Differentiable optimization of the Debye-Wolf integral for light shaping and adaptive optics in two-photon microscopy

Control of light through a microscope objective with a high numerical aperture is a common requirement in applications such as optogenetics, adaptive optics, or laser processing. Light propagation, including polarization effects, can be described under these conditions using the Debye-Wolf diffraction integral. Here, we take advantage of differentiable optimization and machine learning for efficiently optimizing the Debye-Wolf integral for such applications. For light shaping we show that this optimization approach is suitable for engineering arbitrary three-dimensional point spread functions in a two-photon microscope. For differentiable model-based adaptive optics (DAO), the developed method can find aberration corrections with intrinsic image features, for example neurons labeled with genetically encoded calcium indicators, without requiring guide stars. Using computational modeling we further discuss the range of spatial frequencies and magnitudes of aberrations which can be corrected with this approach.

Differentiable model-based adaptive optics for two-photon microscopy

Aberrations limit scanning fluorescence microscopy when imaging in scattering materials such as biological 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 [arXiv:2007.13400]. Here, we extend this approach to two-photon scanning microscopy. The developed sensorless technique finds corrections for aberrations in scattering samples and will be useful for a range of imaging application, for example in brain tissue.

Differentiable model-based adaptive optics with transmitted and reflected light

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.

Adaptive optics with reflected light and deep neural networks

Light scattering and aberrations limit optical microscopy in biological tissue, which motivates the development of adaptive optics techniques. Here, we develop a method for adaptive optics with reflected light and deep neural networks compatible with an epi-detection configuration. Large datasets of sample aberrations which consist of excitation and detection path aberrations as well as the corresponding reflected focus images are generated. These datasets are used for training deep neural networks. After training, these networks can disentangle and independently correct excitation and detection aberrations based on reflected light images recorded from scattering samples. A similar deep learning approach is also demonstrated with scattering guide stars. The predicted aberration corrections are validated using two photon imaging.