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Significance: Large space-bandwidth product is highly desirable in many biomedical imaging. Fourier ptychographic microscopy (FPM) is a computational imaging technique that can significantly increase the space-bandwidth product of a standard microscope. The illuminator of a Fourier ptychographic microscope is not flexible at present, and it is inconvenient to meet different imaging needs. Aim: An illuminator based on a two-axis motorized rotation stage was presented to provide a more flexible illuminating way with the goal of meeting different imaging needs. Approach: The illuminator adopts a concentric illuminating method to provide coherent illumination in any direction on the sample plane. The sampling pattern can be freely designed and changed according to the parameters of the imaging system. A dither removing algorithm was proposed to remove the potential dither influence introduced in the image acquisition process. Results: The illuminator could be conveniently integrated into different imaging systems. The feasibility and flexibility were demonstrated by applying it to imaging systems with numerical aperture of 0.045 and 0.01. The resolution gain is about 4- and 13-fold, respectively. The effectiveness of the dither removing algorithm was validated in both simulation and experiment. Conclusions: A more flexible illuminator for FPM was presented to meet different imaging needs. A dither removing algorithm was proposed to remove dither influence.

Purpose: We present a phase-contrast x-ray tomography study of wild type C57BL/6 mouse hearts as a nondestructive approach to the microanatomy on the scale of the entire excised organ. Based on the partial coherence at a home-built phase-contrast μ - CT setup installed at a liquid metal jet source, we exploit phase retrieval and hence achieve superior image quality for heart tissue, almost comparable to previous synchrotron data on the whole organ scale. Approach: In our work, different embedding methods and heavy metal-based stains have been explored. From the tomographic reconstructions, quantitative structural parameters describing the three-dimensional (3-D) architecture have been derived by two different fiber tracking algorithms. The first algorithm is based on the local gradient of the reconstructed electron density. By performing a principal component analysis on the local structure-tensor of small subvolumes, the dominant direction inside the volume can be determined. In addition to this approach, which is already well established for heart tissue, we have implemented and tested an algorithm that is based on a local 3-D Fourier transform. Results: We showed that the choice of sample preparation influences the 3-D structure of the tissue, not only in terms of contrast but also with respect to the structural preservation. A heart prepared with the evaporation-of-solvent method was used to compare both algorithms. The results of structural orientation were very similar for both approaches. In addition to the determination of the fiber orientation, the degree of filament alignment and local thickness of single muscle fiber bundles were obtained using the Fourier-based approach. Conclusions: Phase-contrast x-ray tomography allows for investigating the structure of heart tissue with an isotropic resolution below 10 μ m . The fact that this is possible with compact laboratory instrumentation opens up new opportunities for screening samples and optimizing sample preparation, also prior to synchrotron beamtimes. Further, results from the structural analysis can help in understanding cardiovascular diseases or can be used to improve computational models of the heart.

We propose a new intrinsic cancer marker in fixed tissue biopsy slides, which is based on the local spatial autocorrelation length obtained from quantitative phase images. The spatial autocorrelation length in a small region of the tissue phase image is sensitive to the nanoscale cellular morphological alterations and can hence inform on carcinogenesis. Therefore, this metric can potentially be used as an intrinsic cancer marker in histopathology. Typically, these correlation length maps are calculated by computing 2D Fourier transforms over image sub-regions – requiring long computational times. In this paper, we propose a more time efficient method of computing the correlation map and demonstrate its value for diagnosis of benign and malignant breast tissues. Our methodology is based on highly sensitive quantitative phase imaging data obtained by spatial light interference microscopy (SLIM).

Bank of England notes of £20 denomination have been studied using infrared spectroscopy in order to generate a method to identify forged notes. An aim of this work was to develop a non-destructive method so that a small, compact Fourier transform infrared spectrometer (FT-IR) instrument could be used by bank workers, police departments or others such as shop assistants to identify forged notes in a non-lab setting. The ease of use of the instrument is the key to this method, as well as the relatively low cost. The presence of a peak at 1400 cm(-1) arising from νasym (CO3(2-)) from the blank paper section of a forged note proved to be a successful indicator of the note's illegality for the notes that we studied. Moreover, differences between the spectra of forged and genuine £20 notes were observed in the ν(OH) (ca. 3500 cm(-1)), ν(C-H) (ca. 2900 cm(-1)) and ν(C=O) (ca. 1750 cm(-1)) regions of the IR spectrum recorded for the polymer film covering the holographic strip. In cases where these simple tests fail, we have shown how an infrared microscope can be used to further differentiate genuine and forged banknotes by producing infrared maps of selected areas of the note contrasting inks with background paper.

