Optical Spectrometers

Transcription

1 Optical Spectrometers Prism Spectrometers Grating Spectrometers Interferential Spectrometers Hyperspectral Spectrometers Credit: Experimental Methods in Physics [ ] EPFL - SB - ICMP - IPEQ CH Lausanne IPEQ - ICMP - SB - EPFL Station 3 CH LAUSANNE

2 Optical spectroscopy light source sample light analyzer light detector 2

3 Content Optical spectroscopy Resolvance (resolving power) Luminosity Prism spectrometer Grating spectrometer Interferential spectrometer Fourier spectrometer Hyperspectral spectrometer 3

4 Optical spectroscopy Definition The emission spectrum of a source, primary or secondary, is characterized by its luminance L ( ). The absorption spectrum is characterized by the absorption factor A ( ). The role of dispersive devices (prism, grating, interferential) is to determine the functions A ( ) and L ( ) with the greatest precision. 4

5 Optical spectroscopy Keep in mind that the important physical parameter is... the frequency,,... even if we measure the wavelength! in the vacuum: λ v = c υ in a medium of index n: λ n = c n υ 5

6 Optical spectroscopy λ v λ n = (n 1) λ v Often in the air, it makes no difference between n and v In fact, in the visible range, the error is not negligible (1-2 Å) 6

7 Dispersive apparatus General properties F: entrance slit C: collimator (objective, mirror, ) D: dispersive element (prism, grating, ) O: objective (mirror) P: image plane (photodetector, CCD, ) 7

8 Dispersive apparatus Figures of merit Resolving power or resolvance R = λ Δλ Luminosity L = E M L s 8

9 Resolvance Ideal case: punctual source (eventually slit) The size of the image, in the plane P, is limited by the diffraction... this is the projection of the contour of the dispersive element in a plane which is perpendicular to a direction that follows the dispersion that is important for calculating the size of the image. 9

10 Resolvance Ideal case: incoherent punctual source D(x) = sin(π x /d ) o ( π x /d ) o 2 d o = f λ w g '' 10

11 Resolvance Rayleigh criterium: Ideal case: 2 punctual sources emitting at two different wavelengths ( and [ + ]) We consider that both wavelengths, and [ + ] are resolved if the centers of their diffraction pattern are separated by at least d 0 11

12 Resolvance 12

13 Resolvance R o = λ Δλ = w '' g dβ dλ The intrinsic resolvance of the system is limited by the size of the dispersive element (or rather by it s projection.), i.e. by the diffraction 13

14 Resolvance Influence of the width of the entrance slit 14

15 Resolvance Influence of the width of the entrance slit E(x) = F(ζ ) D(x ζ)dζ E = F D where F is the function "slit", and D(x) the diffracted intensity in the image plane, of an infinitely thin slit. 15

16 Resolvance Influence of the entrance slit width 16

17 Luminosity versus resolvance Luminosity versus resolvance - a compromise 17

18 Monochromator or spectrometer? Dispersive instruments. prism. grating. interferential Monochromator Monochromator + detector Bandpass filter - monochromator Spectroscope Spectrometer Spectrograph Monochromatic light source Spectral signature 18

19 The prism spectrometer a I( ) S C e O I( + ) S: ponctual source C: collimator O: objectif 19

20 The prism spectrometer a Snell s law d i i1 i t1 i i2 i t2 sin(i n = i1 ) sin(i = t2 ) sin(it1 ) sin(ii2) If the angle of deviation,, is a + d sin( n = 2 ) a sin(2 ) minimum 20

21 The prism spectrometer a I( ) S C e O I( + ) the resolving power is given by: m db dn 0 = = a = e Dm dm dm 21

22 The prism spectrometer Example: To estimate the resolving power, we consider the case of a prism spectrometer working around 0.5 µm (green light). dn n 0 = e. r - n b dm mr - m b e = o abbe (n y - 1) nm? e = 25 mm Crown 3400 Fl int 0.17 nmk Dm TK0.5 nm 22

23 The prism spectrometer Advantages - low sensitivity to polarization - no overlap between different orders - uniform efficiency over the whole spectrum - heavy duty, high damage threshold - scanning and imaging modes Disadvantages - n = n( ) non-linear dependance credit: - material has to be transparent over the whole spectrum - relatively low resolving power, compared to grating instruments (for similar luminosity...) - need for costly achromatic optics - need to control several angles... 23

24 The prism spectrometer source Pellin-Broca s prism At minimum deviation angle, the angle between incident and refracted beam is precisely 90 24

25 The prism spectrometer in the NIR D D ES ED ES ES C ES C R E R S S ED E S: white light source R: reference E: sample C: chopper ES: entrance slit of the spectrometer ED: dispersive element ES: exit slit of the spectrometer D: detector 25

26 The prism spectrometer in the NIR 26

27 The prism spectrometer in the NIR I(z) Beer s law I(z) = I 0 exp(- az) 0 z Transmittance I %T = I0 $ 100 Absorbance A =-log T = log b I 0 I l 27

28 The grating spectrometer 28

29 The grating spectrometer The dispersive element is a grating instead of a prism collimator and objective are replaced by mirror optics (achromatic over a wide spectral range) imaging mode possible using an image detector (CCD or CMOS array) placed in the exit plane 29

30 Grating... intuitive feeling Huygens principle = 0 0 th order = 2π 1 st order = 4π 2 nd order 30

31 Transmission or reflection gratings? transmission grating reflection grating refractive index modulations within a thin layer of material sandwiched between two glass substrates ruled gratings holographic gratings 31

