Further Reading
5.3 Instrumentation
5.3.1 Basic Components for Spectrometric Instrumentation .1 Some Important Optical Units
5.3.1.2 Wavelength Selectors
In order to realize optical measurements at a selected wavelength, detection of radi- ation confined to a narrow spectral band or line is required; this confined distribu- tion in practice is called monochromatic. It should be remembered, however, that true monochromatic light cannot be obtained. There are several ways to obtain monochromatic radiation.
Filters are simple devices. An absorption filter contains properly designed chem- icals either imbedded in or sandwiched between window plates; light is absorbed at undesired wavelengths, leaving a passage of monochromatic light at the wavelength of interest; this device is called a bandpass filter. Alternatively, filters may absorb the radiation selectively below or above a threshold value of wavelength; these devices are called cut-off filters. Quartz and glass are two natural cut-off filters.
Nominal wavelength, effective bandwidth or full-width at half-maxima (FWHM) and per cent transmittance at the nominal wavelength are three important figures to characterize a bandpass-type filter; these are shown in Figure 5.14.
Interference filtersfunction via optical interference phenomenon; the structure and principle of obtaining a monochromatic band is shown in Figure 5.15. Dielectric layer is typically MgF2or CaF2. The beams being transmitted through an interference filter Figure 5.13 An off-axis concave mirror commonly used in spectrometric instruments. m, col-
limating off-axis; x, optical axis and f, focal point
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Figure 5.14 Absorption filters. Q, quartz as a cut-off filter, 50% T at 180 nm; G, glass as a cut-off filter, 50% T at 350 nm and B, bandpass filter, nominal wavelength is 500 nm, 60% T at 500 nm, effective bandwidth, eb, is 40 nm
Figure 5.15 Interference filters. o, oncoming radiation, spectrally continuous and m, mono- chromatic band of radiation; W, window; M, metal layer; d, dielectric layer, MgF2 or CaF2; t, thickness of dielectric layer
are those which form constructive interference where their path difference is a multi- ple of a wavelength. It can be shown that
λ⫽2tn/N (5.16)
where tis the thickness of the dielectric layer in nm,nits refractive index and N, an integer, is the order of interference. Therefore an interference filter whose value of 2tnmatches 600 nm will transmit the wavelengths of 600, 300 and 200 nm for the values of N⫽1, 2 and 3, respectively. The wavelengths at higher orders, such as 150 and 120 nm, will be stopped by quartz windows. Undesired wavelengths at any order can be eliminated by using a proper cut-off filter. Interference filters are available in UV, VIS and IR regions up to about 14λm. Absorption filters have effective band- widths that range from 20 to 300 nm, where interference filter bandwidth values range from 0.2 to 1.5% of the nominal wavelength, amounting to a range of 0.4–12 nm in UV–VIS region. In general, the bands obtained through interference filters are more monochromatic, but the maximum transmittance values are lower as compared to absorption filters. Therefore, in general, interference filters provide better spectral purity associated with higher costs when compared to absorption filters.
Prismsand gratingsare devices that are capable of dispersing a continuous radi- ation into its monochromatic components. Prisms are transparent materials that are cut with perfectly polished faces; they disperse light, because refractive index is dependent on wavelength of radiation as shown in Figure 5.2. Since the slope of the curves in this figure is not constant, dispersion by a prism is not linear, being better for the lower wavelengths of a spectral region where the change in refractive index per unit change of wavelength is larger. Schematic representation of dispersion by a prism is shown in Figure 5.16.
Gratingsare surfaces with fine-ruled parallel grooves on them; they may be of transmission or reflectiontype; and the latter is more popular. Reflection gratings cause the oncoming parallel rays to undergo diffraction, so that outcoming rays will be of the same wavelength when they form constructive interference. The condition
Figure 5.16 Schematic representation for dispersion of white light into its monochromatic components by a prism
for constructive interference for a particular wavelength is shown in Figure 5.17 and can be expressed by the grating formula
Nλ⫽d(sin i⫾sin r) (5.17)
where λis the wavelength,N, an integer, is the order of diffraction,dthe distance between the grooves (lines),iis the angle of incidence and ris the angle of reflec- tion. The angle of reflection has a positive sign when both the incident and the reflected rays are on the same side of the grating normal; otherwise a negative sign is assigned to this term. Dispersion by a grating is almost linear on a scale of wave- lengths; this property is in contrast to non-linear dispersion by prisms. While linear dispersion is an advantage for gratings, they have the problem of high orders in a manner similar to the interference filters; there are no order problems for prisms.
