DOI: 10.5061/dryad.cnp5hqccd
title: Data from: Adaptive optical imaging with entangled photons

description: Adaptive optics (AO) has revolutionized imaging in fields from astronomy
 to microscopy by correcting optical aberrations. In label-free
 microscopes, however, conventional AO faces limitations due to the absence
 of guidestar and the need to select an optimization metric specific to the
 sample and imaging process. Here, we propose an AO approach leveraging
 correlations between entangled photons to directly correct the point
 spread function (PSF). This guidestar-free method is independent of the
 specimen and imaging modality. We demonstrate the imaging of biological
 samples in the presence of aberrations using a bright-field imaging setup
 operating with a source of spatially-entangled photon pairs. Our approach
 performs better than conventional AO in correcting specific aberrations,
 particularly those involving significant defocus. Our work improves AO for
 label-free microscopy and could play a major role in the development of
 quantum microscopes.
description: # Adaptive optical imaging with entangled photons
 [https://doi.org/10.5061/dryad.cnp5hqccd](https://doi.org/10.5061/dryad.cnp5hqccd) Dataset includes all experimental data presented in the figures of the main article. Context and experimental procedure are described in the article. Fig 3a: Direct intensity reference image of a honeybee mouthpiece. No aberrations present in the system and no correction displayed on SLM. Fig 3b: Blurred direct intensity image of honeybee with aberrations. No correction displayed on SLM. Fig 3c: Corrected direct intensity image of honeybee with aberrations and correction displayed on SLM. Fig 3d: Sum-coordinate projection showing the spatial structure of photon pairs' correlations. From same acquisition as Fig 3a. No aberrations and no correction on SLM. Fig 3e: Sum-coordinate projection in the presence of aberrations. From same acquistion as Fig 3b. No correction on SLM. Fig 3f: Sum-coordinate projection after correction. From same acquisition as Fig 3c. Fig 3g: Image of correction phase mask found by optimising sum-coordinate projection. Fig 3h: Plot and gaussian fits of sum-coordinate projection central value as a function of correction coefficient for two different Zernike modes (Z-33 and Z13). Fig 4a: Plots of image quality metrics as a function of defocus aberration strength for an object with 3-d structure (three thin wires). Metrics are (in order): Power-in-Bucket (PIB), image contrast, low spatial frequencies, and central value of sum-coordinate projection. Includes scatter plots of data and line plots of fits. **Figs 4b-4g each contain a direct intensity image (large), a 1d image cross section (line plot), and a sum-coordinate projection image (inset) for different aberration corrections with 3 wires object. All cross-sections are column 75 of direct intensity image. Each image is stored in a different sheet with the corresponding title as: 'Large image' or 'Inset image'** Fig 4b: Defocus aberration and no correction. Fig 4c: Defocus aberration and correction found via optimising Power-in-Bucket metric. Fig 4d: Defocus aberration and correction found via optimising image contrast metric. Fig 4e: Defocus aberration and correction found via optimising low spatial frequencies metric. Fig 4f: Defocus aberration and correction found via optimising peak of sum-coordinate projection. Fig 4g: Reference with no aberration or correction. Fig 5a: Direct intensity image of left half of SPDC beam. No aberration or correction. Fig 5b: Direct intensity image of right half of SPDC beam with honeybee leg object. No aberration or correction. Fig 5d: Image of correction phase mask found by optimising sum-coordinate projection central value.\ **Figs 5e-g each contain show an image of honeybee leg extracted from diagonal elements of 2-photon spatial G2 (large) and sum-coordinate projection (inset). Each image is stored in a different sheet with the corresponding title as: 'Large image' or 'Inset image'** Fig 5e: No aberration or correction. Fig 5f: With aberration and no correction. Fig 5g: With aberration and correction. ## Description of the data and file structure Data are saved as .xlsx files and can be read into arrays using e.g. Matlab's `readmatrix()` function. Each subfigure has its own file: for figure X, subfigure y, the file is titled FigureXy.xlsx. For files containing image data, the columns represent the x pixel coordinate and the rows represent the y-pixel coordinate. Numeric values in each cell correspond to the value of the chosen pixel. Units depend on the quantity being plotted (i.e. direct intensity or correlations) and are given in all figures in the manuscript. Images shown in the paper are plotted using Matlab's imagesc() function, with the color axis scaling indicated on the image colorbars. For subfigures that include two images, e.g. Figures 4 b-g, the large image is saved in the first sheet, and the inset image is saved in the second sheet. Data from scatter and line plots are saved as rows. For a given set, the x data is the first row and the y data is the second. Figure 3h contains two sets of data and two fits for the plots of the projection peak vs correction coefficient. Units are given in paper. * Experimental data is stored in first sheet and the numerical fit is stored in the second. * The x and y values for the first set (blue plots, Zernike Z-33), are stored in rows 1 and 2, respectively. * The x and y valeys for the second set (red plots, Zernike Z13), are stored in rows 3 and 4, respectively. Figure 4a similarly is a plot of multiple sets of data and fits. As with Figure 3h, experimental data and fits are stored in separate sheets. Units are given in paper. They are organised as follows: * Rows 1 and 2: x and y coordinates (resp.) for the yellow plots (power in bucket) * Rows 3 and 4: x and y coordinates (resp.) for the red plots (contrast) * Rows 5 and 6: x and y coordinates (resp.) for the blue plots (low freq.) * Rows 7 and 8: x and y coordinates (resp.) for the purple plots (quantum)