Phase reconstruction from undersampled intensity patterns

We demonstrate the uniqueness and convergence of phase recovery from high-spatial-frequency and undersampled intensity data. Furthermore, this is accomplished without the ambiguities that arise in phase unwrapping and without the need to employ a priori information. The method incorporates the technique of line integration of the phase gradient to find the first approximation to the phase and the algorithm of synthetic interferograms to find the unknown phase with high accuracy. The method may be used with any experimental method that at a certain data processing step obtains generalized sine and cosine intensity functions.     

Unambiguous coherence retrieval from intensity measurements

It is demonstrated that the members of different classes of two-dimensional fields that have the same intensity distributions everywhere in free space but different coherence properties can be identified by measuring the fields' intensities after passing the fields through an anamorphic optical system, such as a cylindrical lens. In this way the ambiguity in coherence determination from intensity measurements alone, present for the case of two-dimensional fields, is removed.     

Substrate temperature control from RHEED intensity measurements

Substrate temperature is an importance parameter controlling nucleation and growth dynamics during the thin film epitaxy in MBE system. The most covenant methods able to determine the substrate temperature is based on some calibration procedures, where substrate temperature is calculated as a function of electric power dissipated in heater system. This paper presents possibility of substrate temperature control based on reflection high-energy electron diffraction (RHEED) intensity measurements as in situ technique. Temperature dependence of the specularly reflected electron beam intensity versus the substrate temperature is predicted by dynamical theory of electron scattering. The theoretical RHEED intensity dependence versus Si(1 1 1) substrate temperature was obtained from one-dimensional rocking-curve calculation.     

Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field

The recording of the volume speckle field from an object at different planes combined with the wave propagation equation allows the reconstruction of the wavefront phase and amplitude without requiring a reference wave. The main advantage of this single-beam multiple-intensity reconstruction (SBMIR) technique is the simple experimental setup because no reference wave is required as in the case of holography. The phase retrieval technique is applied to the investigation of diffusely transmitting and reflecting objects. The effects of different parameters on the quality of reconstructions are investigated by simulation and experiment. Significant enhancements of the reconstructions are observed when the number of intensity measurements is 15 or more and the sequential measurement distance is 0.5 mm or larger. Performing two iterations during the reconstruction process using the calculated phase also leads to better reconstruction. The results from computer simulations confirm the experiments. Analysis of transverse and longitudinal intensity distributions of a volume speckle field for the SBMIR technique is presented. Enhancing the resolution method by shifting the camera a distance of a half-pixel in the lateral direction improves the sampling of speckle patterns and leads to better quality reconstructions. This allows the possibility of recording wave fields from larger test objects.     

Improved phase imaging from intensity measurements in multiple planes

Problems stemming from quantitative phase imaging from intensity measurements play a key role in many fields of physics. Techniques based on the transport of intensity equation require an estimate of the axial derivative of the intensity to invert the problem. Derivation formulas in two adjacent planes are commonly used to experimentally compute the derivative of the irradiance. Here we propose a formula that improves the estimate of the derivative by using a higher number of planes and taking the noisy nature of the measurements into account. We also establish an upper and lower limit for the estimate error and provide the distance between planes that optimizes the estimate of the derivative.     

Phase correction of linear time invariant systems with digitalall-pass filters

A novel phase correction method is presented, which starts from phase data that may be corrupted with (measurement) noise. Due to an appropriate choice of the model, the phase intercept distortion is avoided. Some practical examples and experimental results are given     

Detection of crack growth in concrete from ultrasonic intensity measurements

Results of monitoring crack growth in concrete during uniaxial compression using ultrasonic methods offer the possibility of determining the internal properties of a concrete member both during and after loading without causing any damage. The ultrasonic transducers were designed to monitor pulse transmission in both the axial and lateral directions throughout a uniaxial compression test. The waveforms received at various stages of loading were digitized, stored and analysed after the test. The crack growth was inferred from the intensity of these ultrasonic waveforms. Axial stresses/strains and transverse strains were also recorded by the use of a data acquisition system. Four different mix proportions were tested and the results obtained are discussed and compared with other available results.     

