Telescope to Observe Planetary Systems (TOPS): a high throughput 1.2-m visible telescope with a small inner working angle

The Telescope to Observe Planetary Systems (TOPS) is a proposed space mission to image in the visible (0.4-0.9 micron) planetary systems of nearby stars simultaneously in 16 spectral bands (resolution R~20). For the ~10 most favorable stars, it will have the sensitivity to discover 2 R_E rocky planets within habitable zones and characterize their surfaces or atmospheres through spectrophotometry. Many more massive planets and debris discs will be imaged and characterized for the first time. With a 1.2m visible telescope, the proposed mission achieves its power by exploiting the most efficient and robust coronagraphic and wavefront control techniques. The Phase-Induced Amplitude Apodization (PIAA) coronagraph used by TOPS allows planet detection at 2 lambda/d with nearly 100% throughput and preserves the telescope angular resolution. An efficient focal plane wavefront sensing scheme accurately measures wavefront aberrations which are fed back to the telescope active primary mirror. Fine wavefront control is also performed independently in each of 4 spectral channels, resulting in a system that is robust to wavefront chromaticity.Comment: 12 pages, SPIE conference proceeding, May 2006, Orlando, Florid

Tomographic inversion using ℓ1\ell_1-norm regularization of wavelet coefficients

We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ to within its assigned errors.Comment: 19 pages, 14 figures. Submitted to GJI July 2006. This preprint does not use GJI style files (which gives wrong received/accepted dates). Corrected typ

Feasibility of thickness mapping using ultrasonic guided waves

Detection and sizing of corrosion in pipelines and pressure vessels over large, partially accessible areas is of growing interest in the petrochemical and nuclear industries. Traditionally, conventional ultrasonic thickness gauging and eddy current techniques have been used to precisely measure the thickness in structures. These techniques only allow the measurement of the local thickness under the probe. Consequently obtaining the remnant thickness of a specimen over a large area requires the probe to be scanned, which is a long and tedious process. Moreover, with these techniques, the scanning may become impossible when the area of inspection is inaccessible. There is therefore a need for a rapid, accurate, long range inspection technique to measure the remaining thickness in corrosion patches. Low frequency guided waves are now routinely used to screen large area of pipes and other structures for cracks and corrosion. Their detection and location capability is very good, but the standard screening technique only gives a rough estimate of the remaining wall thickness. Guided waves have multiple properties which can be used for thickness mapping over large partially accessible areas e.g. dispersion and cutoff frequency thickness product of the high order modes. The present work aims to demonstrate the potential of guided waves for thickness mapping over large partially accessible areas. It starts with a general introduction on ultrasonic guided waves and a literature review of the different techniques for the evaluation of thickness with guided waves. The severity of the errors introduced in time-of-flight tomography for thickness reconstruction by breaking the assumption of the ray theory are investigated. As these errors are significant, the possibility of using the cutoff property of the high order modes is investigated in a frequency range where the ray theory is valid. It is found that the attenuation due to the scattering of the waves in corrosion is too large for this technique to work. Finally the use of low frequency guided wave for diffraction tomography is examined. Finite element simulations of a 64 element circular array on a plate show that when the scattering mechanism of the object to be reconstructed satisfies the Born approximation the reconstruction of the thickness is accurate. However the practical implementation is more challenging when the incident field is not known. Experimental results demonstrate that ultimately the scattering from the array of transducer is a major source of error in the tomographic reconstruction, but when there is no scattering from the array of transducers the reconstructions are very similar to the finite element simulations

POLOCALC: a Novel Method to Measure the Absolute Polarization Orientation of the Cosmic Microwave Background

We describe a novel method to measure the absolute orientation of the polarization plane of the CMB with arcsecond accuracy, enabling unprecedented measurements for cosmology and fundamental physics. Existing and planned CMB polarization instruments looking for primordial B-mode signals need an independent, experimental method for systematics control on the absolute polarization orientation. The lack of such a method limits the accuracy of the detection of inflationary gravitational waves, the constraining power on the neutrino sector through measurements of gravitational lensing of the CMB, the possibility of detecting Cosmic Birefringence, and the ability to measure primordial magnetic fields. Sky signals used for calibration and direct measurements of the detector orientation cannot provide an accuracy better than 1 deg. Self-calibration methods provide better accuracy, but may be affected by foreground signals and rely heavily on model assumptions. The POLarization Orientation CALibrator for Cosmology, POLOCALC, will dramatically improve instrumental accuracy by means of an artificial calibration source flying on balloons and aerial drones. A balloon-borne calibrator will provide far-field source for larger telescopes, while a drone will be used for tests and smaller polarimeters. POLOCALC will also allow a unique method to measure the telescopes' polarized beam. It will use microwave emitters between 40 and 150 GHz coupled to precise polarizing filters. The orientation of the source polarization plane will be registered to sky coordinates by star cameras and gyroscopes with arcsecond accuracy. This project can become a rung in the calibration ladder for the field: any existing or future CMB polarization experiment observing our polarization calibrator will enable measurements of the polarization angle for each detector with respect to absolute sky coordinates.Comment: 15 pages, 5 figures, Accepted by Journal of Astronomical Instrumentatio

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Optimization Of Zonal Wavefront Estimation And Curvature Measurements