We propose a nonscanning three-dimensional (3-D) fluorescence imaging technique using the transport of intensity equation (TIE) and free-space Fresnel propagation. In this imaging technique, a phase distribution corresponding to defocused fluorescence images with a point-light-source-like shape is retrieved by a TIE-based phase retrieval algorithm. From the obtained phase distribution, and its corresponding amplitude distribution, of the defocused fluorescence image, various images at different distances can be reconstructed at the desired plane after Fresnel propagation of the complex wave function. Through the proposed imaging approach, the 3-D fluorescence imaging can be performed in multiple planes. The fluorescence intensity images are captured with the help of an electrically tunable lens; hence, the imaging technique is free from motion artifacts. We present experimental results corresponding to microbeads and a biological sample to demonstrate the proposed 3-D fluorescence imaging technique.

Longitudinal neutron resonance spin echo (LNRSE) spectroscopy offers very high energy resolution due to the self correction of the resonant spin flippers, and a wide dynamical range nominally exceeding six orders of magnitude in resolution down to sub-ps range. In this paper, the technical realisation how to achieve such low Fourier times at the spectrometer RESEDA at the MLZ Garching is described. The requirements of data collection and data analysis in the limit of very low Fourier times, notably those related to the breakdown of the spin echo approximation, are discussed. A method to infer the scattering function from the experimental data under large energy tansfers beyond the spin echo approximation is presented.

A clinical need exists for low-cost and noninvasive imaging tools capable of detecting inflammation in the joints of inflammatory arthritis patients. Previous studies have reported an optical contrast between inflamed and noninflamed joints resulting from distinct absorption and scattering properties. Accurate classification using nonocclusion-based continuous wave, transillumination imaging was limited to patient-specific changes during follow-up examination as opposed to single time-point examination, which was attributed to high intersubject variability. In distinction from previous work, optical images were acquired from the dorsal side with illumination on the palmar side and features about the spatial distribution of transmitted light along the joint were assessed using a normalized Fourier transform method. Results using this approach demonstrated an area under receiver operator curve of up to 0.888 for detecting inflammation in a pilot study involving single time-point examination of 144 joints from 21 rheumatology patients. This workflow may enable future development of clinically viable, low-cost devices for assessing inflammation in arthritis patients, without the need for cuff occlusion or comparison to baseline.

The molecular imaging of paper cross sections containing the wet-strength additive poly(amidoamine)–epichlorohydrin (PAE) was effected by Fourier transform infrared (FT-IR) spectroscopic imaging. Thin cross sections of laboratory sheet samples were prepared and transferred onto CaF2 substrates. A laboratory sheet sample without PAE acted as a reference. Principal component analysis (PCA) was applied to identify and to reveal the distribution of PAE across the section. Differences in the loading plots of the fourth and fifth principal components for the sheets with and without PAE were found in the region of the amide I, amide II, and amine bands within a variance of 0.4–0.8 %. The score images of the PCA reveal inhomogeneous distribution of PAE. Small areas of higher concentration of PAE occur across the cross section. The aim of this study was to demonstrate that FT-IR spectroscopic imaging provides spatially resolved quantitative information about the chemical composition of paper, which was successfully achieved.

The work presented in this paper details the design and performance characteristics of a new hyperspectral visible imaging technique. Rather than using optical filters or a dispersing element, this design implements Fourier transform spectroscopy to achieve spectral discrimination. One potentially powerful application of this new technology is the nondestructive analysis and authentication of written and printed documents. Document samples were prepared using red, blue, and black inks. The samples were later altered using a different ink of the same color. While the alterations are undetectable to the naked eye, the alterations involving the blue and black inks were easily detected when the spectrally resolved images were viewed. Analysis of the sample using the red inks was unsuccessful. A 2004 series $20 bill was imaged to demonstrate the application to document authentication. The results argue that counterfeit detection and quality control during printing are plausible applications of Fourier transform hyperspectral visible imaging. All of the images were subjected to fuzzy c-means cluster analysis in an effort to objectively analyze and automate image analysis. Our results show that cluster analysis can distinguish image features that have remarkably similar visible transmission spectra.

The most important quantitative aspects of computational structural crystallography can be introduced in a satisfactory way using 1D truncated and periodic Gaussian functions to represent the atoms in a crystal lattice. This paper describes in detail and demonstrates 1D structural crystallography starting with the definition of such truncated Gaussians. The availability of the computer programme CRONE makes possible the repetition of the examples provided in the paper as well as the creation of new ones.