Gabor Holography Research Articles

Gabor Holography with Speckle-Free Spherical Wave in Hard X-ray Region

Gabor-type holographic imaging in the hard X-ray region is carried out using a speckle-free coherent spherical wave that is generated by combined use of an X-ray focusing optic and a spatial filter at the focal point. A Fresnel zone plate with an outermost zone width of 100 nm is used as the X-ray focusing device, and a nickel pinhole of 1 µm diameter is used as the spatial filter. Using the coherent X-ray beam at the beamline 20XU of SPring-8, sub-optical spatial resolution is achieved at an X-ray energy of 8.5 keV.

Spatial light interference microscopy (SLIM)

We present spatial light interference microscopy (SLIM) as a new optical microscopy technique, capable of measuring nanoscale structures and dynamics in live cells via interferometry. SLIM combines two classic ideas in light imaging: Zernike’s phase contrast microscopy, which renders high contrast intensity images of transparent specimens, and Gabor’s holography, where the phase information from the object is recorded. Thus, SLIM reveals the intrinsic contrast of cell structures and, in addition, renders quantitative optical path-length maps across the sample. The resulting topographic accuracy is comparable to that of atomic force microscopy, while the acquisition speed is 1,000 times higher. We illustrate the novel insight into cell dynamics via SLIM by experiments on primary cell cultures from the rat brain. SLIM is implemented as an add-on module to an existing phase contrast microscope, which may prove instrumental in impacting the light microscopy field at a large scale.

Superresolved phase-shifting Gabor holography by CCD shift

Holography in the Gabor regime is restricted to weak diffraction assumptions. Otherwise, diffraction prevents an accurate recovery of the object's complex wavefront. We have recently proposed a modified Gabor-like setup to extend Gabor's concept to any sample provided that it be non-diffusive. However, the resolution of the final image becomes limited as a consequence of the additional elements considered in the proposed setup. In this paper we present an experimental approach to overcome such a limitation in which the former configuration is used while the CCD camera is shifted to different off-axis positions in order to generate a synthetic aperture. Thus, once the whole image set is recorded and digitally processed for each camera position, we merge the resulting band-pass images into one image by assembling a synthetic aperture. Finally, a superresolved image is recovered by Fourier transformation of the information contained in the generated synthetic aperture. Experimental results validate our concepts for a gain in resolution of close to 2.

Vacuum-ultraviolet Gabor holography with synchrotron radiation

We present the realization of high-resolution holographic microscopy using the original Gabor geometry and imaging with radiation in the vacuum-ultraviolet (VUV) spectral region. Synchrotron VUV radiation with a wavelength of 13.8 nm was focused on a small pinhole generating a highly divergent light cone suitable for digital in-line holography. Objects of different thickness and materials have been used to test the imaging properties of holographic microscopy in the VUV wavelength range. The effective numerical aperture was limited by the illuminated area of the detector, yielding a theoretical resolution below 1 μm and an experimental one of approximately 1 μm.

Ultrafast extreme ultraviolet holography: dynamic monitoring of surface deformation

We demonstrate femtosecond time-resolved dynamic Gabor holography using highly coherent extreme ultraviolet light generated by high harmonic upconversion of a femtosecond laser. By reflecting this light from an impulsively heated surface, we implement a simple and robust single-reflection geometry for phase-sensitive holographic detection at extreme UV wavelengths. Using this setup, we study the ultrafast deformation and subsequent acoustic oscillations within a thin metal film. These measurements exhibit subpicometer spatial sensitivity in the vertical dimension.

Sub 400 nm spatial resolution extreme ultraviolet holography with a table top laser

We report sub-400 nm spatial resolution with Gabor holography obtained using a highly coherent table top 46.9 nm laser. The hologram was recorded in high resolution photoresist and subsequently digitized with an atomic force microscope. The final image was numerically reconstructed with a Fresnel propagator. Optimal reconstruction parameters and quantification of spatial resolution were obtained with a wavelet analysis and image correlation.

Diffraction pattern from thermal neutron incoherent elastic scattering and the holographic reconstruction of the coherent scattering length distribution

The diffraction of spherical waves ( waves) interacting with a periodic scattering length distribution produces characteristic intensity patterns known as Kossel and Kikuchi lines (collectively called lines). The -line signal can be inverted to give the three-dimensional structure of the coherent scattering length distribution surrounding the source of waves---a process known as ``Gabor holography'' or, simply, ``holography.'' This paper outlines a kinematical formulation for the diffraction pattern of monochromatic plane waves scattering from a mixed incoherent and coherent -wave scattering length distribution. The formulation demonstrates that the diffraction pattern of plane waves incident on a sample with a uniformly random distribution of incoherent scatterers is the same as that from a sample with a single incoherent scatterer per unit cell. In practice, one can therefore reconstruct the holographic data from samples with numerous incoherent -wave scatterers per unit cell. Thus atomic resolution thermal neutron holography is possible for materials naturally rich in incoherent thermal neutron scatterers, such as hydrogen (e.g., biological and polymeric materials). Additionally, holographic inversions from single-wavelength data have suffered from the so-called conjugate or twin-image problem. The formulation presented for holographic inversion---different from those used previously []---eliminates the twin-image problem for single-wavelength data.

