What makes a good image?

Transcription

1 Optical Imaging 1

2 What makes a good image? A point in the object is mapped (as much as possible) into a point in the image. The image is a scaled version of the object. 2

3 A flat plane in the object is transformed to a flat plane in the image. All colors are focused on the same plane in the image. 3

4 Point-to-point imaging across a single refracting surface xx, yy cc tt = OOOOOO = nn 1 ss oo + nn 2 ss ii = nn 1 ll oo + nn 2 ll ii nn 1 ss oo + nn 2 ss ii = nn 1 xx 2 + yy 2 + nn 2 ss oo + ss ii xx 2 + yy 2 Cartesian oval 4

5 Collimating the light exiting from a point source with a refracting surface yy cc tt = OOOOOO = nn ii ss oo + nn tt tt = nn ii ll oo + nn tt ll ii AA xx, yy DD ll oo ll ii FF 1 nn ii nn tt xx ss oo tt nn tt 2 nn ii 2 xx 2 nn ii 2 yy nn ii nn tt nn ii ss oo xx = 0 hyperbola 5 if nn tt > nn ii

6 Hyperbola as a section of a cone: 6

7 Possible applications of hyperboloid lenses: Collimating a point source Focusing a collimated optical beam Imaging a point into a point 7

8 Cross sections of a cone: 8

9 nn tt 2 nn ii 2 xx 2 nn ii 2 yy nn ii nn tt nn ii 2 ss oo xx = 0 if nn tt < nn ii ellipse nn ii nn tt 9

10 Aspherical surfaces: They perform well only for a specific condition Ideal performance No longer ideal performance Aspherical surfaces are typically more expensive to manufacture (compared to spherical surfaces) aspherical surfaces 10 spherical surfaces

11 Spherical surface ll oo R S V φφ C P ss oo nn 1 A nn 2 ll ii ss ii ss oo SSSS ss ii VVVV ll oo SSSS ll ii AAAA RR VVVV cc tt = OOOOOO = nn 1 ll oo + nn 2 ll ii ll oo = RR 2 + ss oo + RR 2 2 RR ss oo + RR cos φφ ll ii = RR 2 + ss ii RR 2 2 RR ss ii RR cos ππ φφ 11

12 OOOOOO = nn 1 RR 2 + ss oo + RR 2 2 RR ss oo + RR cos φφ + nn 2 RR 2 + ss ii RR RR ss ii RR cos φφ dd OOOOOO dd cos φφ = 0 nn 1 RR ss oo + RR ll oo + nn 2 RR ss ii RR ll ii = 0 nn 1 ll oo φφ + nn 2 ll ii φφ = 1 RR nn 2 ss ii ll ii φφ nn 1 ss oo ll oo φφ Therefore, given nn 1, nn 2, ss oo and RR, different values of φφ will lead to different values of ss ii 12

13 Spherical aberration: Different values of φφ will lead to different values of ss ii ss oo 13

14 Paraxial approximation: ll oo A R S V φφ C P ll ii ss oo ss ii nn 1 nn 2 paraxial = close to the axis φφ 0 cos φφ 1 S ll oo ssoo φφ ss ii ll ii C P ss oo ll oo nn 1 nn 2 ss ii ll ii 14

15 The equation nn 1 ll oo φφ + nn 2 ll ii φφ = 1 RR nn 2 ss ii ll ii φφ nn 1 ss oo ll oo φφ under the paraxial approximation becomes: nn 1 ss oo + nn 2 ss ii = 1 RR nn 2 nn 1 Given nn 1, nn 2, ss oo and RR, different values of φφ close to the axis (i.e., under the paraxial approximation) will lead to a single and uniquely-defined value of ss ii 16

16 Single spherical surface under paraxial approximation: nn 1 ss oo + nn 2 ss ii = 1 RR nn 2 nn 1 nn 1 = 1.00 nn 2 = 1.50 RR = 10.0 cccc So (cm) Si (cm) S ss oo nn 1 nn 2 RR C P 1.E ss ii 16

