Diffraction-limited microscopy

The product of the refractive index n and sin 9 is known as the numerical aperture 

For most transmission spectroscopic measurements made with a microscope, the sample is in contact with air and so n is usually approximately equal to 1. Since for most microscopes 9 40°, NA is usually close to 0.6 (sin 40° = 0.64). Thus, the spatial resolution is approximately equal to 2. (We note here that the Abbe resolution is often defined as 2/2, but this performance is only accomplished for coherent illumination.) For mid-infrared measurements at the highest spatial resolution, it is customary to set the microscope aperture to give the diffraction-limited resolution at 1000 cm (2 = 10 pm) so that the resolution at longer wavelengths is set by the value at 1000 cm (about 10 pm). Better resolution is achieved in attenuated total reflection (ATR), especially when the internal reflection element (IRE) is silicon (n = 3.4) or germanium (n = 4.0), but achieving optical spatial resolution better than about 3 pm is essentially impossible for diffraction-limited mid-infrared measurements. 

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For diffraction-limited microscopy, it may be thought that the image should be focused on the CCD such that the Airy disk fills one pixel. However, Adar et al. [41]... 

Within the last years, single-molecule fluorescence imaging became possible at room temperature and ambient conditions, first with the use of scanning near-field optical microscopy and ultra-high spatial optical resolution (about 100 nm), and later with the use of diffraction limited microscopy techniques (resolution about 300 nm) such as the epi-fluorescence microscopy, internal reflection microscopy, and scanning confocal microscopy. 

Raman microscopy is more developed than its IR counterpart. There are several reasons for this. First, the diffraction limit for focusing a visible beam is about 10 times smaller than an IR beam. Second, Raman spectroscopy can be done in a backscattering geometry, whereas IR is best done in transmission. A microscope is most easily adapted to a backscattermg geometry, but it is possible to do it in transmission. 

X-Ray Microscopy. Because of the short wavelength of x-rays, they have, for nearly 100 years, held out the hope of being utilized in order to significantly lower the diffraction limit of resolution when visible light is used. The difficulties of focusing x-rays and the relative weakness of x-ray sources have, until recently, fmstrated efforts to teach that goal (25). 

Similarly, the first-order expansion of the p° and a of Eq. (5.1) is, respectively, responsible for IR absorption and Raman scattering. According to the parity, one can easily understand that selection mles for hyper-Raman scattering are rather similar to those for IR [17,18]. Moreover, some of the silent modes, which are IR- and Raman-inactive vibrational modes, can be allowed in hyper-Raman scattering because of the nonlinearity. Incidentally, hyper-Raman-active modes and Raman-active modes are mutually exclusive in centrosymmetric molecules. Similar to Raman spectroscopy, hyper-Raman spectroscopy is feasible by visible excitation. Therefore, hyper-Raman spectroscopy can, in principle, be used as an alternative for IR spectroscopy, especially in IR-opaque media such as an aqueous solution [103]. Moreover, its spatial resolution, caused by the diffraction limit, is expected to be much better than IR microscopy. 

Figures 21(a) and 21(b) show the SEM micrographs of the freeze-fractured cross-section of the film used in the construction of the bag. There are two distinct layers and possibly a third very much thinner tie layer. The outside layer is a layer of nominal thickness 13 pm. The inside layer is much thicker and is approximately 70 pm thick. At the interface between the outer and inner layers the apparent very thin tie layer is about 1 pm thick. This is too thin to be identified by FUR microscopy on a cross-section of the sample, since the technique is diffraction-limited, which means that layers of about 10 pm thickness or greater can only be readily identified [1]. The tie layer thickness is also probably too thin for fingerprinting by Raman microspectroscopy on a cross-section the lateral spatial resolution of Raman microspectroscopy is about 1-2 pm.

Rust, M. J., Bates, M. and Zhuang, X. (2006). Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). Nat. Methods 3, 793-5. 

For samples thicker than the depth of field, the images are blurred by out-of-focus fluorescence. Corrections using a computer are possible, but other techniques are generally preferred such as confocal microscopy and two-photon excitation microscopy. It is possible to overcome the optical diffraction limit in near-field scanning optical microscopy (NSOM). 

Characterization is the foundahon for the development and commercialization of new zeolites and zeolite-containing catalysts and adsorbents. Chapter 4 provides an overview of the most commonly employed characterization techniques and emphasizes the uhlity and limitations of each of these methods. An example is provided as to how a multi-technique characterization approach is necessary in order to determine the structure of a newly invented zeolite. Techniques covered in this chapter include X-ray powder diffraction, electron microscopy, infrared (IR) spectroscopy, nuclear magnetic resonance (NMR) spectroscopy and physical/ chemical methods. 

Hell, S., and Wichmann, J. 1994. Breaking the diffraction limit by stimulated emission Stimulated-emission depletion fluorescence microscopy. Opt. Lett. 19 780-82. 

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