Thin Phase Objects Research Articles

Single-plane and multiplane quantitative phase imaging by self-reference on-axis holography with a phase-shifting method.

A new quantitative phase imaging approach is proposed based on self-reference holography. Three on-axis interferograms with different values of the phase filter are superposed. The superposition yields a more accurate phase map of the wavefront emerging from the object, compared with standard off-axis interferometry. Reduced temporal noise levels in the measured phase map and efficient phase recovery process for optically thin and thick transmissive phase objects highlight the applicability of the suggested framework for various fields ranging from metrology to bio-imaging. Qualitative phase imaging is also done online without altering the optical configuration. Qualitative phase detections of multiple planes of interest are converted to quantitative phase maps of the multiplane scene by a rapid phase contrast-based phase retrieval algorithm, from a single camera exposure and with no moving parts in the system.

Lensless Three-Dimensional Quantitative Phase Imaging Using Phase Retrieval Algorithm.

Quantitative phase imaging (QPI) techniques are widely used for the label-free examining of transparent biological samples. QPI techniques can be broadly classified into interference-based and interferenceless methods. The interferometric methods which record the complex amplitude are usually bulky with many optical components and use coherent illumination. The interferenceless approaches which need only the intensity distribution and works using phase retrieval algorithms have gained attention as they require lesser resources, cost, space and can work with incoherent illumination. With rapid developments in computational optical techniques and deep learning, QPI has reached new levels of applications. In this tutorial, we discuss one of the basic optical configurations of a lensless QPI technique based on the phase-retrieval algorithm. Simulative studies on QPI of thin, thick, and greyscale phase objects with assistive pseudo-codes and computational codes in Octave is provided. Binary phase samples with positive and negative resist profiles were fabricated using lithography, and a single plane and two plane phase objects were constructed. Light diffracted from a point object is modulated by phase samples and the corresponding intensity patterns are recorded. The phase retrieval approach is applied for 2D and 3D phase reconstructions. Commented codes in Octave for image acquisition and automation using a web camera in an open source operating system are provided.

Quantitative measurement of thin phase objects: comparison of speckle deflectometry and defocus-variant lateral shear interferometry.

The two techniques of lateral shear interferometry and speckle deflectometry are analyzed in a common optical system for their ability to measure phase gradient fields of a thin phase object. The optical system is designed to introduce a shear in the frequency domain of a telecentric imaging system that gives a sensitivity of both techniques in proportion to the defocus introduced. In this implementation, both techniques successfully measure the horizontal component of the phase gradient field. The response of both techniques scales linearly with the defocus distance, and the precision is comparative, with a random error in the order of a few rad/mm. It is further concluded that the precision of the two techniques relates to the transverse speckle size in opposite ways. While a large spatial coherence width, and correspondingly a large lateral speckle size, makes lateral shear interferometry less susceptible to defocus, a large lateral speckle size is detrimental for speckle correlation. The susceptibility for the magnitude of the defocus is larger for the lateral shear interferometry technique as compared to the speckle deflectometry technique. The two techniques provide the same type of information; however, there are a few fundamental differences. Lateral shear interferometry relies on a special hardware configuration in which the shear angle is intrinsically integrated into the system. The design of a system sensitive to both in-plane phase gradient components requires a more complex configuration and is not considered in this paper. Speckle deflectometry, on the other hand, requires no special hardware, and both components of the phase gradient field are given directly from the measured speckle deformation field.

Differential-phase-contrast knife-edge scan method for precise evaluation of X-ray nanobeam

A differential-phase-contrast knife-edge scan method is proposed to precisely evaluate X-ray nanofocusing beam profiles. A thin phase object can be used as a knife edge in this method, whereas the conventional absorption knife-edge scan method requires a thick opaque edge. The precision of the focal beam profile measurement was confirmed by numerical calculation. The performance test was carried out at the undulator beamline 20XU of SPring-8, by evaluating the focal spot profile of a tantalum Fresnel zone plate with an outermost zone width of 25 nm. The edge pattern of a tantalum test chart with a thickness of 500 nm was used as the knife edge. The measured beam profile with a size of 25 nm ± 1 full-width at half-maximum was carefully compared with the theoretical values and found to be in good agreement.

Imaging adherent cells in the microfluidic channel hidden by flowing RBCs as occluding objects by a holographic method.

