Miniaturized Spectrometers Chapter 1. 1 Miniaturized Spectrometers. 1.1 General Set-up

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1 Miniaturized Spectroeters Chapter 1 1 Miniaturized Spectroeters 1.1 General Set-up The classical spectroeter consists of an input slit, a rotating dispersive eleent (pris or grating), an output slit and a single detector. This arrangeent allows the separation of polychroatic radiation into its spectral coponents. The ain advantages are the high sensitivity and the low stray light. Several drawbacks, such as the non-parallel easureent, the oveable eleents and the space consuing diensions, were overcoe by the developent of array spectroeters. This kind of spectroeter uses a detector array instead of a single detector and therefore only needs fixed coponents. 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 easureent Gratings Most tie gratings are used as the dispersive eleent in array spectroeters. They have the advantages of higher dispersion and lower production costs than priss. The basic grating equation is as follows: λ sin Θ = sin Θi + (1) d with θ i and θ - angles of the incident as well as the diffracted wave directions to the noral of the grating surface, λ - wavelength, d - grating period and - order of diffraction (integer value, = 0, ±1, ±2,...). This equation is valid for reflexion gratings, whose grooves are perpendicular to the plane of incidence. Gratings in spectroeters are ore often than not used in reflectance ode. The equation shows, that for 0 the radiation of different wavelengths will be separated angularly. This effect is called dispersion. Furtherore, each wavelength is diffracted into different discrete angles according to the order, causing an abiguity. Spectroeters usually use the dispersed light of one order. Influences of other orders and the non-dispersive zeroth order have to be suppressed. Fig. 1 shows the angular separation for onochroatic and polychroatic radiation, caused by a grating. Fig. 1 Angular separation of ono and polychroatic radiation

2 Chapter 1 Miniaturized Spectroeters It deonstrates the overlap between the different orders - the diffraction angle for = 1 in the red region coincidences with the corresponding angle of half of the wavelength for = 2. The free spectral range (range without overlap) becoes saller for higher diffraction orders. As entioned above, the order of diffraction can have negative or positive values. The coon convention, also used here, calls the order positive, if the angle of diffraction exceeds the angle of incidence and lies on the opposite side of the grating noral. The grating equation deterines the angles of diffraction, but gives no inforation about 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 of this order. Syetric profiles as the sinusoidal 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 saw tooth profile. The angle of the swots has to satisfy the condition of the regular reflexion law to reflect the incident bea into the angle of the chosen diffraction order. This is called blazing and the condition can be et exactly for one wavelength only, the blaze wavelength. It is practical to shift this wavelength in the region, where the other coponents of the syste have low effectivity, e.g. the light source or the detector, to achieve a hoogenisation of the syste s perforance. The change of diffraction angle corresponding to a sall 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: dθ dλ = d cosθ (2) The linear dispersion dl/dλ is the product of the exit focal length f of the spectroeter and its angular dispersion: dl = dλ f dθ dλ = f d cos Θ (3) It defines the extend of the spectru on the detector array Spectroeter Set-up Array spectroeters consist of an input slit, a grating, possibly other optical iaging eleents, a line detector and a stable housing. Several standard optical arrangeents are used for spectroeters. The basic deand for the design is to use colliated light for the dispersion - this iproves the easureent accuracy. One can distinguish between plane grating set-ups and concave grating spectroeters. The latter type cobines diffraction and iaging in one eleent. If plane gratings are applied, it is necessary to use additional optical eleents for bea shaping, preferably spherical or aspherical irrors for ray colliation and focusing. 2 Basics of Spectral Measureent JETI Technische Instruente GbH 2005

