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We examine the physical limitations and performance of spatially coherent imaging systems under defocused conditions using a modified two-point resolution criterion. By comparing coherent and incoherent illumination regimes, in defocused conditions, we highlight the peculiar advantages of coherent systems in resolving closely spaced features while maintaining a high depth of field. The analysis identifies two primary contributions to image degradation in coherent defocused systems: image broadening and interference-related contrast reduction. Through a specifically designed analytical framework, this study confirms that resolution degradation in coherent imaging is characterized by a square root dependence on defocusing distance, irrespective of the numerical aperture. This behavior starkly contrasts with incoherent imaging, where the resolution deteriorates linearly with defocusing and exhibits a strong dependence on the system's numerical aperture. Furthermore, we provide explicit analytical expressions for contrast loss and minimum resolvable object size under defocused coherent conditions, offering deeper insights into their relation with system parameters. These results corroborate the superior performance of coherent imaging in resolving fine details in defocused environments, challenging conventional optical paradigms. Our findings not only extend the theoretical understanding of coherent imaging but also establish practical guidelines to optimize optical systems for high-resolution applications. [ABSTRACT FROM AUTHOR]

Recent advancements in quantum and quantum-inspired imaging techniques have enabled high-resolution 3D imaging through photon correlations. These techniques exhibit reduced degradation of image resolution for out-of-focus samples compared to conventional methods (i.e., intensity-based incoherent imaging). A key advantage of these correlation-based approaches is their independence from the system numerical aperture (NA). Interestingly, both improved resolution of defocused images and NA-independent scaling are linked to the spatial coherence of light. This suggests that while correlation measurements exploit spatial coherence, they are not essential for achieving this imaging advantage. This discovery has led to the development of optical systems that achieve similar performance by using spatially coherent illumination and relying on intensity measurements: direct 3D imaging with NA-independent resolution was recently demonstrated in a correlation-free setup using LED light. Here, we explore the physics behind the enhanced performance of defocused coherent imaging, showing that it arises from the modification of the sample's spatial harmonic content due to diffraction, unlike the blurring seen in conventional imaging. The results we present are crucial for understanding the implications of the physical differences between coherent and incoherent imaging, and are expected to pave the way for the practical application of the discovered phenomena. [ABSTRACT FROM AUTHOR]

Wide‐field imaging is widely adopted due to its fast acquisition, cost‐effectiveness, and ease of use. Its extension to direct volumetric applications, however, is burdened by the trade‐off between resolution and depth of field (DOF), dictated by the numerical aperture of the system. It is demonstrated that such trade‐off is not intrinsic to wide‐field imaging, but stems from the spatial incoherence of light: images obtained through spatially coherent illumination are shown to have resolution and DOF independent of the numerical aperture. This fundamental discovery enables to demonstrate an optimal combination of coherent resolution‐DOF enhancement and incoherent tomographic sectioning for scanning‐free, wide‐field 3D microscopy on a multicolor histological section. [ABSTRACT FROM AUTHOR]

We examine the physical limitations and performance of spatially coherent imaging systems under defocused conditions using a modified two-point resolution criterion. By comparing coherent and incoherent illumination regimes, in defocused conditions, we highlight the peculiar advantages of coherent systems in resolving closely spaced features while maintaining a high depth of field. The analysis identifies two primary contributions to image degradation in coherent defocused systems: image broadening and interference-related contrast reduction. Through a specifically designed analytical framework, this study confirms that resolution degradation in coherent imaging is characterized by a square root dependence on defocusing distance, irrespective of the numerical aperture. This behavior starkly contrasts with incoherent imaging, where the resolution deteriorates linearly with defocusing and exhibits a strong dependence on the system’s numerical aperture. Furthermore, we provide explicit analytical expressions for contrast loss and minimum resolvable object size under defocused coherent conditions, offering deeper insights into their relation with system parameters. These results corroborate the superior performance of coherent imaging in resolving fine details in defocused environments, challenging conventional optical paradigms. Our findings not only extend the theoretical understanding of coherent imaging but also establish practical guidelines to optimize optical systems for high-resolution applications.