17 Two unique configurations: nn 1 ss oo + nn 2 ss ii = 1 RR nn 2 nn 1 ss ii nn 1 = 1 ff oo RR nn 2 nn 1 ff oo = nn 1 RR ss oo ff oo nn 2 nn 1 FF oo : focal point on the object side FF oo ff oo nn1 nn 2 nn 1 FF ii : focal point on the image side ss oo nn 2 = 1 ff ii RR nn 2 nn ss 1 ff ii = nn 2 RR ii ff ii nn 2 nn 1 FF ii nn 2 ff ii 17

18 Sign convention: yy S 1 P 1 yy oo S FF oo V RR C FF ii P xx yy ii ss oo ff oo ff ii ss ii ss oo SSSS ss ii VVVV ff oo FF oo VV ff ii VVFF ii RR VVVV yy oo SS SS 1 yy ii PP PP 1 All positive values in the figure below 18

19 Optical axis RR 1 CC 2 RR 2 CC 1 oopppppppppppp aaaaaaaa 19

20 Spherical lens or refraction on a sequence of two surfaces under paraxial approximation RR 1 RR 2 VV 1 VV 2 S PP 1 ss oo,1 d nn mm nn ll nn mm ss ii,1 nn mm ss oo,1 + nn ll ss ii,1 = 1 RR 1 nn ll nn mm 20

21 Spherical lens RR 1 RR 2 S VV 1 VV 2 P PP 1 ss oo,1 d ss ii,2 ss ii,1 ss oo,2 nn mm nn ll nn mm nn mm ss oo,1 + nn ll ss ii,1 = 1 RR 1 nn ll nn mm nn ll ss oo,2 + nn mm ss ii,2 = 1 RR 2 nn mm nn ll ss ii,1 = VV 1 PP 1 = VV 1 VV 2 + VV 2 PP 1 = d ss oo,2 21

22 Spherical lens Surface 1 Surface 2 nn mm ss oo,1 + nn ll ss ii,1 = 1 RR 1 nn ll nn mm nn ll ss oo,2 + nn mm ss ii,2 = 1 RR 2 nn mm nn ll nn mm ss oo,1 + nn ll ss ii,1 + nn ll ss oo,2 + nn mm ss ii,2 = 1 RR 1 nn ll nn mm + 1 RR 2 nn mm nn ll nn mm 1 ss oo,1 + 1 ss ii,2 + nn ll 1 ss ii,1 + 1 ss oo,2 = nn ll nn mm 1 RR 1 1 RR 2 22

23 i) Object at infinity RR 1 RR 2 ss oo,1 = ss oo,1 = nn mm ss ii,1 ff ii,1 = nn ll RR 1 nn ll nn mm VV 1 yy 1 HH 2 VV 2 FF ii FF yy 2 ii,1 d nn ll eeffff ss ii,2 = bbbbbb ss ii,1 = ff ii,1 ss oo,2 nn mm ss ii,2 bbbbbb VV 2 FF ii eeffff HH 2 FF ii yy 2 = bbbbbb yy 1 eeeeee = ss oo,2 ff ii,1 1 = 1 bbbbbb eeeeee ff ii,1 ss oo,2 23

24 nn mm 1 ss oo,1 + 1 ss ii,2 + nn ll 1 ss ii,1 + 1 ss oo,2 = nn ll nn mm 1 RR 1 1 RR 2 ss oo,1 = ss ii,2 = bbbbbb ss ii,1 = ff ii,1 nn mm bbbbbb + nn ll 1 ff ii,1 + 1 ss oo,2 = nn ll nn mm 1 RR 1 1 RR 2 1 bbffff = 1 eeeeee ff ii,1 ss oo,2 nn mm eeeeee ff ii,1 ss oo,2 + nn ll ff ii,1 + ss oo,2 ff ii,1 ss oo,2 = nn ll nn mm 1 RR 1 1 RR 2 ss oo,2 ff ii,1 ff ii,1 + ss oo,2 = dd nn mm eeeeee nn ll dd 1 2 = nn ll nn mm 1 ff ii,1 RR 1 RR 2 ss oo,2 ff ii,1 24

