Applications of algorithmic differentiation to phase retrieval algorithms

Jurling, Alden S.; Fienup, James R.

doi:10.1364/josaa.31.001348

Cited by 107 publications

(66 citation statements)

References 8 publications

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“…Alternatively, we can also frame phase retrieval as a nonlinear minimization problem, where we minimize an error metric using a gradient-based approach. The gradient-based approach is flexible and can include in the forward model a large variety of the physical phenomena related to the probing light (such as partial coherence [17], source fluctuations [18], and errors in positions [19,20]), or the detection process (such as the measurement noise [21,22] and the finite size of the pixel [23]). As such, this method has been the focus of much recent literature, leading to the development of steepest descent methods [16,24,25], conjugate gradient methods [4,16,26], Gauss-Newton methods [27], and quasi-Newton methods [28].…”

Section: Introductionmentioning

confidence: 99%

Using automatic differentiation as a general framework for ptychographic reconstruction

Kandel¹,

Maddali²,

Allain³

et al. 2019

Opt. Express

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Coherent diffraction imaging methods enable imaging beyond lens-imposed resolution limits. In these methods, the object can be recovered by minimizing an error metric that quantifies the difference between diffraction patterns as observed, and those calculated from a present guess of the object. Efficient minimization methods require analytical calculation of the derivatives of the error metric, which is not always straightforward. This limits our ability to explore variations of basic imaging approaches. In this paper, we propose to substitute analytical derivative expressions with the automatic differentiation method, whereby we can achieve object reconstruction by specifying only the physics-based experimental forward model. We demonstrate the generality of the proposed method through straightforward object reconstruction for a variety of complex ptychographic experimental models.

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Section: Introductionmentioning

confidence: 99%

Using automatic differentiation as a general framework for ptychographic reconstruction

Kandel¹,

Maddali²,

Allain³

et al. 2019

Opt. Express

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show abstract

“…The pupil electric field, though, cannot be directly measured. It is typically reconstructed from multiple focused and defocused images using phase retrieval algorithms [21][22][23][24] . However, all the phase retrieval algorithms assume a certain light propagation model, so they do not have the ability to diagnose any errors from an incorrect optical layout prescription.…”

Section: Model Calibrationmentioning

confidence: 99%

Identification and adaptive control of a high-contrast focal plane wavefront correction system

Sun

Kasdin

Vanderbei

2018

J. Astron. Telesc. Instrum. Syst.

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All coronagraphic instruments for exoplanet high-contrast imaging need wavefront correction systems to reject optical aberrations and create sufficiently dark holes. Since the most efficient wavefront correction algorithms (controllers and estimators) are usually model-based, the modeling accuracy of the system influences the ultimate wavefront correction performance. Currently, wavefront correction systems are typically approximated as linear systems using Fourier optics. However, the Fourier optics model is usually biased due to inaccuracies in the layout measurements, the imperfect diagnoses of inherent optical aberrations, and a lack of knowledge of the deformable mirrors (actuator gains and influence functions). Moreover, the telescope optical system varies over time because of instrument instabilities and environmental effects. In this paper, we present an expectation-maximization (E-M) approach for identifying and real-time adapting the linear telescope model from data. By iterating between the E-step (a Kalman filter and a Rauch smoother) and the M-step (analytical or gradient-based optimization), the algorithm is able to recover the system even if the model depends on the electric fields, which are unmeasurable hidden variables. Simulations and experiments in Princeton's High Contrast Imaging Lab demonstrate that this algorithm improves the model accuracy and increases the efficiency and speed of the wavefront correction.

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“…By breaking up the gradient computation into small pieces, it becomes much less daunting to compute analytic gradients for complicated forward models. The idea of algorithmic differentiation has recently been made more accessible for image reconstruction and phase retrieval by Jurling and Fienup [25]. We have followed their formulation of algorithmic differentiation in order to compute the required gradients.…”

Section: Nonlinear Optimizationmentioning

confidence: 99%

Rotation and translation registration of bandlimited interferometric images using a chirp z-transform

2016

Self Cite

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Image reconstruction algorithms for wide-field spatio-spectral interferometry require knowledge of registration parameters associated with low-resolution image measurements at various baseline orientations, such that the images can be registered to within the fine resolution of the final desired image. We have developed an image registration procedure that combines a nonlinear optimization algorithm with the sub-pixel precision of chirp z-transform resampling, particularly for rotation and translation, of bandlimited images with non-radially symmetric aberrations. We show the accuracy of this image registration technique on simulated images that have a complexity comparable to scenes observed experimentally with NASA's wide-field imaging interferometry testbed. Registration to within a tenth of a pixel for translation and within three arcminutes for rotation is demonstrated at the largest simulated noise levels.

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Applications of algorithmic differentiation to phase retrieval algorithms

Cited by 107 publications

References 8 publications

Using automatic differentiation as a general framework for ptychographic reconstruction

Using automatic differentiation as a general framework for ptychographic reconstruction

Identification and adaptive control of a high-contrast focal plane wavefront correction system

Rotation and translation registration of bandlimited interferometric images using a chirp z-transform

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