Resolution noise limited

The best resolution will be obtained when Cp is a maximum, and Cp depends on the imaging mode as well as on the specimen feature. Much of the calculation of resolution limits for radiation sensitive materials becomes a calculation of Cp. Calculations have been made assuming that the feature of interest is an isolated fragment of a polyethylene crystal. Reasonable estimates of C and / led to a resolution limit of 5 nm for both bright and dark field in the TEM [126]. Similar values have been obtained for biologically important molecules [127]. 

In normal microscope operation, a large flux is used to focus the image and adjust the specimen position. This would be enough to destroy many sensitive samples and must be avoided. An image intensifier is less efficient at detecting electrons than photographic film, so it cannot improve the resolution of the recorded image. It does produce 

As described in Section 3.2.3, when a finite number of electrons N are used to form an image, there will be a noise limit to resolution. Consider a radiation dose of J enm incident on a feature of size dnm, contrast C. If / is 

A similar calculation for scanning electron microscope images has the same basic equation, dmin = 5/C(Jfy. Differences between STEM and conventional TEM in the imaging of radiation-sensitive materials relate to the different values of C and/expected. These considerations are by 

Jenkins and H.E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 2001). 

Welford, Optics (Oxford University Press, Oxford, 1988). 

Slayter and H.S. Slayter, Light and Electron Microscopy (Cambridge University Press, Cambridge, 1992). 

As described in Section 3.2.3, when a finite number of electrons N are used to form an image, there will be a noise limited resolution. Consider a radiation dose of / e nm incident on a feature of size d nm, contrast C. If / is the fraction of the incident electrons that contribute to the image, there will he N = Jf electrons in the image of that feature. The statistical noise is d(Jf) and the signal is C(d Jf). If the signal to noise ratio k is required to be five or more, then k = Cd Jff d = k/CiJff 5/C(Jff.  

If the TEM image is recorded on film with a resolution of 100 iim, limited by the focusing screen, the magnification needs to be 20,000 x or more to see 5 nm structure in the object. For a structure like the polyethylene crystal that can only take 300 e nm , the incident electron dose at the film can be no more than (300//20,000 ) e nm = 0.75/ e The film 

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The Rayleigh resolution criterion can be satisfied within noise limits if spatial frequencies are recorded to the Scherzer point resolution ... 

Deconvolution of spectra, such as infrared absorption spectra, provides researchers with a tool that they can use to carry out a particular experiment. It provides an extra measure of flexibility in the design of experiments and in the observation process. In dispersive infrared spectroscopic systems, Blass and Halsey (1981) have shown that effective resolution-acquisitiontime trade-offs may be made, owing to the fact that dispersive infrared spectroscopy is usually detector noise limited. Acquisition rates are therefore optical throughput dependent, which is equivalent to saying that acquisition rates are resolution dependent. Blass and Halsey (1981) show that, for a constant signal-to-noise ratio,... 

Because infrared spectrophotometry is detector noise limited, a profitable trade-off is possible between signal-to-noise ratio and resolution. Such a trade-off may be useful when deconvolution is used to recover resolution lost by opening monochromator slits to increase acquisition rates. In any system where degrading the resolution improves the signal-to-noise ratio nonlinearly, a potentially useful trade-off is possible. 

Random noise on the correlation function broadens the calculated distribution, limiting resolution. 

N. Bobroff, Position measurement with a resolution and noise-limited instrument. Rev. Sci. Instrum. 57(6), 1152-1157 (1986)... 

SNR/i is used to denote the analyte shot noise limit, and a. Da, La refer only to analyte variables. Recall that ts is the measurement time for each resolution element and does not necessarily equal the total measurement time As expected, SNR varies with... 

The analyte shot noise limit illustrates the fundamental Importance of multichannel detection for improving SNR. Equations (4.15) and (4.16) are valid for each resolution element in the system in a single or multichannel spectrometer (but not for a multiplex spectrometer). As noted in Section 3.4 and Eq. (3.9), a spectrometer that can monitor Nk resolution elements simultaneously increases the measurement time for each resolution element by a factor of Nr over the time required for a single-channel system. Since Im = NrIs,... 

A primary source is used which emits the element-specific radiation. Originally continuous sources were used and the primary radiation required was isolated with a high-resolution spectrometer. However, owing to the low radiant densities of these sources, detector noise limitations were encounterd or the spectral bandwidth was too large to obtain a sufficiently high sensitivity. Indeed, as the width of atomic spectral lines at atmospheric pressure is of the order of 2 pm, one would need for a spectral line with 7. = 400 nm a practical resolving power of 200 000 in order to obtain primary radiation that was as narrow as the absorption profile. This is absolutely necessary to realize the full sensitivity and power of detection of AAS. Therefore, it is generally more attractive to use a source which emits possibly only a few and usually narrow atomic spectral lines. Then low-cost monochromators can be used to isolate the radiation. 

At wavelengths below 250 nm, however, detector noise limitations may occur especially with high-resolution spectrometers. For integration times exceeding the 1 s level, the full precision is normally achieved. In the case of CCD detection, readout noise may also become important. 

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