Source-linked AI summary
Low Photon Count Phase Retrieval Using Deep Learning
Alexandre Goy, Kwabena Arthur, Shuai Li, George Barbastathis
TL;DR
The paper models experimental camera measurements under photon-counting and detector noise. It evaluates reconstructions using correlation coefficients against ground truths and compares simulated measurements with experimental data.
Problem
Low-light measurements require modeling photon-counting and detector noise when evaluating image reconstructions.
Method
The acquisition process is simulated using calibrated ground truths, Fresnel propagation, Poisson photon statistics, detector quantum efficiency, camera gains, excess noise, and dark noise.
Results
Reconstruction correlation coefficients are presented with experimental data for comparison.
Takeaways & Limitations
Correlation with ground truths provides the stated basis for comparing simulated and experimental reconstructions.
Abstract
from arXiv · showhide
Imaging systems' performance at low light intensity is affected by shot noise, which becomes increasingly strong as the power of the light source decreases. In this paper we experimentally demonstrate the use of deep neural networks to recover objects illuminated with weak light and demonstrate better performance than with the classical Gerchberg-Saxton phase retrieval algorithm for equivalent signal over noise ratio. Prior knowledge about the object is implicitly contained in the training data set and feature detection is possible for a signal over noise ratio close to one. We apply this principle to a phase retrieval problem and show successful recovery of the object's most salient features with as little as one photon per detector pixel on average in the illumination beam. We also show that the phase reconstruction is significantly improved by training the neural network with an initial estimate of the object, as opposed as training it with the raw intensity measurement.
Negative Pearson correlation coefficient
The negative Pearson correlation coefficient (NPCC) measures reconstruction similarity for two images and is minimized by perfect agreement.
- NPCC is defined for two images A and B using pixel-wise deviations from their respective averages.
- The average of each image is denoted by an overbar in the NPCC expression.
- NPCC reaches -1 for a perfect match and takes higher values otherwise.
SLM calibration
The SLM’s complex transmittance was experimentally calibrated across gray levels using interferometric measurements, with filtered mean curves adopted for subsequent use.
- The SLM’s phase difference and amplitude ratio between gray levels were measured using a Mach-Zehnder interferometer and off-axis holography.
- Phase shift and intensity ratio were calibrated as functions of gray level using 10 measurements at each graph point.
- Low-pass-filtered mean curves were used as the final calibration curves.
Photon count calibration
Photon counts were calibrated from measured beam power, detector response, and the fraction of the illumination beam captured by the camera.
- Average photons per detector pixel were based on Silicon photodetector measurements and filter attenuation factors for each experiment.
- The camera captured 69% of the incident beam power after fitting the measured beam with an Airy-pattern model.
- The reported photon count refers to photoelectrons after accounting for detector quantum efficiency, and the time-averaged count varies spatially.
- Photon energy was 3.139 × 10^-19J, with 2ms integration, 0.6 quantum efficiency, and 1,006,008 total pixels.
Simulations
Numerical simulations reproduced the experimental acquisition process by propagating calibrated images and adding detector noise, then comparing reconstruction correlations across datasets.
- Synthetic camera measurements matched the experimental measurements in size and bit depth, using calibrated ground truths and Fresnel propagation via fast Fourier transforms.
- The simulated noisy detector signal included Poisson photon statistics, quantum efficiency, camera gains, excess gain noise, and dark noise.
- Reconstruction correlation coefficients from simulations were compared with experimental data in Fig. 5 for IC layouts and ImageNet images.