Convolution, Rotation, and Data Fusion with Orthogonal Expansions

This dissertation investigates certain special function classes, namely Hermite and Bessel functions, and uncovers some useful properties relating multiplication, convolution, rotation, and coordinate conversion. These mathematical operations are performed on the underlying basis functions and are thus continuous in nature, lending itself to higher accuracy and computational speed. Some integral transformations involving these special functions (e.g. Abel transform, 3h integrals, 3J integrals) possess recurrence relations, and so given a nite set of analytic starting conditions, higher order forms of these integrals can be obtained quickly. It will be shown how these integrals and the aforementioned special function properties are used in engineering applications including data fusion, deconvolution, continuum normal mode analysis, cryo-electron microscopy (cryo-EM) and small angle X-ray scattering (SAXS)

Quantum field theory of photons with orbital angular momentum

A quantum-field-theory approach is put forward to generalize the concept of classical spatial light beams carrying orbital angular momentum to the single-photon level. This quantization framework is carried out both in the paraxial and nonparaxial regimes. Upon extension to the optical phase space, closed-form expressions are found for a photon Wigner representation describing transformations on the orbital Poincaré sphere of unitarily related families of paraxial spatial modes

Predicting blur visual discomfort for natural scenes by the loss of positional information

The perception of blur due to accommodation failures, insufficient optical correction or imperfect image reproduction is a common source of visual discomfort, usually attributed to an anomalous and annoying distribution of the image spectrum in the spatial frequency domain. In the present paper, this discomfort is related to a loss of the localization accuracy of the observed patterns. It is assumed, as a starting perceptual principle, that the visual system is optimally adapted to pattern localization in a natural environment. Thus, since the best possible accuracy of the image patterns localization is indicated by the positional Fisher Information, it is argued that blur discomfort is strictly related to a loss of this information. Following this concept, a receptive field functional model is adopted to predict the visual discomfort. It is a complex-valued operator, orientation-selective both in the space domain and in the spatial frequency domain. Starting from the case of Gaussian blur, the analysis is extended to a generic type of blur by applying a positional Fisher Information equivalence criterion. Out-of-focus blur and astigmatic blur are presented as significant examples. The validity of the proposed model is verified by comparing its predictions with subjective ratings. The model fits linearly with the experiments reported in independent databases, based on different protocols and settings

Clifford wavelets for fetal ECG extraction

Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother's ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. For this aim, we propose in this paper a wavelet/multi-wavelet method allowing to extract perfectly the feta ECG parameters from the abdominal mother ECG. The method is essentially due to the exploitation of Clifford wavelets as recent variants in the field. We prove that these wavelets are more efficient and performing against classical ones. The experimental results are therefore due to two basic classes of wavelets and multi-wavelets. A first-class is the classical Haar Schauder, and a second one is due to Clifford valued wavelets and multi-wavelets. These results showed that wavelets/multiwavelets are already good bases for the FECG processing, provided that Clifford ones are the best.Comment: 21 pages, 8 figures, 1 tabl

Predicting the Blur Visual Discomfort for Natural Scenes by the Loss of Positional Information

The perception of the blur due to accommodation failures, insufficient optical correction or imperfect image reproduction is a common source of visual discomfort, usually attributed to an anomalous and annoying distribution of the image spectrum in the spatial frequency domain. In the present paper, this discomfort is attributed to a loss of the localization accuracy of the observed patterns. It is assumed, as a starting perceptual principle, that the visual system is optimally adapted to pattern localization in a natural environment. Thus, since the best possible accuracy of the image patterns localization is indicated by the positional Fisher Information, it is argued that the blur discomfort is strictly related to a loss of this information. Following this concept, a receptive field functional model, tuned to common features of natural scenes, is adopted to predict the visual discomfort. It is a complex-valued operator, orientation-selective both in the space domain and in the spatial frequency domain. Starting from the case of Gaussian blur, the analysis is extended to a generic type of blur by applying a positional Fisher Information equivalence criterion. Out-of-focus blur and astigmatic blur are presented as significant examples. The validity of the proposed model is verified by comparing its predictions with subjective ratings. The model fits linearly with the experiments reported in independent databases, based on different protocols and settings.Comment: 12 pages, 8 figures, article submitted to Vision Research (Elsevier) Journal in July 202

Laser link acquisition for the GRACE follow-on laser ranging interferometer

[no abstract

Wave Front Sensing and Correction Using Spatial Modulation and Digitally Enhanced Heterodyne Interferometry

This thesis is about light. Specifically it explores a new way sensing the spatial distribution of amplitude and phase across the wavefront of a propagating laser. It uses spatial light modulators to tag spatially distinct regions of the beam, a single diode to collect the resulting light and digitally enhanced heterodyne interferometry to decode the phase and amplitude information across the wavefront. It also demonstrates how using these methods can be used to maximise the transmission of light through a cavity and shows how minor aberrations in the beam can be corrected in real time. Finally it demonstrate the preferential transmission of higher order modes. Wavefront sensing is becoming increasingly important as the demands on modern interferometers increase. Land based systems such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) use it to maximise the amount of power in the arm cavities during operation and reduce noise, while space based missions such as the Laser Interferometer Space Antenna (LISA) will use it to align distant partner satellites and ensure that the maximum amount of signal is exchanged. Conventionally wavefront sensing is accomplished using either Hartmann Sensors or multi-element diodes. These are well proven and very effective techniques but bring with them a number of well understood limitations. Critically, while they can map a wavefront in detail, they are strictly sensors and can do nothing to correct it. Our new technique is based on a single-element photo-diode and the spatial modulation of the local oscillator beam. We encode orthogonal codes spatially onto this light and use these to separate the phases and amplitudes of different parts of the signal beam in post processing. This technique shifts complexity from the optical hardware into deterministic digital signal processing. Notably, the use of a single analogue channel (photo-diode, connections and analogue to digital converter) avoids some low-frequency error sources. The technique can also sense the wavefront phase at many points, limited only by the number of actuators on the spatial light modulator in contrast to the standard 4 points from a quadrant photo-diode. For ground-based systems, our technique could be used to identify and eliminate higher-order modes, while, for space-based systems, it provides a measure of wavefront tilt which is less susceptible to low frequency noise. In the future it may be possible to couple the technique with an artificial intelligence engine to automate more of the beam alignment process in arrangements involving multiple cavities, preferentially select (or reject) specific higher order modes and start to reduce the burgeoning requirements for human control of these complex instruments