3 Miniaturized Spectroeters Chapter 1 The following figures show exaples for both types of set-up (so-called ounts). Fig. 2 Schees of Czerny-Turner and flat field concave grating spectrograph The advantage besides the lack of oving parts is the quasi-parallel easureent of the whole spectru, which reduces the easuring tie. Further advantages are the robustness and the sall diensions. The flat field arrangeent is further advantageous because of fewer optical eleents, which have to be adjusted. This type of grating offers a plane focal line, which can be detected by the plane detector array without rearkable focusing errors. Nevertheless, plane grating spectroeters as the Czerny-Turner show iproved optical properties because of better copensation possibilities of iaging errors. Usually, the ost efficient diffraction order of the grating is detected by the array; the detection of other orders is avoided by design or suppressed by several eans (filters, ray traps). One has to say, that array spectroeters show soe disadvantages, too: The integral illuination over the full wavelength range increases the stray light, copared with onochroatic set-ups. Furtherore, the sensitivity is lower than of a onochroator, which can even be fitted out with a photo ultiplier. The precision and resolution is norally less than that of laboratory instruents with a turnable dispersive eleent. The first array spectroeters included original gratings, anufactured by holography (interference of a splitted laser bea) or echanical ruling. Holographic gratings show less stray light because of their better surface quality than those of echanically proceeded ones. Furtherore, it is possible to produce holographic gratings with reduced iaging errors by a special design of the exposure arrangeent. Such aster gratings are replicated into epoxy layers (with an aluiniu reflexion layer and a protection coating) to reduce the costs of the spectroeter. A further price reduction is obtained with a replication of the aster gratings by injection oulding into a plastics aterial, e.g. PMMA. This technique is useable for less deanding applications because of a deterioration of the optical properties.

4 Chapter 1 Miniaturized Spectroeters The radiation inside the spectroeter coonly propagates in free space (air or glass). The Zeiss spectroeter MMS is an exaple for this design. Fig. 3 Free space spectroeter MMS UV (Carl Zeiss Jena) Another kind of spectroeter is based on the propagation in a slab wave guide (the LIGA spectroeter). The solution offers the possibility of an extree iniaturization. This spectroeter, anufactured by Boehringer Ingelhei icroparts GbH (Gerany), is shown in the following figure. Fig. 4 Waveguide VIS spectroeter (Boehringer Ingelhei icroparts Dortund) Modern array spectroeters are often fitted out with a fiber optic input for a ore convenient adaption to the easuring situation. There are used single/ ultiode fibers with or without an additional slit or fiber bundles designed as cross section transforer fro cylindrical to rectangular (slit) shape. The detectors used in UV/VIS spectroeters are silicon-based CCD or photodiode arrays. CCD arrays show a higher sensitivity, but diode arrays offer a uch better dynaics. The proper selection of the detector array for a special application can iprove the perforance of the whole syste or can just ake it possible. Further inforation about the ode of operation and the application oriented selection of detector arrays can be obtained fro chapter 2 of these basics (Line Arrays for Miniaturized Spectroeters). 4 Basics of Spectral Measureent JETI Technische Instruente GbH 2005

5 Miniaturized Spectroeters Chapter Spectroeter Paraeters Wavelength Range Array spectroeters are available for wavelengths fro the UV (200 n) and VIS to IR (...3 µ). Wavelength ranges of coercial array spectroeters are indicated in the following figure: Fig. 5 Schee of partial electroagnetic spectru and of wavelength ranges of coercial spectroeters The size of the spectroeter is deterined by the wavelength range in connection with the desired optical resolution (see below), deanding in a certain focal length. JETI s series of specbos instruents currently covers the range of n, specbos 1001 UV n and the JETI spectraval series easures between 350 and 850 n Resolution Several definitions are used for the resolution of a spectroeter. One has to distinguish clearly between the optical or spectral and the digital or pixel resolution. The optical resolution λ is defined by the wavelength difference of two peaks close together in one spectru and of sae intensity, which can be separated. The dip between the peaks has to reach a iniu of at least 19 %, related to the axiu intensity. This definition is called the Rayleigh criterion. Fig. 6 Definition of the optical resolution (Rayleigh and FWHM)

