Mathematical Modelling of Optical Coherence Tomography

In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for different positions of the mirror. Different approaches are addressed depending on the different assumptions made about the optical properties of the sample. This procedure is applied to a full field OCT system and an extension to standard (time and frequency domain) OCT is briefly presented.Comment: 28 pages, 5 figures, book chapte

Development of correction algorithm for pulsed terahertz computed tomography (THz-CT)

For last couple of decades, there has been a considerable improvement in Terahertz (THz) science, technology, and imaging. In particular, the technique of 3-D computed tomography has been adapted to the THz range. However, it has been widely recognized that a fundamental limitation to THz computed tomography imaging is the refractive effects of the sample under study. The finite refractive index of materials in the THz range can severally refract THz beams which probe the internal structure of a sample during the acquisition of tomography data. Refractive effects lead to anomalously high local absorption coefficients in the reconstructed image near the material’s boundaries. Three refractive effects are identified: (a) Fresnel reflection power losses at the boundaries, (b) an increase in path length of the probing THz radiation, and (c) steering of the THz beam by the sample such that the emerging THz radiation is no longer collected by the THz detector. In addition, the finite size of the THz beam dominates the measured THz transmission when the edges of the sample are probed using THz tomography. These boundary phenomena can dominate in the reconstructed THz-CT images making it difficult to distinguish any hidden finer structural defect(s) inside the material. In this dissertation, an algorithm has been developed to remove these refractive and finite beam size effects from THz-CT reconstructed images. The algorithm is successfully implemented on cylindrical shaped objects. A longer term goal of the research is to study the internal structure of natural cork wine stoppers by pulsed Terahertz tomography (THz-CT). It has previously been shown that THz imaging can detect the internal structure of natural cork. Moreover, the internal structure of natural cork stoppers dominates the diffusion of gasses and liquids through the cork. By using THz computed tomography, one can recreate a 3D image of the sample’s internal structure which could then be used to predict non-destructively the diffusion properties of the cork. However, refractive and boundary effects which arise in the THz tomographic image masks the presence of the cork’s internal structure. Applying the correction algorithms which are developed in this dissertation to natural cork stoppers suppresses the refractive and boundary anomalies enabling better visualization of the cork’s internal structure

Mathematics and Algorithms in Tomography

This is the eighth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, sonar, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, vector tomography, and texture analysis

Flame front propagation velocity measurement and in-cylinder combustion reconstruction using POET

The objective of this thesis is to develop an intelligent diagnostic technique POET (Passive Optical Emission Tomography) for the investigation of in cylinder combustion chemiluminescence. As a non-intrusive optical system, the POET system employs 40 fibre optic cables connected to 40 PMTs (Photo Multiplier Tube) to monitor the combustion process and flame front propagation in a modified commercial OHV (Over Head Valve) Pro 206 IC engine. The POET approach overcomes several limitations of present combustion research methods using a combination of fibre optic detection probes, photomultipliers and a tomographic diagnostics. The fibre optic probes are placed on a specially designed cylinder head gasket for non-invasively inserting cylinder. Each independent probe can measure the turbulent chemiluminescence of combustion flame front at up to 20 kHz. The resultant intensities can then be gathered tomographically using MART (Multiplicative Algebraic Reconstruction Technique) software to reconstruct an image of the complete flame-front. The approach is essentially a lensless imaging technique, which has the advantage of not requiring a specialized engine construction with conventional viewing ports to visualize the combustion image. The fibre optic system, through the use of 40, 2m long thermally isolated fibre optic cables can withstand combustion temperatures and is immune from electronic noise, typically generated by the spark plug. The POET system uses a MART tomographic methodology to reconstruct the turbulent combustion process. The data collected has been reconstructed to produce a temporal and spatial image of the combustion flame front. The variations of lame turbulence are monitored by sequences of reconstructed images. Therefore, the POET diagnostic technique reduces the complications of classic flame front propagation measurement systems and successfully demonstrates the in-cylinder combustion process. In this thesis, a series of calibration exercises have been performed to ensure that the photomultipliers of the POET system have sufficient temporal and spatial resolution to quantitatively map the flow velocity turbulence and chemiluminescence of the flame front. In the results, the flame has been analyzed using UV filters and blue filters to monitor the modified natural gas fuel engine. The flame front propagation speed has been evaluated and it is, on average, 12 m/s at 2280 rpm. Sequences of images have been used to illustrate the combustion explosion process at different rpm

Spatial Vector Microwave Measurement

V této práci je představena nová interferometrická měřicí metoda pro měření koeficientu přenosu mezi dvěma anténami. Jestliže je přenos mezi anténami realizován odrazem od nějakého předmětu, lze metodu využít např. pro mikrovlnné zobrazování. Navržený systém obsahuje referenční větev obsahující anténu, která přímo ozařuje přijímací anténu a testovací větev, kde anténa ozařuje testovaný objekt. Elektromagnetická vlna z testovacího kanálu je od testovacího objektu odražena do přijímací antény, kde interferuje s vlnou z referenční větve. Pro jednoznačné získání fázového posunu mezi referenční a testovací vlnou jsou provedena postupně minimálně dvě interferometrická měření, kdy je v referenčním kanálu nastaven vhodný fázový posun a amplituda přenosu. Při měření můžeme provést více nezávislých interferometrických měření a vzniklá redundance může být využita ke zmenšení nejistot měření. Dále byl popsán způsob geometrické representace měření, který umožňuje názorně odhadnout nejisty měření. Nejistoty měření byly určeny i na základě numerické Monte Carlo metody. Navržená konfigurace byla ověřena jak přesným měřením za použití vektorového analyzátoru pro ověření nejistot měření, tak původní konfigurací pro ověření funkčnosti celého konceptu. Navrženou metodou bylo provedeno mikrovlnné zobrazování metodou inverzní syntetické apertury a byla tak ověřena použitelnost navrženého systému.This work presents a new interferometric measuring method for measuring the transmission coefficient between two antennas. If the transmission between the antennas is realized by a reflection from an object, the method can be used, e.g., for microwave imaging. The proposed system contains a reference branch containing an antenna that directly irradiates the receiving antenna and a test branch where the antenna irradiates the object under test. The electromagnetic wave from the test channel is reflected from the test object into the receiving antenna where it interferes with the wave from the reference channel. To achieve a unambiguous phase shift between the reference and test waves, at least two interferometric measurements are performed sequentially, with a suitable phase shift and the amplitude of the transmission being set in the reference channel. We can perform more independent interferometric measurements while redundancy can be used to reduce measurement uncertainty. Furthermore, a method of geometric representation of the measurement has been described which makes it possible to clearly estimate the measurement uncertainty. Measurement uncertainties were determined by the numerical Monte Carlo method. The proposed configuration has been verified by accurate measurements using a vector analyzer to verify measurement uncertainties, and the original configuration to verify the functionality of the entire concept. Microwave imaging using the inverse synthetic aperture method was performed to verify the usability of the proposed system

Mathematics and Algorithms in Tomography

This was the ninth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, emission tomography, X-ray CT, and vector tomography along with a wide range of mathematical analysis