Optical Imaging 1
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
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
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
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 2 + 2 nn ii nn tt nn ii ss oo xx = 0 hyperbola 5 if nn tt > nn ii
Hyperbola as a section of a cone: 6
Possible applications of hyperboloid lenses: Collimating a point source Focusing a collimated optical beam Imaging a point into a point 7
Cross sections of a cone: 8
nn tt 2 nn ii 2 xx 2 nn ii 2 yy 2 + 2 nn ii nn tt nn ii 2 ss oo xx = 0 if nn tt < nn ii ellipse nn ii nn tt 9
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
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
OOOOOO = nn 1 RR 2 + ss oo + RR 2 2 RR ss oo + RR cos φφ + nn 2 RR 2 + ss ii RR 2 + 2 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
Spherical aberration: Different values of φφ will lead to different values of ss ii ss oo 13
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
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
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+10 30 100 37.5 50 50 40 60 30 90 35 70 30 90 25 150 21 630 20.5 1230 20.1 6030 ss ii 16
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
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
Optical axis RR 1 CC 2 RR 2 CC 1 oopppppppppppp aaaaaaaa 19
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
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
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
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
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 1 + 1 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
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 1 1 1 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 2 2 25
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
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
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
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
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
Effective Focal Length (efl): dd RR 0 nn mm eeeeee = nn 1 ll nn mm 1 RR 1 RR 2 2 + 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
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
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
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
To simplify the notation in the following equations: eeeeee ff 35
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
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
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
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
Imaging formation for positive focal length lens eeeeee > 00 nn ll > nn mm 40
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 0.54 41
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 0.72 42
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 1.00 43
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 1.73 44
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 2.04 45
Imaging formation for negative focal length lens eeeeee < 00 nn ll > nn mm 46
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 0.39 47
Combining multiple lenses 48
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 + 1 = 1 ss oo,1 ss ii,1 ff 1 1 + 1 = 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
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 + 1 = 1 ss oo,2 ss ii,2 ff 2 1 + 1 dd ff 1 bbffff = 1 ff 2 1 dd ff 1 + ff 1 eeeeee ff 1 dd 50 = 1 ff 2
1 eeeeee = 1 ff 1 + 1 ff 2 dd ff 1 ff 2 1 + 1 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
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
Multiple lenses 53
Extending the concepts to multiple lenses 54
Example: zoom lens mm TT = ss ii ss oo = ff ff ss oo ff ss oo 55
Mirrors 56
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
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
Spherical mirror under paraxial approximation CC FF 60
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
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
Imaging formation with a concave mirror 63
Imaging SS CC FF VV 64
Imaging SS CC FF VV 65
Imaging SS CC FF VV 66
Imaging SS = CC FF VV 67
Imaging CC SS FF VV 68
Imaging CC FF SS VV 69
Imaging formation with a convex mirror 70
Imaging SS VV FF CC 71
Survey of Optical Instruments 72
Eyes 73
compound eye simple eye human eye pinhole eye 74
Human Eye Cornea: RR 1 + 7.8 mmmm RR 2 +6.4 mmmm nn 1.376 tt +0.6 mmmm Double, positive lens Iris controls amount of collected light (pupil size 2-8 mm in diameter) Retina: thin layer (0.1-0.5 mm) of light receptor cells (rods & cones); concave light sensitive screen Rods: 120 10 6, 2 µm, black/white, high sensitivity Cones: 6 10 6, 6 µm, color sensitive Aqueous humor: nn 1.336 tt +3.0 mmmm Eye lens: RR 3 +10.1 mmmm RR 4 6.1 mmmm Vitreous humor: nn 1.337 tt +16.9 mmmm ffl: +15.6 mmmm nn 1.386 1.406 tt +4.0 mmmm bfl: at retina Macula (3 mm): cones/rods = 2 Fovea (0.3 mm): just cones (1.0 1.5 µm) Accommodation: change in the efl to form an image at the retina, 75 done by the eye lens
Eyeglasses 76
77
A few definitions: Diopters: bending power DD dddddddddddddddd 1 eeeeee mmmmmmmmmmmm nn mm eeeeee = nn 1 ll nn mm 1 RR 1 RR 2 2 + 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
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
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
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
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 + 1 = 1 ss oo ss ii ff gggg eyeglass eye retina 1 0.25 mm + 1 = 1 = DD dddddddddddddddd dd nnnn ff gggg SS ii dd nnpp SS oo DD dddddddddddddddd = 4 1 dd nnpp mmmmmmmmmmmm 82
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
1 ff = 1 + 1 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
Magnifiers Create an image of a nearby object that is larger than the image seen by the unaided eye
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
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
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
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
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
Example: ss oo = ff = 10 cccc LL = MMMM = dd oo DD = 25 cccc 1 10 cccc = 2.5 XX 91
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
Working details of eyepieces MMMM = dd oo ff = dd oo DD MMMM = 25.4 cccc ff MMMM = 10X ff = 2.54 cccc 93
Objectives Purpose: to create a magnified image of an object. 94
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 0.10. 95
Numerical Aperture Quantifies the amount of gathered light by the optical component. NNNN nn ssssss θθ 96
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
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
Optical Telescopes Purpose: collect and focus light to form a magnified image of a distant object. 99
Refracting Telescopes The primary light gathering element is a lens. primary eyepiece 100
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
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 1848. The 24-inch (61 cm) refracting telescope in Flagstaff, Arizona. 102
Galilean Telescope MMMM = ββ αα = h ff ee h ffoo = ff oo ff ee Image is upright, not reversed. 103
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
Newtonian Telescope Primary mirror is parabolic. Secondary mirror is flat. 105
Gregorian Telescope Primary mirror is parabolic. Secondary element is an elliptical concave mirror. 106
Cassegrain Telescope Primary mirror is parabolic. Secondary element is an hyperboloid convex mirror. 107
Ritchey-Chretien Telescope Primary mirror is hyperbolic. Secondary element is a hyperbolic convex mirror. 108
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