6 Chapter 1 Miniaturized Spectroeters Another ore practical definition is related to the easured width of a narrow spectral line. Its easured bandwidth λ FWHM (FWHM full with at half axiu) gives inforation about the broadening of the line. This bandwith aounts to about 4/5 of the resolution according to the Rayleigh criterion. The optical resolution is deterined by the width of the input slit, the focal length of the optical syste and the dispersion of the grating. λ FWHM is inversely proportional to the linear dispersion dl/dλ and directly proportional to the output slit width w : d λ = w' λ (4) dl This equation can easily be used for the estiation of a spectroeter resolution, especially with 1:1 iaging, where the width of the input slit equals to the width of the output slit (w = w ). The saller the slit width, the higher is the resolution. However, reduced slit width reduces the optical energy, entering the spectroeter, too. This can cause sensitivity probles for a spectroetric syste. Coon resolution values of iniaturized VIS spectroeters lie in the region of n, values even below 1 n are possible. The core diaeter of the input fiber influences the optical resolution, if it acts as the input slit. A separate paraeter is the pixel or digital resolution. This is the spectral bandwidth, which is detected by one pixel of the array and is deterined by the width of the pixel and the dispersion of the spectru. Coon values are n/pixel. JETI spectroeters are available with 0.6 to 4 n/pixel. The digital resolution is related to the spectral resolution via the iaging properties of the spectroeter. The ratio of digital to spectral resolution should be 3 to detect precisely a peak in the spectru (rule of thub) Stray Light Stray light is radiation of false wavelengths, which strikes a pixel of the detector array. It is caused by iperfections of the grating, dust, reflexion of non-used orders at the spectroeter housing or errors of the other optical eleents. This paraeter influences the precision of a spectroscopic easuring syste in a crucial way. It gets easured by a broadband illuination of the input slit through a color filter with long pass characteristics. The Schott glass GG 495 is a filter coonly used therefore. The stray light S is the ratio of the transission in the blocked wavelength region below the filter edge e.g. at 420n (τ(420 n)) to the transission in the non-blocked region e.g. at 600n (τ(600 n)). τ (420n) S[%] = 100% (5) τ (600n) It shows the influence of the light of longer wavelengths, passing the filter, on the unwanted intensity in the blocked region. A easured spectru is shown in the following figure. 6 Basics of Spectral Measureent JETI Technische Instruente GbH 2005

7 Miniaturized Spectroeters Chapter 1 Fig. 7 Measureent of stray light In case of a low stray light level (as in fig. 7) an additional neutral density filter is used for the easureent in the non-blocked region, which will be reoved for the easureent in the blocked region. τ (420n) τ ( NDfilter) SL[%] = 100% (6) τ (600n) A standard easureent ethod is described in the ASTM standard test ethod E 387 (available fro Detailed inforation about odifications of the easureent procedure and their influence on the result can be obtained fro the Agilent technical note "Measuring the stray light perforance of UV-visible spectrophotoeters" (available at: Search. asp). Another often applied stray light easuring ethod uses a onochroatic light source (e.g. a HeNe laser). The intensities at the laser wavelength and at another wavelength, several 10 n away fro the laser wavelength are easured. The ratio of the latter to the forer is a easure for the stray light of the syste. This easuring ethod provides uch better values, but is ore distant to the ain practical applications, where a broadband illuination is used. Therefore, the ethod, described first, is recoended. The stray light causes a non-linearity of the signal at lower power levels and thus liits the easuring range of the syste. For exaple: the signal in the blue region of a VIS spectroeter depends on the incident intensity in the other regions of the spectru. This effect cannot be copensated precisely by atheatical calculations in the software. Every specification of stray light has to be given in connection with the used easuring conditions. One has to keep in ind, that the higher the bandwidth of the light entering the spectroeter, the higher the easured stray light ratio. The value, easured with a long pass filter with an edge in the red region of the spectru is not coparable with a value, easured with a yellow edge filter (see the following figure).

