Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 1 In this chapter we discuss basic spectroscopic instruments and techniques employed to measure wavelength and line profiles or to realize the sensitive detection of radiation. 4.1 Spectrographs and Monochromators S pectrographs are optical instruments which form images S 2 ( ) of an entrance slit S 1 which are laterally separated for different wavelengths of the incident radiation. This lateral dispersion is achieved either by spectral dispersion in prisms or by diffraction on plane or concave reflection gratings. Figure 4.1 shows the schematic arrangement of optical components in a prism spectrograph. The light source L illuminates the entrance slit S 1 which is placed in the focal plane of the collimator lens L 1. Behind L 1 the parallel light beam passes through the prism P where it is diffracted by an angle depending on the wavelength . The camera lens L 2 forms an images S 2 ( ) of the entrance slit S 1. The position x( ) of this image in the focal plane of L 2 is a Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 2 Fig Prism spectrograph. function of the wavelength . The linear dispersion dx/d of the spectrograph depends on the spectral dispersion dn/d of the prism material and on the focal length of L 2. LL0L0 L1L1 L2L2 S1S1 S 2 ( 2 ) S 2 ( 1 ) Prism x Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 3 In spectrographs a photoplate or photographic film is placed in the focal plane of L 2. The whole spectral range = 1 (x 1 )- 2 (x 2 ) covered by the lateral extension x=x 1 -x 2 of the photoplate can be simultaneously recorded. If the exposure of the photoplate remains within the linear part of the photographic density range, the density D a (x) of the developed photoplate at the position x( ) (4.1) is proportional to the spectral irradiance I( ) integrated over the exposure time T. The sensitivity factor C( ) depends on the wavelength and further more on the developing procedure and the history of the photoplate. The photoplate can accumulate the incident radiant power over long periods (up to 50 hours). Photographic detection can be used for both pulsed and continuous wave light sources. The spectral range is limited by the spectral sensitivity of available photoplates and covers the wavelength range between 200~1000nm. Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 4 When a reflecting grating is used to separate the spectral line S 2 ( ), the two lenses L 1 and L 2 are commonly replaced by two spherical mirrors M 1 and M 2 which image the entrance slit onto the plane of observation, as shown in Fig An exit slit S 2, selecting an interval x 2 in the focal plane, lets only a limited range through to the photoelectric detector. Turning the grating allows the different spectral regions to be turned across the fixed exit slit S 2. Note that different spectral regions are detected not simultaneously, but successively. The signal received by the detector is proportional to the product of the exit-slit area h x 2 with the spectral intensity, where the integration extends over the spectral range dispersed within the width x 2 of S 2. Just according to the kind of detection we distinguish between spectrographs and monochromators. In general, the name spectrometer is often used for both types of spectroscopic instruments in literature. Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 5 Fig Grating monochromator. S1S1 G M1M1 M2M2 Photodetector S2S2 Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 6 Some basic characteristics of spectrometers are listed as follows: 1.Light-gathering power. It is determined by the maximum acceptance angle for the incident radiation, measured by the ratio a/f of diameter a to focal length f of the collimating lens L 1 or of the mirror M 1. 2.Spectral transmittance T( ). It is limited by the transparency of the lenses and prism in the prism spectrograph or by the reflectivity R( ) of the mirrors and grating in grating spectrograph. 3.Spectral resolving power / ( ) which specifies the minimum separation of two spectral lines that can just be resolved. 4.Free spectral range of the instrument, i.e., the wavelength in which the wavelength can unambiguously determined from the position x( ). The light-gathering power of a spectrometer is defined as the product of the area A of the entrance slit and the maximum acceptance angle . That is Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 7 For a prism spectrometer the maximum solid angle of acceptance, =F/f 1 2, is limited by the effective area F=h a of the prism with height h and width a, f 1 is the focal length of collimator lens L 1. For a grating spectrometer the optimized imaging of a light source onto the entrance slit is achieved when the solid angle of the incoming light matches the acceptance angle (a/d) 2 of the spectrometer, as shown in Fig The spectral resolving power of any dispersing instrument is defined by the expression. (4.3) where stands for the minimum separation of the central wavelengths 1 and 2 of two closely spaced lines which are considered to be just resolved. Rayleighs criterion for the resolution of two nearly overlapping lines is shown in Fig.4.4. We define two lines with equal intensities to be just resolved if the dip between the two maxima drops to (8/ 2 ) 0.8 of I max. Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 8 Fig Optimized grating spectrometer. a M1M1 =(a/d) 2 d g2g2 g1g1 =(g 2 /g 1 ) The fundamental limit on the spectral resolving power which clearly depends on the size a of the limiting aperture and on the angular dispersion of the instrument. The limiting aperture is determined by the size of prism or grating. So, the spectral resolving power Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 9 Fig. 4.4 Rayleighs criterion. of a spectrometer is basically determined by the prism or grating. Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 10 Note that the entrance slit imposes a limitation on the transmitted intensity at small slit widths. The useful width b min of the entrance slit is given by It is demonstrated that the resolution of the instrument cannot be increased much by decreasing the entrance slit width b below b min. A practically attainable resolving power of a spectrometer for an entrance slit width b below b min is Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments Grating Spectrometer In a grating spectrometer the grating is a central component which consists of straight grooves with great number (~10 5 ). The grooves of the grating are parallel to the entrance slit. The grooves have been ruled onto an optically smooth glass substrate or have been produced by holographic techniques. The whole grating surface is coating with a highly reflecting layer (metal or dielectric film). The many grooves, which are illuminated coherently, can be regarded as small radiation sources, each of them diffracting the light incident onto this small groove with a width of about the wavelength, into a large range of angles around the direction of geometrical reflection. The total reflected light is a coherent super-position of these many partial contributions. Only in those directions where all partial waves emitted from the different grooves are in phase the constructive interference of these partial waves results in a large total intensity, while in all directions the total destructive interference occur. Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 12 Fig Illustration of the grating equation (4.7). Note that the path length difference between the reflected lights by the two adjacent grooves is S=d(sin sin ). Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 13 Figure 4.8 shows a parallel light beam incident onto two adjacent grooves. At an angle of incidence to the grating normal one obtains constructive inference condition for those directions of the reflected light m=0, 1, 2, (4.7) where is the wavelength of the incident monochromatic light. In (4.7) the plus sign means that and are on the same side of the grating normal; otherwise the minus sign is taken, which is the case shown in Fig For a special case in which =which means the light is reflected back into the direction of the incident light. Such an arrangement is called a Littrow grating mount, the condition (4.7) for constructive interference reduces to (4.8) Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 14 We now examine the intensity distribution I() of the reflected light when a monochromatic plane wave is incident onto a grating. For simplicity, consider the case in which the plane wave is normally incident onto the grating, that is =0. The incident plane wave can be expressed as E=Aexp(i(t-kz)). The path difference between partial waves reflected by any two adjacent grooves is S=dsin, and the corresponding phase difference is given by the total amplitude of the partial waves reflected from all N grooves in the direction is (4.10) The Littrow grating acts as a wavelength-selective reflector because light is only reflected if the incident light wavelength satisfies the condition (4.8). Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 15 where R is reflectivity of the grating, which depends on the reflection angle , and A g is the amplitude of the partial wave incident onto each groove. Because the intensity of the reflected wave is related to its amplitude A R by I R = 0 cA R A R *, we find from(4.10) (4.11) This is the grating equation (4.7) for the special case =0 and means that the path difference between the partial waves reflected by adjacent grooves The intensity distribution I R is plotted in Fig4.6 for two different gratings with different total groove number N. The principal maxima occur for =2m, which is, according to (4.9) equivalent to dsin =m (4.12) with Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 16 is an integer multiple of the wavelength . The integer m is called the order of the interference. The function (4.11) has N-1 minima with Fig Intensity distribution I( ) for different numbers of grooves. Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 17 I R =0 between two successive principal maxima. The intensity of the N-2 small maxima, which are caused by incomplete destructive interference, decreases proportional to 1/N with increasing groove number N. It is not hard to image that for a real grating with great number of grooves, the reflected intensity I R ( ) at a given wavelength will have very sharply defined maxima only in those direction as defined by (4.12). The small side maxima are completely negligible. Note that the reflectivity R( , ) is not only dependent on the reflection angle but also on the slope of the grooves. In order to achieve the optimum value of R(, ) the slope of the grooves must be carefully designed. We define a particular angle (blaze angle) for obtaining the optimum value of the reflectivity. From Fig. 4.7 one infers in the case of specular reflection i=r, with i= - and r= + , the condition for the blaze angle The incident angle is determined by the particular construction of the spectrometer and the angle for which the constructive interference occurs =( - )/2, Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 18 depends on the wavelength. Therefore the blaze angle has to be specified for the derived spectral range and the spectrometer type. The corresponding wavelength is called the blazed wavelength of the grating. Usually the second order diffraction (m=2) is employed to increase the spectral resolution by a factor 2 without losing much intensity in the practical spectrometer, if the blaze angle is correctly chosen to satisfy (4.19) and (4.18) with m=2. Differentiating the grating equation (4.7) with respect to we obtain Fig Illustration of blaze angle. Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 19 (4.13) The spectral resolving power is the product of the diffraction order m with the total number N of grooves. This illustrates that the angular dispersion is determined solely by the angles and and not by the number of grooves. The resolving power can be derived as following (4.15) Substituting from (4.7), We find (4.14) the angular dispersion at a given angle of incident Laser Spectroscopy/SJX Chap. 4 Components of Spectroscopic Instruments 20 Summarizing the considerations above we find that the grating acts as a wavelength-selective mirror, reflecting light of a given wavelength only into definite directions m, m is the mth diffraction order.