25 nn mm eeeeee nn ll dd 1 2 = nn ll nn mm 1 ff ii,1 RR 1 RR 2 ss oo,2 ff ii,1 ff ii,1 = nn ll RR 1 nn ll nn mm ss oo,2 = ff ii,1 dd = nn ll RR 1 nn ll nn mm dd = nn ll RR 1 dd nn ll nn mm nn ll nn mm 2 nn mm eeeeee dd nn ll nn mm 1 2 = nn ll nn mm 1 nn ll RR 1 RR 1 RR 2 nn ll RR 1 dd nn ll nn mm nn ll RR 1 2 nn mm eeeeee dd nn ll nn mm 1 2 = nn ll nn mm dd nn ll nn mm nn ll RR 1 RR 1 RR 2 RR 1 RR 2 nn ll RR 1 2 nn mm eeeeee = nn 1 ll nn mm 1 RR 1 RR 2 + dd nn ll nn mm nn ll RR 1 RR

26 1 bbffff = 1 eeeeee ff ii,1 ss oo,2 bbbbbb = eeeeee ss oo,2 ff ii,1 ss oo,2 = ff ii,1 dd bbbbbb = eeeeee ss oo,2 ff ii,1 = eeeeee ff ii,1 dd ff ii,1 = eeeeee eeeeee dd ff ii,1 ff ii,1 = nn ll RR 1 nn ll nn mm bbbbbb = eeeeee eeeeee dd nn ll nn mm nn ll RR 1 26

27 Recap: object at infinity RR 1 RR 2 ss oo,1 = VV 1 HH 2 VV 2 FF ii bbbbbb eeffff nn mm nn ll nn mm d HH 2 FF ii eeffff nn mm eeeeee = nn 1 ll nn mm 1 RR 1 RR 2 + dd nn ll nn mm nn ll RR 1 RR 2 2 VV 2 FF ii bbbbbb = eeeeee eeeeee dd nn ll nn mm nn ll RR 1 HH 2 VV 2 = eeeeee dd nn ll nn mm nn ll RR 1 27

28 ii) Image at infinity RR 1 RR 2 ss oo,1 = ffffff =? ss ii,2 = FF oo VV 1 HH 1 VV 2 ffffff eeffff nn mm nn ll nn mm d 28

29 Reverse the lens and the rays: RR 2 RR 1 VV 2 HH 1 VV 1 FF oo ffffff eeffff nn mm nn ll nn mm d nn mm eeeeee = nn 1 ll nn mm 1 + dd nn ll nn mm RR 2 RR 1 nn ll RR 2 RR 1 eeeell = eeeeee 2 ffffff = eeeeee eeeeee dd nn ll nn mm nn ll RR 2 29

30 Back to original configuration: RR 1 RR 2 ss ii,2 = FF oo VV 1 HH 1 VV 2 ffffff eeffff nn mm nn ll nn mm d FF oo VV 1 = FF oo HH 1 VV 1 HH 1 ffffff = eeeeee eeeeee dd nn ll nn mm nn ll RR 2 VV 1 HH 1 = eeeeee dd nn ll nn mm nn ll RR 2 30

31 Effective Focal Length (efl): dd RR 0 nn mm eeeeee = nn 1 ll nn mm 1 RR 1 RR dd nn ll nn mm 1 nn nn ll RR 1 RR ll nn mm 1 2 RR 1 RR 2 Typical case: nn ll nn mm > 0 31