Imaging through turbid media is a challenging topic. A liquid is considered turbid when dispersed particles provoke strong light scattering, thus destroying the image formation by any standard optical system. Generally, colloidal solutions belong to the class of turbid media since dispersed particles have dimensions ranging between 0.2 μm and 2 μm. However, in microfluidics, another relevant issue has to be considered in the case of flowing liquid made of a multitude of occluding objects, e.g. red blood cells (RBCs) flowing in veins. In such a case instead of severe scattering processes unpredictable phase delays occur resulting in a wavefront distortion, thus disturbing or even hindering the image formation of objects behind such obstructing layer. In fact RBCs can be considered to be thin transparent phase objects. Here we show that sharp amplitude imaging and phase-contrast mapping of cells hidden behind biological occluding objects, namely RBCs, is possible in harsh noise conditions and with a large field-of view by Multi-Look Digital Holography microscopy (ML-DH). Noteworthy, we demonstrate that ML-DH benefits from the presence of the RBCs, providing enhancement in terms of numerical resolution and noise suppression thus obtaining images whose quality is higher than the quality achievable in the case of a liquid without occlusive objects.

Directional edge enhancement in optical tomography of thin phase objects

In this paper, we make a proposal to obtain the Hilbert-transform for each entry of the projection data leaving the slice of a thin phase object. These modified projections are stacked in such a way that they form a modified sinogram called Hilbert-sinogram. We prove that the inverse Radon-transform of this sinogram is the directional Hilbert-transform of the slice function, and the reconstructed image is the directional edge enhancement of the distribution function on the slice. The Hilbert-transform is implemented by a 4f optical Fourier-transform correlator and a spatial filter consisting of a phase step of π radians. One important feature of this proposal is to perform a turn of 180° in the spatial filter at a certain value of the projection angle within the range [0°, 360°]. The desired direction of enhancement can be chosen by the proper selection of such turning angle. We present both the mathematical modeling and numerical results.

Direct full compensation of the aberrations in quantitative phase microscopy of thin objects by a single digital hologram

Aberrations and the distortions due to the imaging optics can be compensated in quantitative phase microscopy of thin phase objects by digital holography using a single hologram. The reconstructed quantitative phase microscopy phase distribution map can be directly corrected in the reconstructed image plane by a numerical method. To remove this unwanted aberration, in the special case of thin objects, the authors perform a two-dimensional fit with the Zernike polynomials of the reconstructed unwrapped phase. Subtraction of the fitted polynomial from the original phase map gives quantitative phase microscopy phase map free of aberrations.

The Use of Phase and Amplitude Information of Reconstructed Exit Waves

Exit waves can be reconstructed from through focus series of HREM images or by off-axis holography [1]. We have applied the through focus method to reconstruct exit waves, using algorithms developed by Van Dyck and Coene [2]. Electron microscopy was performed with a Philips CM30ST electron microscope with a field emission gun operated at 300 kV. The high resolution images were recorded using a Tietz software package and a 1024x1024 pixel Photometrix CCD camera having a dynamic range of 12 bits. The reconstructions were done using 15-20 images with focus increments of 5.2 nm. The resulting exit waves were corrected posteriorly for the three fold astigmatism.The exit wave is complex; consequently it contains phase and amplitude. Since in the very thin regions the specimen acts as a thin phase object, such a thin area will show little contrast, an example of which is shown in Figure 1.

Coherent nanodiffraction from phase objects: carbon nanotubes

Electron diffraction patterns obtained with a coherent incident beam of diameter 1 nm or less do not, in general, show a center of symmetry even for thin phase objects. Experimental observations of nanodiffraction patterns obtained from the walls of carbon nanotubes show asymmetries in the intensities of the first-order reflections from the carbon-layer stacking periodicity which are in agreement with calculations from a simple theoretical model. It is suggested that the measurement of such asymmetries may provide evidence regarding the structures of nanotubes of non-circular cross-section and of the end regions of tubes.

Scattering integrals at solid-solid interfaces

Solid/solid interfaces can be imaged in the transmission electron microscope by means of refraction/reflection arising from the difference in mean electrostatic potential between the two adjoining solids. Standard approximations used in high energy electron diffraction and microscopy are not directly applicable to treatment of this effect. Two modified procedures are discussed: an adaption of the integral expression for the scattering amplitude and a modified thin phase object approximation. Calculations of diffraction patterns and in-focus contrast from an abrupt interface are shown as examples.

Proof of the Necessity and Sufficiency of Conditions for Thin Phase Imagery

A proof is given of the necessity and sufficiency of conditions on a spatial filtering system for imaging of thin phase objects.

Dependence of the optical contrast of vesicle walls on lamellarity and curvature

Using photometric phase-contrast microscopy it was possible to discern the number of lammellae in thin walls of artificial phospholipid-vesicles. By comparing the contrast of spheres and elongated tubes with same diameters we could analyse the dependence of the contrast on both principal curvatures. The characteristics of the intensity distribution of the light in the image plane of the phase-contrast microscope is discussed for thin hollow phase objects.

Phase and amplitude contrast in electron microscopy of stained biological objects

For biological objects negatively stained with heavy atom material, electron microscope images show best contrast for image detail on the scale of 10--20 A when a small objective aperture is used. In images taken under the optimum phase contrast imaging conditions of Scherzer, the required image detail is lost in unwanted noise. Both of these conditions may be described in terms of phase contrast imaging for a thin phase object. Calculations of image intensities and noise are reported for a model object consisting of heavy and light atoms randomly distributed to simulate a negatively stained protein molecule. The results are consistent with experimental observations.

