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The computational correction of defocus and aberrations in optical coherence tomography (OCT) is a promising approach to achieve high-resolution imaging with deep imaging depth without hardware costs. However, the techniques are not well understood due to the lack of an accurate theoretical model and investigation tools. The image formation theory of optical coherence tomography (OCT) with optical aberrations is formulated. Based on the theory, a numerical simulation method is developed and computational refocusing (CR) and aberration correction (CAC) methods are designed. The newly designed CAC method is applied to the OCT images of a microparticle phantom and in vivo human retina. The results show that the CAC method can correct the optical aberrations and improve the image quality. The theoretical model-based approach is a powerful tool for understanding the OCT imaging properties and designing new processing methods.

High-numerical-aperture optical coherence tomography (OCT) enables sub-cellular imaging but faces a trade-off between lateral resolution and depth of focus. Computational refocusing can correct defocus in Fourier-domain OCT, yet its limitations remain unaddressed theoretically. We model the pupil-based lateral imaging process to analyze defocus and the constraints of computational refocusing in point-scanning OCT and spatially-coherent full-field OCT (FFOCT). The maximum correctable defocus (MCD) is primarily limited by confocality in point-scanning OCT, while spatially-coherent FFOCT has no such constraint, achieving virtually infinite MCD. This makes spatially-coherent FFOCT particularly suitable for optical coherence microscopy.

We construct an image formation theory that covers the majority of optical microscopy techniques that use diverse coherent or incoherent light-matter interactions. The theories of individual microscopy methods could not previously be connected with other systems because of the absence of a common theoretical framework. Using the general principles of quantum physics and applying a four-dimensional representation, we unify the image formation theories of optical systems ranging from classical microscopy to cutting-edge instruments into a single framework in which light is replaced with quantum fields and the interactions are represented using double-sided Feynman diagrams. Our universal methodology requires a four-dimensional aperture that enables sufficient understanding of the associations between the different imaging types and interprets image formation appropriately for all systems, including optical coherence tomography.

We construct an accurate imaging theory for optical coherence tomography/microscopy (OCT/OCM) without approximations to calculate precise optical resolution and imaging characteristics. Our theory represents a broadband light source using a four-dimensional (4D) pupil function with a dimension for light frequency (reciprocal of wavelength) as the fourth axis in 4D frequency space. Consequently, 4D space-time representation is required in real space, connected to the 4D frequency space by a 4D Fourier transform. Our theory provides insight into a peculiar image formation in OCT/OCM, particularly when an apparatus has a high numerical aperture (NA) optical system to handle aberrations and dispersions simultaneously.

Dynamic optical coherence tomography (DOCT) statistically analyzes fluctuations in time-sequential OCT signals, enabling label-free and three-dimensional visualization of intratissue and intracellular activities. Current DOCT methods, such as logarithmic intensity variance (LIV) and OCT correlation decay speed (OCDS) have several limitations.Namely, the DOCT values and intratissue motions are not directly related, and hence DOCT values are not interpretable in the context of the tissue motility. We introduce a new DOCT algorithm that provides more direct interpretation of DOCT in the contexts of dynamic scatterer ratio and scatterer speed in the tissue.The detailed properties of the new and conventional DOCT methods are investigated by numerical simulations, and the experimental validation with in vitro and ex vivo samples demonstrates the feasibility of the new method.

We demonstrate a method that reduces the noise caused by multi-scattering (MS) photons in an \invivo optical coherence tomography image. This method combines a specially designed image acquisition (i.e., optical coherence tomography scan) scheme and subsequent complex signal processing. For the acquisition, multiple cross-sectional images (frames) are sequentially acquired while the depth position of the focus is altered for each frame by an electrically tunable lens. In the signal processing, the frames are numerically defocus-corrected, and complex averaged. Because of the inconsistency in the MS-photon trajectories among the different electrically tunable lens-induced defocus, this averaging reduces the MS signal. This method was validated using a scattering phantom and in vivo unanesthetized small fish samples, and was found to reduce MS noise even for unanesthetized in vivo measurement.

Wedemonstratedeep-learningneuralnetwork(NN)-baseddynamicopticalcoherence tomography (DOCT), which generates high-quality logarithmic-intensity-variance (LIV) DOCT images from only four OCT frames. The NN model is trained for tumor spheroid samples using a customized loss function: the weighted mean absolute error. This loss function enables highly accurate LIV image generation. The fidelity of the generated LIV images to the ground truth LIV images generated using 32 OCT frames is examined via subjective image observation and statistical analysis of image-based metrics. Fast volumetric DOCT imaging with an acquisition time of 6.55 s/volume is demonstrated using this NN-based method.

