Optical and X-ray tomography is of considerable importance for biomedical imaging. This thesis is centred on Non-Reciprocal Broken-Ray Tomography (NRBRT), a tomographic imaging technique that applies to both optical and X-ray tomography. NRBRT is based on angularly-selective measurements of fluorescent or Compton scattered radiation, and the image reconstruction algorithm assumes that the measured signal is predominantly single-scattered. NRBRT enables simultaneous reconstruction of the total attenuation coefficient at two energies, in addition to the fluorescent contrast agent concentration (in fluorescence optical tomography) and the electron density (in X-ray tomography). The overarching objective of this thesis is to further develop the NRBRT technique for optical and X-ray tomography, specifically, the implementation, validation, and detection optimisation through numerical experiments, to guide future implementation.

Numerical experiments were performed to validate optical NRBRT under ideal detection conditions (detecting only the single-scattered radiation and perfectly angularly-selective point detectors). Excellent image quality was obtained for samples without the addition of Poisson noise (for all property models, the Structural Similarity Index Measure (SSIM) values were > 0.93). The image quality decreased with noise; however, in all cases, the SSIM values were > 0.62. This was furthered by considering more realistic measurements. Forward datasets were generated for the first time using Monte Carlo simulations, where all fluorescent radiation in the detector’s geometrical, energy, and angular collimation characteristics were measured. Optical NRBRT was demonstrated for samples of up to four scattering lengths in size. The effects of the detector characteristics (the area and acceptance angle) were also investigated. This study validated the principles and image reconstruction formalism of optical NRBRT.

Next, a dual-modality imaging approach was validated. NRBRT was combined with another existing imaging technique to overcome the difficulty related to incomplete measurement datasets in samples with exclusive accumulation of the contrast agent in the inhomogeneity. Good image quality was maintained for NRBRT even when fewer measurements were used compared to performing NRBRT independently, the SSIM error metrics only decreased in the range of 0.00 to 0.10. Samples with isotropic scattering demonstrated better image quality (SSIM ≈ 0.8) than those with anisotropic scattering (SSIM ≈ 0.6).

Finally, X-ray NRBRT was validated for a range of energies and detection characteristics using Monte Carlo simulations. As the incident irradiation energy was reduced, the primary cause of poorer image quality was increased noise in the measured signals. However, despite these high noise levels (3.8%), good image quality was maintained (SSIM 0.78 − 0.99). Furthermore, it demonstrated that the single-scattering approximation in NRBRT formalism takes longer to break down when measuring Compton scattered radiation.