Photon-starved imaging through turbulence at the diffraction limit

TL;DR

Ground-based imaging under atmospheric turbulence and photon scarcity challenges conventional adaptive optics and blind deconvolution. The authors introduce TAP-BD, a hardware-software co-design that uses phase-diverse coded-detection via a sequence of SLM phase patterns to enrich information, followed by a two-stage, physics-informed ADMM optimization that jointly recovers the object $O$ and turbulence phase $\Phi$, with a Poisson denoiser to mitigate shot noise. TAP-BD demonstrates robust reconstructions with only a handful of measurements, significantly outperforming direct imaging and neural baselines in photon-starved, severe turbulence regimes, and achieves substantial computational gains. The work enables photon-efficient, turbulence-resilient imaging for long-range remote sensing, space situational awareness, and related applications.

Abstract

Ground-based imaging systems struggle to achieve diffraction-limited resolution when atmospheric turbulence and photon scarcity act simultaneously. In this regime, conventional adaptive optics, speckle imaging, and blind deconvolution lack sufficient information diversity to reliably estimate either the scene or the turbulence. We present Turbulence Aware Poisson Blind Deconvolution (TAP-BD), a framework designed for robust image recovery in these extreme conditions. TAP-BD extracts more information from coded-detection through phase diversity and decodes it with a physics-informed optimization that incorporates low photon Poisson statistics. Experiments show that TAP-BD provides reliable reconstructions of both scene and turbulence using only a few tens of measurements, even under strong aberrations and photon-starved conditions where existing methods fail. This capability enables photon-efficient, turbulence resilient imaging for applications such as space situational awareness and long-range remote sensing.

Figures (4)

• Figure 1: Turbulence-Aware Poisson blind deconvolution (TAP‐BD) framework. (A) Hardware setup: A spatial light modulator (SLM) sequentially imposes phase diversity patterns $\{\Gamma_i \}$ on the incoming distorted wavefront, generating multiple coded-measurements $\{I_i \}$. (B) TAP-BD reconstruction pipeline: Each measurement is first denoised via a Poisson denoiser. An iterative solver then jointly recovers the target $O$ and turbulence phase $\Phi$ by leveraging both the denoised intensities $\{P_i \}$ and the known SLM patterns $\{\Gamma_i \}$. (C) Plots show target PSNR (top) and phase RMSE (bottom) after reconstruction for the coded (red) versus DI (black). Cramer-Rao lower bounds (CRLBs) are also plotted for phase RMSE (dashed). The lower CRLB for the coded detection reflects higher information content. TAP-BD achieves better performance than DI by leveraging this additional information.
• Figure 2: Comparative simulation of TAP‐BD and NeuWS: (A) varying measurement count $M$ (at fixed turbulence strength $D/r_0=20$ and total photon budget $5\times10^8$) and (B) varying turbulence severity $D/r_0$ (at fixed $M=100$ and total photon budget $1\times10^9$). The left panels show turbulent only measurement $I_1$ with flat phase diversity $\Gamma_1$, reconstructed targets $\hat{O}$ and estimated turbulence phases $\hat{\Phi}$ for each method. The right panels show corresponding target PSNR and phase RMSE. Note that we modified NeuWS to incorporate the assumption of uniform intensity across the circular pupil aperture to match with TAP-BD simulating phase-only distortion at the pupil plane. Both methods use 1000 iterations/epochs. Poisson denoiser was not used for TAP-BD in these simulations.
• Figure 3: Experimental reconstruction under varying turbulence severity level $D/r_0$ and measurement count M, averaged over five distinct turbulence phases per $D/r_0$. (A) Example reconstruction results at $D/r_0=20$: The top panel shows the turbulent measurement $I_1$ with flat phase diversity $\Gamma_1$, diffraction-limited image of the USAF 1951 target O and ground truth turbulence phase $\Phi$. The bottom plot illustrates how increasing $M$ boosts reconstruction quality, as measured by target PSNR, and phase RMSE (bottom-right). (B) Contour plots of the target PSNR (top) and phase RMSE (bottom) as functions of $D/r_0$ and $M$. All experiments were conducted with a high photon flux ($\sim2.13\times10^7$ photons per single measurement), using a 5 mm aperture and 1000 iterations per reconstruction. A Poisson denoiser was not employed.
• Figure 4: Experimental reconstruction under low photon levels, averaged over five distinct turbulence phases at fixed $D/r_0=16$. (A) Example reconstructions. The left panel shows ground truth elements: the diffraction limited image of ‘Purdue train’ target $O$, the turbulent PSF $h_1$ with flat phase diversity $\Gamma_1$ and the turbulence phase $\Phi$. The right panels illustrate reconstruction results at different photon levels. The first row shows raw measurements $I_1$, highlighting how shot noise becomes dominant as photon count decreases. The second row presents Poisson-denoised measurements $P_1$. Rows three to five display the reconstructed target $\hat{O}$, estimated PSF $\hat{h_1}$ and retrieved phase $\hat{\Phi}$. (B) Target PSNR and phase RMSE with and without Poisson denoising. In the low-photon regime, denoising significantly boosts PSNR and lowers phase RMSE. Shaded regions denote the $\pm$ one standard deviation computed over five independent trials with different turbulence phases. All experiments used a 3 mm aperture, $M=48$ measurements, and 1000 iterations per reconstruction.