TDMS: an open source time domain Maxwell solver for simulating optical coherence tomography image formation

Realistic modelling of image formation in optical coherence tomography, which models light propagation in the sample using Maxwell’s equations, is useful for applications such as training researchers and clinicians, image interpretation and technique development. Such models, however, require specialised knowledge of numerical techniques for solving Maxwell’s equations, and for modelling optical systems. Here I present a freely available, open source package, aimed at making such simulations accessible to researchers throughout the optical coherence tomography community. Time Domain Maxwell Solver (TDMS) is based on the finite difference time domain (FDTD) and pseudo spectral time domain (PSTD) methods, and includes functionallity required to model optical systems typically found in OCT systems. TDMS includes several use case examples aimed at making it easy for users with limited background in simulation to use the package

Three-dimensional full wave model of image formation in optical coherence tomography

We demonstrate, what we believe to be, the first mathematical model of image formation in optical coherence tomography, based on Maxwell’s equations, applicable to general three-dimensional samples. It is highly realistic and represents a significant advance on a previously developed model, which was applicable to two-dimensional samples only. The model employs an electromagnetic description of light, made possible by using the pseudospectral time-domain method for calculating the light scattered by the sample which is represented by a general refractive index distribution. We derive the key theoretical and computational advances required to develop this model. Two examples are given of image formation for which analytic comparisons may be calculated: point scatterers and finite sized spheres. We also provide a more realistic example of C-scan formation when imaging turbid media. We anticipate that this model will be important for various applications in OCT, such as image interpretation and the development of quantitative techniques

X-ray phase-contrast imaging with polychromatic sources and the concept of effective energy

Grating-based quantitative polychromatic x-ray phase imaging is currently a very active area of research. It has already been shown that, in such systems, the retrieved differential phase depends upon the spectral properties of the source, the gratings, the detector, and the sample. In this paper, we show that the retrieved sample absorption also depends upon the spectral properties of the gratings. Further, we compare the spectral dependence of both retrieved phase and absorption for the grating interferometer and coded aperture techniques. These results enable us to conclude that in both cases quantitative phase imaging systems cannot be described by an effective energy which is independent of the sample. This has important implications for applications where an absolute measure of phase is important and in tomography

A simplified approach to quantitative coded aperture X-ray phase imaging

We recently demonstrated how quantitative X-ray phase contrast imaging may be performed with laboratory sources using the coded aperture technique. This technique required the knowledge of system parameters such as, for example, the source focal spot size and distances between elements of the imaging system. The method also assumes that the absorbing regions of the apertures are perfectly absorbing. In this paper we demonstrate how quantitative imaging can be performed without knowledge of individual system parameters and with partially absorbing apertures. We also show that this method is analogous to that employed in analyser based imaging which uses the rocking curve of an analyser crystal

Synthesizing scanning-mode acquisition in full-wave modelling of OCT

“Full-wave” models of OCT imaging systems based on Maxwell’s Equations are beginning to emerge as feasible alternatives to well established approximate models. These models are however computationally taxing when dealing with large samples. Here, in an effort to reduce the computational burden, we present a means of synthesizing full-wave scanning-mode OCT image formation using only a single simulation of a plane wave incident on a given sample medium. The method involves an angular spectrum approach which synthesizes the signal for arbitrary scan positions, and arbitrary illumination conditions. This is demonstrated to reduce the required simulation time by an order of magnitude when synthesizing OCT B-scans, as compared to previous methods which require a separate simulation for each scan position