Laser beam reading of video records

In optical video recording the information is usually read from the disk by a scanning laser beam. We apply the theory of imaging in partially coherent light to this, situation. We assume that the disk is a thin phase object, and that the information pattern consists of tracks of a width that is small compared to the diameter of the reading spot. We obtain simple expressions for the amplitudes of the signals generated by the playback system. Also intermodulation products and cross talk between the tracks are considered.

Preparation and properties of alumina supermicrogrid

It is often required in high resolution electron microscopy to use very thin supporting films for the reduction of random noise. When the specimen is crystalline film, it is also desirable that the thickness is controlled to be less than a hundred angstroms so that the specimen can be dealt with as a thin phase object. In both cases, a suitable supporting technique is necessary to secure the stability and mechanical strength of these very thin films and perhaps very small fragments of a few hundred angstroms in size. The present work was undertaken to prepare rigid supporting films by means of chemical thinning of alumina films produced by the anodic oxidation of aluminium plate. The overall procedure is outlined in Fig. 1.The aluminium to be oxidized is cut in a form of a 1cm × 2cm plate from extra pure foil whose thickness ranges between 15 to 30μm.

Imaging of tilted, extended, thin phase-objects

In images of extended strongly tilted specimens, different parts of the object are subject to different defocus. This makes it possible to obtain, by a single exposure, an overall view of the transfer properties of the objective [1,2]; on the other hand, in reconstruction work it requires the use of correcting procedures [3]. The importance of both points seems to justify formal investigation--restricted here to thin phase objects. The geometrical data are shown in Fig. 1; the axis of tilt is normal to the plane of the drawing and is used as coordinate axis X2. Representing the scattered amplitude by u(k1,k2) where spatial frequencies k by δ = λk represent the inclination δ of the different components of the wave field a(x1,x2,z), one hasPutting z = x1 one finds for the amplitude immediately beyond the object(1)

Discrimination of individual atoms in the molecular images of chlorinated copper phthalocyanine

For the establishment of solid approaches to the target of discriminating individual atoms in molecular images, it still seems to be necessary to deal with radiation resistant compounds with known structures. The use of thin specimen crystals renders several advantages, as they keep molecules in suitable orientations with tolerably small atomic displacements due to the thermal vibration. Rows of stacked molecules increase the contrast in the projected images, although the thickness must be such that the specimen can be regarded as a thin phase object. Two dimensional periodicity of projected images facilitates the spacial averaging which increases the s/n ratio as predicted by Kuo and Glaeser, reducing the exposure time and consequently the radiation damage. In order to realize the atomic resolution, the improvement in the instrumental characteristics is indispensable as well. The 500kV electron microscope constructed by Kobayashi et al. has the capability of achieving the ultimate resolution of 1.5A, and played the principal role in the present attempt to reach the atomic resolution.

Complex Image Determination in Electron Microscopy

Expressions are derived for the unaberrated complex scattering potential of thin (< 100 A) phase objects in terms of the sum and difference of the image intensities formed in successive experiments with complementary half-plane apertures inserted in the back-focal plane of the objective lens of an electron microscope.

Lattice images of Nb22O54and V6O13in the 1000 kV electron microscope

Abstract According to the calculation of the phase factor the resolution limit for the 1000kV electron microscope at present available, equipped with a goniometer stage, is 2 Å which is about half that for the 100 kV instrument. The crystal structure of Nb22O54 was resolved in detail in a two-dimensional lattice image by the 1000 kV electron microscope; the potential distribution of oxygen ions appeared to be imaged to some extent in addition to that of the niobium ions. The effect of defocus and aperture size on the image contrast could be explained qualitatively on the basis of thin phase object contrast theory. For a V6O13crystal with a relatively small unit cell the lattice image, exhibiting the crystal structure fairly clearly, was obtained with moderately high contrast.

Contrast in High Resolution Images of Crystals

An attempt is made to understand experimentally observed high resolution electron microscope images. Iijima has obtained images that are good representations of the crystal potentials for a resolution of about 3Å using a defocus corresponding to the “optimum defocus condition”. This is to be expected for a thin phase object. However, Iijima's images are obtained from crystals having thicknesses of 100Å and greater for which the maximum phase change is more than 10 radians, and so the thin phase object approximation is not expected to be valid. These images must therefore be explained by other means.Many beam calculations have been made on thick crystals using a trial crystals structure as shown in Fig. 1. A metal atom sits at the centre of each octahedral site with oxygen atoms at the corners. This structure contains blocks of 3 x 3 octahedra of the type found in disordered samples of Ti2Nb10O29 as shown in Fig. 2.