Prisms and gratings can disperse the polychromatic light into its monochromatic components, but they are not capable of forming images. While a spectrum is meas- ured, radiation must be dispersed into the monochromatic components with band- widths as small as required. A monochromator is a device that can use a polychromatic (white) image and form many monochromatic images to be used for spectral measurements at different wavelengths. One should be reminded that the term white may be used instead of continuous radiation, while it means really white only for the VIS region; in other regions it refers to the sum of all the frequencies covered by that region.
A typical monochromator has the following components:
1. A dispersing device, which is a prism or a grating.
2. Entrance slit: this is the start of the optical journey in a monochromator. A white image is focused on the entrance slit
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Figure 5.17 Diffraction on a reflection grating surface. Outcoming rays are parallel to each other have the same wavelength. GN, grating normal; i, angle of incidence and r, angle of reflection
3. Collimators: these are lenses, or more commonly, mirrors. These units realize focusing and defocusing as required, so that the monochromatic images are formed on the exit slit.
4. Exit slit is the end of the optical journey in a monochromator. Many mono- chromatic images adjacent to each other are formed on a focal plane; one or more images are selected by exit slit(s).
The description above applies to a classical monochromator; the developed novel designs have deviations from this format. A monochromator is protected by dust, dirt or extraneous radiation by a tightly closed metal box; internal surfaces are coated with non-reflective, matt black paint. The terms monochromatorand polychromator are often used in a loose manner; the latter is more proper for a system that is using more than one wavelengths selected at the exit slits at a time. A typical monochro- mator design is shown in Figure 5.18.
Alternatively, more than one wavelength, in practice up to ⬃60, may be selected simultaneously by using many slits and detectors; a popular polychromator design, Rowland Circle, is shown in Figure 5.19. It must be noted that in this design approach, no collimators are used since the concave grating is able to both disperse the light and form the image.
The images at consecutive wavelengths are ordered on a plane perpendicular to the optical axis; this is called the focal plane, as shown in Figure 5.18, extending from the points f to p. By rotating the grating, the conditions for the grating formula is met for another wavelength, so that the corresponding monochromatic band is allowed to reach the exit slit. The bandwidth of monochromatic radiation does depend on the width of the exit slit. Narrower slits result in smaller bandwidths for the monochromatic image at the exit slit. For a dispersion element forming mono- chromatic images,resolutionis the measure of its ability in forming adjacent images
Figure 5.18 A Czerny–Turner monochromator. S1and S2are the entrance and exit slits; G is reflection grating; M1and M2are off-axis mirrors used as collimators. Until G, white light is shown, after G the light shown is monochromatic; focal plane is from f to p
with wavelength differences as small as possible. Therefore both dispersion and res- olution are the performance characteristics for a monochromator; while the former is a rather intrinsic property of the system, the latter is a measure of performance and is meaningful when considered with a defined slit width only.
Angular dispersionis given by dr/dλ, where dris the change in the angle of reflec- tion for a grating and refraction for a prism, as shown in Figures 5.16 and 5.17. The linear dispersion,D, is equal to dy/dλor Fdr/dλ, where Fis the focal length of a monochromator and dyis the physical displacement on the focal plane for dλ, the wavelength difference as shown in Figure 5.20.Fcorresponds to the focal length of the off-axis collimator mirrors and is also called as the focal length of the mono- chromator. The more common expression for the dispersion ability is the reciprocal linear dispersion,D⫺1:
D⫺1⫽dλ/dy⫽(1/F) dλ/dr (5.18)
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Figure 5.19 A polychromator of the Rowland Circle type; S1, entrance slit; CG, concave grating; D1, D2, D3, detectors
Common units for D⫺1are nm/mm and this figure of merit is mentioned to express the intrinsic dispersion ability for a monochromator.
The angular dispersion of a grating can be found by differentiating the grating for- mula while iis held as a constant. The following expression is obtained for a given angle of incidence,i:
dr/dλ⫽N/(dcos r) (5.19)
It can be shown that
D⫺1⫽(1/F) dλ/dr⫽(dcos r)/NF (5.20) Resolution of a monochromator is defined in several ways. When λis an average of two wavelengths that can form separate adjacent images on the focal plane and ∆λ is their difference,resolving power, Ris given as follows:
R⫽λ/∆λ⫽NN⬘ (5.21)
where Nis the diffraction order and N⬘the number of lines illuminated on the grat- ing surface. N⬘is a function of the monochromator design and the width of the grat- ing. While the above equation is the definition for resolving power R, most users prefer to employ D⫺1, reciprocal linear dispersion, or spectral bandwidth to express resolution performance of a system.