Diffraction limits the minimum resolvable feature on remotely observed targets to $\lambda R_{c}/A_{c}$, where $\lambda$ is the operating wavelength, $R_{c}$ is the range to the target and $A_{c}$ is the diameter of the observing aperture. Resolution is often further reduced by scatter or turbulence. Here we show that analysis of scattered coherent illumination can be used to achieve resolution proportional to $\lambda R_{s}/A_{s}$, where $R_{s}$ is the range between the scatterer and the target and $A_{s}$ is the diameter of the observed scatter. Theoretical analysis suggests that this approach can yield resolution up to 1000× better than the diffraction limit. We present laboratory results demonstrating $>30\times$ improvement over direct observation. In field experiments, we use a 23.5 cm aperture telescope at 100 m to resolve 27.78 $\mu$m features, improving on diffraction limited resolution by $>10\times$. The combination of lab and field results demonstrates the potential of scatter analysis to achieve multiple order of magnitude improvements in resolution in applications spanning microscopy and remote sensing.

The coherent nature of imaging in synthetic aperture radar (SAR) inevitably gives rise to speckle noise, a challenge exacerbated by the constrained bandwidth and limited look angles. Among the despeckling algorithms, convolutional neural networks (CNNs) have dominated the forefront of SAR image despeckling, showcasing state-of-the-art performance. CNN-based SAR image despeckling methods excel in learning complex features in an image, while they often struggle with a tendency to induce blurring, leading to a loss of texture information in SAR imagery. We hypothesize that this is mainly caused by the inappropriate use of generic loss functions for despeckling that tend to yield a washed-out blurring effect or introduce artifacts during the denoising process. In this article, we propose a new loss function for an existing CNN architecture that is designed to reduce washed-out blurring effects and is capable of enhancing edges and small-scale features while suppressing noise. The loss function we propose is based on the logarithm of discrete cosine transform images, with a perspective to maintain a nuanced equilibrium between high- and low-energy features in an image, meanwhile maintaining acceptable noise suppression. In comparison to established loss functions applied in SAR image despeckling, experimental results show that the CNNs trained with the proposed loss function not only enhance multiple objective metrics but also exhibit considerable advantages in terms of visual effects.

The problem of diffraction of slow neutrons with a de Broglie wavelength λ ~10-10 m in a crystal with a deformed lattice is considered. Based on the Hamilton equations describing the dynamic diffraction of slow neutrons, the features of the formation of a dynamic diffraction field in a lattice in various regions of the deformation field characteristics, including weak fields, slowly changing fields and rapidly changing fields are discussed. Using a particular example of a deformation field with a displacement field quadratic in coordinates, analytical solutions are obtained for the wave functions of transmitted and reflected lattice waves. [ABSTRACT FROM AUTHOR]

For traditional imaging systems, high imaging quality and system miniaturization are often contradictory. In order to meet the requirements of high imaging quality and system miniaturization, this paper proposes a method to correct the aberration of coherent imaging optical systems. The method is based on the idea of phase recovery and the imaging principle of a coherent imaging system to recover the aberrations at the exit pupil of the system. According to the recovered aberrations, conjugate filters are constructed to correct the image quality in the frequency domain. The imaging quality of the system is improved without changing the original optical path, and the simplicity of the system is guaranteed. To solve the pupil frequency domain aberration more accurately, this paper adopts the dual competition and parallel recombination strategy based on the genetic algorithm and introduces the disaster model. The improved genetic algorithm can effectively restrain the appearance of the "precocity" phenomenon. Finally, the paraxial imaging optical path is simulated and verified by experiments. The results show that, after aberration correction, the image sharpness is improved and the edge information is richer, which verifies the feasibility of the coherent imaging system image quality enhancement method proposed in this paper. [ABSTRACT FROM AUTHOR]

Fourier ptychography (FP) is a computational imaging technique with the advantage that it can obtain large field-of-view (FOV) and high-resolution (HR) imaging. We propose an algorithm for Fourier ptychography based on reweighted amplitude flow (RAF) with regularization by denoising (RED) and deep decoder (DD), which is an untrained deep generative model. The proposed method includes two loops, using reweighted amplitude flow with regularization by denoising as an inner loop for phase retrieval and deep decoder for further denoising as an outer loop in the Fourier ptychography recovery system. The proposed method does not need any training dataset, just adds a little computer time during the image recovery process. The proposed method has no bias due to training images, which is different from other deep learning methods. The experimental results show that the proposed method can improve the reconstruction quality in both PSNR and SSIM.

