Resolving power

Resolving power is related to granularity and is defined as the ability of an emulsion to record separate adjacent lines. The resolving power of an emulsion usually is given in terms of the maximum number of lines that can be resolved per millimeter. For example, a resolution of 50 means that 50 equally spaced lines is the maximum that can be observed per millimeter using suitable magnification for observation. 

FIGURE 6-8. Spectral sensitivity curves of three commonly used spectral plates and films. [From a copyrighted Kodak publication. Courtesy Eastman Kodak Co.] 

As mentioned previously, most commercial magnetic sector ICP-MS systems offer up to 10,000 resolving power (10% valley definition), which is high enough to resolve 

FIG U RE 8.2 Ion transmission with a magnetic sector instrument decreases as the resolution increases. 

Resolution Required to Resolve Some Common Polyatomic Interferences from a Selected Group of Isotopes 

The RP for other analyzer types that do not provide approximately constant peak widths across the mJz range is conventionally defined by Equation [6.1]  

In the present context of quantitative analysis of target analytes present at trace levels in complex matrices, the importance of high resolving power lies in the additional degree of detection selectivity that it provides. A particularly important example where this is essential is that of PCDDs ( dioxins ) discussed later in Section 11.4.1. It is also true that higher RP implies that the positions of the peaks along the m/z axis are more precisely defined and, in turn, this can facilitate more precise measurements of the m/z value this in turn can provide additional confirmation of analyte identity in cases where this is an important issue (Sections 6.2.3c and 9.4.3b). 

In modern analytical chemistry such methods play an increasing role which have a high resolution with regard to  

Each type of resolved measurement increases the amount of information obtainable by an analytical method, namely with regard to its capability of multielemental, spatial or temporal differentiation. 

In case of variable signal half-width Az as shown in Fig. 7.11b the following general expression applies (Danzer [1975])  

In the case of constant signal half-width it results in Eq. (7.53) whereas, in the case of constant resolution R(z)y it follows that (Kaiser [1970] Danzer [1975]) 

The analytical resolving power is applied in several analytical fields in form of well-known expressions such as, e.g., spectral resolving power Rx = X/AX or mass resolving power RM = M/AM. 

Consider two identical Gaussian curves representing the concentration contribution of equal amounts of two very similar proteins at a distance Ax from each other. Mathematical analysis shows that the run of these two curves has only one maximum if Ax is smaller than two standard deviations, that is, 2a ,. The distance is thus insuflScient for a visible separation of the proteins. For Ac larger than 2x the summation of the two distribution curves shows two maxima and between them one minimum. In this case one can speak about a detectable separation between the two proteins, i.e., two focused protein zones in electrofocusing. As the value of Ac increases, the depth of the minimum between the peaks increases, at first slowly then more rapidly. For Ac = 3.07x the mini- 

When this value is inserted in the equation for xt along with the figures derived from the separation of myoglobins obtained by Vesterberg and Svensson (7) and by Vesterberg (8), a resolving power of 0.01 — 0.02 pH units is obtained. This agrees well with experimentally obtained results. 

In experiments described by Vesterberg and Svensson (7) separating myoglobin IIi from myoglobin 11, Vesterberg (8) calculated the charge of one of the two protein components at the pi value of the other one. He arrived at 0.13 electrostatic unit. The stated pi difference was 0.06 pH unit. 

ISOELECTRIC POINT MEASURED IN ELECTROFOCUSING AND ELECTROPHORESIS, RESPECnVELT 

It is conceivable that weak complexes can form between proteins and carrier ampholytes. There have been no reports of investigations on this subject, which has however been discussed by Vesterberg and Svensson (7) and Vesterberg (49,50). However, when the pi of proteins is determined by electrofocusing, the values seem to be independent of the kind and concentration of the carrier ampholytes. A protein focused at its isoelectric point exists in a surrounding of carrier ampholytes each of which essentially lies at its isoelectric point. Thus it cannot be assumed that a possible complex between a protein and the surrounding carrier ampholytes would cause the isoelectric point to shift. 

