High resolution quantum enhanced phase imaging of cells

TL;DR

The paper tackles the challenge of obtaining quantitative phase information from biological samples while minimizing photon exposure. It introduces a non-interferometric, sub-shot-noise phase imaging approach (NIQPI) that combines spontaneous parametric down-conversion twin beams with a transport-of-intensity equation framework, enabling high-resolution, label-free phase imaging. A key finding is that quantum noise subtraction via NRF and a TIE-based reconstruction yields a substantial quantum advantage in phase fidelity, largely independent of spatial resolution, demonstrated on engineered phase–transmittance objects and unstained sea urchin ova. This method offers fast, scanning-free phase imaging with practical potential for biological microscopy, particularly where phototoxicity or rapid dynamics limit illumination.

Abstract

Recovering both amplitude and phase information from a system is a fundamental goal of optical imaging. At the same time, it is crucial to operate at low photon doses to avoid altering the sample, particularly in biological applications. Quantum imaging provides a powerful route to extract more information per photon than classical techniques, which are ultimately limited by shot-noise. However, the trade-off between quantum noise reduction and spatial resolution has long been regarded as a major obstacle to the application of quantum techniques to small cellular and sub-cellular structures, where they could offer the greatest benefits. Here, we overcome this limitation by demonstrating sub-shot-noise quantitative phase imaging of biological cells based on the transport-of-intensity equation, enabling high-fidelity, label-free imaging of key cellular and sub-cellular features. We achieve high-resolution phase imaging limited only by the numerical aperture, while simultaneously obtaining a resolution-independent quantum advantage. Unlike other quantum imaging approaches, our method operates in a quasi-single-shot, wide-field configuration, retrieves both phase and amplitude information, and does not rely on interferometric measurements, making it intrinsically fast and stable. These results pave the way for the immediate application of sub-shot-noise imaging in biological microscopy.

Figures (7)

• Figure 1: High resolution quantum phase imaging technique (a) Schematic of the non-interferometric quantum phase imaging setup ortolano2023quantum. Signal and idler beams generated by spontaneous parametric down conversion (SPDC) propagate through an $f$-$f$ optical system, producing correlated intensity patterns. A phase-amplitude object, placed near the far field of the source, interacts only with the signal beam. Phase information is retrieved from intensity measurements placing the object at the focal and at the defocused planes ($\pm dz$). (b) Engineered test object consisting of distinct phase and transmittance masks. The phase mask consists of the superposition of a pure phase structure featuring a $\pi$-shaped symbol and a $\varnothing$-shaped symbol. The $\varnothing$ symbol additionally features a transmittance of approximately 0.93. The phase-amplitude object has lateral dimensions of approximately $348\,\mu\mathrm{m} \times 350\,\mu\mathrm{m}$, with thicknesses of about $60$ nm for the $\pi$ structure and $40$ nm for the $\varnothing$ symbol. (c) The four panels show the experimental and simulated quantum advantage in phase estimation using the transmittance-optimized correction factor $k^{(\tau)}_{\text{opt}}$ortolano2023quantum and the newly proposed factor for TIE-based phase retrieval $k^{(TIE)}_{\text{opt}}$ for four different defocusing distances $dz$. The advantage is quantified as the ratio $C(\text{Quant.})/C(\text{Clas.})$, where $C(\text{Quant.})$ ($C(\text{Clas.}))$ are the correlation coefficients between the quantum (classical) phase images and the reference one. The reported mean values and the associated uncertainty bars, corresponding to one standard uncertainty on the mean, are evaluated over an ensemble of approximately $10^3$ images. The ratios, for the different distances $dz$, are plotted as a function of the phase spatial resolution. Red and blue dots represent experimental data using $k^{(\tau)}_{\text{opt}}$ and $k^{(TIE)}_{\text{opt}}$, respectively, with shaded regions showing theoretical predictions. Green highlights indicate areas of optimization gain.
• Figure 2: Experimental reconstruction of transmittance and phase object (a) Transmittance estimations for classical and quantum single-frame images, processed with a factor $\mathcal{D}=3.8$ obtained by averaging over 12 pixels. The object's area occupies $220 \times 220~\text{pix}^2$ with a mean number of photon per pixel of 600. (b) Phase reconstruction at various defocus distances, $dz$, comparing classical and quantum single-frame approaches. The phase estimations at the smallest $dz$ are: classical $\pi = (-0.260 \pm 0.030$) rad, quantum $\pi = (-0.259 \pm 0.022)$ rad (theoretical $\pi$ = $(-0.226 \pm 0.006)$ rad); classical $\varnothing$$= (0.37 \pm 0.02)$ rad, quantum $\varnothing$$= (0.36 \pm 0.02)$ rad (theoretical $\varnothing$ = $(0.35 \pm 0.01)$ rad). Experimental uncertainties are obtained as mean errors calculated over $10^3$ frames.
• Figure 3: Biological quantum phase imaging (a) (Left column) Phase images obtained by averaging 100 frames, serving as a shot-noise-free reference. (Middle column) Classical single-shot phase images, affected by shot-noise. (Right column) Quantum-corrected single-shot phase images showing visibly improved quality and enhanced contrast compared to the classical case. Each row corresponds to a different biological sample, and the same color scale is used within each row. (b) Two areas, corresponding to the square boxes in last row of (a), are cropped. The color scales represent the entire range of the retrieved phase values. Green and blue dots are specific positions chosen for the quantitative analysis. (c) (Left) The average phase values corresponding to the six dots calculated over 100 frames. (Right) Standard deviation of the phase values in correspondence of the six dots.
• Figure 4: Experimental and theoretical behavior of NRF as a function of the parameter $\mathcal{D}$. Red points represent measured NRF values, the blue curve corresponds to theoretical predictions based on Eq. \ref{['eq:NRF']}, and black points indicate the Fano factor, confirming Poissonian photon statistics.
• Figure 5: Photon counts with the object placed at three distances. (Left panel) Photon counts recorded with the object positioned at the focal plane of the imaging system. In this case, only the transmittance mask ($\varnothing$) is visible. When the object is moved to defocused planes at distances $\pm dz$ (middle and right panel), phase variations induce additional intensity modulations, resulting in an overlap of phase and amplitude effects. Nevertheless, the TIE allows decoupling of these contributions, enabling the quantitative and unique retrieval of the sample's phase profile.