32 Positive efl: 1 RR 1 1 RR 2 > 0 RR 1 > 0 RR 2 < 0 RR 1 > 0 RR 2 = RR 1 > 0 RR 2 > 0 RR 1 < RR 2 RR 1 > 0 RR 2 < 0 RR 2 < 0 RR 1 = RR 1 < 0 RR 2 < 0 RR 2 < RR 1 29

33 Negative efl: 1 RR 1 1 RR 2 < 0 RR 1 < 0 RR 2 > 0 RR 1 < 0 RR 2 = RR 1 < 0 RR 2 < 0 RR 1 < RR 2 RR 1 < 0 RR 2 > 0 RR 1 = RR 2 > 0 RR 1 > 0 RR 2 > 0 RR 2 < RR 1 33

34 Principal Planes: VV 1 HH 1 = eeeeee dd nn ll nn mm nn ll RR 2 HH 2 VV 2 = eeeeee dd nn ll nn mm nn ll RR 1 HH 1 HH 2 HH 1 HH 2 HH 1 HH 2 HH 1 HH 2 eeeeee > 0 HH 1 HH 2 HH 1 HH 2 HH 1 HH 2 HH 1 HH 2 eeeeee < 0 34

35 To simplify the notation in the following equations: eeeeee ff 35

36 Spherical lens under paraxial approximation VV 11 HH 11 HH 22 VV 22 FF ii FF ii FF oo VV11 HH 11 HH 22 VV 22 FF oooo 36

37 Lens equation and conjugate points HH 1 HH 2 yy oo ss oo FF ii SS ii SS oo FF oo ff ff yy ii ss ii yy oo = ss oo ff yy ii ff = ff ss ii ff 1 ss oo + 1 ss ii = 1 ff 37

38 Transverse magnification: mm TT yy ii yy oo mm TT > 00 upright mm TT > 11 magnified mm TT < 00 inverted mm TT < 11 de-magnified yy oo yy ii = ff ss ii ff 1 ss oo + 1 ss ii = 1 ff mm TT yy ii yy oo = ss ii ff ff = 1 ss ii ff = ss ii ss oo mm TT yy ii yy oo = ss ii ss oo 38

39 Ray aiming at principal point: HH 1 HH 2 yy oo SS oo ss oo FF oo αα ff ff αα FF ii SS ii yy ii ss ii tttttt αα = yy oo ss oo = yy ii ss ii = tttttt αα αα = αα parallel rays 39

40 Imaging formation for positive focal length lens eeeeee > 00 nn ll > nn mm 40

41 Imaging HH 1 HH 2 FF ii SS ii SS oo FF oo real image mm TT = ss ii ss oo 1.53 ff 2.82 ff

42 Imaging HH 1 HH 2 FF ii SS ii SS oo FF oo real image mm TT = ss ii ss oo 1.73 ff 2.39 ff

43 Imaging HH 1 HH 2 FF ii SS ii SS oo FF oo real image mm TT = ss ii ss oo 2 ff 2 ff

44 Imaging HH 1 HH 2 FF ii SS ii SS oo FF oo real image mm TT = ss ii ss oo 2.71 ff 1.57 ff

45 Imaging virtual image FF ii FF oo SS ii SS oo HH 1 HH 2 mm TT = ss ii ss oo 1.04 ff 0.51 ff

46 Imaging formation for negative focal length lens eeeeee < 00 nn ll > nn mm 46

47 Imaging HH 1 HH 2 SS oo FF ii SS ii virtual image FF oo mm TT = ss ii ss oo 0.60 ff 1.52 ff

48 Combining multiple lenses 48

49 Combining two lenses: HH 1,1 HH 1,2 HH 2,1 HH 2,2 S ss oo,2 ssii,2 P PP 1 ss oo,1 ss ii,1 dd = 1 ss oo,1 ss ii,1 ff = 1 ss oo,2 ss ii,2 ff 2 ss ii,1 = HH 1,2 PP 1 = HH 1,2 HH 2,1 + HH 2,1 PP 1 = d ss oo,2 49

