[Paper Review] Self-Bayesian Aberration Removal via Constraints for Ultracold Atom Microscopy

Emine Altuntaş, I. B. Spielman|arXiv (Cornell University)|Aug 16, 2021

Cold Atom Physics and Bose-Einstein Condensates42 references8 citations

TL;DR

This paper presents a self-Bayesian digital aberration correction method for ultracold atom microscopy using a low-cost, high-NA aspheric lens. By leveraging density-density correlations across defocused images and applying a finite-size constraint via Bayesian regularization, the method recovers near-diffraction-limited resolution without hardware modifications, significantly reducing photon shot noise in quantum back-action-limited measurements.

ABSTRACT

High-resolution imaging of ultracold atoms typically requires custom high numerical aperture (NA) optics, as is the case for quantum gas microscopy. These high NA objectives involve many optical elements each of which contributes to loss and light scattering, making them unsuitable for quantum back-action limited "weak" measurements. We employ a low cost high NA aspheric lens as an objective for a practical and economical-although aberrated-high resolution microscope to image ${^{87}\mathrm{Rb}}$ Bose-Einstein condensates. Here, we present a novel methodology for digitally eliminating the resulting aberrations that is applicable to a wide range of imaging strategies and requires no additional hardware. We recover nearly the full NA of our objective, thereby demonstrating a simple and powerful digital aberration correction method for achieving optimal microscopy of quantum objects. This reconstruction relies on a high quality measure of our imaging system's even-order aberrations from density-density correlations measured with differing degrees of defocus. We demonstrate our aberration compensation technique using phase contrast imaging, a dispersive imaging technique directly applicable to quantum back-action limited measurements. Furthermore, we show that our digital correction technique reduces the contribution of photon shot noise to density-density correlation measurements which would otherwise contaminate the desired quantum projection noise signal in weak measurements.

Motivation & Objective

• To address the challenge of optical aberrations in low-cost, high-NA objectives used for ultracold atom microscopy.
• To enable quantum back-action-limited imaging by digitally correcting aberrations without additional hardware.
• To reduce contamination from photon shot noise in density-density correlation measurements by recovering high-fidelity images prior to windowing.
• To develop a general-purpose, hardware-agnostic method applicable to various imaging strategies in cold-atom experiments.
• To demonstrate near-diffraction-limited performance using only computational reconstruction on experimentally acquired data.

Proposed method

• Employs a Tikhonov-type pseudo-inverse with a Bayesian prior based on spatial compactness of the atomic cloud.
• Uses density-density correlation data from multiple defocus levels to estimate even-order aberrations.
• Applies a finite-size constraint in Fourier space by weighting nearby wavevectors near zeros of the contrast transfer function (CTF).
• Implements a self-consistent Bayesian framework that combines noise modeling with spatial support priors to stabilize inversion.
• Uses periodic Fourier transforms with boundary handling via gradient clamping and zero-weighting at Nyquist-violating points.
• Reconstructs aberration-free images by minimizing a regularized objective function that balances data fidelity and prior knowledge.

Experimental results

Research questions

• RQ1 Can digital aberration correction recover near-diffraction-limited resolution in a low-cost, high-NA aspheric lens system for ultracold atoms?
• RQ2 How can photon shot noise in density-density correlation measurements be reduced without hardware changes?
• RQ3 To what extent can a Bayesian prior based on spatial compactness improve image reconstruction in the presence of CTF zeros?
• RQ4 Can this method be applied to phase contrast imaging in weak-measurement regimes without degrading quantum signal fidelity?
• RQ5 Is the reconstruction robust across varying degrees of defocus and aberration levels in experimental data?

Key findings

• The method recovers nearly the full numerical aperture of the objective, achieving near-diffraction-limited resolution despite significant optical aberrations.
• Aberration correction reduces photon shot noise contributions in density-density correlation measurements by enabling effective windowing on high-fidelity images.
• The Bayesian regularization with finite-size constraints effectively suppresses artifacts and noise amplification in ill-posed inverse problems.
• The technique is demonstrated on experimental 87Rb Bose-Einstein condensate data, enabling non-destructive in-situ imaging of the thermal-to-BEC phase transition.
• The approach is general and applicable to various imaging modalities, including phase contrast, without requiring hardware modifications.
• The method outperforms standard Tikhonov deconvolution by incorporating physical priors derived from system constraints and data correlation.