Monochromators instrumental function

The instrumental function, Q, depends on multiple geometrical parameters the locations and geometry of the source, monochromator(s). 

An optical multichannel Raman instrument functions as a spectrograph rather than as a monochromator due to the absence of an exit slit. The Raman light at the output of a grating instrument is dispersed across a detector consisting of an electronic image sensor that functions as an electronic photographic plate . For optical activity measurements, the components between the laser and the sample are essentially the same as described in the previous section for the scanning instrument. 

The main difficulties encountered in numerical calculations of the instrumental function are associated with the wide range of instrumental parameters [diffractometer radius, sizes of X-ray source, sample, receiving slit, using (or not using) Soller slits in incident and/or diffracted beam, using (or not using) monochromator], the contributions of some of which differ by three orders of magnitude. 

Notably, there is no satisfactory solution, based on a physically meaningful model, for incorporating a monochromator during the calculation of the instrumental function in X-ray powder diffraction. In the context of the proposed method, the case of the diffractometer with a monochromator can be considered as follows. 

Figure 6.25 shows the equatorial instrumental functions with and without taking into account the monochromator. 

Figure 6.27 shows the total instrumental functions with and without a monochromator. (Reprinted from Ref. 54. Permission of the International Union of Crystallography.)... 

To compute the convolution of these two functions, Eq. 2.19 requires that/(v) be reversed left to right [which is trivial in this case, since/(v) is an even function], after which the two functions are multiplied point by point along the wavenumber axis. The resulting points are then integrated, and the process is repeated for all possible displacements, v, of/( relative to B v). One particular example of convolution may be familiar to spectroscopists who use grating instruments (see Chapter 8). When a low-resolution spectrum is measured on a monochromator, the true spectrum is convolved with the triangular slit function of the monochromator. The situation with Fourier transform spectrometry is equivalent, except that the true spectrum is convolved with the sine function/(v). Since the Fourier transform spectrometer does not have any slits,/(v) has been variously called the instrument line shape (ILS) Junction, the instrument function, or the apparatus function, of which we prefer the term ILS function. 

Procedures for determining the spectral responslvlty or correction factors In equation 2 are based on radiance or Irradlance standards, calibrated source-monochromator combinations, and an accepted standard. The easiest measurement procedure for determining corrected emission spectra Is to use a well-characterized standard and obtain an Instrumental response function, as described by equation 3 (17). In this case, quinine sulfate dlhydrate has been extensively studied and Issued as a National Bureau of Standards (NBS) Standard Reference Material (SRM). 

Spectroradiometer An instrument that combines the functions of a radiometer and a monochromator to measure irradiance in finely divided bands. 

When a luminescence spectrum is obtained on an instrument such as that used to produce the spectra in Figure 7.23, it will depend on the characteristics of the emission monochromator and the detector. The transmission of the monochromator and the quantum efficiency of the detector are both wavelength dependent and these would yield only an instrumental spectrum. Correction is made by reference to some absolute spectra. Comparison of the absolute and instrumental spectra then yields the correction function which is stored in a computer memory and can be used to multiply automatically new instrumental spectra to obtain the corrected spectra. The calibration must of course be repeated if the monochromator or the detector is changed. 

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