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.

翻译：通过具有高数值孔径的显微镜目标对光进行控制是选择基因学、适应性光学或激光处理等应用中常见的一项要求。在这些条件下,光传播,包括极化效应,可以用Debye-Wolf difrediction 集成体描述。在这里,我们利用不同的优化和机器学习,以便有效地优化Debye-Wolf 集成的这种应用。对于光成形,我们显示这种优化方法适合于在两光显微镜中设计任意的三维点扩散功能。对于基于不同模型的适应性光学(DAO),开发的方法可以找到带有内在图像特征的畸变校正,例如用基因编码的钙指标标定的神经,而不需要导星。使用计算模型,我们进一步讨论了空间频率和畸变幅度的范围,可以通过这一方法加以纠正。