Low Photon Number Non-Invasive Imaging Through Time-Varying Diffusers

TL;DR

The paper addresses the challenge of optical imaging through dynamic scattering media under ultra-low photon flux. It introduces a data-analysis pipeline that computes the RMS of Fourier magnitudes across a sequence of short-exposure frames to recover the scattering-free Fourier magnitude, followed by phase retrieval to reconstruct the object, without measuring a transmission matrix or shaping the wavefront. The approach is validated in simulations and in fluorescence microscopy, achieving reconstructions with averages of fewer than one photon per pixel per frame (down to around $0.14$ photons per pixel) across thousands of frames. This enables non-invasive imaging behind time-varying diffusers with broad potential applications in LIDAR through fog, astronomy through turbulent atmospheres, and endoscopy, with prospects for faster acquisition via SPAD arrays.

Abstract

Optical imaging plays a crucial role in advancing science and technology, enabling applications in fields ranging from biomedicine to astronomy. However, imaging through scattering media such as biological tissues, fog, or turbulent atmosphere remains a major challenge. Light scattering and absorption in such media make imaging challenging; in the case of time varying scatterers and low-light regime imaging has not been demonstrated so far. We present the first demonstration of non-invasive imaging of dim objects hidden behind dynamic scattering layers, obtaining robust reconstruction even at extremely low photon counts per frame. We achieve this by developing a new data-processing approach. In our experiment, we utilize a photon number resolving camera to capture a sequence of frames, containing on average, less than one photon per pixel. We validate our approach in microscopy, where we reconstruct images of biological samples stained with standard fluorescent dyes. Beyond microscopy, our approach can be applied in LIDAR systems for imaging through fog, and endoscopy using multimode and multicore fibers.

Figures (5)

• Figure 1: Concept of the method. (a) A luminescent, spatially incoherent object is imaged through a time-varying diffuser and recorded with a high-speed, photon-counting camera. (b) A long exposure produces a homogeneous image that carries no spatial information about the object. (c) A single short-exposure frame preserves speckle structure but contains very few photons. (d) In the analysis, we use a series of short frames with a low signal. (e) Summing many such low-signal frames similarly yields a homogeneous image without spatial content. (f) Instead, for each short-exposure frame, we compute the magnitude of its Fourier transform. (g) The root-mean-square (RMS) average of these Fourier magnitudes across the burst recovers the spatial-frequency content of the object. (h) After retrieving the missing Fourier phase using a phase-retrieval algorithm Fienup1982, the object hidden behind the dynamic diffuser can be reconstructed.
• Figure 2: Mathematical background of our method. (a) Direct imaging in a scattering-free system. The image $I$ formed on the camera is a convolution of the object $O$ with the system Point Spread Function (PSF) $h$. (b) Under dynamic scattering, each speckle image $I_i$ formed on the camera is a convolution of the object $O$ with the instantaneous speckle Point Spread Function (PSF) $S_i$. (c) Spatial Fourier transforms of the images shown in (b). (d) The root mean square (RMS) of the Fourier transform moduli, computed across many frames, converges to $|\mathcal{F}\{O\}|\,|\mathcal{F}\{P\}|$, where $P$ denotes the effective PSF of the system as if no scattering were present. (e) The magnitude of the scattering-free Fourier transform is obtained, while its phase is lost. A phase retrieval algorithm Fienup1982 is then used to recover the missing phase information. (f) Reconstruction of the object after phase retrieval.
• Figure 3: Imaging in the photon counting regime -- simulation results. (a) Original object. (b) Image of the object captured with a finite resolution imaging system. (c) Modulus of the Fourier transform of the object (b). (d) Image of the object obscured by the diffuser - a single frame captured by the camera. (e) Single camera frame with Poisson noise. (f) An average of Fourier transforms modulus of 10,000 frames. (g) Reconstructed object image through a dynamic diffuser.
• Figure 4: Imaging of 5$\mu m$ fluorescence micro-spheres through the dynamic complex medium in wide-field microscope. (a) Schematic of the wide-field fluorescence microscope utilized in our experiments. (b) Direct image of the sample without the diffuser (ground truth). (c) Single frame captured by the qCMOS camera. (d) Average of all 1791 frames recorded. (e) Reconstruction result using the phase retrieval algorithm Fienup1982.
• Figure 5: Results comparison of imaging through the dynamic complex medium. (a) Direct images of fluorescent samples without the diffuser. (b) The modulus of the Fourier transforms of the images in column (a). (c) Example camera frames of objects in column (a) obscured by the varying diffuser, with photon counts as low as 0.14 photons per pixel in 1152 frames, highlighted in the second row. (d) The average of the Fourier transform moduli of the frames captured through the dynamic diffuser. (e) Recovered image computed using the phase retrieval algorithm Fienup1982. Rows 1 to 3 present fluorescent microspheres, while row 4 shows Alexa Fluor 568-labeled astrocytes.