Resolving power, R, is a measure of the ability of a spectrometer to separate two close wavelengths and is defined by
![[R=l/dl]](images/Equations/Design1.gif){kind=small}
where l is the average of the
two wavelengths and Dl is the
difference between the two wavelengths. The higher R the
better the resolving power. The resolving power is the inverse of chromatic resolution.
Luminosity is a measure of the 'light-collecting power' of a spectrometer. In an ideal instrument, it depends on the product of the area of the entrance slit and the solid angle subtended by the dispersing element (e.g. by the diffraction grating). It is assumed that all other elements in the spectrometer, e.g. lenses and detectors, are made large enough so as not to reduce the luminosity.
In real spectrometers, the number and quality of optical components can have a dramatic effect on luminosity. The table below compares the effect on luminosity of the optical components in an Echelle grating spectrometer and a Czerny Turner monochromator in both the Visible (VIS) and ultraviolet (UV):
Optical Components |
Energy Through put (%) |
|||||||
| Grating | Cross Dispers. | Mirror | Prism | Lens | Filter | |||
| Echelle in UV | 1 | 1 | 5 | 0 | 1 | 0 | 8.6 | |
| Echelle in VIS | 1 | 1 | 3 | 1 | 4 | 0 | 3.8 | |
| Czerny Turner in UV | 1 | 0 | 2 | 0 | 1 | 0 | 33.2 | |
| Czerny Turner in VIS | 1 | 0 | 3 | 0 | 1 | 1 | 29.9 | |
| Light Loss % Factors | UV | 50 | 32 | 15 | - | 8 | - | |
| VIS | 50 | 84 | 10 | 8 | 8 | 10 | ||
The product of resolving power and luminosity is commonly known as efficiency. In normal operation, reducing the width of the entrance slit will increase the resolving power but reduce the luminosity while the efficiency remains fixed. Efficiency is therefore a useful means for comparing the performance of two spectrometers.
For a grating spectrometer, the efficiency, E, is given by
![[E=Akl/50a]](images/Equations/Design10.gif){kind=small}
where A is the area of the aperture stop of the spectrometer (ideally, the grating), k the order of diffraction, a the grating constant (i.e. the width of a groove on the grating). The length of the entrance slit is assumed to be 1/50th of the focal length of the spectrometer.
The rays emanating from any point on a source and travelling different paths though a spectrometer will not converge to ideal points on the detector. This divergence (blurring) is called aberration. The main types of aberration are:
For further reading see:
J F James and R S Sternberg, The Design of Optical Spectrometers, Chapman & Hall, London (1969).
For a more general but demanding discussion of optical design see
R R Shannon, The Art and Science of Optical Design, Cambridge University Press, Cambridge (1997).
First published on the web: 15 March 2000.
Author: Richard Payling