Determination and correction of aberrations in full field optical coherence tomography using phase gradient autofocus by maximizing the likelihood function

K-Space Approach in Optical Coherence Tomography: Rigorous Digital Transformation of Arbitrary-Shape Beams, Aberration Elimination and Super-Refocusing beyond Conventional Phase Correction Procedures

For the most popular method of scan formation in Optical Coherence Tomography (OCT) based on plane-parallel scanning of the illuminating beam, we present a compact but rigorous K-space description in which the spectral representation is used to describe both the axial and lateral structure of the illuminating/received OCT signals. Along with the majority of descriptions of OCT-image formation, the discussed approach relies on the basic principle of OCT operation, in which ballistic backscattering of the illuminating light is assumed. This single-scattering assumption is the main limitation, whereas in other aspects, the presented approach is rather general. In particular, it is applicable to arbitrary beam shapes without the need for paraxial approximation or the assumption of Gaussian beams. The main result of this study is the use of the proposed K-space description to analytically derive a filtering function that allows one to digitally transform the initial 3D set of complex-valued OCT data into a desired (target) dataset of a rather general form. An essential feature of the proposed filtering procedures is the utilization of both phase and amplitude transformations, unlike conventionally discussed phase-only transformations. To illustrate the efficiency and generality of the proposed filtering function, the latter is applied to the mutual transformation of non-Gaussian beams and to the digital elimination of arbitrary aberrations at the illuminating/receiving aperture. As another example, in addition to the conventionally discussed digital refocusing enabling depth-independent lateral resolution the same as in the physical focus, we use the derived filtering function to perform digital "super-refocusing." The latter does not yet overcome the diffraction limit but readily enables lateral resolution several times better than in the initial physical focus.

Amplitude Zone Plate in Adaptive Optics: Proposal of the Principle

One of the main elements in hardware-based adaptive optics systems is a deformable mirror. There is quite a large number of such mirrors based on different principles and exhibiting varying performance. They constitute a significant portion of the cost of the final optical devices. In this study, we consider the possibility of replacing an adaptive mirror with the adaptive amplitude Fresnel zone plate, implemented using a digital light-processing matrix. Since such matrices are widely used in mass industry products (light projectors), their costs in large batches are 1–2 orders of magnitude lower than the cost of inexpensive deformable mirrors. Numerical modeling for scanning an optical coherence tomography system with adaptive optics is presented. It is shown that wavefront distortions with high spatial frequencies and large amplitudes can be corrected using an amplitude Fresnel zone plate. The results are compared with piezoelectric and microelectromechanical system mirrors.

Simulating scan formation in multimodal optical coherence tomography: angular-spectrum formulation based on ballistic scattering of arbitrary-form beams

We present a computationally highly efficient full-wave spectral model of OCT-scan formation with the following features: allowance of arbitrary phase-amplitude profile of illuminating beams; absence of paraxial approximation; utilization of broadly used approximation of ballistic scattering by discrete scatterers without limitations on their density/location and scattering strength. The model can easily incorporate the wave decay, dispersion, measurement noises with given signal-to-noise ratios and arbitrary inter-scan displacements of scatterers. We illustrate several of such abilities, including comparative simulations of OCT-scans for Bessel versus Gaussian beams, presence of arbitrary aberrations at the tissue boundary and various scatterer motions. The model flexibility and computational efficiency allow one to accurately study various properties of OCT-scans for developing new methods of their processing in various biomedical applications.

Digital adaptive optics based on digital lateral shearing of the computed pupil field for point scanning retinal swept source OCT

A novel non-iterative digital adaptive optics technique is presented in which the wavefront error is calculated using the phase difference between the pupil field and its digital copies translated by a pixel along the horizontal and vertical direction in the pupil plane. This method provides slope data per pixel, thus can generate > 50k local slope data samples for a circular pupil of diameter 256 pixels with high accuracy and dynamic range. It offers more than 12x faster computational speed in comparison to the sub-aperture based digital adaptive optics method. Furthermore, it is independent of any system parameters, the light distribution in the pupil plane, or the intensity of the image. The technique is useful in applications such as interferometric or digital holography based microscopy, metrology, and as digital wavefront sensor in adaptive optics, where focusing of light in the sample is involved that creates a guide star or where the sample itself exhibits guide star-like structures. This technique is implemented in a point scanning swept-source OCT at 1060 nm, and a large wavefront error with a peak to valley of 20 radians and root mean square error of 0.71 waves is detected and corrected in case of a micro-beads phantom sample. Also, human photoreceptor images are recovered from aberrated retinal OCT volumes acquired at eccentricities of 2 and 2.5 degrees from the fovea in vivo.