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.