We demonstrate a deep-learning-based scatterer density estimator (SDE) that processes local speckle patterns of optical coherence tomography (OCT) images and estimates the scatterer density behind each speckle pattern. The SDE is trained using large quantities of numerically simulated OCT images and their associated scatterer densities. The numerical simulation uses a noise model that incorporates the spatial properties of three types of noise, i.e., shot noise, relative-intensity noise, and non-optical noise. The SDE's performance was evaluated numerically and experimentally using two types of scattering phantom and in vitro tumor spheroids. The results confirmed that the SDE estimates scatterer densities accurately. The estimation accuracy improved significantly when compared with our previous deep-learning-based SDE, which was trained using numerical speckle patterns generated from a noise model that did not account for the spatial properties of noise.

Polarization-sensitive optical coherence tomography (PS-OCT) is a promising biomedical imaging tool for differentiation of various tissue properties. However, the presence of multiple-scattering (MS) signals can degrade the quantitative polarization measurement accuracy. We demonstrate a method to reduce MS signals and increase the measurement accuracy of Jones matrix PS-OCT. This method suppresses MS signals by averaging of multiple Jones matrix volumes measured using different focal positions. The MS signals are decorrelated among the volumes by focus position modulation and are thus reduced by averaging. However, the single scattering signals are kept consistent among the focus-modulated volumes by computational refocusing. We validated the proposed method using a scattering phantom and a postmortem medaka fish. The results showed reduced artifacts in birefringence and degree-of-polarization uniformity measurements, particularly in deeper regions in the samples. This method offers a practical solution to mitigate MS-induced artifacts in PS-OCT imaging and improves quantitative polarization measurement accuracy.

A new formulation of lateral imaging process of point-scanning optical coherence tomography (OCT) and a new differential contrast method designed by using this formulation are presented. The formulation is based on a mathematical sample model called the dispersed scatterer model (DSM), in which the sample is represented as a material with a spatially slowly varying refractive index and randomly distributed scatterers embedded in the material. It is shown that the formulation represents a meaningful OCT image and speckle as two independent mathematical quantities. The new differential contrast method is based on complex signal processing of OCT images, and the physical and numerical imaging processes of this method are jointly formulated using the same theoretical strategy as in the case of OCT. The formula shows that the method provides a spatially differential image of the sample structure. This differential imaging method is validated by measuring in vivo and in vitro samples.

An organoid is a three-dimensional (3D) in vitro cell culture emulating human organs. We applied 3D dynamic optical coherence tomography (DOCT) to visualize the intratissue and intracellular activities of human induced pluripotent stem cells (hiPSCs)-derived alveolar organoids in normal and fibrosis models. 3D DOCT data were acquired with an 840-nm spectral domain optical coherence tomography with axial and lateral resolutions of 3.8 {\mu}m (in tissue) and 4.9 {\mu}m, respectively. The DOCT images were obtained by the logarithmic-intensity-variance (LIV) algorithm, which is sensitive to the signal fluctuation magnitude. The LIV images revealed cystic structures surrounded by high-LIV borders and mesh-like structures with low LIV. The former may be alveoli with a highly dynamics epithelium, while the latter may be fibroblasts. The LIV images also demonstrated the abnormal repair of the alveolar epithelium.

This short textbook was written for someone who newly start studying, doing research, or development about optical coherence tomography (OCT) or using OCT. The first chapter summarizes the concept and the history of OCT. In the second chapter, the technologies of OCT are summarized, which includes the mathematical principle, hardware implementation, the instructions for designs such as interferometer and wavelength selections, and theories of resolutions and sensitivity. In the third chapter, some examples of ophthalmic applications of OCT are described. In the last chapter, instructions for next learning steps are given.

Jones-matrix optical coherence tomography (JM-OCT) is an extension of OCT that provides multiple types of optical contrasts of biological and clinical samples. JM-OCT measures the spatial distribution of the Jones matrix of the sample and also its time sequence. All contrasts (i.e., multi-contrast OCT images) are then computed from the Jones matrix. The contrasts obtained from the Jones matrix include the conventional and polarization-insensitive OCT intensity, cumulative and local phase retardation (birefringence), degree-of-polarization uniformity quantifying the polarization randomness of the sample, signal attenuation coefficient, sample scatterer density, Doppler OCT, OCT angiography, and dynamic OCT. JM-OCT is a generalized version of OCT because it measures the generalized form of the sample information; i.e., the Jones matrix sequence. This review summarizes the basic conception, mathematical principle, hardware implementation, signal and image processing, and biological and clinical applications of JM-OCT. Advanced technical topics, including JM-OCT-specific noise correction and quantity estimation and JM-OCT's self-calibration nature, are also described.

