Abstract-This paper analyzes DONE, an online optimization algorithm that iteratively minimizes an unknown function based on costly and noisy measurements. The algorithm maintains a surrogate of the unknown function in the form of a random Fourier expansion (RFE). The surrogate is updated whenever a new measurement is available, and then used to determine the next measurement point. The algorithm is comparable to Bayesian optimization algorithms, but its computational complexity per iteration does not depend on the number of measurements. We derive several theoretical results that provide insight on how the hyper-parameters of the algorithm should be chosen. The algorithm is compared to a Bayesian optimization algorithm for an analytic benchmark problem and three applications, namely, optical coherence tomography, optical beam-forming network tuning, and robot arm control. It is found that the DONE algorithm is significantly faster than Bayesian optimization in the discussed problems, while achieving a similar or better performance.
In this report, which is an international collaboration of OCT, adaptive optics, and control research, we demonstrate the data-based online nonlinear extremum-seeker (DONE) algorithm to guide the image based optimization for wavefront sensorless adaptive optics (WFSL-AO) OCT for in vivo human retinal imaging. The ocular aberrations were corrected using a multi-actuator adaptive lens after linearization of the hysteresis in the piezoelectric actuators. The DONE algorithm succeeded in drastically improving image quality and the OCT signal intensity, up to a factor seven, while achieving a computational time of 1 ms per iteration, making it applicable for many high speed applications. We demonstrate the correction of five aberrations using 70 iterations of the DONE algorithm performed over 2.8 s of continuous volumetric OCT acquisition. Data acquired from an imaging phantom and in vivo from human research volunteers are presented.
Several sensor-less wavefront aberration correction methods that correct nonlinear wavefront aberrations by maximizing the optical coherence tomography (OCT) signal are tested on an OCT setup. A conventional coordinate search method is compared to two model-based optimization methods. The first model-based method takes advantage of the well-known optimization algorithm (NEWUOA) and utilizes a quadratic model. The second model-based method (DONE) is new and utilizes a random multidimensional Fourier-basis expansion. The model-based algorithms achieve lower wavefront errors with up to ten times fewer measurements. Furthermore, the newly proposed DONE method outperforms the NEWUOA method significantly. The DONE algorithm is tested on OCT images and shows a significantly improved image quality.
The transfer function for optical wavefront aberrations in single-mode fiber based optical coherence tomography is determined. The loss in measured OCT signal due to optical wavefront aberrations is quantified using Fresnel propagation and the calculation of overlap integrals. A distinction is made between a model for a mirror and a scattering medium model. The model predictions are validated with measurements on a mirror and a scattering medium obtained with an adaptive optics optical coherence tomography setup. Furthermore, a one-step defocus correction, based on a single A-scan measurement, is derived from the model and verified. Finally, the pseudo-convex structure of the optical coherence tomography transfer function is validated with the convergence of a hill climbing algorithm. The implications of this model for wavefront sensorless aberration correction are discussed.
The quality of fluorescence microscopy images is often impaired by the presence of sample induced optical aberrations. Adaptive optical elements such as deformable mirrors or spatial light modulators can be used to correct aberrations. However, previously reported techniques either require special sample preparation, or time consuming optimization procedures for the correction of static aberrations. This paper reports a technique for optical sectioning fluorescence microscopy capable of correcting dynamic aberrations in any fluorescent sample during the acquisition. This is achieved by implementing adaptive optics in a non conventional confocal microscopy setup, with multiple programmable confocal apertures, in which out of focus light can be separately detected, and used to optimize the correction performance with a sampling frequency an order of magnitude faster than the imaging rate of the system. The paper reports results comparing the correction performances to traditional image optimization algorithms, and demonstrates how the system can compensate for dynamic changes in the aberrations, such as those introduced during a focal stack acquisition though a thick sample.
In this manuscript, we present a lens setup for large defocus and astigmatism correction. A deformable defocus lens and two rotational cylindrical lenses are used to control the defocus and astigmatism. The setup is calibrated using a simple model that allows the calculation of the lens inputs so that a desired defocus and astigmatism are actuated on the eye. The setup is tested by determining the feedforward prediction error, imaging a resolution target, and removing introduced aberrations.
Abstract:In scanning microscopy and optical coherence tomography, aberrations of the wavefront cause a loss in intensity and resolution. Intensity and resolution are quantified using Fresnel propagation, Fraunhofer diffraction, and the calculation of overlap integrals. IntroductionHigh resolution optical imaging in biomedicine is of paramount importance in the study of biological processes and in medical diagnosis. Scanning optical microscopy and optical coherence tomography are two high resolution optical imaging techniques that are based on point scanning of an optical beam over a sample. A scanning optical microscope, such as a confocal microscope, is a sequential imaging system which scans an optical beam over the sample to obtain a full image of the sample. In theory, a diffraction-limited spot is used for scanning.Optical aberrations, either in tissue or in the imaging system, can significantly decrease the spatial resolution and imaging depth. Adaptive optics (AO) can improve the performance of such systems through correction of the wavefront [1]. Thorough knowledge of the effect of aberrations on the system performance can improve the performance of AO through more efficient aberration correction and/or the development of accurate image quality metrics.Here we model the effect of system aberrations in fiber-based scanning optical microscopes to identify their influence on the measured intensity and spatial resolution. The influence of aberrations on the intensity is calculated using the back coupling efficiency of light from a single mode fiber (SMF) to a mirror reflector. The RMS radius of the intensity distribution in the focal plane quantifies the image spatial resolution. Good agreement is observed between calculations and analytical theory. For some aberrations a maximum in the intensity is not a sufficient criterion for optimal system performance.
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