Phase-contrast

OBJECT PLANE OBJECTIVE FOCAL PLANE IMAGE PLANE 

At the back-focal plane of objective lens, the diffraction pattern is considered as the Fourier transform (FT) of the object function. 

Y and Z are the magnitudes of reciprocal vector R, corresponding to the magnitude (x, y and z) of vector r in the real space. Since the electron waves pass the objective lens, the objective lens can affect the wave characteristics. The effect of the objective lens on the wave function can be represented by a transfer function, 7TR). Thus, the actual wave function on the back-focal plane becomes the following function. 

Wave theory tells us that the wave function of electrons on the image plane (florescent screen) should be the Fourier transform of F (R). For treatment simplicity, we may ignore the image magnification and rotation on the image plane. Then, the wave function on the image plane becomes f (r). 

The results should be read as the convolution product of/(r) by t(r), where t(r) is the Fourier transform of T(R). The transfer function plays an important role in image formation. The transfer function can be written as the following equation. 

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It is shown how phase contrast X-ray microtomography can be realised with a (commercial) polychromatic X-ray microfocus tomograph provided the source size and the resolution of the detector are sufficiently small and the distance between source and detector is sufficiently large. The technique opens perspectives for high resolution tomography of light objects... 

A much better way would be to use phase contrast, rather than attenuation contrast, since the phase change, due to changes in index of refraction, can be up to 1000 times larger than the change in amplitude. However, phase contrast techniques require the disposal of monochromatic X-ray sources, such as synchrotrons, combined with special optics, such as double crystal monochromatics and interferometers [2]. Recently [3] it has been shown that one can also obtain phase contrast by using a polychromatic X-ray source provided the source size and detector resolution are small enough to maintain sufficient spatial coherence. 

This opens perspectives for obtaining phase contrast information in a microfocus tomographic system Recently we have developed a desktop X-ray microtomographic system [4] with a spot size of 8 micrometer (70 KeV) and equipped with a (1024) pixel CCD, lens coupled to a scintillator. The system is now commercially available [5], The setup is sketched in Figure 1 In this work we used the system to demonstrate the feasibility for phase contrast microtomography. 

Consider a microtomographic system as depicted in Figure 1. It can be shown that in this geometry [6] the phase contrast signal is... 

From (1) it is clear that the phase contrast can be interpreted simply in terms of tbe variation (second order derivative) of the projected image density, and increases with improving resolution of the system, in agreement with the findings of [3]. 

Let us now consider the phase contrast at a sharp phase edge, as is the case for a planar... 

It should be noted that these results are only preliminary and have to be considered as a proof of concept. As is clear from eq. (2) the phase contrast can be improved drastically by improving the global resolution and sensitivity of the instrument. Currently, a high resolution desktop system is under construction [5] in which the resolution is much better than that of the instrument used in this work, and in which the phase contrast is expected to be stronger by one order of magnitude. 

It has been demonstrated that phase contrast microtomography is feasible with a desktop (commercial) X-ray microtomographic system The observations agree well with the theoretical predictions. This opens perspectives for high resolution microtomography of light objects. 

Except for the phase-contrast detector in STEM [9], STEM and SEM detectors do not track the position of the recorded electron. The spatial information of an image is fonned instead by assigning the measured electron current to the known position of the scaimed incident electron beam. This infomiation is then mapped into a 2D pixel array, which is depicted either on a TV screen or digitalized in a computer. 

Figure Bl.17.5. Examples of CTFs for a typical TEM (spherical aberration = 2.7 mm, 120 keV electron energy). In (a) and (b) the idealistic case of no signal decreasing envelope fimctions [77] are shown, (a) Pure phase contrast object, i.e. no amplitude contrast two different defocus values are shown (Scherzer focus of 120 mn imderfocus (solid curve), 500 mn underfocus (dashed curve)) (b) pure amplitude object (Scherzer focus of 120 mn underfocus) (c) realistic case mcluding envelope fimctions and a mixed weak...

Light microscopy allows, in comparison to other microscopic methods, quick, contact-free and non-destmctive access to the stmctures of materials, their surfaces and to dimensions and details of objects in the lateral size range down to about 0.2 pm. A variety of microscopes with different imaging and illumination systems has been constmcted and is conunercially available in order to satisfy special requirements. These include stereo, darkfield, polarization, phase contrast and fluorescence microscopes. 

Figure Bl.18.6. Schematic representation of Zemike s phase contrast method. The object is assumed to be a relief grating in a transparent material of constant index of refraction. Phase and amplitude are varied by the Zemike diaphragm, such that an amplitude image is obtained whose contrast is, m principle, adjustable.

At this point it is worth comparing the different techniques of contrast enliancements discussed so far. They represent spatial filtering teclmiques which mostly affect the zeroth order dark field microscopy, which eliminates the zeroth order, the Schlieren method (not discussed here), which suppresses the zerotii order and one side band and, finally, phase contrast microscopy, where the phase of the zeroth order is shifted by nil and its intensity is attenuated. 

As already discussed, transparent specimens are generally only weakly visible by their outlines and flat areas caimot be distinguished from the surroundings due to lack of contrast. In addition to the phase contrast teclmiques, light interference can be used to obtain contrast [8, 9]. 

Zernike F 1942 Phase contrast, a new method for the microscopic observation of transparent objects I Physica 9 686... 

Tdrdk P, Sheppard C J R and LaczikZ 1996 Dark field and differential phase contrast imaging modes in confocal microscopy using a half aperture stop Optik 103 101-6... 

PHARMSEARCH Phase behavior Phase change recording Phase contrast Phase diagram Phase diagrams... 

There ate four main approaches to x-ray imaging contact radiography, scanning x-ray microscopy, holographic x-ray microscopy, and shadow projection x-ray microscopy. In the future, there will likely be phase-contrast imaging and photoelectron x-ray microscopy. 

Fig. 27. Phase contrast photomicrographs showing particle formation via phase inversion.

The im< e mode produces an image of the illuminated sample area, as in Figure 2. The imj e can contain contrast brought about by several mechanisms mass contrast, due to spatial separations between distinct atomic constituents thickness contrast, due to nonuniformity in sample thickness diffraction contrast, which in the case of crystalline materials results from scattering of the incident electron wave by structural defects and phase contrast (see discussion later in this article). Alternating between imj e and diffraction mode on a TEM involves nothing more than the flick of a switch. The reasons for this simplicity are buried in the intricate electron optics technology that makes the practice of TEM possible. 

Figure 5 Images of a thin region of an epitaxial film of Ge on Si grown by oxidation of Ge-implanted Si (a) conventional TEM phase contrast image with no compositional information and b) high-angle dark-field STEM image showing atomically sharp interface between Si and Ge. (Courtesy of S.J. Pennycook)...

In the second half of the 20th century, a number of advanced variants of optical microscopy were invented. They include phase-contrast microscopy (invented in France) and multiple-beam interference microscopy (invented in England), methods... 

Fibres longer than 5 im and with an aspect ratio >3 1 as determined by the membrane filter method at 400-450X magnification (4 mm objective) phase contrast illumination. 

Tamayo, J. and Garcia, R., Effects of elastic and inelastic interactions on phase contrast images in tapping-mode scanning force microscopy. Appl. Phys. Lett., 71(16), 2394-2396 (1997). 

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