Differentiable model-based adaptive optics with transmitted and reflected light

Abstract

Aberrations limit optical systems in many situations, for example when imaging in biological tissue. Machine learning offers novel ways to improve imaging under such conditions by learning inverse models of aberrations. Learning requires datasets that cover a wide range of possible aberrations, which however becomes limiting for more strongly scattering samples, and does not take advantage of prior information about the imaging process. Here, we show that combining model-based adaptive optics with the optimization techniques of machine learning frameworks can find aberration corrections with a small number of measurements. Corrections are determined in a transmission configuration through a single aberrating layer and in a reflection configuration through two different layers at the same time. Additionally, corrections are not limited by a predetermined model of aberrations (such as combinations of Zernike modes). Focusing in transmission can be achieved based only on reflected light, compatible with an epidetection imaging configuration.

Differentiable model-based adaptive optics for two-photon microscopy

“…Sample aberrations introduce an unknown phase function into the optical setup. To mirror this situation computationally, a phase surface is added as a set of free parameters to the model [1]. This unknown phase surface needs to be adjusted through optimization in such a way that it describes the introduced sample aberration.…”

“…More recently, the development of machine learning frameworks such as Tensorflow has enabled optimizing computationally demanding models in many areas of physics and engineering (for example [14,15,16,17,18,19,20,21]) and also in optical imaging [18,1,22]. This approach can be applied for adaptive optics [1].…”

“…More recently, the development of machine learning frameworks such as Tensorflow has enabled optimizing computationally demanding models in many areas of physics and engineering (for example [14,15,16,17,18,19,20,21]) and also in optical imaging [18,1,22]. This approach can be applied for adaptive optics [1]. Using a differentiable model of the optical system, focusing in transmission through a single aberrating layer as well as in a reflection, epidetection configuration through two aberrating layers was achieved [1].…”

“…This approach can be applied for adaptive optics [1]. Using a differentiable model of the optical system, focusing in transmission through a single aberrating layer as well as in a reflection, epidetection configuration through two aberrating layers was achieved [1]. Here, we extend this differentiable model-based adaptive optics method to scanning two-photon microscopy with a high numerical aperture objective as used for in vivo imaging in brain tissue.…”

“…Model-based approaches for adaptive optics take advantage of a computational model of the optical setup. Such models can be combined with the optimization techniques of machine learning frameworks to find aberration corrections, as was demonstrated for focusing a laser beam through aberrations onto a camera [1]. Here, we extend this approach to two-photon scanning microscopy.…”