Minimum resolution criterion

Once the retention surfaces are known, any criterion may in principle be used to calculate the response surface and to locate the optimum composition. One of the criteria used by Glajch et al. is the threshold minimum resolution criterion (section 4.3.3). This is done by means of a graphical procedure, referred to as overlapping resolution mapping or ORM. This procedure involves the location of areas in the triangle where the resolution Rs exceeds a certain threshold value. This is repeated for all pairs of solutes and the results are combined to form a single figure. 

Figure 4.14 shows a screen dump of an isothermal gas chromatographic simulation from a commercial gas chromatographic optimization program. The Temperature, Pressure, and Column tabs in the display permit the user to set elution conditions, including multiramp temperature and pressure programming, which were not exercised for this example. The Auto-Optimize tab carries out a minimum-resolution-oriented optimization calculation, which determines a set of conditions that lie within specified limits and meet the minimum resolution criterion. 

Several ways to formalize the concept of robustness are presented in this book. Robustness can be formalized and expressed as a variance of the quality criterion which is done in Chapter 7. Another way to formalize robustness is the percentage change of the response, which is done in Chapter 8. It is also possible to express robustness in more complicated ways, examples of those are given in Chapters 2 and 4. In Chapter 6 a maxi-min formalization is chosen select the TLC-solvent composition in such a way that the minimum resolution between two pair of solutes is maximized. 

A second criterion should express the robustness of the separation more subtle than the number of spot cross-overs. The minimum resolution at different temperatures and relative humidities can be combined to an average and a minimum value. 

Like CRF-1, CRF-2 also favors short analysis times and well resolved peaks. However, there is no threshold value for resolution, and the compromise between resolution and analysis time is not as well defined as in CRF-1. Inclusion of analysis time in the denominator of an objective function may result in the loss of some resolution, compensated for by a rapid analysis time (51). This is likely to occur to some extent when the resolution threshold is defined in excess of 1 to 1.25, since the peak-valley ratio utilized by CRF-2 does not diminish to an appreciable extent until the resolution falls below this range. Note that as the resolution drops below 1 to 1.25, however, CRF-2 decreases rapidly, and it is unlikely that a short analysis time will compensate for such poor resolution (33). Nevertheless, if a user-specified minimum resolution is an absolute requirement, it is probably better to use a threshold criterion such as CRF-1 in which the desired resolution is stipulated by the user. 

Explain the Rayleigh criterion for minimum resolution size ... 

For example, suppose one would like to optimize the separation of substances in a chromatogram and that the minimum resolution (Rsmin) between two adjacent peaks is the criterion which defines the quality of the separation. Imagine that Rsmin < 1.0 is considered unacceptable, that Rsmm > 3.0 will make the analysis too long, and that Rs ,in = 2.0 would lead to a good separation with a reasonable analysis time. For this example, t = 2.0, Kmin = I -0, and y ,ax = 3.0. Therefore for values of Rsmin <1.0 and Rsnun 3.0, d = 0 and the values of Rsmi between 1.0 and 3.0 will be scaled according to equations (19) and (20). 

The resolution or "resolving power" of a light microscope is usually specified as the minimum distance between two lines or points in the imaged object, at which they will be perceived as separated by the observer. The Rayleigh criterion [42] is extensively used in optical microscopy for determining the resolution of light microscopes. It imposes a resolution limit. The criterion is satisfied, when the centre of the Airy disc for the first object occurs at the first minimum of the Airy disc of the second. This minimum distance r can then be calculated by Equation (3). 

This criterion may be used during a sequential optimization process (see chapter 5), leading to an acceptable result and to completion of the optimization process once the threshold value has been reached. Alternatively, it may be used to establish ranges of conditions in the parameter space for which the result will be acceptable. This latter approach has been followed by Glajch et al. [415], by Haddad et al. [424] and by Weyland et al. [425] and was referred to as resolution mapping by the former. Within the permitted area(s) secondary criteria are then required to select the optimum conditions. For example, the conditions at which the k value of the last peak (k is minimal while the minimum value for Rsexceeds 1 may be chosen as the optimum. Such a composite criterion can be described as... 

Weyland et al. [560,561] used this method to optimize ternary mobile phase compositions for the separation of sulfonamides by RPLC. They fitted the retention surfaces to a quadratic model similar to eqn.(3.39), and also used a combination of a threshold resolution and minimum analysis time (min tm fl / vmin> 1.25 eqn.4.24) [560]. This criterion may yield a good optimum if the optimization is performed on the final analytical column (see table 4.11). 

It can be seen in the chromatogram of figure 6.11 that four peaks (the three antioxidants plus an unknown impurity) are amply resolved to the baseline. This implies that all values for the peak-valley ratio P are equal to 1 and that the criterion has become very insensitive to (minor) variations in the resolution between the different peak pairs. In the area of the parameter space in which four well-resolved peaks are observed, the only remaining aim of the optimization procedure is to approach the desired analysis time of 4 minutes. The irrelevance of the minimum time tmin is illustrated by the occurrence of the first peak in figure 4.9 well within the value of 1.5 min chosen for this parameter. 

Figure 3-10 shows how light from an infinitely narrow slit is focused to cover the face of the prism at the angle of minimum deviation. Two beams emerge of wavelengths X and X + A, which just meet the Rayleigh criterion for resolution. The beams are separated by the angle A0. Thus, A0 = Xja, where a is the beam width. Consequently... 

In 1873, Ernst Abbe established the resolution limit of optical microscopes The minimum distance, d, between two structural elements to be imaged as two objects instead of one is given by d = A/(2 NA), where X is the wavelength of light and NA the numerieal aperture of the objective lens. The physical root for resolution limit is related to optical diffraction and loss of evanescent waves in far-field the evaneseent waves carry high-frequency subwavelength spatial information of an object and decay exponentially with distance from the objeet. With white lights, optical microscope resolution is limited at about 200-250 nm. For about one hundred years, the Abbe criterion was considered the fundamental limit of optical microscope resolution. 

This limitation on the resolution of images by diffraction is quantified in terms of the so-caUed Rayleigh criterion the imaging process is said to be diffraction limited when the first diffraction minimum of the image of one source point coincides with the maximum of a neighbouring one. The numerical value for the Rayleigh diffraction angle A0r, is... 

The first acceptance criterion for the resolution of USI A-47 is that the plant shall have, as a minimum, control-grade protection against SG overfill by main feedwater, consistent with the requirements and guidance of GL 89-19. Also, in accordance with GL 89-19, technical specifications and plant operating procedures shall ensure in-service verification of the availability of the overfill protection. 

The acceptance criterion for the resolution of GSI B-56, is that emergency diesel generator design, operation, and periodic testing shall ensure, as a minimum, a starting reliability of. 95 per demand, as identified in Regulatory Guides 1.9, Rev. 3 (DRAFT) and 1.155. 

Lord Rayleigh introduced a criterion of resolution for diffraction-limited line profiles, where two lines are considered to be just resolved if the central diffraction maximum of the profile Ii(X — X ) coincides with the first minimum of h X — X2) [4.3]. 

The topic of polymer nanocomposites pertains to the synthesis, characterization, and applications of polymer materials with at least one or more dimensions less than 100 nm. According to the Rayleigh criterion, the maximum resolution or the minimum detectable size achievable was believed to be half the wave length of light, that is, 200 nm. The first clay nanocomposite was commercialized by Toyota with a belt cover made of a nylon-6 matrix filled with 5% clay. General Motors commercialized the first exterior trim application of nanocomposite in their 2002 mid-sized vans. 

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