Coherent diffraction microscopy (CDM) is a potential approach to image micromaterials at atomic resolution without crystals. Due to the lack of high-angle scattering, the achieved resolution is limited to several nanometers. Small-angle scattering allows researchers to reveal high-resolution 3D structures of specimens by fitting 1D diffraction signals. However, prerequisite 3D models and non-unique solutions restrict the potential to image general specimens. Under the assumption of an ensemble containing large amounts of identical specimens with the same orientation, the intensity distribution of the diffraction pattern of the whole ensemble is approximated to the form factor of a single specimen multiplied by the number of identical specimens. Since the diffraction intensities are contributed from the whole ensemble, the signal can be significantly extended to high-frequency regions. The feasibility of ensemble diffraction microscopy (EDM) was demonstrated by a designed sample using both totally and partially coherent X-ray sources at Taiwan Photon Source (TPS). The reconstructed images show excellent consistency with the image of a scanning electron microscope. This work represents a new protocol for directly characterizing the structures of nanomaterials, or potentially biomacromolecules, from accumulated X-ray scattering data.

A light ray in space is characterized by two vectors: (i) a transverse spatial vector associated with the point where the ray intersects a given spherical cap; (ii) an angular-frequency vector which defines the ray direction of propagation. Given a light ray propagating from a spherical emitter to a spherical receiver, a linear equation is established that links its representative vectors on the emitter and on the receiver. The link is expressed by means of a matrix which is not homogeneous, since it involves both spatial and angular variables (having distinct physical dimensions). Indeed, the matrix becomes a homogeneous rotation matrix after scaling the previous variables with appropriate dimensional coefficients. When applied to diffraction, in the framework of a scalar theory, the scaling operation results directly in introducing fractional-order Fourier transformations as mathematical expressions of Fresnel diffraction phenomena. Linking angular-frequency vectors and spatial frequencies results in an interpretation of the notion of a spherical angular spectrum. Accordance of both homogeneous and non-homogeneous ray matrices with the Huygens–Fresnel principle is examined. The proposed ray-matrix representation of diffraction is also applied to coherent imaging through a lens. [ABSTRACT FROM AUTHOR]

In the present communication, a detailed investigation has been made to realize a compact four hololens imaging system for the precision measurement of fracture parameters. The crack tip opening displacements (CTODs) were calculated using measured crack mouth opening displacement (CMOD) and crack opening displacement (COD) to determine all the important fracture parameters. It has been demonstrated that the effect of the zero-order diffraction halo can be avoided by measuring the CMOD and CTOD in the first-order diffraction halo to obtain better results. Experiments were conducted on an aluminium (Al) beam specimen with a central edge crack subjected to three-point bending under different loading conditions. The experimental and theoretical results are found to be in good agreement. The investigation presented in the paper strongly supports the argument that the sensitivity and accuracy of measurements in speckle metrology can be significantly enhanced using low-cost holographic optics. [ABSTRACT FROM AUTHOR]

In case of in-line inspection of optical functional micro-structured surfaces with phase response as well as amplitude response, higher resolution than the diffraction limit and phase measurability are needed. We proposed a novel coherent super-resolution method named complex-amplitude-response SIM (structured illumination microscopy). An equation is derived that enables extraction of frequencies higher than the diffraction limit of the complex-amplitude response distribution of a sample from multiple acquired images, which had not been obtained previously. This equation was validated through theoretical analysis by using images calculated by numerical optical simulation that were assumed to be acquired. Numerical analyses using the derived equation and simulations of image acquisition revealed that the proposed method is able to measure phase- and amplitude-response distributions of samples with a resolution higher than the diffraction limit. It was demonstrated that the proposed method is able to separate two points at a submicron distance of 500 nm under conditions of visible light and long W.D. (NA 0.2) and measure the phase difference with a maximum error of approximately 0.03 rad (∼π/100). When the amplitude response distribution of a sample is uniform and consists only of phase responses, the structure of the sample cannot be observed by standard optical microscopy. Numerical simulations revealed that the proposed method is able to visualise such samples with fine periodic phase responses on the submicron scale (∼500 nm) beyond the diffraction limit. Furthermore, we have shown that the proposed method is able to detect phase defects in ultra-fine optical functional structures with periods of less than 100 nm, which is expected to characterise the next generation metasurfaces. • Long working distance optical measurement of submicron-structured surfaces with amplitude and phase response distributions. • The proposed method enables extraction of high frequencies of a sample beyond the diffraction limit not only for amplitude but also phase response measurement. • Visualisation of fine periodic phase structures under constant amplitude distribution condition beyond the diffraction limit. • Phase defect of 20 nm in ultra-fine periodic phase structures can be detected in long working distance measurement. [ABSTRACT FROM AUTHOR]