Approximate image synthesis in optical coherence tomography

Full-wave models of OCT image formation, which are based on Maxwell’s equations, are highly realistic. However, such models incur a high computational cost, particularly when modelling sample volumes consistent with those encountered in practice. Here, we present an approximate means of synthesizing volumetric image formation to reduce this computational burden. Instead of performing a full-wave scattered light calculation for each A-scan, we perform a full-wave scattered light calculation for a normally incident plane wave only. We use the angular spectrum field representation to implement beam focussing and scanning, making use of an assumption similar to the tilt optical memory effect, to approximately synthesize volumetric data sets. Our approach leads to an order of magnitude reduction in the computation time required to simulate typical B-scans. We evaluate this method by comparing rigorously and approximately evaluated point spread functions and images of highly scattering structured samples for a typical OCT system. Our approach also reveals new insights into image formation in OCT

Development of a reliable and reproducible phantom manufacturing method using silica microspheres in silicone

Optically scattering phantoms composed of silica microspheres embedded in an optically clear silicone matrix were manufactured using a previously developed method. Multiple problems, such as sphere aggregation, adsorption to the cast, and silicone shrinkage, were, however, frequently encountered. Solutions to these problems were developed and an improved method, incorporating these solutions, is presented. The improved method offers excellent reliability and reproducibility for creating phantoms with uniform scattering coefficient. We also present evidence of decreased sphere aggregation

Coherent X-ray imaging across length scales

Contemporary X-ray imaging techniques span a uniquely wide range of spatial resolutions, covering five orders of magnitude. The evolution of X-ray sources, from the earliest laboratory sources through to highly brilliant and coherent free-electron lasers, has been key to the development of these imaging techniques. This review surveys the predominant coherent X-ray imaging techniques with fields of view ranging from that of entire biological organs, down to that of biomolecules. We introduce the fundamental principles necessary to understand the image formation for each technique as well as briefly reviewing coherent X-ray source development. We present example images acquired using a selection of techniques, by leaders in the field

Tool for simulating the focusing of arbitrary vector beams in free-space and stratified media

Vectorial models of focused beams are important to a variety of fields including microscopy, lithography, optical physics, and biomedical imaging. This has led to many models being developed, which calculate how beams of various profiles are focused both in free space and in the presence of stratified media. The majority of existing models begin with a vectorial diffraction formula, often referred to as the Debye–Wolf integral, which must be evaluated partially analytically and partially numerically. The complexity of both the analytic and numerical evaluations increases significantly when exotic beams are modeled, or, a stratified medium is located in the focal region. However, modern-day computing resources permit this integral to be evaluated entirely numerically for most applications. This allows for the development of a vectorial model of focusing in which the focusing itself, interaction with a stratified medium, and incident beam specification are independent, allowing for a model of unprecedented flexibility. We outline the theory upon which this model is developed and show examples of how the model can be used in applications including optical coherence tomography, high numerical aperture microscopy, and the properties of cylindrical vector beams. We have made the computer code freely available

Analysing the impact of non-parallelism in Fabry-Perot etalons through optical modelling

Fabry-Perot (FP) etalons, composed of two parallel mirrors, are used widely as optical filters and sensors. In certain applications, however, such as when FP etalons with polymer cavities are used to detect ultrasound, the mirrors may not be perfectly parallel due to manufacturing limitations. As little is known about how the mirrors being non-parallel impacts upon FP etalon performance, it is challenging to optimize the design of such devices. To address this challenge, we developed a model of light propagation in non-parallel FP etalons. The model is valid for arbitrary monochromatic beams and calculates both the reflected and transmitted beams, assuming full-wave description of light. Wavelength resolved transmissivity simulations were computed to predict the effect that non-parallel mirrors have on the sensitivity, spectral bandwidth and peak transmissivity of FP etalons. Theoretical predictions show that the impact of the non-parallel mirrors increases with both mirror reflectivity and incident Gaussian beam waist. Guidelines regarding the maximum angle allowed between FP mirrors whilst maintaining the sensitivity and peak transmissivity of a parallel mirror FP etalon are provided as a function of mirror reflectivity, cavity thickness and Gaussian beam waist. This information, and the model, could be useful for guiding the design of FP etalons suffering a known degree of non-parallelism, for example, to optimize the sensitivity of polymer based FP ultrasound sensors