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arXiv:2511.20790 · Optics Express

Super-resolution microscopy via fluctuation-enhanced spatial mode demultiplexing

Stanislaw Kurdzialek

physics.opticsquant-phSubmitted Nov 25, 2025• Announced Nov 27, 2025• 0 citations
v1 · Nov 25, 2025v2 · Sep 14, 2026
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Abstract

We introduce a superresolution technique that combines spatial mode demultiplexing (SPADE) with emitter blinking. We show that temporal fluctuations not only enhance the precision of SPADE imaging, but also drastically simplify the measurement required to recover full object information -- in the presence of fluctuations, SPADE can be replaced by the much simpler image inversion interferometry. Both gains are enabled by exploiting temporal cumulants of the detected signal.

Journal reference
Optics Express 34(20), 37096 (2026)
DOI
10.1364/OE.605623
Comments
9+5 pages, 4 figures

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We introduce a superresolution technique that combines spatial mode demultiplexing (SPADE) with emitter blinking. We show that temporal fluctuations not only enhance the precision of SPADE imaging, but also drastically simplify the measurement required to recover full object information -- in the presence of fluctuations, SPADE can be replaced by the much simpler image inversion interferometry. Both gains are enabled by exploiting temporal cumulants of the detected signal.
We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing (SPADE) with noisy detectors. We show that in the presence of noise, the resolution of the measurement is limited by the signal-to-noise ratio (SNR) and the minimum resolvable spatial separation has a characteristic dependence of [Formula: see text]. Several detection techniques, including direct photon counting, as well as homodyne and heterodyne detection are considered.
I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE can estimate its second or higher moments much more precisely than direct imaging can fundamentally do in the presence of photon shot noise. I also prove that SPADE can approach the optimal precision allowed by quantum mechanics in estimating the location and scale parameters of a subdiffraction object. Realizable with far-field linear optics and photon counting, SPADE is expected to find applications in both fluorescence microscopy and astronomy.
High-resolution array detectors are widely used in single-particle tracking, but their performance is limited by excess noise from background light and dark current. As pixel resolution increases, the diminished signal per pixel exacerbates susceptibility to noise, degrading tracking accuracy. To overcome this limitation, we use spatial-mode demultiplexing (SPADE) as a noise-robust approach for estimating the motion characteristics of an optical pointlike source. We show that SPADE efficiently concentrate the information into a few key spatial modes, drastically reducing the number of detectors while maintaining high estimation precision. Furthermore, we enhance the robustness of the estimation against excess noise by elaborately designing the modes to be decomposed. We demonstrate, both theoretically and experimentally, that a SPADE with two specific modes outperforms direct imaging in estimating the microoscillation frequency of an optical point source in the presence of excess noise.
Super-resolution microscopy is crucial for imaging sub-wavelength biological structures. However, most techniques rely on nonlinear saturation or stochastic switching of emitters, limiting imaging speed and increasing phototoxicity. Here, we achieve deep super-resolution without employing saturation or stochastic dynamics, instead using a form of spatial mode demultiplexing. By shaping the point-spread function of the emitted light, our Structured Detection Microscope (SDM) redistributes information away from high shot-noise regions of the image, enhancing sensitivity to sub-diffraction emitter separations in two-dimensions and without mode-sorting optics. Implementing SDM within a high-numerical aperture total internal reflection fluorescence microscope, we demonstrate imaging of fluorophores attached to DNA nanorulers with separations as small as 50 nm at resolutions surpassing 40 nm - fivefold below the diffraction limit. This shows that spatial mode demultiplexing can achieve far sub-wavelength resolution and is applicable to biologically relevant samples. By enabling super-resolution biomolecular imaging without emitter saturation and stochasticity, our work opens the door to better understanding biological structure, function and dynamics.
Imaging systems measuring intensity in the far field succumb to Rayleigh's curse, a resolution limitation dictated by the finite aperture of the optical system. Many proof-of-principle and some two-dimensional imaging experiments have shown that, by using spatial mode demultiplexing (SPADE), the field information collected is maximal, and, thus, the resolution increases beyond the Rayleigh criterion. Hitherto, the SPADE approaches are based on resolving the lateral splitting of a Gaussian wave function. Here, we consider the case in which the light field originates from a biphoton source, i.e., spontaneous parametric down-conversion, and a horizontal separation is introduced in one of the two photons. We show that a separation induced in the signal photon arm can be superresolved using coincidence measurements after projecting both photons on Hermite-Gauss modes. Remarkably, the Fisher information associated with the measurement is enhanced compared to the ordinary SPADE techniques by K\sqrt{K}K​, where KKK is the Schmidt number of the two-photon state that quantifies the amount of spatial entanglement between the two photons.
The development of super-resolution techniques, i.e., allowing for efficient resolution below the Rayleigh limit, became one of the important branches in contemporary optics and metrology. Recent findings show that perfect spatial mode demultiplexing (SPADE) into Hermite-Gauss modes followed by photon counting enables one to reach the quantum limit of precision in the task of estimation of separation between two weak stationary sources in the sub-Rayleigh regime. In order to check the limitations of the method, various imperfections such as misalignment or crosstalk between the modes were considered. Possible applications of the method in microscopy call for the adaptive measurement scheme, as the position of the measured system can evolve in time, causing non-negligible misalignment. In this paper, we examine the impact of Brownian motion of the center of the system of two weak incoherent sources on adaptive SPADE measurement precision limits. The analysis is carried out using Fisher information, from which the limit of precision can be obtained by Cramér-Rao bound. As a result, we find that Rayleigh's curse is present in such a scenario; however, SPADE measurement can outperform perfect direct imaging. What is more, a suitable adjustment of the measurement time between alignments allows measurement with near-optimal precision.