Production of Reflection Point Sources for Hard X-Ray Gabor Holography

The production of point X-ray sources for hard X-rays of approximately 8 keV is proposed and their application to Gabor holography is examined. Small X-ray sources less than 100 nm in diameter are obtained by total reflection from a limited surface area at grazing incidence. A microstrip plated with heavy metal on a glass plate is used for a one-dimensional small X-ray source and crossed glass rods for a two-dimensional X-ray source. A virtual source width smaller than approximately 80 nm is demonstrated. Young's X-ray interference fringes are obtained using beams reflected from two microstrips. Gabor X-ray holograms of a gold wire and a diatom are recorded with a virtual point source and their reconstructed images are numerically obtained.

Holographic testing of terahertz antennas

In the light of future applications involving terahertz antenna measurements, this paper revisits Gabor (1949) holography as a direct method for recovering phase, offering some interesting advantages for near-field measurements. In particular, we examine the theory and parameterization of planar near-field Gabor holography and comment on the requirements for scanner precision at terahertz frequencies.

On X-ray in-line Gabor holography with a partially coherent source

Partially coherent X-ray in-line Gabor holography is studied based on the theory of partial coherence. Using asymptotic expansion methods, the relations between the coherent degree and the resolution (contrast) are obtained. Both transverse and longitudinal resolution and image contrast decrease when the coherent degree decreases and the improvement of X-ray coherence has little effect on the imaging quality if the coherence is high enough. The numerical examples are in good agreement with the analytic results. A criterion on the coherent length is proposed based on the calculating results to get high quality holography.

Soft-x-ray Gabor holography by use of a backilluminated CCD camera

A soft-x-ray Gabor hologram was recorded directly by means of a cooled backilluminated CCD camera, and numerical reconstruction was performed. Synchrotron radiation from a bending magnet with beam line 11A at the Photon Factory, National Laboratory for High Energy Physics, Japan, was used. X rays were monochromatized to a wavelength of 2.34 nm with a grasshopper monochromator and focused on a pinhole of diameter 1.0 mum with a zone plate. A specimen was illuminated with soft x rays transmitted through the pinhole, and a shadowgraph with a magnification ratio of 33 at the CCD plane was digitized directly. The transverse resolution of the reconstructed image was estimated to be 1.5 mum, which was in good agreement with a theoretical value.

X-ray Gabor holography

Soft x-ray microscopy offers an approach to transmission imaging of wet, micron-thick biological objects at a resolution superior to that of optical microscopes and with less specimen preparation/manipulation than electron microscopes. Gabor holography has unique characteristics which make it particularly well suited for certain investigations: it requires no prefocussing, it is compatible with flash x-ray sources, and it is able to use the whole footprint of multimode sources. Our method serves to refine this technique in anticipation of the development of suitable flash sources (such as x-ray lasers) and to develop cryo capabilities with which to reduce specimen damage. Our primary emphasis has been on biological imaging so we use x-rays in the water window (between the Oxygen-K and Carbon-K absorption edges) with which we record holograms in vacuum or in air.The hologram is recorded on a high resolution recording medium; our work employs the photoresist poly(methylmethacrylate) (PMMA). Following resist “development” (solvent etching), a surface relief pattern is produced which an atomic force microscope is aptly suited to image.

Subnanosecond in-line soft x-ray holography using germanium laser in the 20 nm wavelength region

Near- and far-field characteristics of a germanium soft x-ray laser at the wavelengths of 23.2–23.6 nm ( J = 2-1 transitions) and 19.6 nm ( J = 0-1 transition) are given for quantitative evaluation of the germanium laser for holographic applications. In-line Gabor holography of simple structured objects, such as thin opaque fibers and a standard electron microscope test specimen, is demonstrated. The holograms were recorded on PMMA (polymethyl methacrylate) photoresists and Ilford Q-plates. The holograms recorded on PMMA were retrieved with an atomic force microscope. The object image was reconstructed by numerical reconstruction with phase retrieval algorithm, resulting in a clear, ghost-free image with sharp edges which infer sub- μ m resolution. Future directions for x-ray laser holography are briefly discussed.

Comparison of phase retrieval methods for optical diffraction tomography

We compare three different phase retrieval methods for applications in optical diffraction tomography (ODT). The first method is based on Gabor holography and is limited by the 'twin-image' problem. The second is an iterative approach for which the uniqueness of the retrieved phase is questionable. In the third method the phase is measured by phase shifting interferometry (PSI), but this technique is more demanding experimentally. Using realistic computer simulations, which include noise and lens aberrations, we show that the PSI method determines the phase accurately. The iterative method gives equally accurate results in most cases. But in some cases this method produces a false phase. This problem is demonstrated using both simulated and experimental intensity data. The images reconstructed from the false phases are found to be severely distorted. We also show that the uniqueness problem can be avoided by increasing the distance between the scattering object and the measurement line.