Object reconstruction from adaptive compressive measurements in feature-specific imaging

Static feature-specific imaging (SFSI), where the measurement basis remains fixed/static during the data measurement process, has been shown to be superior to conventional imaging for reconstruction tasks. Here, we describe an adaptive approach that utilizes past measurements to inform the choice of measurement basis for future measurements in an FSI system, with the goal of maximizing the reconstruction fidelity while employing the fewest measurements. An algorithm to implement this adaptive approach is developed for FSI systems, and the resulting systems are referred to as adaptive FSI (AFSI) systems. A simulation study is used to analyze the performance of the AFSI system for two choices of measurement basis: principal component (PC) and Hadamard. Here, the root mean squared error (RMSE) metric is employed to quantify the reconstruction fidelity. We observe that an AFSI system achieves as much as 30% lower RMSE compared to an SFSI system. The performance improvement of the AFSI systems is verified using an experimental setup employed using a digital micromirror device (DMD) array.     

Noise-robust stress intensity factor determination from kinematic field measurements

Stress intensity factors are often estimated numerically from a given displacement field through an interaction integral formalism. The latter method makes use of a weight, the virtual crack extension field, which is under-constrained by first principles. Requiring a least noise sensitivity allows one to compute the optimal virtual crack extension. Mode I and mode II specialized fields are obtained and particularized for a given displacement functional basis. The method is applied to an experimental case study of a crack in a silicon carbide sample, whose displacement field is obtained by a digital image correlation technique. The optimization leads to a very significant uncertainty reduction up to a factor 100 of the non-optimized formulation. The proposed scheme reveals additional performances with respect to the integral domain choice and assumed crack tip geometry, which are shown to have a reduced influence.     

Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements

Optical imaging and localization of objects inside a highly scattering medium, such as a tumor in the breast, is a challenging problem with many practical applications. Conventional imaging methods generally provide only two-dimensional (2-D) images of limited spatial resolution with little diagnostic ability. Here we present an inversion algorithm that uses time-resolved transillumination measurements in the form of a sequence of picosecond-duration intensity patterns of transmitted ultrashort light pulses to reconstruct three-dimensional (3-D) images of an absorbing object located inside a slab of a highly scattering medium. The experimental arrangement used a 3-mm-diameter collimated beam of 800-nm, 150-fs, 1-kHz repetition rate light pulses from a Ti:sapphire laser and amplifier system to illuminate one side of the slab sample. An ultrafast gated intensified camera system that provides a minimum FWHM gate width of 80 ps recorded the 2-D intensity patterns of the light transmitted through the opposite side of the slab. The gate position was varied in steps of 100 ps over a 5-ns range to obtain a sequence of 2-D transmitted light intensity patterns of both less-scattered and multiple-scattered light for image reconstruction. The inversion algorithm is based on the diffusion approximation of the radiative transfer theory for photon transport in a turbid medium. It uses a Green s function perturbative approach under the Rytov approximation and combines a 2-D matrix inversion with a one-dimensional Fourier-transform inversion to achieve speedy 3-D image reconstruction. In addition to the lateral position, the method provides information about the axial position of the object as well, whereas the 2-D reconstruction methods yield only lateral position.     

Image reconstruction in spherical-wave intensity diffraction tomography

A reconstruction theory for intensity diffraction tomography (I-DT) has been proposed that permits reconstruction of a weakly scattering object without explicit knowledge of phase information. We investigate the I-DT reconstruction problem assuming an incident (paraxial) spherical wave and scanning geometries that employ fixed source-to-object distances. Novel reconstruction methods are derived by identifying and exploiting tomographic symmetries and the rotational invariance of the problem. An underlying theme is that symmetries in tomographic imaging systems can facilitate solutions for phase-retrieval problems. A preliminary numerical investigation of the developed reconstruction methods is presented.     

