ARMA model for random periodic processes

In this thesis, we construct ARMA model for random periodic processes. We stress on the mixed periodicity and randomness of the model and redefined the definition of sample autocovariance function. We prove the asymptotic normality of Yule-Walker estimation and innovation estimation for coefficients in causal and invertible case. We also prove the central limit theorem for random periodic processes. Under this and ergodic theorem, we prove the asymptotic normality of maximum likelihood estimation for non-causal autoregressive model for random periodic processes. We simulate ARMA model for randomperiodic processes to two examples and compare the results with classical ARMA model.</div

Investigating ultrasound–light interaction in scattering media

Significance: Ultrasound-assisted optical imaging techniques, such as ultrasound-modulated optical tomography, allow for imaging deep inside scattering media. In these modalities, a fraction of the photons passing through the ultrasound beam is modulated. The efficiency by which the photons are converted is typically referred to as the ultrasound modulation’s “tagging efficiency.” Interestingly, this efficiency has been defined in varied and discrepant fashion throughout the scientific literature. Aim: The aim of this study is the ultrasound tagging efficiency in a manner consistent with its definition and experimentally verify the contributive (or noncontributive) relationship between the mechanisms involved in the ultrasound optical modulation process. Approach: We adopt a general description of the tagging efficiency as the fraction of photons traversing an ultrasound beam that is frequency shifted (inclusion of all frequency-shifted components). We then systematically studied the impact of ultrasound pressure and frequency on the tagging efficiency through a balanced detection measurement system that measured the power of each order of the ultrasound tagged light, as well as the power of the unmodulated light component. Results: Through our experiments, we showed that the tagging efficiency can reach 70% in a scattering phantom with a scattering anisotropy of 0.9 and a scattering coefficient of 4  mm⁻¹ for a 1-MHz ultrasound with a relatively low (and biomedically acceptable) peak pressure of 0.47 MPa. Furthermore, we experimentally confirmed that the two ultrasound-induced light modulation mechanisms, particle displacement and refractive index change, act in opposition to each other. Conclusion: Tagging efficiency was quantified via simulation and experiments. These findings reveal avenues of investigation that may help improve ultrasound-assisted optical imaging techniques

Analytical description of high-aperture STED resolution with 0-2π\pi vortex phase modulation

Stimulated emission depletion (STED) can achieve optical super-resolution, with the optical diffraction limit broken by the suppression on the periphery of the fluorescent focal spot. Previously, it is generally experimentally accepted that there exists an inverse square root relationship with the STED power and the resolution, yet without strict analytical description. In this paper, we have analytically verified the relationship between the STED power and the achievable resolution from vector optical theory for the widely used 0-2$\pi$ vortex phase modulation. Electromagnetic fields of the focal region of a high numerical aperture objective are calculated and approximated into polynomials, and analytical expression of resolution as a function of the STED intensity has been derived. As a result, the resolution can be estimated directly from the measurement of the saturation power of the dye and the STED power applied.Comment: (19 pages