32 Grating spectrometer - basic equations Notations = incident angle = diffraction angle k = diffraction order N = total number of grooves n = grooves density [grooves/mm] = wavelength [nm] b = grating step D V = + = total deviation angle 32

33 Grating spectrometer-basic equations D V = b - a D V is fixed by the geometry k = diffraction order n = grooves density sin(a) + sin(b) = 2 $ sin b a + b 2 l $ cos b b - a 2 l = 10-6 $ k $ n $ m 33

34 Grating spectrometer-basic equations example of configuration 34

35 Grating spectrometer imaging mode The image detector is placed in a plane which is not perpendicular to the axis defined by the central wavelength (to minimize the infuence of the aberrations). 35

36 Grating spectrometer Superposition of the different orders of diffraction k $ m =cste cannot be avoided the use of blocking filter can help 36

37 Grating spectrometer angular dispersion and intrinsic resolvance m 0 0 = = '' Dm wg db dm m 0 0 = = '' wg Dm k $ n $ 10-6 = w cos b g $ k $ n = k $ N m 0 0 = = wg $ Dm sin(a) + sin(b) 10-6 $ m 37

38 Grating spectrometer blazed gratings 1st order it is possible to concentrate most of the diffracted energy in the first order for a given wavelength if = The grating equation shows that the angles of the diffracted orders only depend on the grooves' period, and not on their shape. By controlling the crosssectional profile of the grooves, it is possible to concentrate most of the diffracted energy in a particular order for a given wavelength. A triangular profile is commonly used. This technique is called blazing 38

39 Grating spectrometer blazed gratings Usually the blazed angle is defined for a Littrow configuration to be independent of the angle of total deflection (D V is imposed by the geometry of the monochromator) 39

40 Grating spectrometer blazed gratings 40

41 Grating spectrometer Ebert- Fastie design one concave mirror one planar grating slits are placed in the focal plane of the mirror advantages simple inexpensive disadvantages off-axis configuration, performances strongly limited by aberrations 41

42 Grating spectrometer Czerny - Turner 42

43 Grating spectrometer Aberration in PGS systems 43

44 Aberration in PGS spectrometer Aberration in PGS systems 44

45 Grating spectrometer Concave gratings (ACGH) 45

46 Grating spectrometer Anamorphism 46

47 Grating spectrometer Bandpass and resolution 47

48 Grating spectrometer Quasi-littrow configuration 48

49 Grating spectrometer F - value N.A. = sin X 1 f/value = 2 NA 49

50 Grating spectrometer Radiometry and spectrometry... geometry extent 50

51 Grating spectrometer One example: Jobin-Yvon HR

52 Grating spectrometer Examples: Triax Series 52

53 PF spectrometer [Fabry-Perot] 53

54 Interferential spectrometer 54

55 Iterferential spectrometer 55

56 Interferential spectrometer S = 2nd cos i E trans = E 5 inc tt + trrte -jk 0 S + trrrrte -jk 02S +...? 56

57 Interferential spectrometer avec R = r 2 et T = t 2 4R F = (1 - R) 2 c c o 0 = = S 2nd cos i I trans = I inc b ro 1 + F sin 2 o 0 l 1 57

58 Interferential spectrometer 58

59 Interferential spectrometer FWHM = r 2 sin c m. F r F = p 1 finesse o 0 = Do o 1 = $ o0 FWHM o = $ p =m $ p o0 0 F=380, = 30.6, 0 = 15 GHz, m = =

60 Interferential spectrometer 60

61 Hyperspectral spectrometer LCPF 61

62 Interferential spectrometer LCPF 62

63 Interferential spectrometer LCPF 63

64 Spectral imaging filter 64

65 Spectral imaging filter 65

66 Acousto-optic spectrometer.. AOTF Texte 66

67 Acousto-optic spectrometer.. AOTF Texte 67

68 Acousto-optic spectrometer.. AOTF Texte 68

69 Acousto-optic spectrometer.. AOTF Texte 69

70 FTIR spectrometer 70

71 FTIR spectrometer 71

72 FTIR spectrometer I o1 (x) = B(o 1 ) $ cos 2ro 1 x I o2 (x) = B(o 2 ) $ cos 2ro 2 x I (x) = I 1 (x)+ I 2 (x) 72

73 FTIR spectrometer The mesured intensity (interferogram) in fonction of the displacement, x, is given by: I(x) = 2r 1 3 # -3 B(o) $ cos(2rox)do we observe immediately that the spectral information B(V) is nothing else than the Fourier transform of the measured intensity: B(o) = 3 # -3 I(x) $ cos(2rox)dx 73

74 FTIR spectrometer 74

75 FTIR spectrometer 75

76 Hyperspectral Visual perception of colors 76

77 Hyperspectral 77

78 Hyperspectral 78

79 Hyperspectral 79

80 Hyperspectral 80

81 Hyperspectral 81

82 Hyperspectral 82

83 Hyperspectral 83

84 Hyperspectral 84

85 Hyperspectral 85

86 Minimum Deviation by a Prism i i1 a i t2 d sin(i n = i1 ) sin(i = t2 ) sin(it1 ) sin(ii2) i t1 i i2 a = i + i t1 i2 d = i + i -a i1 t2 arcsin n sin arcsin sin i d = i + ; $ ca- ' i1 1mE -a i1 n 86

87 Minimum deviation angle d i i1 a i t2 d i t1 i i2 n=1.5 i i1 87