Generalized stress intensity factors in linear elastostatics

The solution of two-dimensional linear elastostatic problems in the neighborhood of singular points is discussed. A reliable and efficient method for computing the eigenpairs that characterize the exact solution and their coefficients, called the generalized stress intensity factors, by the finite element method is demonstrated.Examples, representing three very different kinds of singular points demonstrate that the method works well and produces results of high accuracy. Importantly, the method is applicable to anisotropic materials, multi-material interfaces, and cases where the singularities are characterized by complex eigenpairs.Research performed while the author served as a visiting assistant professor at Washington University in St. Louis.     

Direct reconstruction of complex refractive index distribution from boundary measurement of intensity and normal derivative of intensity

We present an optical tomographic reconstruction method to recover the complex refractive index distribution from boundary measurements based on intensity, which are the logarithm of intensity and normal derivative of intensity. The method, which is iterative, repeatedly implements the forward propagation equation for light amplitude, the Helmholtz equation, and computes appropriate sensitivity matrices for these measurements. The sensitivity matrices are computed by solving the forward propagation equation for light and its adjoint. The results of numerical experiments show that the data types ln(I) and partial differential I/ partial differential n reconstructed, respectively, the imaginary and the real part of the object refractive index distribution. Moreover, the imaginary part of the refractive index reconstructed from partial differential I/ partial differential n and the real part from ln(I) failed to show the object's inhomogeneity. The value of the propagation constant, k, used in our simulations was 50, and this value resulted in smoothing of the reconstructed inhomogeneities. Thus we have shown that it is possible to reconstruct the complex refractive index distribution directly from the measured intensity without having to first find the light amplitude, as is done in most of the currently available reconstruction algorithms of diffraction tomography.     

Image reconstruction by backprojection from frequency-domain optical measurements in highly scattering media

The reconstruction of the location and optical properties of objects in turbid media requires the solution of the inverse problem. Iterative solutions to this problem can require large amounts of computing time and may not converge to a unique solution. Instead, we propose a fast, simple method for approximately solving this problem in which calculated effective absorption and reduced scattering coefficients are backprojected to create an image of the objects. We reconstructed images of objects with centimeter dimensions embedded in a diffusive medium with optical characteristics similar to those of human tissue. Data were collected by a frequency-domain spectrometer operating at 120 MHz with a laser diode light source emitting at 793 nm. Intensity and phase of the incident photon density wave were collected from linear scans at different projection angles. Although the positions of the objects are correctly identified by the reconstructed images, the optical parameters of the objects are recovered only qualitatively.     

Time-dependent linear systems derivable from a variational principle

This paper presents a study of time-varying linear systems of second order ordinary differential equations, which can be derived from a Lagrangian after multiplication by a suitable matrix. It concerns a generalization of previous studies on systems with constant coefficients. After a simplification of the Helmholtz conditions, it is shown that the problem is reduced to a purely algebraic one, provided one can solve a matrix differential equation which produces the transformation to canonical form of the given system. This further leads to a theoretical characterization of all systems admitting a multiplier. Various algebraic relations are derived, involving constant matrices only, which can help to detect, prior to any integration procedure, whether or not: a multiplier exists. They are referred to as the generalized commutativity conditions. The first of these, which is sufficient for the existence of a Lagrangian, is shown to allow also a simple construction of a quadratic first integral, and to have some other interesting features. The paper ends with an example.     

Aberration measurement in confocal microscopy: Phase retrieval from a single intensity measurement

Abstract

A simplified method for aberration measurement in confocal microscopy is proposed. The method is based on analysis of the Fourier spectrum of the confocal interference axial response. With this method, both the complex pupil function and the complex defocus signal can be recovered from only a single measurement, and no electro-optic phase modulator is needed. This method has been demonstrated both theoretically and experimentally.