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| General Setup of miniaturized spectrometers | |
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| The classical spectrometer consists of an input slit, a rotating dispersive element (prism or grating), an output slit and a single detector. This arrangement allows the separation of multichromatic radiation into its spectral components. The main advantages are the high sensitivity and the low stray light. Several drawbacks, as the non parallel measurement, the moveable elements and the space consuming dimensions, were overcome by the development of array spectrometers. This kind of spectrometer uses a detector array instead of a single detector and therefore needs only fixed components. Meanwhile they are widely used in PC coupled, stand alone as well as hand held devices and begin to find their applications even in the online process measurement.
Most of the time gratings are used as the dispersive element in array spectrometers. They have the advantages of higher dispersion and lower production costs than prisms. The basic grating equation is as follows:
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| with qi and qm - angles of the incident as well as diffracted wave directions to the normal of the grating surface, l - wavelength, d - grating period and m - order of diffraction (integer value, m = 0, 1, 2, ...). This equation is valid for reflexion gratings, whose grooves are perpendicular to the plane of incidence. Gratings in spectrometers are mostly used in reflectance mode. The equation shows, that for m ¹0 radiation of wavelengths is separated angularly. This effect is called dispersion. Furthermore each wavelength is diffracted into different discrete angles according to the order m, causing an ambiguity. Spectrometers normally use the dispersed light of one order. Influences of other orders and the non dispersive zeroth order have to be supressed. The following figure shows the angular separation for monochromatic and polychromatic radiation, caused by a grating. | |
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It demonstrates the overlap between the different orders - the diffraction angle for m = 1 in the red region coincidences with the corresponding angle of the half wavelength for m = 2. The free spectral range (range without overlap) becomes smaller for higher diffraction orders. As mentioned above, the order of diffraction can have negative or positive values. The common convention, also used here, calls the order positive, when the angle of diffraction exceeds the angle of incidence and lies on the opposite side of the grating normal. The grating equation determines the angles of diffraction, but has nothing to do with the intensity distribution into the different orders. The fraction of light intensity diffracted in one order, related to the entire incident intensity is called diffraction efficiency.Symmetric profiles as the sinusiodal shape of the gratings in fig. 1 are not very effective. The efficiency can be tuned by varying the shape and depths of the grooves. An increased efficiency is obtained by a sawtooth profile. The angle of the sawtooths has to satisfy the condition of the regular reflexion law to reflect the incident beam into the angle of the chosen diffraction order. This is called blazing and the condition can be met exactly for one wavelength only, the blaze wavelength. It is practical to lay this wavelength in the region, where the other componets of the system have low effectivity, e.g. the light source or the detector, to achieve a homogenization of the system's performance.
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The change of diffraction angle corresponding to a small change in wavelength is called angular dispersion of a grating. The following equation is obtained by differentiating the grating equation to the wavelength with fixed angle of incidence:
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The linear dispersion dl/dl is the product of the exit focal length f of the spectrometer and its angular dispersion:
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It defines the extend of the spectrum on the detector array.
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Array spectrometers consist of an input slit, a grating, possibly another optical imaging elements, a line detector and a stable housing. Several basic optical arrangements are used for spectrometers. The basic demand for the design is to use collimated light for the dispersion - this improves the measurement accuracy . One can distinguish between plane gratings set-up and concave grating spectrometers. The latter type combines diffraction and imaging in one element. If plane gratings are applied, it is necessary to use additional optical elements for beam shaping, preferably spherical or aspherical mirrors for ray collimation and focusing.
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| The following figure ( Schemes of a Czerny-Turners and flat field concave grating spectrograph) how examples for both types of set-up (so-called mounts). | |
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The advantages besides the lack of moving parts are the quasi parallel measurement of the whole spectrum, which reduces the measuring time. Further advantages are the robustness and the small dimensions. The flat field arrangement is further advantegous because of fewer optical elements, which have to be adjusted. This type of grating offers of a plane focal line, which can be detected by plane detector array without remarkable focusing errors. Nevertheless, plane grating spectrometers as the Czerny-Turner show improved optical properties because of better compensation possibilities of imaging errors. Usually the most efficient diffraction order of the grating is detected by the array, the detection of other orders is avoided by design or suppressed by several means (filters, ray traps). One has to say, that array spectrometers show some disadvantages, too: The integral illumination over the full wavelengths range increases the stray light, compared with monochromatic set-up. Furthermore, the sensitivity is lower than of a monochromator, which can even be fitted out with a photo multiplier. The precision and resolution is normally less than that of laboratory instruments with turnable dispersive element. The first array spectrometers included original gratings, manufactured by holography (interference of a splitted laser beam) or mechanical ruling. Holographic gratings show less stray light because of their better surface quality than mechanically proceeded ones. Furthermore, it is possible to produce holographic gratings with reduced imaging errors by a special design of the exposure arrangement.
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Such master gratings are replicated into epoxy layers (with an aluminum reflexion layer and a protection coating) to reduce the costs of the spectrometer. A further price reduction is obtained with a replication of the master gratings by injection moulding into a plastics material, e.g. PMMA. This technique is useable for less demanding applications because of a deterioration of the optical properties. The light inside the spectrometer commonly propagates in free space (air or glass).
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Modern array spectrometers are often fitted out with a fiber optic input for a more convenient adaption to the measuring problem. There are used single multimode fibers with or without an additional slit or fiber bundles designed as cross section transformer from cylindrical to rectangular (slit) shape. In this case the input slit width w is determined by fiber core diameter.The detectors used in UV/VIS spectrometers are silicon-based CCD or photodiode arrays. CCD arrays show a higher sensitivity, but diode arrays offer a much better dynamics. The proper selection of the detector array for an special application can improve the performance of the whole system or can just make it possible.
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Last change 08/13/2007 09:37 AM
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