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Coherent X-ray imaging techniques, such as in-line holography, exploit the high brilliance provided by diffraction-limited storage rings to perform imaging sensitive to the electron density through contrast due to the phase shift, rather than conventional attenuation contrast. Thus, coherent X-ray imaging techniques enable high-sensitivity and low-dose imaging, especially for low-atomic-number (Z) chemical elements and materials with similar attenuation contrast. Here, the first implementation of in-line holography at the NanoMAX beamline is presented, which benefits from the exceptional focusing capabilities and the high brilliance provided by MAX IV, the first operational diffraction-limited storage ring up to approximately 300 eV. It is demonstrated that in-line holography at NanoMAX can provide 2D diffraction-limited images, where the achievable resolution is only limited by the 70 nm focal spot at 13 keV X-ray energy. Also, the 3D capabilities of this instrument are demonstrated by performing holotomography on a chalk sample at a mesoscale resolution of around 155 nm. It is foreseen that in-line holography will broaden the spectra of capabilities of MAX IV by providing fast 2D and 3D electron density images from mesoscale down to nanoscale resolution.

We have developed a guided ptychography iterative engine (gPIE) algorithm that applies the concept of optimization to the conventional ePIE (extended ptychography iterative engine) approach. Instead of accessing a random or spiral trajectory among the collected diffraction patterns to implement the phase-retrieval, gPIE guides the searching direction through the local minimum and minimizes the cost function, which is the difference between the calculated intensities and the experimental ones, to approach the global minimum. Compared with ePIE, gPIE robustly reconstructs a more accurate sample and illumination, thus revealing the correct surface topology. The feasibility of gPIE was verified experimentally by acquiring sequential diffraction patterns from a UV laser.

The advancement of new promising techniques in the field of biomedical imaging has always been paramount for the research community. Recently, ultrasound tomography has proved to be a good candidate for non-invasive and safe diagnostics. In particular, breast cancer imaging may benefit from this approach, as frequent screening and early diagnosis require decreased system size and costs compared to conventional imaging techniques. Furthermore, a major advantage of these approaches consists in the operator-independent feature, which is very desirable compared to conventional hand-held ultrasound imaging. In this framework, the authors present some imaging results on an experimental campaign acquired via an in-house ultrasound tomographic system designed and built at the University of Naples Parthenope. Imaging performance was evaluated via different tests, showing good potentiality in structural information retrieval. This study represents a first proof of concept in order to validate the system and to consider further realistic cases in near future applications. [ABSTRACT FROM AUTHOR]

In the framework of non-destructive testing and imaging, ultrasound tomography can have an important role in several applications, especially in the biomedical field. The motivation beyond the use of this imaging technique lies in the possibility of obtaining quantitative imaging which is also operator-independent, conversely to conventional approaches. Thus, the need for public data sets for testing inverse scattering approaches is always persisting. To this aim, this paper introduces an experimental multiple-input-multiple-output ultrasound tomographic database whose acquisitions were performed by an air-matched in-house system designed and built by the Authors. The proposed database provides several cases with single and multiple objects of different shapes, sizes, and materials, to be imaged in laboratory-controlled conditions. Therefore, these scenarios can represent interesting options for the preliminary testing of tomographic ultrasound imaging approaches. [ABSTRACT FROM AUTHOR]

Coherent X‐ray imaging techniques, such as in‐line holography, exploit the high brilliance provided by diffraction‐limited storage rings to perform imaging sensitive to the electron density through contrast due to the phase shift, rather than conventional attenuation contrast. Thus, coherent X‐ray imaging techniques enable high‐sensitivity and low‐dose imaging, especially for low‐atomic‐number (Z) chemical elements and materials with similar attenuation contrast. Here, the first implementation of in‐line holography at the NanoMAX beamline is presented, which benefits from the exceptional focusing capabilities and the high brilliance provided by MAX IV, the first operational diffraction‐limited storage ring up to approximately 300 eV. It is demonstrated that in‐line holography at NanoMAX can provide 2D diffraction‐limited images, where the achievable resolution is only limited by the 70 nm focal spot at 13 keV X‐ray energy. Also, the 3D capabilities of this instrument are demonstrated by performing holotomography on a chalk sample at a mesoscale resolution of around 155 nm. It is foreseen that in‐line holography will broaden the spectra of capabilities of MAX IV by providing fast 2D and 3D electron density images from mesoscale down to nanoscale resolution. [ABSTRACT FROM AUTHOR]