Subnanosecond In-Line Soft X-Ray Holography Using Germanium Laser in the 20 nm Wavelength Region

Near- and far-field characteristics of a germanium soft x-ray laser at the wavelengths of 23.2-23.6 nm (J = 2-1 transitions) and 19.6 nm (J = 0-1 transition) are given for quantitative evaluation of the germanium laser for holographic applications. In-line Gabor holography of simple structured objects, such as thin opaque fibers and a standard electron microscope test specimen, is demonstrated. The holograms were recorded on PMMA (polymethyl methacrylate) photoresists and llford Q-plates. The holograms recorded on PMMA were retrieved with an atomic force microscope. The object image was reconstructed by numerical reconstruction with phase retrieval algorithm, resulting in a clear, ghost-free image with sharp edges which infer sub-μm resolution. Future directions for x-ray laser holography are briefly discussed.

X-ray Gabor holography: Recent progress

Gabor holography is well positioned to exploit flash x-ray sources, such as x-ray lasers and free electron lasers, as well as ultra-bright third generation synchrotron sources as a sub-50 nm resolution imaging technique for biological samples. Gabor holography requires no optics (except for a monochromator with λ/Δλ ~ 500) and no sample prefocusing since the image is focused in the reconstruction process. Furthermore, sample alignment is eased since the area of illumination can be quite large. In fact, Gabor holography can be used to image large fields with multimode sources with the resulting numerical aperture, and hence resolution, being limited by the size of a single mode. However, Gabor holography is not a real time technique so there is no rapid feedback to improve the immediate experiment. In addition, the resolution has been limited by shortcomings in the reconstruction methods.Our primary emphasis has been on biological imaging so we use x-rays in the water window (between the O-K and C-K absorption edges).

A linear-field scanning-force microscope: Application to x-ray gabor holography

We have built a linear field Scanning Force Microscope to readout x-ray Gabor holograms recorded in photoresist. A field linearity yielding one half or less pixel registration error (for 10-50nm pixel sizes) across the scanned hologram is needed so that the resulting reconstruction is not significantly degraded. The desire for a large (75μm)2 and linear scanning field necessitated designing our own stage since these conditions could not be met commercially.Gabor holography is well positioned to exploit flash x-ray sources, such as x-ray lasers and free electron lasers, as well as ultra-bright third generation synchrotron sources as a sub-50nm resolution imaging technique for biological samples. Gabor holography requires no optics (except for a monochromator with λ/Δλ ∽ 500) and no sample prefocusing since the image is focused in the reconstruction process. Furthermore, sample alignment is eased since the area of illumination can be quite large. In fact, Gabor holography can be used to image large fields with multimode sources with the resulting numerical aperture, and hence resolution, being limited by the size of a single mode.

Resolution in x-ray microscopes

X-ray microscopes can be roughly grouped into two categories: soft x-ray microscopes (λ ≈ 1-10 nm) which are able to image specimens at up to 30 nm resolution with some elemental mapping capabilities, and hard x-ray microprobes (E ≈ 3-100 keV) which are able to map trace chemical compositions and produce tomograms at ∼ 2 μm resolution. In both cases, the sample can be hydrated and in air, its thickness can be range from a few μm (with soft x rays) to a few mm (hard x rays), and the radiation dose delivered is considerably lower than what is involved in the equivalent electron microscopy technique.Some x-ray microscopes are lensless instruments. In contact microscopy and Gabor holography, soft x rays passing through the sample are recorded directly on high resolution photoresists (e.g., PMMA). Shinozaki et al. have studied the x-ray exposure properties of PMMA in detail, and have concluded that a detector resolution limit of 20 nm or better should be attainable.

Twin-image elimination in Gabor holography

It is shown that the “twin-image” may be eliminated from images of real (e.g., thin and purely absorptive) objects generated by Gabor holography using straightforward linear filtering. The technique tends to emphasize otherwise small contributions from the “intermodulation term” and an algorithm is demonstrated that can estimate the intermodulation term and, therefore, largely eliminate its effects from the processed image. Holograms of complex objects are analyzed and it is shown that they may be reconstructed without twin image effects provided the objects obey a size constraint that is similar to, but less stringent and more precise than, the conventional Fraunhofer condition.

X-ray Microscopy with the NSLS Soft X-ray Undulator

Soft x-rays are attractive for microscopy because they tend to be less damaging to specimens than charged probes. In addition their interactions with specimens can result in element-specific information and the penetration depth is adjustable by choice of the beam energy. Resolution on the order of 50 nm has been demonstrated, and further improvements are anticipated.The experimental program at the NSLS X1A beamline is dedicated to soft x-ray microscopy. We are developing two types of instruments, both dependent on the remarkable brightness of the undulator source. One of these uses a Fresnel zone plate to focus the beam to a small size. This microprobe is used either to study biological specimens, or, in a different apparatus, to study surfaces by photoelectron microscopy. The other type of instrument makes use of x-rays diffracted by the specimen. In this category we are involved in the development of Gabor holography, Fourier transform holography, and in imaging by soft x-ray diffraction.