Optical testing in adverse environments, ophthalmology and applications where characterization by curvature is leveraged all have a common goal: accurately estimate wavefront shape. This dissertation investigates wavefront sensing techniques as applied to optical testing based on gradient and curvature measurements. Wavefront sensing involves the ability to accurately estimate shape over any aperture geometry, which requires establishing a sampling grid and estimation scheme, quantifying estimation errors caused by measurement noise propagation, and designing an instrument with sufficient accuracy and sensitivity for the application. Starting with gradient-based wavefront sensing, a zonal least-squares wavefront estimation algorithm for any irregular pupil shape and size is presented, for which the normal matrix equation sets share a pre-defined matrix. A Gerchberg–Saxton iterative method is employed to reduce the deviation errors in the estimated wavefront caused by the pre-defined matrix across discontinuous boundary. The results show that the RMS deviation error of the estimated wavefront from the original wavefront can be less than λ/130~ λ/150 (for λ equals 632.8nm) after about twelve iterations and less than λ/100 after as few as four iterations. The presented approach to handling irregular pupil shapes applies equally well to wavefront estimation from curvature data. A defining characteristic for a wavefront estimation algorithm is its error propagation behavior. The error propagation coefficient can be formulated as a function of the eigenvalues of the wavefront estimation-related matrices, and such functions are established for each of the basic estimation geometries (i.e. Fried, Hudgin and Southwell) with a serial numbering scheme, where a square sampling grid array is sequentially indexed row by row. The results show that with the wavefront piston-value fixed, the odd-number grid sizes yield lower error propagation than the even-number grid sizes for all geometries. The Fried geometry either allows sub-sized wavefront estimations within the testing domain or yields a two-rank deficient estimation matrix over the full aperture; but the latter usually suffers from high error propagation and the waffle mode problem. Hudgin geometry offers an error propagator between those of the Southwell and the Fried geometries. For both wavefront gradient-based and wavefront difference-based estimations, the Southwell geometry is shown to offer the lowest error propagation with the minimum-norm least-squares solution. Noll’s theoretical result, which was extensively used as a reference in the previous literature for error propagation estimate, corresponds to the Southwell geometry with an odd-number grid size. For curvature-based wavefront sensing, a concept for a differential Shack-Hartmann (DSH) curvature sensor is proposed. This curvature sensor is derived from the basic Shack-Hartmann sensor with the collimated beam split into three output channels, along each of which a lenslet array is located. Three Hartmann grid arrays are generated by three lenslet arrays. Two of the lenslets shear in two perpendicular directions relative to the third one. By quantitatively comparing the Shack-Hartmann grid coordinates of the three channels, the differentials of the wavefront slope at each Shack-Hartmann grid point can be obtained, so the Laplacian curvatures and twist terms will be available. The acquisition of the twist terms using a Hartmann-based sensor allows us to uniquely determine the principal curvatures and directions more accurately than prior methods. Measurement of local curvatures as opposed to slopes is unique because curvature is intrinsic to the wavefront under test, and it is an absolute as opposed to a relative measurement. A zonal least-squares-based wavefront estimation algorithm was developed to estimate the wavefront shape from the Laplacian curvature data, and validated. An implementation of the DSH curvature sensor is proposed and an experimental system for this implementation was initiated. The DSH curvature sensor shares the important features of both the Shack-Hartmann slope sensor and Roddier’s curvature sensor. It is a two-dimensional parallel curvature sensor. Because it is a curvature sensor, it provides absolute measurements which are thus insensitive to vibrations, tip/tilts, and whole body movements. Because it is a two-dimensional sensor, it does not suffer from other sources of errors, such as scanning noise. Combined with sufficient sampling and a zonal wavefront estimation algorithm, both low and mid frequencies of the wavefront may be recovered. Notice that the DSH curvature sensor operates at the pupil of the system under test, therefore the difficulty associated with operation close to the caustic zone is avoided. Finally, the DSH-curvature-sensor-based wavefront estimation does not suffer from the 2π-ambiguity problem, so potentially both small and large aberrations may be measured

Lay-up characterization and elastic property determination in composite laminates

This dissertation focuses on two important nondestructive evaluation and materials characterization problems related to composite laminates: ply lay-up characterization and elastic property determination. For ply lay-up characterization, we have developed a shear wave transmission technique to effectively detect ply lay-up errors in composite laminates. The effects of fiber orientation on normal-incident shear waves propagating through a composite laminate have been investigated both theoretically and experimentally. To facilitate rotation, EMATs (electromagnetic acoustic transducers) were used to generate and receive the shear waves. It was found that the transmitted shear waves when the EMAT transmitter and receiver were perpendicular to each other had a great sensitivity to ply lay-up errors. This technique has been successfully demonstrated on both cured and uncured composite laminates. For elastic property determination, we have first applied the simultaneous velocity and thickness imaging technique to map out small changes in ultrasonic velocity (hence elastic constant) when the material thickness was unknown or varied spatially. Applications to several industrial materials have demonstrated the usefulness of this technique for both materials characterization and flaw detection in metals and composite laminates. We have also extended this technique to generate images of sample surface contours and cross-sectional profiles when the velocity was unknown. Next, we have extended the synthetic aperture scanning method using planar transducers in an immersion leaky wave reflection or transmission measurement to allow the use of focused transducers. The complex transducer point approach has been used to model the receiver output voltage and to analyze the transducer beam effects on the result of a synthetic aperture scan. It was found that the large angular beam spread of focused transducers can be used for rapid mapping of the reflection or transmission coefficient and the associated dispersion spectrum. A novel stepwise, targeted procedure has also been developed to allow efficient reconstruction of material elastic property with only minimal use of the highly redundant dispersion spectrum data. Experiments on both isotropic and anisotropic plates showed that this method can be used for rapid evaluation of the elastic behavior of composite laminates and other plate materials with a reasonably good accuracy