Noninterferometric quantitative phase imaging with soft x rays

Naked eye direction of arrival estimation with a Fresnel lens

Direction of arrival (DoA) estimation is of primary importance in a broad range of wireless applications, where electromagnetic waves play a role. While a vast majority of existing techniques is based on phase lag comparison in antenna arrays, intensity-based approaches are valuable in a range of low budget applications. Here we demonstrate a direct visible to a naked eye DoA device, based on a Fresnel zone plate lens, aperture, and a light-emitting diode indicator. Being a low budget device, it still allows achieving up to 90° angle of view, 19° of angular resolution, and 11° of angular accuracy at 10 GHz operational frequency. The demonstrated approach provides fast DoA visualization and can be used to adjust point-to-point communication links, identify radio wave pollution sources at home conditions and several others.

Digital holography from shadowgraphic phase estimates

We show experimentally that the recently proposed iterative shadowgraphic method can be applied to in-line digital holography, provided a suitable regularization step is introduced. We show that the method correctly solves the "twin-image" problem using just two samples of the intensity field scattered by a phase object. Field retrieval accuracy is significantly improved when compared to a reconstruction obtained with the defocusing variation algorithms.

Sphere-to-sphere diffraction propagation method for a phase-retrieval algorithm in the measurement of optical surfaces

We present an improved phase-retrieval algorithm that is based on the Sziklas and Siegman coordinate transformation (SSCT) and applied to optical surface testing. With the SSCT, a spherical-wave diffraction problem can be transformed into a plane-wave diffraction problem, and the fast Fourier transform can be applied directly in propagation computations. Compared with conventional diffraction propagation methods, the proposed method is simple and relatively fast, and the computation efficiency for the phase-retrieval algorithm can be increased to a certain degree. Analysis and simulation were performed for this method, and simulation results exhibit correct diffraction computation and good phase-retrieval capability. A practical 200 mm diameter, f/5 spherical surface was tested; testing results showed good agreement with that of a ZYGO interferometer, which confirmed the feasibility and accuracy of the proposed method.

Phase retrieval from a high-numerical-aperture intensity distribution by use of an aperture-array filter

Almost all noninterferometric phase-retrieval methods used in coherent diffractive imaging have been based on the measurement system with low numerical aperture, in which Fresnel or Fraunhofer approximation is valid to express the wave propagation between an object and a detector. In microscopy, which is a typical application of coherent diffractive imaging, the measurement of the diffraction intensity with high numerical aperture is required for object reconstruction at high spatial resolution. We here propose an extension procedure to apply the previous phase-retrieval method using an aperture-array filter [J. Opt. Soc. Am. A25, 742 (2008)] to the system with high numerical aperture, in which the first Rayleigh-Sommerfeld integral for spherical waves is utilized instead of the Fresnel integral for parabolic waves. Computer-simulated examples in the high-numerical-aperture system demonstrate object reconstruction at high lateral resolution and retrieval of information in the depth direction of an object.

Phase front retrieval by means of an iterative shadowgraphic method

In this paper, we propose an iterative shadowgraphic method (ISM) as an interesting alternative to existing methods for self-referencing optical phase retrieval. Two defocused images of the intensity distribution of the light scattered by a weakly absorbing phase object were sufficient to retrieve the transverse phase distribution of the distorted illuminating beam. An algorithm was developed to correct for diffraction effects in phase maps retrieved with a simple shadowgraphic method. We provide a mathematical proof of the convergence of the algorithm to the true profile of the sought phase object. Several numerical tests were performed of the algorithm showing its capability of recovering the full details of the original phase distribution with increased resolution as compared with the simple shadowgraphic method. The convergence of the ISM was also compared numerically with that of a nonoptimized Gerchberg-Saxton-type algorithm and found to be faster and not affected by stagnation problems.

Optical imaging of cell mass and growth dynamics

Using novel interferometric quantitative phase microscopy methods, we demonstrate that the surface integral of the optical phase associated with live cells is invariant to cell water content. Thus, we provide an entirely noninvasive method to measure the nonaqueous content or "dry mass" of living cells. Given the extremely high stability of the interferometric microscope and the femtogram sensitivity of the method to changes in cellular dry mass, this new technique is not only ideal for quantifying cell growth but also reveals spatially resolved cellular and subcellular dynamics of living cells over many decades in a temporal scale. Specifically, we present quantitative histograms of individual cell mass characterizing the hypertrophic effect of high glucose in a mesangial cell model. In addition, we show that in an epithelial cell model observed for long periods of time, the mean squared displacement data reveal specific information about cellular and subcellular dynamics at various characteristic length and time scales. Overall, this study shows that interferometeric quantitative phase microscopy represents a noninvasive optical assay for monitoring cell growth, characterizing cellular motility, and investigating the subcellular motions of living cells.

Quantitative phase imaging with a scanning transmission x-ray microscope

We obtain quantitative phase reconstructions from differential phase contrast images obtained with a scanning transmission x-ray microscope and 2.5 keV x rays. The theoretical basis of the technique is presented along with measurements and their interpretation.

