Joint phase retrieval and alignment via deep learning for advancing 3D refractive index measurement in interferometric tomography

Quantitative phase tomography

High-resolution imaging in thick biological tissues beyond a few transport mean free path of photons remains a formidable challenge to modern science and technology. Recent advancements in optical tomography have enabled the reconstruction of the three-dimensional (3D) refractive index distribution in biological samples, which is crucial in the prediction of light propagation in that sample. Here we propose a new technique for imaging second harmonic radiating imaging probes (SHRIMPs) through a tissue using harmonic holography based on the extracted refractive index map. We analyze the spatiotemporal intensity distribution of light pulses using a new model that separate scattering by orders (times of deflections) and show that wide-field excitation and detection of the SHG in tissues beyond one cm thickness is possible with resonant nonlinear plasmonic nanocavities as the SHRIMP. We demonstrate with numerical simulations that the 3D image of SHRIMPs can be extracted by matching the measured second harmonic speckle pattern with that predicted for each point in the sample given the refractive index. We analyze the impact of measurement error in the refractive index on the SNR of the recovered image. We further discuss the influence of the frequency-domain memory effect.

As an expansion of coherent diffraction imaging, ptychographic iterative engine (PIE) not only inherits advantages such as ultra-high resolution and compact optical system, but also expands the field of view in quantitative imaging, thus PIE is widely used in short wavelength imaging such as X-ray and electron beam imaging, and then extended to visible light field. However, PIE requires coherent illumination for both phase and amplitude retrieval, while traditional X-ray or electron beam sources often cannot satisfy this strict coherent condition, which leads to poor-quality information retrieval with low signal-to-noise ratio. Though several proposed methods such as multiple wavelength and multi-mode algorithms can eliminate incoherency influence to some extent, various details such as quantitative spectrum of illuminating source should be obtained before information retrieval, which complicates computing procedures. In addition, it is hard to acquire the spectrum of the illuminating source in most cases. In order to acquire high-quality information based on PIE with partially coherent illumination, a newly designed enhanced phase retrieval method for weakly scattering samples in PIE with partially coherent illumination is presented in this paper, in which only the bright field of the diffraction patterns is used in the iterative procedures mimicking the coherent cases especially for weakly scattering samples without any prior illuminating details. The bright field area can be regarded as purely coherent diffraction patterns composed of a strengthened zeroth order beam and a weakened diffracted beam. While the dark-field area generated by interference of diffracted beams cannot satisfy the requirement for coherence, therefore, dark-field diffraction patterns should be excluded in sample information extraction and only the bright field is used for phase retrieval via iterative process. Compared with the proposed multiple wavelength and multi-mode algorithms, the proposed method can simplify sample reconstructing procedures due to needing no prior knowledge. Moreover, in order to enhance the information of weakly scattering samples in retrieval, high order iteration method is also introduced in the paper. Since the bright field can be regarded as purely coherent diffraction patterns composed of a strengthened zeroth order beam and a weakened diffracted beam. For weakly scattering sample, the weakened diffracted beam is much lower than zeroth order beam, thus it is difficult to acquire high-contrast information with classical PIE algorithms. Introducing high order iterative tactic, the contrast of weakly scattering sample is obviously improved and the details of weakly scattering sample can be retrieved clearly. Both theoretical analysis and numerical simulations are illustrated in detail, proving the robustness and availability of the designed method: high-contrast phase information can be obtained with the proposed method, while traditional phase retrieval algorithm almost loses all details of the sample. In order to mimic the real experimental situation, a 30 dB white noise is added into the simulation, the details of weakly scattering sample phase information can also be retrieved clearly by using the bright field of the diffraction patterns with high order iteration method. With the newly designed enhanced phase retrieval method for weakly scattering samples with partially coherent illumination, sample retrieval via PIE can not only use ordinary X-ray source or electron beam as illumination source, thereby avoiding the dependence on complete coherent source, but also obviously improve the retrieval quality of the sample characteristics, which widely expands the application fields of the PIE.

A method of tomographic phase retrieval is developed for multi-material objects whose components each has a distinct complex refractive index. The phase-retrieval algorithm, based on the Transport-of-Intensity equation, utilizes propagation-based X-ray phase contrast images acquired at a single defocus distance for each tomographic projection. The method requires a priori knowledge of the complex refractive index for each material present in the sample, together with the total projected thickness of the object at each orientation. The requirement of only a single defocus distance per projection simplifies the experimental setup and imposes no additional dose compared to conventional tomography. The algorithm was implemented using phase contrast data acquired at the SPring-8 Synchrotron facility in Japan. The three-dimensional (3D) complex refractive index distribution of a multi-material test object was quantitatively reconstructed using a single X-ray phase-contrast image per projection. The technique is robust in the presence of noise, compared to conventional absorption based tomography.