50 Object at infinity: HH 1,1 HH 1,2 HH 2,1 HH 2,2 ss oo,1 = yy 1 dd ss ii,1 = ff 1 HH 2 FF ii yy 2 eeeeee ss ii,2 = bbbbbb ss oo,2 FF ii,1 yy 2 = bbbbbb yy 1 eeeeee = ss oo,2 1 ff 1 bbbbbb = ff 1 = eeeeee ss oo,2 ff 1 eeeeee ff 1 dd = 1 ss oo,2 ss ii,2 ff dd ff 1 bbffff = 1 ff 2 1 dd ff 1 + ff 1 eeeeee ff 1 dd 50 = 1 ff 2

51 1 eeeeee = 1 ff ff 2 dd ff 1 ff dd ff 1 bbffff = 1 ff 2 bbbbbb = ff 2 ff 1 dd ff 1 + ff 2 dd ffffff = ff 1 ff 2 dd ff 1 + ff 2 dd 51

52 Example: combination of eyeglass & eye eyeglass mm TT = ss ii ss oo = ff ff ss oo ff 1 = ff gggg ff 2 = ff eeeeee dd = ff eeeeee eeeeee = ff eeeeee bbbbbb = ff eeeeee ff gggg dd ff gggg 52

53 Multiple lenses 53

54 Extending the concepts to multiple lenses 54

55 Example: zoom lens mm TT = ss ii ss oo = ff ff ss oo ff ss oo 55

56 Mirrors 56

57 How to convert a spherical wave into a plane wave (and vice-versa) using a mirror? xx nn cc tt = OOOOOO = nnff VV + nn VVVV = nn FFFF + nn AAAA DD AA(xx, yy) FFVV + VVVV = FFFF + AAAA yy PP FF VV ff + dd = xx 2 + ff yy 2 + dd yy ff yy = 1 4 ff xx2 parabola dd 57

58 58

59 Spherical mirror xx 2 + yy RR 2 = RR 2 xx RR yy CC FF VV xx 2 + yy 2 + RR 2 2 yy RR = RR 2 paraxial approx. yy RR 1 yy 1 2 RR xx2 ff = RR 2 59

60 Spherical mirror under paraxial approximation CC FF 60

61 Sign convention for mirrors: real object ss oo > 0 virtual image ss oo < 0 real image VV ss ii > 0 virtual image ss ii < 0 RR < 0 RR > 0 ff > 0 ff < 0 ff = RR 2 61

62 Mirror equation under paraxial approximation yy ii yy oo = ss ii ff ff = ff ss oo ff yy oo SS CC yy ii FF VV 1 ss oo + 1 ss ii = 1 ff ff ss ii ss oo 62

63 Imaging formation with a concave mirror 63

64 Imaging SS CC FF VV 64

65 Imaging SS CC FF VV 65

66 Imaging SS CC FF VV 66

67 Imaging SS = CC FF VV 67

68 Imaging CC SS FF VV 68

69 Imaging CC FF SS VV 69

70 Imaging formation with a convex mirror 70

71 Imaging SS VV FF CC 71

72 Survey of Optical Instruments 72

73 Eyes 73

74 compound eye simple eye human eye pinhole eye 74

75 Human Eye Cornea: RR mmmm RR mmmm nn tt +0.6 mmmm Double, positive lens Iris controls amount of collected light (pupil size 2-8 mm in diameter) Retina: thin layer ( mm) of light receptor cells (rods & cones); concave light sensitive screen Rods: , 2 µm, black/white, high sensitivity Cones: , 6 µm, color sensitive Aqueous humor: nn tt +3.0 mmmm Eye lens: RR mmmm RR mmmm Vitreous humor: nn tt mmmm ffl: mmmm nn tt +4.0 mmmm bfl: at retina Macula (3 mm): cones/rods = 2 Fovea (0.3 mm): just cones ( µm) Accommodation: change in the efl to form an image at the retina, 75 done by the eye lens