Imaging red blood cell dynamics by quantitative phase microscopy

Red blood cells (RBCs) play a crucial role in health and disease, and structural and mechanical abnormalities of these cells have been associated with important disorders such as Sickle cell disease and hereditary cytoskeletal abnormalities. Although several experimental methods exist for analysis of RBC mechanical properties, optical methods stand out as they enable collecting mechanical and dynamic data from live cells without physical contact and without the need for exogenous contrast agents. In this report, we present quantitative phase microscopy techniques that enable imaging RBC membrane fluctuations with nanometer sensitivity at arbitrary time scales from milliseconds to hours. We further provide a theoretical framework for extraction of membrane mechanical and dynamical properties using time series of quantitative phase images. Finally, we present an experimental approach to extend quantitative phase imaging to 3-dimensional space using tomographic methods. By providing non-invasive methods for imaging mechanics of live cells, these novel techniques provide an opportunity for high-throughput analysis and study of RBC mechanical properties in health and disease.

A method for phase reconstruction from measurements obtained using a configured detector with a scanning transmission X-ray microscope

We developed a technique for performing quantitative phase reconstructions from differential phase contrast images obtained using a configured detector in a scanning transmission X-ray microscope geometry. The technique uses geometric optics to describe the interaction of the X-ray beam with the specimen, which allows interpretation of the measured intensities in terms of the derivative of the phase thickness. Integration of the resulting directional derivatives is performed using a Fourier integration technique. We demonstrate the approach by reconstructing simulated measurements of a 0.5-µm-diameter gold sphere at 7-keV photon energy.

Diffraction phase and fluorescence microscopy

We have developed diffraction phase and fluorescence (DPF) microscopy as a new technique for simultaneous quantitative phase imaging and epi-fluorescence investigation of live cells. The DPF instrument consists of an interference microscope, which is incorporated into a conventional inverted fluorescence microscope. The quantitative phase images are characterized by sub-nanometer optical path-length stability over periods from milliseconds to a cell lifetime. The potential of the technique for quantifying rapid nanoscale motions in live cells is demonstrated by experiments on red blood cells, while the composite phase-fluorescence imaging mode is exemplified with mitotic kidney cells.

Thermal and cold neutron phase-contrast radiography

In this paper, we will discuss a phase-contrast imaging method that avoids the complications of interferometry to provide phase contrast in weakly absorbing samples. A transversely coherent neutron beam is used with the traditional radiography scheme. Images taken with this scheme show dramatic intensity variations due to sharp changes in the neutron wave refractive index. With some numerical processing these images may be used to reconstruct a quantitative phase radiograph of specimens imaged with this technique.

Resolution extension and exit wave reconstruction in complex HREM

Direct methods in real and reciprocal space are developed for structural reversion. The direct method in real space involves the use of a novel method to retrieve the phase in the image plane using transport of intensity equation/maximum entropy method (TIE/MEM) and exit wave reconstruction by self-consistent propagation. Since the exit wave is restored from the complex signal in the image planes, no image model between the exit wave and image is assumed. The structural information in the reconstructed exit wave is then further extended by a "complex" maximum entropy method as a direct method in reciprocal space to extrapolate the phase to higher frequencies.

Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging

We outline a new approach to X-ray projection microscopy in a scanning electron microscope (SEM), which exploits phase contrast to boost the quality and information content of images. These developments have been made possible by the combination of a high-brightness field-emission gun (FEG)-based SEM, direct detection CCD technology and new phase retrieval algorithms. Using this approach we have been able to obtain spatial resolution of < 0.2 micro m and have demonstrated novel features such as: (i) phase-contrast enhanced visibility of high spatial frequency image features (e.g. edges and boundaries) over a wide energy range; (ii) energy-resolved imaging to simultaneously produce multiple quasi-monochromatic images using broad-band polychromatic illumination; (iii) easy implementation of microtomography; (iv) rapid and robust phase/amplitude-retrieval algorithms to enable new real-time and quantitative modes of microscopic imaging. These algorithms can also be applied successfully to recover object-plane information from intermediate-field images, unlocking the potentially greater contrast and resolution of the intermediate-field regime. Widespread applications are envisaged for fields such as materials science, biological and biomedical research and microelectronics device inspection. Some illustrative examples are presented. The quantitative methods described here are also very relevant to projection microscopy using other sources of radiation, such as visible light and electrons.

Quantitative phase-amplitude microscopy II: differential interference contrast imaging for biological TEM

Although phase contrast microscopy is widespread in optical microscopy, it has not been as widely adopted in transmission electron microscopy (TEM), which has therefore to a large extent relied on staining techniques to yield sufficient contrast. Those methods of phase contrast that are used in biological electron microscopy have been limited by factors such as the need for small phase shifts in very thin samples, the requirement for difficult experimental conditions, or the use of complex data analysis methods. We here demonstrate a simple method for quantitative TEM phase microscopy that is suitable for large phase shifts and requires only two images. We present a TEM phase image of unstained Radula sp. (liverwort spore). We show how the image may be transformed into the differential interference contrast image format familiar from optical microscopy. The phase images contain features not visible with the other imaging modalities. The resulting technique should permit phase contrast TEM to be performed almost as readily as phase contrast optical microscopy.

Differential interference contrast x-ray microscopy with twin zone plates

X-ray imaging in differential interference contrast (DIC) with submicrometer optical resolution was performed by using a twin zone plate (TZP) setup generating focal spots closely spaced within the TZP spatial resolution of 160 nm. Optical path differences introduced by the sample are recorded by a CCD camera in a standard full-field imaging and by an aperture photodiode in a standard scanning transmission x-ray microscope. Applying this x-ray DIC technique, we demonstrate for both the full-field imaging and scanning x-ray microscope methods a drastic increase in image contrast (approximately 20x) for a low-absorbing specimen, similar to the Nomarski DIC method for visible-light microscopy.