The principal limitation in many areas of astronomy, especially for directly imaging exoplanets, arises from instability in the point spread function (PSF) delivered by the telescope and instrument. To understand the transfer function, it is often necessary to infer a set of optical aberrations given only the intensity distribution on the sensor—the problem of phase retrieval. This can be important for post-processing of existing data, or for the design of optical phase masks to engineer PSFs optimized to achieve high-contrast, angular resolution, or astrometric stability. By exploiting newly efficient and flexible technology for automatic differentiation, which in recent years has undergone rapid development driven by machine learning, we can perform both phase retrieval and design in a way that is systematic, user-friendly, fast, and effective. By using modern gradient descent techniques, this converges efficiently and is easily extended to incorporate constraints and regularization. We illustrate the wide-ranging potential for this approach using our new package, Morphine. Challenging applications performed with this code include precise phase retrieval for both discrete and continuous phase distributions, even where information has been censored such as heavily saturated sensor data. We also show that the same algorithms can optimize continuous or binary phase masks that are competitive with existing best solutions for two example problems: an apodizing phase plate coronagraph for exoplanet direct imaging, and a diffractive pupil for narrow-angle astrometry. The Morphine source code and examples are available open-source, with an interface similar to the popular physical optics package Poppy.

中文翻译：

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具有自动微分的相位检索和设计：教程

许多天文学领域的主要限制，特别是对于直接成像系外行星，源于望远镜和仪器提供的点扩散函数 (PSF) 的不稳定性。为了理解传递函数，通常需要仅根据传感器上的强度分布来推断一组光学像差——相位恢复问题。这对于现有数据的后处理或设计光学相位掩模以设计优化的 PSF 以实现高对比度、角分辨率或天体测量稳定性非常重要。通过开发新的高效灵活的自动微分技术，近年来在机器学习的驱动下经历了快速发展，我们可以以系统，用户友好，快速和有效的方式进行相位检索和设计。通过使用现代梯度下降技术，这可以有效地收敛，并且很容易扩展到包含约束和正则化。我们使用我们的新软件包吗啡来说明这种方法的广泛潜力。使用此代码执行的具有挑战性的应用包括离散和连续相位分布的精确相位检索，即使信息已被审查，例如高度饱和的传感器数据。我们还表明，对于两个示例问题，相同的算法可以优化与现有最佳解决方案竞争的连续或二元相位掩码：用于系外行星直接成像的变迹相位板日冕仪，以及用于窄角天体测量的衍射光瞳。Morphine 源代码和示例是开源的，其界面类似于流行的物理光学包 Poppy。