We accurately reconstruct three-dimensional (3-D) refractive index (RI) distributions from highly ill-posed two-dimensional (2-D) measurements using a deep neural network (DNN). Strong distortions are introduced on reconstructions obtained by the Wolf transform inversion method due to the ill-posed measurements acquired from the limited numerical apertures (NAs) of the optical system. Despite the recent success of DNNs in solving ill-posed inverse problems, the application to 3-D optical imaging is particularly challenging due to the lack of the ground truth. We overcome this limitation by generating digital phantoms that serve as samples for the discrete dipole approximation (DDA) to generate multiple 2-D projection maps for a limited range of illumination angles. The presented samples are red blood cells (RBCs), which are highly affected by the ill-posed problems due to their morphology. The trained network using synthetic measurements from the digital phantoms successfully eliminates the introduced distortions. Most importantly, we obtain high fidelity reconstructions from experimentally recorded projections of real RBC sample using the network that was trained on digitally generated RBC phantoms. Finally, we confirm the reconstruction accuracy using the DDA to calculate the 2-D projections of the 3-D reconstructions and compare them to the experimentally recorded projections.

We discuss theoretical, experimental and numerical aspects of several new techniques for quantitative phase-contrast tomography using, for example, unfiltered radiation from a polychromatic X-ray microfocus source. The proposed algorithms allow one to reconstruct the three-dimensional distribution of complex refractive index in a sample consisting of one or more constituent materials, given one or more projection images per view angle. If the sample is weakly absorbing or consists predominantly of a single material, these reconstruction algorithms can be simplified and fewer projections may be required for an unambiguous quantitative reconstruction of the spatial distribution of the refractive index. In the case of weakly absorbing samples, the reconstruction algorithm is shown to be achromatic and stable with respect to high-spatial-frequency noise, in contrast to conventional tomography. A variation of the algorithm exploits the natural combination of binary tomography with a phase-retrieval method that makes explicit use of the single-material nature of the sample. Such consistent use of <i>a priori </i>knowledge dramatically reduces the number of required projections, implying significantly reduced dose and scanning time when compared to most alternative phase-contrast tomography methods. Experimental demonstrations are also given, using data from a point-projection X-ray microscope. The refractive index distribution, in test samples of both a polymer fibre scaffold and an adult mouse, is accurately reconstructed from polychromatic phase-contrast data. Applications of the new techniques to rapid non-destructive testing in materials science and biomedical imaging are considered.

The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete Fourier transforms due to their high computational efficiency. However, the mathematics underpinning these algorithms is typically formulated using continuous mathematics, which can result in a loss of spatial resolution in the reconstructed images. Herein we investigate how phase retrieval algorithms for propagation-based phase-contrast X-ray imaging can be rederived using discrete mathematics and result in more precise retrieval for single- and multi-material objects and for spectral image decomposition. We validate this theory through experimental measurements of spatial resolution using computed tomography (CT) reconstructions of plastic phantoms and biological tissues, using detectors with a range of imaging system point spread functions (PSFs). We demonstrate that if the PSF substantially suppresses high spatial frequencies, the potential improvement from utilising the discrete derivation is limited. However, with detectors characterised by a single pixel PSF (e.g. direct, photon-counting X-ray detectors), a significant improvement in spatial resolution can be obtained, demonstrated here at up to 17%.

Imaging systems' performance at low light intensity is affected by shot noise, which becomes increasingly strong as the power of the light source decreases. In this Letter, we experimentally demonstrate the use of deep neural networks to recover objects illuminated with weak light and demonstrate better performance than with the classical Gerchberg-Saxton phase retrieval algorithm for equivalent signal over noise ratio. The prior contained in the training image set can be leveraged by the deep neural network to detect features with a signal over noise ratio close to one. We apply this principle to a phase retrieval problem and show successful recovery of the object's most salient features with as little as one photon per detector pixel on average in the illumination beam. We also show that the phase reconstruction is significantly improved by training the neural network with an initial estimate of the object, as opposed to training it with the raw intensity measurement.

A method for routine, but precise measurements of refractive index is described. The method is fast and accurate. It is based on the analysis of interference fringes, and uses positions of the fringe maxima and/or minima and a precise measurement of sample thickness to extract refractive index. An extremely dense dataset of refractive index values over the entire spectral range of interest can be routinely obtained.