The optical scattering coefficient (μs) in the dermis layer of human skin obtained with optical coherence tomography (OCT) has shown to have a strong correlation with the blood glucose concentration (BGC), which can be used for noninvasive BGC monitoring. Unfortunately, the nonhomogeneity in the skin may cause inaccuracies for the BGC analysis. In this paper, we propose a 2D correlation analysis method to identify 2D regions in the skin with μs sensitive to BGC variations and only use data in these regions to calculate μs for minimizing the inaccuracy induced by nonhomogeneity and therefore improving the accuracy of OCT-based BGC monitoring. We demonstrate the effectiveness of the 2D method with OCT data obtained with in vivo human forearm skins of nine different human subjects. In particular, we present a 3D OCT data set in a two-dimensional (2D) map of depth vs. a lateral dimension and calculate the correlation coefficient R between the μs and the BGC in each region of the 2D map with the BGC data measured with a glucose meter using finger blood. We filter out the μs data from regions with low R values and only keep the μs data with R values sufficiently high (R-filter). The filtered μs data in all the regions are then averaged to produce an average μs data. We define a term called overall relevancy (OR) to quantify the degree of correlation between the filtered/averaged μs data and the finger-blood BGC data to determine the optimal R value for such an R-filter with the highest obtained OR. We found that the optimal R for such an R-filter has an absolute value (|R|) of 0.6 or 0.65. We further show that the R-filter obtained with the 2D correlation method yields better OR between μs and the BGC than that obtained with the previously reported 1D correlation method. We believe that the method demonstrated in this paper is important for understanding the influence of BGC on μs in human skins and therefore for improving the accuracy of OCT-based noninvasive BGC monitoring, although further studies are required to validate its effectiveness. [ABSTRACT FROM AUTHOR]

In the framework of non-destructive testing and imaging, ultrasound tomography can have an important role in several applications, especially in the biomedical field. The motivation beyond the use of this imaging technique lies in the possibility of obtaining quantitative imaging which is also operator-independent, conversely to conventional approaches. Thus, the need for public data sets for testing inverse scattering approaches is always persisting. To this aim, this paper introduces an experimental multiple-input-multiple-output ultrasound tomographic database whose acquisitions were performed by an air-matched in-house system designed and built by the Authors. The proposed database provides several cases with single and multiple objects of different shapes, sizes, and materials, to be imaged in laboratory-controlled conditions. Therefore, these scenarios can represent interesting options for the preliminary testing of tomographic ultrasound imaging approaches.

For in-line surface inspection of microfluidic devices, optical measurement techniques with sub-micrometer resolution and a long working distance (W.D.) objective lens are needed. Structured illumination microscopy (SIM) is a good candidate to achieve high resolution. In micro-structured surface inspection, however, measurement needs to be carried out through coherent imaging, and thus conventional incoherent SIM cannot be applied directly due to interference of light from a sample. In this study, equations are reformulated by considering amplitude and phase of light waves. As a result, we found that higher spatial frequencies of samples can be derived even through coherent imaging by using multiple interference images. Based on this proposed coherent SIM, an optical measurement method with a long W.D. objective lens and sub-micrometer resolution for in-line surface inspection of sub-micro- and micro-structured surfaces is proposed. We analyzed resolution and performance of the proposed method from a theoretical and numerical perspective based on Fourier optics and imaging theory. The results verified that even with a long W.D. objective lens, the concept of the proposed method allows us to achieve sub-micrometer resolution in spite of non-fluorescence observation. This cannot be achieved by standard microscopy and the conventional incoherent SIM. We also conducted numerical analysis considering external disturbance that can occur in practical in-line inspection. The results revealed that the proposed method is capable to resolve two points with a distance less than half a micrometer with the maximum measurement error of no larger than 5%, under the condition where a maximal phase error of reference light is 2π/20 i.e., 20 nm error in length. These values are practical in in-line inspection. • Submicron-structured surface measurement with a long working distance objective lens. • Equations of structured illumination microscopy are reformulated for coherent imaging. • Interference with a reference light allows for high resolution for coherent imaging. • Distance shorter than 500 nm is measured even with phase errors of reference light. [ABSTRACT FROM AUTHOR]

