Mass resolution definition

Improving the mass resolution (definition is covered in Section 5.1.1.1.1) reduces this m/q spread, thereby allowing for the separation of secondary ion signals of similar (nominal) m/q ratios. Minimal spread is noted in the FT-ICR mass spectra shown in Figure 5.2(c) where an extremely High Mass Resolution (HMR) was used (Smith et al. 2013). 

Figure 5.3 Mass resolution definitions referred to as the (a) single-ion method and (b) the double-ion method for flat-top peaks. The same definitions apply to round topped peaks.

Figure 2.172 (a-c) Comparison of different mass resolution definitions 10% valley (equal to 5% peak height) and FWHM (Munster and Taylor, 2009). 

Peak Width. Peak width depends on the mass resolution. A resolution of 1 mass unit is sufficient to distinguish ions in most qualitative/quantitative small molecule applications. A typical definition of unit resolution is when the peak width at half-height is about 0.6 to 0.8 mass unit. The profile scan of ions on a typical benchtop LC-MS has a bandwidth of about 1 mass unit (Figure 13.1). 

Because slits in the range 0.1 to 1mm width are used in mass spectrometers, the separated ion beams have a defined breath b close to the slits. The capability of the mass spectrometer for separating ion beams with different masses m and m+Ara is characterized by the mass resolution R (or resolving power) using the following definition ... 

Figure 3.15 Demonstration of two definitions of mass resolution (R = m/4m) 10 % valley definition and peak width definition.

Resolving Power (RP) A measurement of how effectively a mass analyzer can distinguish between two peaks at different, but similar m/z. Mathematically, the formula M/ AM is used, where M is the m/z value for one of the peaks and AM is the spacing, in unified atomic mass units, between the peaks. Most commonly, AM is the mass resolution, either via the 10% valley or FWHM definitions (see below). (Note that the definition used will affect the resolving power calculated.) Resolving power of 500-1000 approximately corresponds to unit resolution (e.g., at m/z 700 and FWHM resolution of 0.7, RP = 1000). 

FWHM Full width at half-maximum. Mass resolution is often difficult to determine at or near the base of a peak due to baseline noise and peak overlap. It is more common to measure the width of the peak halfway to the peak maximum, where a clean measurement is possible. The most common alternative to FWHM was the 10% valley definition, in which the peak width at 10% of height was examined. This latter definition is common in the literature, especially for magnetic sector mass spectrometers, but is currently used much less frequently than FWHM. The choice of FWHM or 10% valley has an impact on the calculation of resolving power. 

If delayed extraction increases the mass resolution without degradation of sensitivity compared with continuous extraction, it also has limitations. Indeed, delayed extraction complicates the mass calibration procedure. It can only be optimized for part of the mass range at a time and is less effective at high mass. Delayed extraction partially decouples ion production from the flight time analysis, thus improving the pulsed beam definition. However, calibration, resolution and mass accuracy are still affected by conditions in the source. For instance, in the usual axial MALDI-TOF experiments, optimum focusing conditions depend on laser pulse width and fluence, the type of sample matrix, the sample preparation method, and even the location of the laser spot on the sample. 

The mass resolution of magnetic instruments is expressed as M/AM where AM is the mass difference between mass M and the next higher mass from which it is being separated. An overlap of the two peaks leading to a 10% valley has been selected arbitrarily for a working definition of unit resolution. 

In quadmpole and ion trap spectrometers, it is customary to use the unit resolution definition, which means that each mass can be separated from the next integer mass (500 from 501, 2000 from 2001, etc.). The comparison and conversion between the different resolution definitions is not trivial, considering that they are strongly dependent on peak shape (Gaussian, triangular, trapezoidal, Lorent-zian, etc.).9... 

Figure 5 There are two definitions of mass resolution. These are based on either two overlapping peaks of equal intensity separated by AM (a) or a single well-defined peak with AM defined as the full-width at half-maximum height (FWHM) (b).

There are two commonly used definitions for mass resolution (R). The first, used with magnetic sector instruments, is defined as the ability to separate two neighboring ions in a mass spectrum where AMx is the difference in mjz between the two peaks. The two peaks should be of equal size and similar shape and the degree of overlap (x) should be specified (Figure 5(a)). The latter is often specified as 10 or 50% of the valley height. M is the average of the two masses. 

A rapid sampling method for direct aerosol analysis using FD-mass spectrometer has been described . In a predominantly inorganic aerosol three alkali metal cations and a number of cluster ions of intact salts have been identified under the conditions of high mass resolution (R 15,000, 10 per cent valley definition) using photographic registration. 

By definition, the mass resolution of a mass spectrometer is its ability to distinguish between two neighboring ions that differ only slightly in their mass (Am). Mathematically, it is the inverse of resolving power (RP), given as... 

Fortunately, some of the weaknesses may be overridden by using better hardware. Thus, higher mass resolution helps in molecular formula determination (Sections 8.7 and 8.8). Additional spectroscopic analyses (e.g. AAS, AES) provide additional information for element composition determination if available, e.g. the empirical formula (cf. Definition 1.25). Under such circumstances the molecular formula determination is unambiguous in many cases. 

In a traditional PTR-MS, the detector is a quadrupole and its mass resolution is rather limited, the ratios of mass to charge (tn/z) of the product ions cannot be served for a definite indicator of the identity of trace gases because numerous isomeric or isobaric compounds have the same or close molecular weight. In addition, mass overlap from probable fragmentation and cluster ions may be in operation. In particular, when a mixture containing unknown VOC components is investigated, it is inevitable to meet with a question how to identify the compounds. 

Figure 2.4 Mass resolution, (a) Calculation of the resolution offered by a mass spectrometer on the basis of the width of a spectral peak at 5% peak height (Am) at mass m. (b) 10% valley definition calculation of the resolution required to resolve the peaks of two ions showing a mass difference of m2 - m. ...

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