8 Chapter 1 Miniaturized Spectroeters GG495 RG2 Fig. 8 Stray light easureents with GG 495 and RG 2 The stray light of array spectroeters is ainly higher than of onochroators due to the lack of an output slit ADC Resolution The analog intensity distribution of the optical spectru on the detector array has to be converted pixelwise to a digital signal by an analog digital converter (ADC). Coon electronic resolutions are bit ( counts full scale). These nubers are finally reduced by the dark spectru of the line array and the driving of the converter. The ADC resolution should be in a suitable ratio to the stray light of the spectroeter and to the dynaics of the detector array. The dynaics D of the entire syste is deterined by the ADC resolution R ADC, divided by the noise signal Φ. R D = ADC (7) Φ A 12 bit spectroeter with a noise signal of 4 counts offers a dynaics of about Integration Tie The light intensity coupled into a spectroeter and illuinating a pixel, results in a proportional signal fro the AD converter. The exposure tie of the light to the pixel is called integration tie and is a ain paraeter to adjust the ADC signal. A level between 2/3 and full scale is suited for best easuring results, using the full dynaics of the syste. Off scale peaks or regions in the spectru have to be avoided. Coon values for the integration tie of array spectroeters are s. Several instruents, as the JETI spectroradioeter, specbos 1201, spectraval CAM and spectraval VIS, are equipped with an autoatic integration tie adaption. 8 Basics of Spectral Measureent JETI Technische Instruente GbH 2005

9 Miniaturized Spectroeters Chapter Spectral sensitivity The sensitivity of a spectroscopic syste E(λ) is another iportant issue in any applications, especially in fluorescence detection, and is a ain criterion for the choice of a spectroeter. It is easured in counts/ Ws and eans the ADC signal r [counts] divided by the optical energy P (λ) t int [Ws], entering the spectroeter optical input. r E( λ ) = (8) P( λ) t int The spectral sensitivity has to be specified for a given wavelength ainly because of the spectral dependencies of the grating efficiency and the detector sensitivity. The easureent can be done with bandpass filtered white light illuination or a onochroator, fro which the radiant flux P (λ) is known. Of course, sensitivity data have to be related to the ADC resolution of the read out electronics. The ain uncertainity in sensitivity easureents is caused by the easuring error of P (λ), coupled into the spectroeter. The spectral sensitivity can be adapted in certain liits to the application by a proper selection of the spectroeter s detector array (see chapter 2 "Line Arrays for Miniaturized Spectroeters") Wavelength and Intensity Calibration The AD converter delivers the spectral signal in counts for each pixel of the line array. The pixels are nubered and these nubers have to be transfored into the corresponding wavelength. This can be done by a ultiorder polyno as follows: 2 3 λ( n) = k + k n + k n + k n + K+ k i n i (9) where n is the pixel nuber, k 0 [n] the wavelength of the first pixel, k 1 [n/pixel] the pixel resolution and k 2, k 3,.., k i are the higher order coefficients. This approxiation with a polyno gives a wavelength precision, which has to be taken into consideration in the application. The choice for the order of the polyno depends on the non-linear behaviour of the spectroeter. The linear approxiation is sufficient for a LIGA Spectroeter, whereas a higher order polyno is necessary for the Zeiss MMS. The calibration can be done by relating the peaks of a suited spectral lap (e.g. Hg in the VIS range) to the corresponding pixel and subsequent calculation of the k-paraeters by regression (e.g. in Excel). JETI offers a special fit progra for this purpose. This progra can be used to easure the spectra, indicate the peaks, calculate the k-paraeters and check the result. A spline fit is used to get a subpixel precision. A easy way to check the calibration of a spectroeter for soebody who has no special spectral lap is to use a coon fluorescent lap (F11, possibly on top of the lab), which has a spectru as shown in the following diagra. The intense peaks of 546 and 614 n can be used for a roughly test of the calibration.

10 Chapter 1 Miniaturized Spectroeters Fig. 9 Typical spectru of a F11 (TL 84) lap Soething else, soeties ixed with the wavelength calibration, is the calibration of the intensity axis. A non-calibrated spectroeter as the JETI specbos 1001 has an intensity axis (y- axis) in counts or percent. Therefore, only relative easureents of light sources, e.g. the spectral distribution of LED, are possible. One has to keep in ind, that the obtained spectru is weighted with the instruent function (grating efficiency, transittance, detector sensitivity). Spectroeters with calibrated intensity axis are called spectroradioeters (see chapter 3.4). 10 Basics of Spectral Measureent JETI Technische Instruente GbH 2005