76 Eyeglasses 76

77 77

78 A few definitions: Diopters: bending power DD dddddddddddddddd 1 eeeeee mmmmmmmmmmmm nn mm eeeeee = nn 1 ll nn mm 1 RR 1 RR dd nn ll nn mm 1 nn nn ll RR 1 RR ll nn mm 1 2 RR 1 RR 2 1 eeeeee nn ll 1 1 RR 1 1 RR 2 Far Point: longest distance the accommodated eye can image at the retina. Normal eyes: larger than 5 m. Near Point: shortest distance the eye can accommodate an image at the retina. Normal eyes: about 25 cm. 78

79 Nearsightedness (myopia): Eye focal length is shorter than normal, too much bending power. Far point is too close. Objects beyond far point appear blurred. Eyeglass correction Objects closer than far point appear sharp. The corrective action of an eyeglass is done by adding a negative (diverging) lens to bring distant objects closer than the far point. 79

80 1 + 1 = 1 ss oo ss ii ff gggg ss oo = correction for distant objects dd ffff ss ii = dd ffff eyeglass to form an image at far point ff gggg = dd ffff DD dddddddddddddddd = 1 dd ffff mmmmmmmmmmmm 80

81 Farsightedness (hyperopia): Image of distant objects falls behind the retina for the unaccommodated (relaxed) eye. Near point is larger than normal (~ 25 cm). Eyeglass correction Any object closer than the near point cannot be imaged at the retina. A positive (converging) eyeglass lens is needed for correction. 81

82 ss oo = 25 cccc targeted object distance to form a sharp image. unaided eye eye retina ss ii = dd nnpp eyeglass to form an image at the eye near point. SS oo dd nnpp = 1 ss oo ss ii ff gggg eyeglass eye retina mm + 1 = 1 = DD dddddddddddddddd dd nnnn ff gggg SS ii dd nnpp SS oo DD dddddddddddddddd = 4 1 dd nnpp mmmmmmmmmmmm 82

83 Maintaining image magnification while wearing glasses: ff eeeeee HH 1 HH 2 ff eeeeee FF oo,eeeeee eye bbffll uu ff eeeeee HH1 HH 2 FF oo,eeeeee eyeglass dd eye bbffll aa retina If dd = ff eeeeee then mm TT is the same as the unaided eye. 83

84 1 ff = ff gggg ff eeeeee dd ff gggg ff eeeeee dd = ff eeeeee ff = ff eeeeee mm TT = ss ii ss oo = ff ff ss oo bbbbbb = ff eeeeee ff gggg dd ff gggg 84

85 Magnifiers Create an image of a nearby object that is larger than the image seen by the unaided eye

86 Unaided eye αα uu yy oo dd oo yy oo αα uu dd oo (near point) Aided eye virtual image ff yy ii object yy oo αα aa αα aa yy ii LL ss ii ss oo ll LL = ll + ss ii 86

87 MMMM = Magnification power: MMMM αα aa yy ii LL yyoo ddoo = yy ii yy oo dd oo LL = ss ii ss oo dd oo LL = 1 + ss ii ff dd oo LL = αα uu 1 + LL ll ff dd oo LL virtual image ff yy ii object yy oo αα aa αα aa yy ii LL ss ii ss oo ll LL = ll + ss ii MMMM = 1 + LL ll ff dd oo LL 87

88 a) Magnification power: ll = ff ff yy ii object yy oo αα aa ss ii LL = ll + ss ii ss oo ll = ff MMMM = 1 + LL ll ff dd oo LL = dd oo ff = dd oo DD 88

89 b) Magnification power: ll = 0 ff yy ii object yy oo ss ii LL = ss ii ss oo ll = 0 MMMM = 1 + LL ll ff dd oo LL = 1 + LL ff dd oo LL ss ii = dd oo LL = dd oo MMMM = 1 + dd oo DD 89

