Solving inverse scattering problems in biological samples by quantitative phase imaging

Quantitative phase imaging (QPI), a method that precisely recovers the wavefront of an electromagnetic field scattered by a transparent, weakly scattering object, is a rapidly growing field of study. By solving the inverse scattering problem, the structure of the scattering object can be reconstructed from QPI data. In the past decade, 3D optical tomographic reconstruction methods based on QPI techniques to solve inverse scattering problems have made significant progress. In this review, we highlight a number of these advances and developments. In particular, we cover in depth Fourier transform light scattering (FTLS), optical diffraction tomography (ODT), and white‐light diffraction tomography (WDT).

     

Coherent effects in inverse compton scattering in the high frequency region

The conditions under which a cooperative emission from different friges occurs in the scattering between a relativistic electron beam and two interfering laser beams are discussed. In particular, the conditions to have an electron grating are discussed.     

Channel spin mixing ratios in high resolution proton inelastic scattering

A simple method of determining both the magnitudes and phase for channel spin mixing is described. An example is presented and a variety of applications discussed.     

Absorption and scattering imaging of tissue with steady-state second-differential spectral-analysis tomography

A novel approach to reconstructing both the absorption and the scattering properties of a turbid medium simultaneously from steady-state broadband spectral measurements is presented that utilizes second-differential fitting to the water spectrum to estimate the optical path length in tissue. Theoretical and experimental evidence is provided to demonstrate the robust accuracy of the spectroscopy approach and reconstructed absorption images. The steady-state broadband CCD system has the potential to provide accurate chromophore imaging without the technological complexity of time- or frequency-domain systems.     

Non-linear pair production in scattering of photons on ultra-short laser pulses at high energy

We consider scattering of a photon on a short intense laser pulse at high energy. We argue that for ultra-short laser pulses the interaction is coherent over the entire length of the pulse. At low pulse intensity I the total cross section for electron–positron pair production is proportional to I  . However, at pulse intensities higher than the characteristic value Is$I_s$, the total cross section saturates – it becomes proportional to the logarithm of intensity. This non-linear effect is due to multi-photon interactions. We derive the total cross section for pair production at high energies by resuming the multi-photon amplitudes to all orders in intensity. We calculate the saturation intensity Is$I_s$ and show that it is significantly lower than the Schwinger's critical value. We discuss possible experimental tests.     

Bulk evaluation of ductile damage development using high resolution tomography and laminography

Ductile fracture of metals is accompanied at the microscopic scale with the appearance of damage, in the form of small cavities. Damage progress is divided into three distinct and consecutive phases: initiation, growth and coalescence. This article illustrates the use of three-dimensional nondestructive imaging to study this damage development. Two techniques, mainly based on the attenuation of X-rays are now used for this type of studies at high resolution: tomography and laminography. The interest of laminography is that samples with larger dimensions (in the form of sheets) than the conventional tomography ones can be used. Examples of images obtained with the two techniques, as well as quantification using X-ray tomography, are presented.     

Nondestructive evaluation of nanoscale structures: inverse scattering approach

In this paper, we demonstrate how subwavelength images of nanoscale structures can be obtained from the measurements of electromagnetic fields scattered by the objects, via an enhanced inverse scattering approach, which takes into account the multiple-scattering effect and allows the detectors to be placed in the far field. Specifically, the method is a combination of the transverse electric (TE) incidence and the subspace-based optimization method (SOM). It is observed that a wide continuous range of integer values of leading singular values can yield satisfactory reconstruction results, and even if the antennas for radiating and receiving the electromagnetic wave can only be arranged on one side of the scatterers, due to the limitation in the real world, the proposed method is still capable of achieving high resolution for the reconstructed patterns with rapid convergence rates and robust immunity to high noise corruption (33%).     

Imaging of human breast tissue using polarization sensitive optical coherence tomography

We report a study on the use of polarization sensitive optical coherence tomography (PSOCT) for discriminating malignant (invasive ductal carcinoma), benign (fibroadenoma) and normal (adipocytes) breast tissue sites. The results show that while conventional OCT, that utilizes only the intensity of light back-scattered from tissue microstructures, is able to discriminate breast tissues as normal (adipocytes) and abnormal (malignant and benign) tissues, PS-OCT helps in discriminating between malignant and benign tissue sites also. The estimated values of birefringence obtained from the PSOCT imaging show that benign breast tissue samples have significantly higher birefringence as compared to the malignant tissue samples.     