Ptychographic X‐ray computed tomography is a quantitative three‐dimensional imaging technique offered to users of multiple synchrotron radiation sources. Its dependence on the coherent fraction of the available X‐ray beam makes it perfectly suited to diffraction‐limited storage rings. Although MAX IV is the first, and so far only, operating fourth‐generation synchrotron light source, none of its experimental stations is currently set up to offer this technique to its users. The first ptychographic X‐ray computed tomography experiment has therefore been performed on the NanoMAX beamline. From the results, information was gained about the current limitations of the experimental setup and where attention should be focused for improvement. The extracted parameters in terms of scanning speed, size of the imaged volume and achieved resolutions should provide a baseline for future users designing nano‐tomography experiments on the NanoMAX beamline. [ABSTRACT FROM AUTHOR]

X‐ray free‐electron lasers (FELs) are being recognized as a powerful tool in an ever‐increasing number of research fields, but are very limited as to the number of experiments that they can support. This work shows that more beamtime could be made available by using 'parasitic' geometries, where a secondary experiment uses the X‐ray beam that the primary experiment does not utilize. The first successful ptychography experiment, a scanning coherent diffractive imaging technique, in a parasitic geometry at an X‐ray FEL is demonstrated. Utilizing the CXI hutch at the Linac Coherent Light Source (LCLS), it is shown that the obtained data are of high quality and that characterizing the beam using ptychography can be much faster than traditional imprinting methods. [ABSTRACT FROM AUTHOR]

Coherent illumination of an optically rough surface creates random phase variations in the reflected electric field. Free-space propagation converts these phase variations into irradiance variations in both the pupil and image planes, known as pupil- and image-plane speckle. Infrared imaging systems are often parameterized by the quantity Fλ/d , which relates the cutoff frequencies passed by the optical diffraction MTF to the frequencies passed by the detector MTF. We present both analytical expressions and Monte-Carlo wave-optics simulations to determine the relationship between image-plane speckle contrast and the first-order system parameters utilized in Fλ/d (focal length, aperture size, wavelength, and detector size). For designers of active imaging systems, we provide input on speckle mitigation using Fλ/d to consider in system design. [ABSTRACT FROM AUTHOR]

A novel method of pixel reassignment (PRA) is proposed to achieve transverse superresolution in the confocal microscopy. Inspired by it, for the first time, we report a pixel-reassigned spectral-domain optical coherence tomography (OCT) with ~1.5 times transverse resolution improvement both in numerical simulations and imaging experiments. PRA is implemented by transversely shifting the detection fiber from the on-axis position to five off-axis positions, capturing cross-sectional images at each shifting step of the detection fiber and digitally reassigning them together to give a sharper image with moderately extended depth of focus and enhanced intensity. So, we believe that the PRA technique will improve the imaging performance and be beneficial to the development of the OCT community.

We demonstrate a computational, frequency-diverse, phaseless imaging technique at microwave frequencies that minimizes the impacts of phase calibration and alignment errors on image reconstruction. Phase calibration error is introduced by means of misaligning the sub-antennas forming an aperture, causing unwanted phase shifts between the forward model and adjoint operation. It is shown that by leveraging phase retrieval techniques, distinguishable images can still be reconstructed in the presence of significant phase errors, while complex-based reconstructions - those relying on measurement of both phase and amplitude - produce heavily corrupted images. Using a frequency-diverse imaging system consisting of a cavity-backed metasurface antenna that operates at microwave frequencies in the K-band (17.5-26.5 GHz), we demonstrate the complex-based and phaseless images of various objects, from a simple subwavelength conducting element to more complex metal structures. We verify that the combination of the phase retrieval approach with the frequency-diverse imager significantly improves the robustness of the composite imaging system to phase errors. While frequency-diverse computational imaging systems have significant advantages in terms of hardware, their reliance on a near-exact forward model places heavy requirements on system calibration. The phase retrieval approach developed here has the potential to alleviate this reliance, increasing the feasibility of such systems.

We present a detailed characterization of noise sources in multiple reference optical coherence tomography (MR-OCT) compared to time-domain OCT (TD-OCT). The noise characteristics were modeled based on the TD-OCT noise model and modified for MR-OCT and confirmed with measurements. The MR-OCT sensitivity characteristics are significantly affected by the reflection from the partial mirror, which also introduces a natural attenuation in the reference arm, partially matching the reflectivity intensity profile of human tissue. At optimal balance between sample and reference arm and using balanced detection, the peak sensitivity was measured to be 95 dB, which is close to simple Fourier-domain systems. The results provide a better understanding of the application range for MR-OCT and higher order effects observed, suggesting a nontrivial noise model for MR-OCT.

