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Adaptive X-ray mirrors are being adopted on high-coherent-flux synchrotron and X-ray free-electron laser beamlines where dynamic phase control and aberration compensation are necessary to preserve wavefront quality from source to sample, yet challenging to achieve. Additional difficulties arise from the inability to continuously probe the wavefront in this context, which demands methods of control that require little to no feedback. In this work, a data-driven approach to the control of adaptive X-ray optics with piezo-bimorph actuators is demonstrated. This approach approximates the non-linear system dynamics with a discrete-time model using random mirror shapes and interferometric measurements as training data. For mirrors of this type, prior states and voltage inputs affect the shape-change trajectory, and therefore must be included in the model. Without the need for assumed physical models of the mirror's behavior, the generality of the neural network structure accommodates drift, creep and hysteresis, and enables a control algorithm that achieves shape control and stability below 2 nm RMS. Using a prototype mirror and ex situ metrology, it is shown that the accuracy of our trained model enables open-loop shape control across a diverse set of states and that the control algorithm achieves shape error magnitudes that fall within diffraction-limited performance.

We present a computational method for field-varying aberration recovery in optical systems by imaging a weak (index-matched) diffuser. Using multiple images acquired under plane wave illumination at distinct angles, the aberrations of the imaging system can be uniquely determined up to a sign. Our method is based on a statistical model for image formation that relates the spectrum of the speckled intensity image to the local aberrations at different locations in the field-of-view. The diffuser is treated as a wide-sense stationary scattering object, eliminating the need for precise knowledge of its surface shape. We validate our method both numerically and experimentally, showing that this relatively simple algorithmic calibration method can be reliably used to recover system aberrations quantitatively.

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Fourier ptychographic microscopy is a computational imaging technique that provides quantitative phase information and high resolution over a large field-of-view. Although the technique presents numerous advantages over conventional microscopy, model mismatch due to unknown optical aberrations can significantly limit reconstruction quality. A practical way of correcting for aberrations without additional data capture is through algorithmic self-calibration, in which a pupil recovery step is embedded into the reconstruction algorithm. However, software-only aberration correction is limited in accuracy. Here, we evaluate the merits of implementing a simple, dedicated calibration procedure for applications requiring high accuracy. In simulations, we find that for a target sample reconstruction error, we can image without any aberration corrections only up to a maximum aberration magnitude of λ/40. When we use algorithmic self-calibration, we can tolerate an aberration magnitude up to λ/10 and with our proposed diffuser calibration technique, this working range is extended further to λ/3. Hence, one can trade off complexity for accuracy by using a separate calibration process, which is particularly useful for larger aberrations.