Direct Zernike Coefficient Prediction from Point Spread Functions and Extended Images using Deep Learning

TL;DR

Aberrations degrade optical imaging and traditional adaptive optics often rely on iterative optimization. This work trains a ResNet50 to map up to $n_z\le3$ phase-diverse images to $25$ Zernike coefficients ($Z_3$–$Z_{27}$), enabling direct aberration retrieval without explicit phase sensing. Results on simulated PSF and extended 2D samples show a best RMSE of $0.1020$ rad for PSF with defocus bias and $0.1479$ for extended images, with a single prediction often sufficing and iterative refinements offering further gains. The approach promises rapid aberration correction with minimal image acquisition, supporting deployment in real microscopy contexts and potentially reducing exposure and acquisition time.

Abstract

Optical imaging quality can be severely degraded by system and sample induced aberrations. Existing adaptive optics systems typically rely on iterative search algorithm to correct for aberrations and improve images. This study demonstrates the application of convolutional neural networks to characterise the optical aberration by directly predicting the Zernike coefficients from two to three phase-diverse optical images. We evaluated our network on 600,000 simulated Point Spread Function (PSF) datasets randomly generated within the range of -1 to 1 radians using the first 25 Zernike coefficients. The results show that using only three phase-diverse images captured above, below and at the focal plane with an amplitude of 1 achieves a low RMSE of 0.10 radians on the simulated PSF dataset. Furthermore, this approach directly predicts Zernike modes simulated extended 2D samples, while maintaining a comparable RMSE of 0.15 radians. We demonstrate that this approach is effective using only a single prediction step, or can be iterated a small number of times. This simple and straightforward technique provides rapid and accurate method for predicting the aberration correction using three or less phase-diverse images, paving the way for evaluation on real-world dataset.

Figures (6)

• Figure 1: An example of an input simulated psf dataset with defocus $Z_4$ as the bias mode providing the phase-diversity. a), b), and c) show simulated images of the PSF at different focal planes when a random set of Zernike modes, as presented in d), are applied. e) shows the ground truth psf without any aberration.
• Figure 2: An example of an input simulated extended 2D sample dataset with defocus $Z_4$ as the bias mode providing the phase-diversity. a), b), and c) show simulated images of the 2D sample at different focal planes when a random set of Zernike modes, as presented in d), are applied. e) shows the ground truth 2D sample without any aberration.
• Figure 3: Overview of framework: The ResNet50 is trained to predict the Zernike coefficients from $n_z$ phase-diversity images captured at different planes ($n_z$ not more than three in this study). The predicted Zernike coefficients are used to correct the aberration on the image.
• Figure 4: Subset of results obtained on the simulated psf dataset. From the left to right columns are the ground truth images, the aberrated images and the corrected images after Zernike prediction. In this simulated experiment, the corrected image is calculated from the residual aberration (Ground truth Zernike values minus Predicted Zernikes) re-applied to the ground truth image.
• Figure 5: Iterative Zernike coefficient prediction on the simulated psf dataset. From the left to right columns are the ground truth images, the aberrated images and the corrected images after Zernike prediction at 1$^{st}$, 2$^{nd}$ and 3$^{rd}$ iterations. At the 1$^{st}$ iteration, the corrected image is calculated from the residual aberration (Ground truth Zernike values minus Predicted Zernikes) re-applied to the ground truth image. At each subsequent iteration, the network predicts the aberration remaining in the previous corrected image and the calculated residual aberration is again applied on the ground truth image.