Optical coherence tomography (OCT) was used to image the internal structure of a rat cochlea (ex vivo). Immediately following sacrifice, the temporal bone of a Sprague-Dawley rat was harvested. Axial OCT cross sectional images (over regions of interest, 1×1 mm to 2×8 mm) were obtained with a spatial resolution of 10-15 μm. The osseous borders of the lateral membranous labyrinth overlying the cochlea and the scala vestibuli, media, and tympani which were well demarcated by the modiolus, Reissner's and the basilar membranes were clearly identified. OCT can be used to image internal structures in the cochlea without violating the osseous labyrinth, and may potentially be used to diagnose inner ear pathology in vivo in both animal and human subjects.

Optical coherence tomography (OCT) was used to image the internal structure of a rat cochlea (ex vivo). Immediately following sacrifice, the temporal bone of a Sprague-Dawley rat was harvested. Axial OCT cross sectional images (over regions of interest, 1×1 mm to 2×8 mm) were obtained with a spatial resolution of 10-15 μm. The osseous borders of the lateral membranous labyrinth overlying the cochlea and the scala vestibuli, media, and tympani which were well demarcated by the modiolus, Reissner's and the basilar membranes were clearly identified. OCT can be used to image internal structures in the cochlea without violating the osseous labyrinth, and may potentially be used to diagnose inner ear pathology in vivo in both animal and human subjects.

• Elements of matrix for Collins' integral have been derived for optical systems with multi-optical elements and an aperture stop in the context of Abbe's imaging theory. • Elements of matrix for Collins' integral have been derived for optical systems with multi-optical elements and an aperture stop in the context of Rayleigh's imaging theory. • The equivalence between Abbe's and Rayleigh's imaging theories has been derived rigorously using Collins' integral. • A convenient and applicable theoretical tool for studies on coherent imaging systems has been provided. Diffraction effect resulting from the entrance pupil of the optical imaging system was proposed by Abbe. An equivalent view regarding diffraction effect from the exit pupil was considered by Rayleigh. In the present work, the relation of the two effects is first established using Collins' integral and the Fresnel diffraction formula. For a general optical system including multiple optical elements and an aperture stop, we develop an approach in that the elements of the matrix for Collins' integral are derived. Subsequently, we perform optical experiments to verify our developed approach. [ABSTRACT FROM AUTHOR]

• Holographic images can be combined coherently to increase image resolution and field of view. • The choice of illumination and observation geometries affect the point-spread and transfer characteristics of the imaging system. • Phase contrast imaging in transmission and reflection geometries is possible. This paper discusses a modular implementation of synthetic aperture interferometry (SAI) using inexpensive telecommunications technologies that can be expanded for use in optical instruments with arbitrarily large fields of view. Exploiting multiple image sensors and multiple illumination sources, transmission and reflection SAI geometries, capable of emulating the phase contrast and interference modes of conventional interference microscopes, are considered. The point-spread and transfer characteristics of these geometries are illustrated for the case of a transmission mode instrument. It is shown that although imaging is strictly field dependent (i.e. shift-variant), the response of modular instruments is periodic and with careful choice of illumination and sensor positioning can be made quasi shift-invariant. We demonstrate SAI in a transmission configuration comprising of a single coherent imager that holographically records the field scattered from a test target sequentially illuminated by 16 different plane waves. This set-up is equivalent to a single module of a larger SAI system and since brightfield regions in the individual reconstructed images overlap, provides an ideal platform to examine the effect of tilt and phase offset errors in the illumination. By applying a first order correction and assuming phase continuity over the overlapping regions, we demonstrate a significant improvement in the SAI reconstruction. [ABSTRACT FROM AUTHOR]

A scheme was proposed to achieve wide-field vibrational sum-frequency generation (SFG) microscopy with subdiffraction-limited resolution in one dimension. In this approach, samples are illuminated with a structured visible field and a uniform IR field to induce vibrational sum-frequency generation. With five raw images acquired at five different phases of the visible stripe pattern, a super-resolved vibrational SFG (SR-SFG) image with the resolution triple to that of the original can be reconstructed. Theoretical framework describing the coherent image formation and reconstruction scheme for the SR-SFG imaging system was derived and carried out with numerical simulations to investigate its imaging performance. With a typical imaging system, the lateral resolution was improved from 390 nm of the conventional SFG imaging system, to around 130 nm of the SR-SFG imaging system.

