Resolution criterion

When we say that objects are resolved, we mean that they are rendered so that their separate and distinguishable identities are apparent. The present section briefly formalizes this intuitive idea. 

In the simplest possible case, we wish to distinguish only two objects. In optics the required specification is called a two-point resolution criterion. In spectroscopy a two-point criterion specifies the distance that must separate two spectral lines for them to be called resolved. Essentially similar criteria apply to other fields. 

Previous sections have detailed phenomena that contribute to the degradation of resolution in optical spectra. Concepts useful in specifying resolution criteria have been established. Although transfer and point-spread functions of varying shape can yield identical numbers when a simple two-point criterion is applied, this many-to-one correspondence does not diminish the criterion s usefulness. More rigorous specification of the transfer function virtually requires graphical presentation for human interpretation. Its use therefore demands far more space in text and more time for study. Frequently, the functional form of the transfer function is well known anyway systems being compared are often of similar type. In these cases, the two-point criterion is entirely adequate. 

In optics and spectroscopy, resolution is often limited by diffraction. To a good approximation, the spread function may appear as a single-slit diffraction pattern (Section II). If equal-intensity objects (spectral lines) are placed close to one another so that the first zero of one sine-squared diffraction pattern is superimposed on the peak of the adjacent pattern, they are said to be separated by the Rayleigh distance (Strong, 1958). This separation gives rise to a 19% dip between the peaks of the superimposed patterns. 

It might seem that Lord Rayleigh s proposal is somewhat arbitrary even if two lines are separated by a somewhat smaller distance, it will be apparent that two lines are present rather than one. Sparrow s criterion (Strong, 1958) does, in fact, say that two lines may be termed just resolved when spaced so that the dip first appears. The Rayleigh criterion, however, gives rise to particularly simple expressions for resolving power. 

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Peaks and their number are instead currently detected and measured by an integrator or scanning devices and thus are instead observable quantities. The main drawback is that they are evaluated on the basis of established threshold and resolution criteria that very often are not precise. Nonetheless, the response values, even if poorly defined, can be used to estimate m—a hidden quantity, see above—in a random retention pattern, as described below. 

What meaning do these two-point resolution criteria have in describing the deconvolution process, that is, resolution before and after deconvolution Although width criteria may be applied to derive suitable before-after ratios, the Rayleigh criterion raises an interesting question. Because the diffraction pattern is an inherent property of the observing instrument, would it not be best to reserve this criterion to describe optical performance The effective spread function after deconvolution is not sine squared anyway. 

Other modifications are possible to the same basic approach of seeking a filter that is optimum in the sense of least mean-square error. Backus and Gilbert (1970), for example, derive a linear filter by minimizing a sum of terms in which noise and resolution criteria are separately weighted. Frieden (1975) discusses variations of this technique. 

GC Resolution Criteria for SP-2331 or Equivalent Column. The chromatographic peak separation between unlabeled 2,3,7,8-TCDD and the peaks representing all other unlabeled TCDD isomers shall be resolved with a valley of S 25 percent, where... 

The resolution criteria must be evaluated using measurements made on the selected ion current profile (SICP) for the appropriate ions for each isomer. Measurements are not made from total ion current profiles. 

Further analyses may not proceed until the GC resolution criteria have been met. 

GC Column Resolution Criteria. The chromatographic resolution on the D-5 (or equivalent) column must meet the QC criteria in Paragraph 7.3.2.1. The chromatographic resolution on the SP-2331 (or equivalent) column must meet the QC criteria in Paragraph 7.2.3. In addition, the chromatographic peak separation between the 1,2,3,4,7,8-HxCDD and the 1,2,3,6,7,8-HxCDD in the CC3 solution shall be resolved with a valley of 50 percent. 

As in the case of the piperidine derivatives, azepine drugs in complex with protein were searched for in the PDB using the MSD server. Since the number of hits was very low no resolution criteria was used for this search that yielded one each in azepin and benzothiazepine and five in fused-diazepine (Table 6). 

Limiting resolution criteria Spatial frequency point where MTF( equals 10 % or the spatial frequency where the chart periodicity is lost Spatial frequency point where MTF(f) equals 5 %... 

The spatial resolution criteria given in Equations [3] and [4] apply for diffraction-limited microscope objectives in the far-field limit. In recent years, nearfield techniques have been devised that exceed the diffraction limit by scanning a tapered light source, with a spot size less than the probe wavelength, in close proximity to the sample. 

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