Spectral dispersion reciprocal linear

Spatial resolution is one channel which is typically 25 ym wide. Spectral resolution is the product of the channel width and the reciprocal dispersion of the spectrometer. For example, a spectrometer with a focal length of 0.25 m and grating of 152.5 grooves/mm typically produces a reciprocal linear dispersion of 25 nm/mm. Therefore a 25 ym channel will cover 0.64 nm. A 305 g/mm grating used with the same spectrometer would produce a resolution of 0.32 nm/channel. 

Wavelength Calibration And Spectral Resolution. The wavelength calibration accuracy of the SPD depends, in principle, only on the corresponding accuracy of the spectrometer s reciprocal linear dispersion. In this study, the wavelength-to-diode calibration was proven adequately linear to determine wavelength to within +0.02 nm over the entire 20 nrn spectral window (1024 diodes) of the array, from any pair of known spectral lines. 

The spectral resolution of a detector is defined here as equal to its spatial resolution (in urn ) times the reciprocal linear dispersion of the spectrometer (in nm/um ). It was measured to be 1.5 - 2.5 and 2-4 times poorer for the SPD and SIT, respectively, compared to that of a PMT. All measurements were performed with the same spectometer, utilizing 20 urn slit widths. Because, the proximity focused, microchannel plate (MCP) intensi-fier broadens the line images, the spectral resolution of the ISPD was found to be significantly worse than that of the SPD. Peak widths measured at half maximum intensity were four diodes wide even when only a single diode width was illuminated. 

The reciprocal linear dispersion dX/dx) is the function of the geometric slit width S) and spectral bandpass (AA ,) of the monochromator ... 

The reciprocal linear dispersion for a grating is nearly constant over the entire wavelength region and it is dependent on the number of grooves per unit width, spectral order, and the focal length of the collimator. The resolution of a grating is a function of spectral order (m) and the total number of grooves N) ... 

As commonly used, dispersion is the wavelength separation of two spectral lines which are a unit distance apart at the focal plane of the spectrometer. This is actually reciprocal linear dispersion or dX/f d02, where / is the distance from the grating to the focal plane of the spectrometer. Reciprocal linear dispersion has the dimensions of angstrom units per millimeter. 

The effective bandwidth (also called the spectral bandpass or spectral slit width, which is one half the bandwidth when the two slit widths arc identical, is seen to be the range of wavelengths that exit the monochromator at a given wavelength setting. The effective bandwidth can be related to the reciprocal linear dispersion by writing Equation 7-9 in the form... 

For conversion of geometrical profiles to spectral profiles the geometrical width has to be multiplied by the reciprocal linear dispersion SX/Sx of the instrument giving the width AA° Jtr of ifio optimal instrument profile ... 

Linear dispersion defines the extent to which a spectral interval is spread out across the focal field and is expressed in nanometre per millimetre (nm/mm) -(or its inverse, the reciprocal dispersion in mm/nm). Linear dispersion is associated with an instrument s ability to resolve fine spectral detail. It depends of several parameters such as the focal distances and the widths of entrance and exit slits of the instrument. In general the better the dispersion the greater is the physical separation distance between two given wavelengths (Figure 14.11). 

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