Optimization-based adaptive optics for optical coherence tomography

Optical coherence tomography (OCT) is a technique for non-invasive imaging based on low coherence interferometry. Its main application is found in ophthalmology, where it is used for 3D in vivo imaging of the cornea and the retina. OCT has evolved over the past decade as one of the most important ancillary tests in ophthalmic practice, providing great diagnostic value for disease screening and monitoring. In retinal OCT imaging, the lateral resolution is not determined by the pupil size, but instead it is limited by optical wavefront aberrations of the cornea and lens. These aberrations reduce the OCT image resolution and lower the signal to noise ratio. To obtain high quality OCT images the optical aberrations can be removed using adaptive optics (AO).

In general, AO consists of an adaptive optical element and a wavefront sensor. The adaptive element, such as a deformable mirror, is used to reshape the wavefront and remove the undesired aberrations. The wavefront sensor measures the aberrations by reconstructing the phase of the wavefront, which is used to determine the correction on the wavefront applied by the deformable mirror. However, the use of a wavefront sensor has some disadvantages. It requires light being directed out of the imaging path onto the wavefront sensor. This leads to a loss of signal in the imaging path and can result in non-common optical path errors in the aberrations estimation procedure. Additionally, the use of a deformable mirror and a wavefront sensor leads to a bulky and expensive OCT setup.

The work presented in this thesis has the goal of reducing the cost and bulkiness of an AO-OCT system. First, we investigate the influence of optical wavefront aberrations to the OCT signal strength. The establishment of the relation between aberrations and the OCT signal strength is key to estimating and correcting the aberrations based on single OCT scans. By using Fresnel optical wave propagation and determining the fiber coupling efficiency, we find that the OCT transfer function, i.e. the function that expresses the relation between the aberrations and OCT signal strength, is quasi-convex. We determine both analytically and experimentally the transfer function for both reflective and scattering media, such as a mirror and Scotch tape sample. Additionally, if the OCT system and its optical properties are well-known we demonstrate a method to correct a defocus aberration in one step.

Second, we use the OCT transfer function to develop and determine an efficient wavefront sensorless (WFSL) AO optimization procedure. WFSL-AO methods aim to correct the aberrations without using a wavefront sensor, but instead base the determination of the wavefront on the imaging signal itself. This eliminates the use of the wavefront sensor, its extra cost and its disadvantages from an AO-OCT setup. To keep up with the OCT imaging rate, which is of the order of several tens of kHz, the algorithm has to be computationally efficient. Furthermore, there are no analytic derivatives available for the optimization and the OCT signal is very noisy. Finally, the derivative-free optimization algorithm also has to be able to determine the aberrations accurately when dealing with a minimum number of noisy measurements. We developed the Data-based Online Nonlinear extremum-seeker (DONE) algorithm. Every iteration, the DONE algorithm updates a surrogate function, which is based on random Fourier expansions (RFE) of the OCT transfer function, with a new OCT signal measurement. The optimum of the RFE surrogate function is then found with a well-known (quasi-Newton) optimization method. We demonstrate the effectiveness of the DONE algorithm compared to other optimization algorithms for WFSL-AO on biological and non-biological samples. We conclude that DONE has a smaller convergence error, while maintaining similar or faster convergence speeds compared to the other algorithms.

Third, we demonstrate a fully functional WFSL-AO OCT setup for retinal imaging. We use a state-of-the-art deformable lens with 18 actuators, rather than a deformable mirror, which leads to a smaller and more integrated WFSL-AO setup. The WFSL-AO OCT setup is successfully used for in vivo retinal OCT imaging and demonstrates that the DONE algorithm can remove the ocular wavefront aberrations with the deformable lens during in vivo OCT imaging. By developing a new algorithm and exploring the options for adaptive components, we have succeeded in retinal WFSL-AO OCT.

In a broader perspective, we show that the DONE algorithm is suitable for other applications than WFSL-AO OCT. We demonstrate that the DONE derivative-free optimization algorithm is robust towards noisy measurements for applications in robotics, microscopy and optical beam forming networks.