Echelle gratings

The characteristics and fabrication of echelle (French ladder) gratings were first described by Harrison in 1949 [56]. Further general information about the theory and application of this grating type is given by Schroeder [127] and Boumans and Vrakking [14], 

Only two basic equations have to be used to describe the specific features of an echelle grating. At the blaze maximum in each order the angle of incidence a and the angle of diffraction (3 can be expressed in terms of the small angular difference 5 with respect to the blaze angle 6. With a = 6 - - 5 and p = 6 — 5, well as cos 5 1, the universally 

According to the Rayleigh criterion, the theoretical resolution AAtheor. which could be produced by a spectrometer, is given by the theoretical diffraction-limited resolving power i theor  

A similar formula could be obtained for the angular dispersion S/3/SA differentiating the grating Equation 3.1  

According to Equation 3.1 all diffraction orders of the echelle grating superimpose and cannot be initially distinguished by the detector of a spectrometer. Consequently order separation by an additional dispersing component is essential for unambiguous wavelength determination. 

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Abstract This tutorial shows how fundamental is the role plaid by interferences in many of the physical processes involved in astrophysical signal formating and consequently instmmentation. It is obvious in interferometry. Grating spectroscopy is explained within the same framework as Young experiment, and Fabry-Perot filters are explained as Michelson interferometers.Polarization interferences, used in Lyot filters, are discussed, emphasizing the analogy with echelle gratings. 

Figure 11. Left Littrow configuration for an echelle grating. Right example of the layout of orders (labelled by m) on the detector showing the wavelength ranges covered.

Figure I. Schematic layout of an echelle grating waveguide spectrometer.

To isolate specific emissions of the analyte being analysed (i.e. optical transitions), a high quality optical set-up is required. Dispersive systems using planar, concave or echelle gratings are used in classical spectrophotometers or spectrographs (Figs. ll.lO and 15.6). 

Figure 15.6-— Principle of dispersion in the focalplane using an arrangement comprising an echelle grating and prism. For clarity, the associated optics (collimating and focusing lenses) are not shown in the top figure. In this set-up, the entrance slit is not very high.

Figure 15.7—Optical diagrams for a spectrophotometer with an echelle grating. Model PU 7000 optical system (reproduced by permission of Philips). All spectral lines are captured, which allows a more complete study of the sample. The dynamic range of these instruments is still lower than that of a PMT.

Echelle grating, 279 Eddy diffusion, 18 EDTA, 269 EDXRF, 238 Effective plate, 13 Efficiency coefficient, 14 El, 307... 

Felkel, H. L., Jr., "Evaluation of imaging detector coupled to an echelle grating spectrometer for atomic spectroscopy", Ph.D. Thesis, Purdue University, 1978. 

Heitmann et al. [11] designed a very compact double monochromator, consisting of a 300 mm prism pre-monochromator and a 400 mm echelle grating monochromator, both in Littrow mounting, which is shown schematically in Figure 4.3. The prism monochromator selects the part of the spectrum that is of interest, and the echelle monochromator provides the high dispersion of the selected spectral interval, which is better than 2 pm per pixel at 200 nm (see Welz et al. [10]). 

Obviously, such a high-resolution monochromator requires active wavelength stabilization in order to avoid drift problems. This has been accomplished through an internal neon lamp, mounted on an adjustable stand in front of the intermediate slit between the pre- and echelle-monochromator, so that it can be moved into the beam automatically if necessary. The neon lamp emits many relatively narrow lines in the 580-720 nm range, and, in the absence of any pre-selection, these are separated by the echelle grating into various superimposed orders. This means that without pre-dispersion at least two neon lines for every grating position surely fall on the detector, and can be used for stabilization. The precision of this stabilization is only limited by the stepper motor for grating adjustment, and is better than one-tenth of a pixel width (see Welz et al. [10]). 

However, any spectrometer that uses CS and a double monochromator with an echelle grating makes it possible to reach any line within an extremely short period of time of much less than 1 s, as both the grating and the prism are stepper-motor controlled. This feature allows a fast sequential multi-element determination to be performed with the great advantage that flame conditions and burner... 

Due to its versatility, robustness, and relativel low cost, ICP-AES has started to be considered as routine instrumentation for elemental composition measurements in many laboratories involved in food analysis. Unquestionably, the acceptance of the technique has been further advanced by the commercial availability of rapid, simultaneous, and flexible, sequential instruments based on echelle grating crossed dispersion and solid state detectors. It is expected that novel nebulizer devices for liquid sample introduction will find increased applications in beverage analysis. 

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