Optical coherence tomography (OCT) is one of the most innovative and successfully translated imaging techniques with substantial clinical and economic impacts and acceptance.^1,2 OCT is a non-invasive optical analog to ultrasound (US) with significantly higher resolution ($<1\mu \mathrm{m}$) enabling three- and four-dimensional high-speed (>millions of A-scans/s) imaging with tissue penetration of up to 2 mm, closely matching that of conventional histopathology. The year 2021 marks not only the 30th birthday of OCT (assuming its initiation with the Science paper by Huang et al.³ in 1991) but also the 35th birthday of low-coherence interferometry and optical ranging in biological systems.^4,5 In the last three decades, more than 75,000 OCT related papers have been published (about two thirds in ophthalmology) with continuous yearly increases of published articles.⁶ Breaking through the 1000 publications/year barrier was initiated in 2005/2006 with the introduction of spectral domain OCT (SD OCT). In 2020, the OCT-related scientific output was more than 7800 papers, resulting in nearly one paper every single hour on every single day of the year. Extrapolating this publishing performance, a saturation of yearly publication output at about 9500 can be expected around 2030. After 30 years, it is interesting and important to benchmark this performance with other medical imaging techniques:⁶ multiphoton microscopy (MPM) [including second harmonic generation (SHG) and third harmonic generation (THG)], developed about three decades before OCT,^7,8 has about 50,000 publications so far; photoacoustic imaging (PAI), established in the 1970s,^9,10 has about 15,000 papers; and confocal microscopy, developed in the 1940s,^11,12 has about 145,000. Developed in the 1940s,¹³ US imaging has contributed to about 160,000 papers; positron emission tomography (PET), initiated in the 1970s,^14,15 has about 175,000; computed tomography (CT), developed in the 1930s,¹⁶ has about 750,000; and magnetic resonance imaging (MRI), developed in the late 1940s,¹⁷ has close to 1,000,000 publications. This dominance in publications of radiology and nuclear medicine imaging technologies is also one of the reasons why medical imaging is, in general, associated with MRI, CT, PET, or US. It is important to note, though, that from a medical imaging market perspective, optical imaging technologies dominate with 66% versus 34% for radiology and nuclear medicine imaging technologies. In addition, in the United States alone, about 450,000 physicians use primarily optical imaging techniques; 60,000 use primarily radiologic imaging; and about 130,000 use both.¹⁸

In this paper, we consider the problem of estimating the internal displacement field of an object which is being subjected to a deformation, from optical coherence tomography images before and after compression. For the estimation of the internal displacement field we propose a novel algorithm, which utilizes particular speckle information to enhance the quality of the motion estimation. We present numerical results based on both simulated and experimental data in order to demonstrate the usefulness of our approach, in particular when applied for quantitative elastography, when the material parameters are estimated in a second step based on the internal displacement field.

Optical coherence tomography (OCT) is a widely used imaging technique in the micrometer regime, which gained accelerating interest in medical imaging in the last twenty years. In up-to-date OCT literature, certain simplifying assumptions are made for the reconstructions, but for many applications, a more realistic description of the OCT imaging process is of interest. In mathematical models, for example, the incident angle of light onto the sample is usually neglected or a plane wave description for the light–sample interaction in OCT is used, which ignores almost completely the occurring effects within an OCT measurement process. In this article, we make a first step to a quantitative model by considering the measured intensity as a combination of back-scattered Gaussian beams affected by the system. In contrast to the standard plane wave simplification, the presented model includes system relevant parameters, such as the position of the focus and the spot size of the incident laser beam, which allow a precise prediction of the OCT data. The accuracy of the proposed model—after calibration of all necessary system parameters—is illustrated by simulations and validated by a comparison with experimental data obtained from a 1300 nm swept-source OCT system.

Many diseases like cancer or atherosclerosis bear micro-scale tissue stiffness changes, which can be visualised by optical coherence elastography (OCE). OCE is a promising research field, where a growing number of publications present qualitative displacement maps. Quantitative OCE results have also been presented, but still lack high precision and good reproducibility, which are important for clinical applications. In this work, we compare three reconstruction methods for the Young's modulus in intensity-based quasi-static compressional OCE: uniaxial analysis, strain map based reconstruction facilitating a particle tracking improved optical flow (EOFM), and a novel image-based inverse reconstruction method (IIM). The quality of the proposed reconstruction methods is investigated by comparing their performance on twelve silicone elastomer phantoms with inclusions of varying size and stiffness. While the uniaxial reconstruction is strongly affected by lateral motion, EOFM is capable of deriving precise strain maps from consecutive OCT images during compression. However, for a valid Young's modulus reconstruction additional stress map information is required. IIM performs best, precisely reconstructing Young's modulus of inclusion and background, closely corresponding to separately determined ground truth values. The method offers a significant improvement of the relative error by a factor of ${3.5}$ compared to uniaxial and strain-based analysis.

Quantitative tissue information, like the light scattering properties, is considered as a key player in the detection of cancerous cells in medical diagnosis. A promising method to obtain these data is optical coherence tomography (OCT). In this article, we will therefore discuss the refractive index reconstruction from OCT data, employing a Gaussian beam based forward model. We consider in particular samples with a layered structure, meaning that the refractive index as a function of depth is well approximated by a piecewise constant function. For the reconstruction, we present a layer-by-layer method where in every step the refractive index is obtained via a discretized least squares minimization. For an approximated form of the minimization problem, we present an existence and uniqueness result. The applicability of the proposed method is then verified by reconstructing refractive indices of layered media from both simulated and experimental OCT data.