Coherent X-ray diffraction patterns were recorded by using an X-ray free-electron laser to illuminate barium titanate nanocrystals as a function of time delay after laser excitation. Rather than seeing any significant thermal expansion effects, the diffraction peaks were found to move perpendicular to the momentum transfer direction. This suggests a laser driven rotation of the crystal lattice, which is delayed by the aggregated state of the crystals. Internal deformations associated with crystal contacts were also observed.

Featured Application: This work can be used for fast characterizing the phase modulation of the spatial light modulator (SLM) and shows the applications in coherent imaging by using the SLM. Although digital holography is used widely at present, the information contained in the digital hologram is still underutilized. For example, the phase values of the Fourier spectra of the hologram are seldom used directly. In this paper, we take full advantage of them for characterizing the phase modulation of a spatial light modulator (SLM). Incident plane light beam is divided into two beams, one of which passes the SLM and interferes with the other one. If an image with a single grey scale loads on the SLM, theoretical analysis proves that the phase of the Fourier spectra of the obtained hologram contains the added phase and a constant part relative to the optical distance. By subtracting the phase for the image with the grey scale of 0 from that for the image with other grey scales, the phase modulation can be characterized. Simulative and experimental results validate that the method is effective. The SLM after characterization is successfully used for coherent imaging, which reconfirms that this method is exact in practice. When compared to the traditional method, the new method is much faster and more convenient. [ABSTRACT FROM AUTHOR]

We present a detailed characterization of noise sources in multiple reference optical coherence tomography (MR-OCT) compared to time-domain OCT (TD-OCT). The noise characteristics were modeled based on the TD-OCT noise model and modified for MR-OCT and confirmed with measurements. The MR-OCT sensitivity characteristics are significantly affected by the reflection from the partial mirror, which also introduces a natural attenuation in the reference arm, partially matching the reflectivity intensity profile of human tissue. At optimal balance between sample and reference arm and using balanced detection, the peak sensitivity was measured to be 95 dB, which is close to simple Fourier-domain systems. The results provide a better understanding of the application range for MR-OCT and higher order effects observed, suggesting a nontrivial noise model for MR-OCT. [ABSTRACT FROM AUTHOR]

A proposal for building a Free Electron Laser, EuPRAXIA@SPARC_LAB, at the Laboratori Nazionali di Frascati, is at present under consideration. This FEL facility will provide a unique combination of a high brightness GeV-range electron beam generated in a X-band RF linac, a 0.5 PW-class laser system and the first FEL source driven by a plasma accelerator. The FEL will produce ultra-bright pulses, with up to 10 12 photons/pulse, femtosecond timescale and wavelength down to 3 nm, which lies in the so called “water window”. The experimental activity will be focused on the realization of a plasma driven short wavelength FEL able to provide high-quality photons for a user beamline. In this paper, we describe the main classes of experiments that will be performed at the facility, including coherent diffraction imaging, soft X-ray absorption spectroscopy, Raman spectroscopy, Resonant Inelastic X-ray Scattering and photofragmentation measurements. These techniques will allow studying a variety of samples, both biological and inorganic, providing information about their structure and dynamical behavior. In this context, the possibility of inducing changes in samples via pump pulses leading to the stimulation of chemical reactions or the generation of coherent excitations would tremendously benefit from pulses in the soft X-ray region. High power synchronized optical lasers and a TeraHertz radiation source will indeed be made available for THz and pump–probe experiments and a split-and-delay station will allow performing XUV-XUV pump–probe experiments.

We propose an optical security method for object authentication using photon-counting encryption implemented with phase encoded QR codes. By combining the full phase double-random-phase encryption with photon-counting imaging method and applying an iterative Huffman coding technique, we are able to encrypt and compress an image containing primary information about the object. This data can then be stored inside of an optically phase encoded QR code for robust read out, decryption, and authentication. The optically encoded QR code is verified by examining the speckle signature of the optical masks using statistical analysis. Optical experimental results are presented to demonstrate the performance of the system. In addition, experiments with a commercial Smartphone to read the optically encoded QR code are presented. To the best of our knowledge, this is the first report on integrating photon-counting security with optically phase encoded QR codes.

Fourier ptychography (FP) is a recently developed computational framework for high-resolution high-throughput imaging. In this paper, we will review the latest development of the Fourier ptychographic imaging scheme. We will demonstrate its applications in wide-field imaging, quantitative phase imaging, and adaptive imaging. We will also discuss its potential applications in X-ray optics and transmission electron microscopy.