Phase shifts microscope

With the paraboloid method followed by the maximum-likelihood refinement of the exit-wave function, the inherent effects of the microscope on the exit wave function due to spherical aberration and defocus are eliminated resulting in a complex-valued wave function with the delocalization removed. However, the electron wave function frequently suffers from residual aberrations due to insufficient microscope alignment. In a single image, it is not possible to remove these aberrations, but, with the reconstructed complex wave function, one can use a numerical phase plate to compensate the effect of aberrations by applying appropriate phase shifts (Thustetal. 1996b). 

Powerful methods that have been developed more recently, and are currently used to observe surface micro topographs of crystal faces, include scanning tunnel microscopy (STM), atomic force microscopy (AFM), and phase shifting microscopy (PSM). Both STM and AFM use microscopes that (i) are able to detect and measure the differences in levels of nanometer order (ii) can increase two-dimensional magnification, and (iii) will increase the detection of the horizontal limit beyond that achievable with phase contrast or differential interference contrast microscopy. The presence of two-dimensional nuclei on terraced surfaces between steps, which were not observable under optical microscopes, has been successfully detected by these methods [8], [9]. In situ observation of the movement of steps of nanometer order in height is also made possible by these techniques. However, it is possible to observe step movement in situ, and to measure the surface driving force using optical microscopy. The latter measurement is not possible by STM and AFM. 

If the specimen is moved away from the focal position, then this will cause a phase shift that depends on 6. If the wavenumber in the coupling fluid is k = 2n/Xo, then the z component of the wavevector is kz = k cos 6. Defocusing the specimen by an amount z causes a phase delay of 2zkz, or 2zk cos 0 (the factor of two arises because both the incident wave and the reflected wave suffer a change in path length). Expressing this phase delay as the complex exponential of a phase angle, the response of the microscope with a defocus z is... 

Figure 7 Phase images from the interferometric microscope (p-polarized, 32.6 incidence angle, 800 nm wavelength) during breakout of a 4.7 GPa shock from 250 nm thick Al, using 130 fs pulse length shock drive. The image z-axis scale is phase shift in radians.

In electron interferometry, there are often cases where great precision is required, for example, to measure the thickness distribution in atomic dimensions or to observe microscopic electromagnetic fields. To achieve such precision, phase amplification techniques peculiar to holography have been developed and used. Using these techniques, phase shifts as small as 1/100 of the wavelength can be detected [2.5]. 

AFM experiments are carried out by AFM using a Dimension 3000 microscope coupled to a Nanoscope Ilia electronic controller (Digital Instruments, Veeco-FFI Co., USA). All experiments were performed in tapping mode. The AFM was equipped with the phase extender electronic modulus, making it possible to record the phase shift variations between the instantaneous oscillation of the tip and the oscillation applied to the cantilever in tapping mode. In our case, this phase shift depended strongly on the local moduli between the different components of the material and reflected the surface structure of the thin films [27-34]. 

The initial phase coherence of the spins in the xy plane gradually fades with time, a process which is reflected in the time-dependent disappearance of the transverse magnetization Mxyj that is, a time-dependent signal decay in the detection coil. The spin dephasing is caused by two main processes. First, fluctuating inhomogeneities in the microscopic environment of the individual protons induce phase shifts [289]. The Larmor frequency of the spins remains unaltered at the same time. This phase loss is characterized by the transverse relaxation time T2. Second, static local... 

The phase-shift detection limit of the microscope shall be about 3 degrees measured using the HSE phase shift test slide as outlined below. 

Place the phase-shift test slide on the microscope stage and focus on the lines. The analyst must see line set 3 and should see at least parts of 4 and 5 but, not see line set 6 or 6. A microscope/microscopist combination which does not pass this test may not be used. 

Figure 5. Image path of the phase contrast microscope, convening phase shifts into a noticeable contrast a) Illuminating diaphragm ring b) Condenser, c) Specimen generating a phase shift d) Objective plate e) Phase plate 0 Intermediate image...

Figure 6. A) Image path of a Iwo-beam interference microscope B) Nomarski prism with direction of optical axes and position of interference plane indicated a) Polarizer (45°) b) First Wollaston prism c) Condenser d) Specimen e) Objective f) Second Wollaston prism g) Analyzer (135°) h) Intermediate image Contrast is generated by a phase shift of the polarized and prism-split illuminating beam.s, which are combined by the second prism...

Figure 42. Dependence on li of the phase shift x (/() of a beam enclosing an angle P with the optical axis of the microscope...

The situation is somewhat comparable to positive and negative phase contrast in optical microscopy. The lens imperfections have been used to Introduce a phase shift of jt/2 in the same way as the quarter wavelength ring in the optical microscope. Only beams passing through the "window in which the condition sin X =- I is met, interfere with the required phase relationship that causes the image to represent maxima in projected potential as dark areas. 

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