A feasible high spatiotemporal resolution breast DCE-MRI protocol for clinical settings

Three dimensional bilateral imaging is the standard for most clinical breast dynamic contrast-enhanced (DCE) MRI protocols. Because of high spatial resolution (sRes) requirement, the typical 1–2 min temporal resolution (tRes) afforded by a conventional full-k-space-sampling gradient echo (GRE) sequence precludes meaningful and accurate pharmacokinetic analysis of DCE time-course data. The commercially available, GRE-based, k-space undersampling and data sharing TWIST (time-resolved angiography with stochastic trajectories) sequence was used in this study to perform DCE-MRI exams on thirty one patients (with 36 suspicious breast lesions) before their biopsies. The TWIST DCE-MRI was immediately followed by a single-frame conventional GRE acquisition. Blinded from each other, three radiologist readers assessed agreements in multiple lesion morphology categories between the last set of TWIST DCE images and the conventional GRE images. Fleiss’ κ test was used to evaluate inter-reader agreement. The TWIST DCE time-course data were subjected to quantitative pharmacokinetic analyses. With a four-channel phased-array breast coil, the TWIST sequence produced DCE images with 20 s or less tRes and ~ 1.0×1.0×1.4 mm³ sRes. There were no significant differences in signal-to-noise (P=.45) and contrast-to-noise (P=.51) ratios between the TWIST and conventional GRE images. The agreements in morphology evaluations between the two image sets were excellent with the intra-reader agreement ranging from 79% for mass margin to 100% for mammographic density and the inter-reader κ value ranging from 0.54 (P<.0001) for lesion size to 1.00 (P<.0001) for background parenchymal enhancement. Quantitative analyses of the DCE time-course data provided higher breast cancer diagnostic accuracy (91% specificity at 100% sensitivity) than the current clinical practice of morphology and qualitative kinetics assessments. The TWIST sequence may be used in clinical settings to acquire high spatiotemporal resolution breast DCE-MRI images for both precise lesion morphology characterization and accurate pharmacokinetic analysis.     

Small angle neutron scattering at very high time resolution: Principle and simulations of ‘TISANE’

The time resolution of SANS experiments is generally limited by frame overlap to some ms. We report on a new time-resolved stroboscopic SANS method, called TISANE, offering μs time resolution without a major sacrifice in intensity by making use of very large frame overlap. We may explore a new field in neutron scattering and complement the emerging field of time resolved small angle X-ray scattering. Here we discuss the principle of TISANE, its mathematical treatment and its limitations.     

A high resolution neutron spectrometer for quasielastic scattering on the basis of spin-echo and magnetic resonance

We propose a high resolution neutron spectrometer, which combines the spin-echo principle with the separated coil magnetic resonance technique. The introduction of magnetic resonance instead of static spin-flippers in the spin-echo spectrometer allows the replacement of its high magnetic fields by low guide fields. The new technique represents a generalisation of the conventional spin-echo spectrometer.This property also holds for the double statistical-[8] the double Fourier- [9] and the Fotof-spectrometer [10], but those have not been built to our knowledge     

Highly efficient beamline and spectrometer for inelastic soft X‐ray scattering at high resolution

The design, construction and commissioning of a beamline and spectrometer for inelastic soft X‐ray scattering at high resolution in a highly efficient system are presented. Based on the energy‐compensation principle of grating dispersion, the design of the monochromator–spectrometer system greatly enhances the efficiency of measurement of inelastic soft X‐rays scattering. Comprising two bendable gratings, the set‐up effectively diminishes the defocus and coma aberrations. At commissioning, this system showed results of spin‐flip, d–d and charge‐transfer excitations of NiO. These results are consistent with published results but exhibit improved spectral resolution and increased efficiency of measurement. The best energy resolution of the set‐up in terms of full width at half‐maximum is 108 meV at an incident photon energy tuned about the Ni L₃‐edge.     

Extraction of optical scattering parameters and attenuation compensation in optical coherence tomography images of multilayered tissue structures

A recently developed analytical optical coherence tomography (OCT) model [Thrane et al., J. Opt. Soc. Am. A 17, 484 (2000)] allows the extraction of optical scattering parameters from OCT images, thereby permitting attenuation compensation in those images. By expanding this theoretical model, we have developed a new method for extracting optical scattering parameters from multilayered tissue structures in vivo. To verify this, we used a Monte Carlo (MC) OCT model as a numerical phantom to simulate the OCT signal for heterogeneous multilayered tissue. Excellent agreement between the extracted values of the optical scattering properties of the different layers and the corresponding input reference values of the MC simulation was obtained, which demonstrates the feasibility of the method for in vivo applications. This is to our knowledge the first time such verification has been obtained, and the results hold promise for expanding the functional imaging capabilities of OCT.     

Unitary approximation for radiative high energy scattering processes: Application to Bhabha scattering

We describe how to apply the unitary approximation to high energy scattering processes which involve the radiation of arbitrarily many photons. We compare our results to calculations of inclusive quantities using leading log resummation techniques well known from QCD. In contrast to the latter method the unitary approximation is also appropriate for differential cross sections. The Monte Carlo implementation of the method is discussed and detailed results are given for the case of radiative Bhabha scattering.     

The scattering of ultrasound by cylinders: implications for diffraction tomography

The validity of wave equations employed as system models in acoustical diffraction tomography is investigated using simulations and measurements of the scattering of plane ultrasound waves by cylinders. It is demonstrated by simulation and experiment that it can be appropriate to neglect density fluctuations and shear waves, implying that the commonly used form of the wave equation suitably describes scattering by fluctuations of acoustic speed and absorption. Diffraction tomographic reconstructions of simulated data reveal the importance of absorption, the behavior of the real and imaginary parts of the reconstructed refractive index, and the relative advantages and limitations of the Born and Rytov approximate transformations.