2π phase with transmission higher than 90 %.

Figure 3:

Virtual optical setup and calibration step of the proposed Hadamard microscopy. (a) Virtually designed optical setup for Hadamard microscopy. The normal imaging and spectral imaging paths serve as detection paths for optical sectioning and hyperspectral imaging, respectively. To conduct realistic simulations as close to actual conditions as possible, the virtual setup was designed based on the specifications of commercially available optical components. Additionally, details such as the magnification and NA used in the virtual design were utilized for imaging simulations. (b) Intensity the distribution of the scattering PSF (left), and the intensity d (middle) and spectral distributions (right) of the spectral PSF. Scale bars, 10 μm (left) and 5 μm (middle). (c) Calibration of the Hadamard microscope to define the digital pinhole and slit, which are utilized for optical sectioning and hyperspectral imaging, respectively. The circled cross and dot symbols represent convolution and dot product, respectively.

Figure 4:

Image processing simulation of metasurface-based Hadamard microscopy. The imaging simulations are classified into optical sectioning and hyperspectral imaging. A 4-channel confocal microscopy image was used to create ground truth. For optical sectioning, we first simulated imaging in a scattering environment under Hadamard illumination. After decoding, a simple average produces a blurred wide-field image, whereas an optically sectioned image is obtained by performing element-wise multiplication with digital pinhole before averaging. In contrast, hyperspectral imaging includes the convolution of the spectral PSF. After decoding and multiplying the digital slit, a spectrally dispersed image is obtained. The hyperspectral image was reconstructed by gathering the spectral information distributed along with the digital slit. The circled cross and dot symbols represent convolution and dot product, respectively.

Figure 5:

Comparison of the simulation results with ground truth. (a) The ground truth was compared with the imaging simulation results of metasurface-based Hadamard microscopy. The results show that the optical sectioning achieved by the proposed method is comparable to the ground truth, while the wide-field image is highly blurred due to scattering. Although the hyperspectral image exhibits lower spatial resolution compared to the ground truth, the color distribution closely matched that of the ground truth hyperspectral image. The magenta arrows in the hyperspectral images indicate the spectral sampling point. Scale bar, 50 μm. (b) Comparison of the spectral data acquired at the sampling point (indicated by the magenta arrows in (a)) between the ground truth and the spectral Hadamard microscopy.