90 c) Magnification power: ss oo = ff ff yy ii object yy oo αα aa ss ii = LL = ss oo = ff ll MMMM = 1 + LL ll ff dd oo LL = dd oo ff = dd oo DD 90

91 Example: ss oo = ff = 10 cccc LL = MMMM = dd oo DD = 25 cccc 1 10 cccc = 2.5 XX 91

92 Eyepieces A lens (or a combination of lenses) that is attached to a variety of optical devices such as telescopes and microscopes. Purpose: an eyepiece collimates an intermediate image so the relaxed eye can comfortably image it at the retina. It is so named because it is usually the lens that is closest to the eye when someone looks through the device. 92

93 Working details of eyepieces MMMM = dd oo ff = dd oo DD MMMM = 25.4 cccc ff MMMM = 10X ff = 2.54 cccc 93

94 Objectives Purpose: to create a magnified image of an object. 94

95 Practicalities of objectives The optical component is usually labelled with the magnification and the numerical aperture. The component is designed to operate at a specific object/lens distance (working distance = distance from the first surface of objective to the object). The transverse magnification refers to this optimum operating condition. Transverse magnification from 4X to 100X are common. The objective shown on the further left in the figure above indicates a transverse magnification of 4X (and an image formed at 160 mm from the barrel) and a numerical aperture of

96 Numerical Aperture Quantifies the amount of gathered light by the optical component. NNNN nn ssssss θθ 96

97 One important standard: iiiiiiiiii pppppppppp oooooooooooo pppppppppp wwwwwwwwwwwwww dddddddddddddddd manufacturers standard mm TT = yy ii yy oo = ss ii ss oo = ff ss ii ff ss ii ff = 160 mmmm 160 mmmm mm TT = ff 97

98 Optical Microscope Key components: an objective and an eyepiece working together to form a magnified image of an object. MMMM mmmmmmmmmmmmmmmmmmmm = mm TT, oooooooooooooooo MMMM eeeeeeeeeeeeeeee ss oo ss ii 98

99 Optical Telescopes Purpose: collect and focus light to form a magnified image of a distant object. 99

100 Refracting Telescopes The primary light gathering element is a lens. primary eyepiece 100

101 Keplerian Telescope Two positive lenses separated by the sum of their focal length. MMMM = ββ αα = h ff ee = ff oo h ff ee ffoo Drawback: inverted image. 101

102 The 40-inch (1.02 m) Refractor, at Yerkes Observatory, the largest achromatic refractor ever put into practical astronomical use. Image of a refracting telescope from the Cincinnati Observatory in The 24-inch (61 cm) refracting telescope in Flagstaff, Arizona. 102

103 Galilean Telescope MMMM = ββ αα = h ff ee h ffoo = ff oo ff ee Image is upright, not reversed. 103

104 Reflecting Telescopes The primary element for light gathering is a mirror. No chromatic aberration from the primary element. Avoids bulky and heavy primary lens. No need of a high quality homogenous glass for the primary (no bulky material in the optical path). Easy to fabricate larger apertures (diameters) to gather more light and reach better resolution. 104

105 Newtonian Telescope Primary mirror is parabolic. Secondary mirror is flat. 105

106 Gregorian Telescope Primary mirror is parabolic. Secondary element is an elliptical concave mirror. 106

107 Cassegrain Telescope Primary mirror is parabolic. Secondary element is an hyperboloid convex mirror. 107

108 Ritchey-Chretien Telescope Primary mirror is hyperbolic. Secondary element is a hyperbolic convex mirror. 108

109 Schmidt-Cassegrain Telescope The primary element is a parabolic mirror. The secondary mirror is a spherical convex mirror. A corrector plate is mounted at entrance port of telescope for aberration correction. 109