Degree of polarization uniformity (DOPU) imaging obtained by polarization-sensitive optical coherence tomography (PS-OCT) has the potential to provide biomarkers for retinal diseases. It highlights abnormalities in the retinal pigment epithelium that are not always clear in the OCT intensity images. However, a PS-OCT system is more complicated than conventional OCT. We present a neural-network-based approach to estimate the DOPU from standard OCT images. DOPU images were used to train a neural network to synthesize the DOPU from single-polarization-component OCT intensity images. DOPU images were then synthesized by the neural network, and the clinical findings from ground truth DOPU and synthesized DOPU were compared. There is a good agreement in the findings for RPE abnormalities: recall was 0.869 and precision was 0.920 for 20 cases with retinal diseases. In five cases of healthy volunteers, no abnormalities were found in either the synthesized or ground truth DOPU images. The proposed neural-network-based DOPU synthesis method demonstrates the potential of extending the features of retinal non-PS OCT.

We demonstrate label-free drug response evaluations of human breast (MCF-7) and colon (HT-29) cancer spheroids via dynamic optical coherence tomography (OCT). The MCF-7 and HT-29 spheroids were treated with paclitaxel (PTX, or Taxol) and the active metabolite of irinotecan (SN-38), respectively. The drugs were applied using 0 (control), 0.1, 1, and 10 uM concentrations with treatment times of 1, 3, and 6 days. The samples were scanned using a repeated raster scan protocol and two dynamic OCT algorithms, logarithmic intensity variance (LIV) and late OCT correlation decay speed (OCDSl) analyses, were applied to visualize the tissue and cellular dynamics. Different drug response patterns of the two spheroid types were visualized clearly and analyzed quantitatively by LIV and OCDSl imaging. For both spheroid types, structural corruptions and reduction of LIV and OCDSl were observed. These results may indicate different mechanisms of the drug action. The results suggest that dynamic OCT can be used to highlight drug response patterns and perform anti-cancer drug testing.

This treaties aims to introduce a speculative framework to comprehend modern metrology. In a classical sense, measurement measures physically existing quantities, such as length, mass, and time. By contrast, modern measurement measures a wide spectrum of objects, for example, an imaging biomarker, which is a user-defined pattern. Artificial-intelligence (AI)-based diagnosis is another example. If we regard an optical coherence tomography (OCT) device equipped with diagnostic AI as a comprehensive "measurement system," the object being measured is a "disease," which is not a physical quantity but a concept. To comprehend the wide range of modern measurements, we introduce a speculative, i.e., philosophical and theoretical, model called the "epistemological-metrology model." In this model, we describe the act of measurement as cascading encoding-and-decoding processes. In the encoding processes, three types of objects-to-be measured are considered, which include substance, existence, and concept. Then we classify acts of measurement into "sensing," "understanding," and "reasoning," which measure the substance, existence, and concept, respectively. We note that the measurements in the understanding and reasoning classes are constructive. Namely, they proactively define the quantity-to-be-measured by the measurement modalities themselves. A speculative method to warrant the relevance of such constructive measurements is presented. We investigate several modern OCT-related measurements, including AI-based diagnosis, types of polarization sensitive OCT, and attenuation coefficient imaging, using our theoretical framework.

Label-free metabolic imaging of non-alcoholic fatty liver disease (NAFLD) mouse liver is demonstrated ex vivo by dynamic optical coherence tomography (OCT). The NAFLD mouse is a methionine choline-deficient (MCD)-diet model, and two mice fed MCD diet for 1 and 2 weeks are involved in addition to a normal-diet mouse. The dynamic OCT is based on repeating raster scan and logarithmic intensity variance (LIV) analysis which enables volumetric metabolic imaging with a standard-speed (50,000 A-lines/s) OCT system. Metabolic domains associated with lipid droplet accumulation and inflammation are clearly visualized three-dimensionally. Particularly, the normal-diet liver exhibits highly metabolic vessel-like structures of peri-vascular hepatic zones. The 1-week MCD-diet liver shows ring-shaped highly metabolic structures formed with lipid droplets. The 2-week MCD-diet liver exhibits fragmented vessel-like structures associated with inflammation. These results imply that volumetric LIV imaging is useful for visualizing and assessing NAFLD abnormalities.