The first Born and Rytov approximations of scattering theory are introduced in their less familiar near-field versions. Two algorithms for phase retrieval based on these approximations are then described. It is shown theoretically and by numerical simulations that, despite the differences in their formulation, the two algorithms deliver fairly similar results when used for optical phase retrieval in the near and intermediate fields. The algorithms are applied to derive explicit solutions to four phase-retrieval problems of practical relevance to quantitative phase-contrast imaging and tomography. An example of successful phase reconstruction by use of the Born-type algorithm with an experimental x-ray image is presented.

Polarization-maintaining fiber based macehead shaped interferometric sensor for accurate measurement of refractive index and temperature

In this paper it is shown that temperature, refractive index and density and also convective heat transfer coefficient around a vertical axisymmetric cylindrical wire can be measured by the Michelson Interferometer. In experimental setup, a vertical wire has been put in one of the arms of the Michelson Interferometer. By applying voltage to the wire, temperature gradient is created around the wire. These phenomena curved the linear Michelson fringes. By measuring the fringes shift and applying the Abel transform, the distribution of refractive index can be evaluated. This distribution gives the density distribution. Minimum value for refractive index and density is found on the surface of the wire. For the far distance from the wire, density and refractive index approaches to the room values. Air density was evaluated experimentally, which is compatible with its reported value at definite weather conditions. Considering high reflectance of the wire, its thermal radiation is low and heat mostly transfers by convection. Convective heat transfer coefficient is measured experimentally which agrees with last results.

Flexible Plasma Enhanced Chemical Vapor Deposition (PECVD) technology of Diamond Like Carbon (DLC) thin film preparation on the surface of Si and organic glasses has been elaborated. Modification of PECVD equipment has been implemented by integrating ion and magnetron sources. In this paper toluene (C 7 H 8 ) has been used as a nanocmposite film forming hydrocarbon which decomposition yields to the multi component plasma in vacuum chamber. Nitrogen has been used as a dopand. Investigation of plasma composition influence to the optical and mechanical properties of DLC films has been observed. The presence of sp 3 and sp 2 hybridization states have been proven by Raman spectroscopy and their ratios have been estimated with the help of I D , I G characteristic lines for different technological conditions. High precision refractive index and thickness measurements of DLC films have been implemented by means of laser ellipsometer. Refractive indices of prepared films have been varied in the region 1.5-3.1 and thicknesses have been varied in the region 50-250 nm. Extraordinary change in refractive index has been explained with the help of formation of differently sized sp 2 carbon based clusters in the sp 3 matrix. Different types of carbon and hydrogen bonds have been observed in the obtained structures by means of FTIR. Obvious prospectives of DLC nanocomposite film as a promissing nanophotonic material has been discussed.

Optical properties of thin films and bulk materials at short wavelengths, including 157 nm and shorter, are needed for development of new lithographic processes, new fundamental science, and new metrology in the semiconductor, optical and data storage industries. Variable angle spectroscopic ellipsometry offers non-destructive and precise measurement of thin film thickness and refractive index in the wavelength range from 140 nm to 1700 nm (0.73 eV to 8.9 eV). The addition of short wavelengths allows analysis of multilayer dielectric stacks, often difficult to do using visible spectroscopy alone. Another major application is in study of wide bandgap materials such as SiC and GaN related compound semiconductors for blue lasers and detectors. This paper reviews the present status of spectroscopic ellipsometry applications in the vacuum ultraviolet.

This work describes a simple but novel analytical method for in situ monitoring of the diffusion process of drugs in hydrogels based on refractive index measurements. The diffusion process was monitored by recording the refraction of a laser beam passing through a triangular cell, which allows the determination of changes in the refractive index distribution from the deviated distance of the linear beam. Compared to conventional methods, this new method exhibits advantages such as more simplicity, lower cost, and speed. Further, the refractive index method permits the determination of the concentration distribution of solutes in the hydrogels at any time during the diffusion process under nondestructive circumstances. The precision was determined by successfully applying this new method to the diffusion of a typical antibiotic drug, cefazolin sodium, in agarose gels of various concentrations. By employing Fick's second law, the diffusion behavior was investigated and the diffusion coefficients of cefazolin sodium in agarose gels were therefore obtained. Amsden's physical model based on obstruction effect was applied to the simulation of the diffusion process of cefazolin sodium and turned out to fit the results quite well.