Practical Guide to ICP-MS A Tutorial for Beginners, Second Edition 

FIGURE 8.3 Comparison of resolution between (a) a quadrupole and (b) a magnetic sector instrument for the polyatomic interference of Ar O on Fe+. (From U. Greb and L. Rott-man, Labor Praxis, August 1994.) 

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Liquid chromatography, having a resolving power generally less than that of gas phase chromatography, is often employed when the latter cannot be used, as in the case of samples containing heat-sensitive or low vapor-pressure compounds. 

Note that this relationship is in conPadiction to the well known equation for the calculation of the thickness resolving power given by Halmshaw in 111. The relationship in 111 requires explicit knowledge about built-up factors for scatter correction and the film contrast factory (depending on D) and is only valid for very small wall thickness changes compared to the nominal wall thickness. 

In practice, only a limited number of views are available the scanned sector is typically 180 or 360°, and the angular increment 2°. Moreover the frequency band-width of the employed pulses is very limited, typically one octave. The resolving power of the system is then limited. A typical numerical signal is composed of 1024 samples at a sampling period of 50 nsec. 

When dispersing elements are used, the resolution of the speetrometer is detennined by the entranee slit widtir, the exit slit width, the foeal length and the dispersing element itself Resolving power is defined as... 

The resolution of the Raman spectrum is detemiined by the monoclnomator. Furthennore, since the light bemg measured is in the visible region, usually around 20 000 cnc the resolution of the monoclnomator must be significantly better than that of its IR counterpart because the resolving power is described by Av/v. That is, for... 

Probably the simplest mass spectrometer is the time-of-fiight (TOP) instrument [36]. Aside from magnetic deflection instruments, these were among the first mass spectrometers developed. The mass range is theoretically infinite, though in practice there are upper limits that are governed by electronics and ion source considerations. In chemical physics and physical chemistry, TOP instniments often are operated at lower resolving power than analytical instniments. Because of their simplicity, they have been used in many spectroscopic apparatus as detectors for electrons and ions. Many of these teclmiques are included as chapters unto themselves in this book, and they will only be briefly described here. 

Ultimate resolving power (accurate mass determination) + +++... 

Generally, the attainable resolving power of a TOE instrument is limited, particularly at higher mass, for two major reasons one inherent in the technique, the other a practical problem. First, the flight times are proportional to the square root of m/z. The difference in the flight times (t and t ,+i) for two ions separated by unit mass is given by Equation 26.5. 

An added consideration is that the TOF instruments are easily and quickly calibrated. As the mass range increases again (m/z 5,000-50,000), magnetic-sector instruments (with added electric sector) and ion cyclotron resonance instruments are very effective, but their prices tend to match the increases in resolving powers. At the top end of these ranges, masses of several million have been analyzed by using Fourier-transform ion cyclotron resonance (FTICR) instruments, but such measurements tend to be isolated rather than targets that can be achieved in everyday use. 

Accurate mass measurement requires high resolving power. The difference in degrees of difficulty between measuring an m/z of 28 and one of 28.000 is likely to be large. Table 39.3 shows the broad mass ranges achievable with various analyzers. 

Resolving power (mass). The ability to distinguish between ions differing slightly in mass-to-charge ratio. It can be characterized by giving the peak width, measured in mass units, expressed as a function of mass, for at least two points on the peak, specifically for 50% and for 5% of the maximum peak height. 

Plot X against n and hence obtain the resolving power of a fused quartz prism, wifh a base length of 3.40 cm, at 200 nm, 250 nm, 300 nm and 350 nm. What is the resolution, in nanometres, at these wavelengths How would the resolving power and resolution be affected, quantitatively, by using two such prisms in tandem ... 

It was learned very early that the angular aperture of the substage condenser controls specimen contrast. Decreasing that aperture, usually with a continuously adjustable iris diaphram, greatly increases contrast. It was not, however, appreciated fully until Ernst Abbe s classic contributions (7,8) in the period ca 1880—1889 that decreasing the aperture to increase contrast also decreases the resolving power of the microscope. 

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