Slits are formed by placing two sharp metal edges parallel to each other. Optical requirements usually force that equal sizes for the entrance and exit slits must be used. While the entrance slit allows a certain portion of the radiation coming from the object, the exit slit defines the portion of focal plane images to be sent to detec- tor. Therefore, large slits would allow higher number of photons on detector and this is advantageous to have a stronger light signal; on the other hand, a high wavelength resolution requires smaller slits that cause the degradation of signal power. When the two slit widths are identical, the slit function at exit slit is a triangle whose height is proportional to light power and the base has the units of wavelength, as shown in Figure 5.20 Wavelength dispersion along a focal plane
Figure 5.21. Effective bandwidth is the half-width or FWHM value of this triangle in units of wavelength. When combined with the reciprocal linear dispersion, a useful relation is formed as follows:
∆λeff⫽WD⫺1 (5.22)
where ∆λeffis the effective bandwidth or spectral bandwidth in nm,D⫺1the spectral bandwith in nm/mm and Wthe physical slit in mm. In order to have a complete sep- aration of two images at λ1and λ2,∆λeffshould be equal to the half of the difference between these wavelengths.
Another important property of a monochromator is its light-gathering power, given by the f/number of the system,
f⫽F/d (5.23)
where Fis the focal length and dthe diameter of aperture; dmay correspond to the diameter of a collimator mirror or a lens provided that all of its surface is employed.
By convention, a system having a focal length of 25 cm and a mirror diameter of 2.5 cm would have a light-gathering power equivalent to f/ 10; smaller f/ numbers corre- spond to higher light-gathering powers. However, high resolution requires smaller light-gathering powers because rays are more paraxial and the images are sharper in such systems.
In order to have a high spectral resolving power, a value as small as possible is required for D⫺1. Two different approaches have been used for this purpose.
• Classical grating monochromators use very fine rulings, such as 1200–3600 lines mm⫺1, corresponding to a very small value for d; in addition, the use of a large monochromator with a high Fvalue is advantageous. Normally, the orders of 1 or 2 are used. The angle ris rather small and the equation for D⫺1practi- cally becomes, in most cases,D⫺1⫽d/NF.
• Echelle monochromator design has a different approach than the classical ones.
A relatively high order, such as 40–135, is used; in addition, the angle of reflec- tion,ris large and thus cos ris minimized. A rather coarse grating is used with
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Figure 5.21 Slit function
typically 79 lines mm−1and in contrast to conventional gratings the smaller face of the groove is used to receive and reflect the light as shown in Figure 5.22.
A comparison of performances for the two monochromator designs of the same focal length is given in Table 5.1.
Relatively high orders used for an Echelle monochromator create problems regarding the overlapping wavelengths at different orders at the same point on the focal plane. The overlap due to orders is a problem also with the conventional mono- chromators. However,free spectral range,∆λeff⫽λ/(N⫹1), is rather large for small orders. For example, at N⫽1 and 600 nm, free spectral range is 300 nm, meaning that there are no overlapping orders between 600 and 300 nm. Cut-off filters or wide-band filters are used as order sorters in conventional monochromators.
However, for Echelle monochromators, high N values are used and thus the free spectral range is very narrow. This problem is alleviated by using a prism as an order-sorter after the grating as shown in Figure 5.23. The prism in the Echelle monochromator disperses the light already dispersed by the grating. However, the plane of dispersion by prism is perpendicular to the plane of dispersion by the grat- ing. Therefore, while in a conventional monochromator the focal plane lies on one Figure 5.22 Diffraction on an Echelle grating; N, normal; i, angle of incidence; r, angle of reflection
Table 5.1 Comparison for a conventional and Echelle monochromator Conventional Echelle
Focal length (m) 0.5 0.5
Groove density (lines mm−1) 1200 79
Angle of diffraction,r 10°22⬘ 63°26⬘
Width of grating (mm) 52 128
Order Nat 300 nm 1 75
Resolution at 300 nm 62 400 763 000
Linear dispersion at 300 nm (mm nm⫺1) 0.61 6.65 Reciprocal linear dispersion at 300 nm
(nm mm⫺1) 1.6 0.15
f/ number f/ 9.8 f/ 8.8
dimension, a two-dimensional focal plane is formed in an Echelle monochromator.
The two-dimensional focal plane can accommodate single or multiple detectors as required. Both conventional and Echelle monochromators are used in several spectrometer designs in atomic spectrometry where high resolution is required, especially in emission measurements.