Prof. Jose Sasian OPTI 518. Introduction to aberrations OPTI 518 Lecture 14

Transcription

1 Introduction to aberrations Lecture 14

2 Topics Structural aberration coefficients Examples

3 Structural coefficients Ж Requires a focal system Afocal systems can be treated with Seidel sums

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6 Structural stop shifting parameter nu Y 1 y /2 Using ω on we can express: S y y P P 2Ж S ypyp s s' 2Ж Y 1 s2n Y 1 s' 2 n' s is the distance from the front principal plane to entrance pupil s is the distance from the rear principal plane to exit pupil 2 yp yp yp S S 2Ж 2Ж

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8 Review of concepts Thin lens as the thickness tends to zero t n Shape of a lens and shape factor Conjugate factor to quantify how the lens is used. Related to transverse magnification Must know well first-order optics

9 Shape and Conjugate factors Y ' 1 ' 1 m m nu c c R R X c c R R Lens bending concept

10 Shape X X=0 X=0 X=1 X=-1 X=1.7 X=-1.7 X=3.5 X=-3.5

11 Shape X=-3 X=-2 X=-1 X=0 X=3 X=2 X=1 X=0

12 Shape or bending factor X Quantifies lens shape Optical power of thin lens is maintained Not defined for zero power, R1=R2 X c c R R c c R R

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15 Example: Refracting surface free from spherical aberration Object at infinity Y=1 I n' n n' n n' n 1 2n 2 2n n' n n' n n' n 2 n' n n' n' n n' yp SI yp I n K y 3 P I y 2 P K 4 r 4 n' n yp n n 1 1 SI yp K K 4 n' n n' n' n n' n n' S I 2 n 2 0 K 2 n' Parabola for reflection Ellipse for air to glass Hyperbola for glass to air

16 Note S y y K y K I 2 4 P I n' n P 4 P I n' n The contribution to the structural coefficient from the aspheric cap is 2 Icap n' n 2 K For a reflecting surface is just the conic constant K

17 Icap K

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21 Spherical Mirror A spherical mirror can be treated as a convex/concave plano lens with n=-1. The plano surface acts as an unfolding flat surface contributing no aberration. X I II V L III IV T 1 2 Y Y A 4 B 0 C 1 1 D 4 E 0 F 1 n=1 n=1 n=-1

22 Field curves

23 Field curves Rt~f/3.66 Rm~f/2.66 Rs~f/1.66 Rp~f/0.66

24 Thin lens Spherical aberration and coma I II Fourth-order

25 Spherical aberration of a F/4 lens Asymmetry For high index 4 th order predicts well the aberration

26 Thin lens spherical aberration n=1.517 Y I X

27 Thin lens coma aberration n=1.517 Y II X

28 This lens Aplanatic solutions Y ' 1m ' 1m X=4 Y=5 n=1.5

29 N=1.5 N=2 N=2.5 N=3 N=3.5 N=4 Thin lens Spherical and Y=0 I II Strong index dependence

30 Thin lens special cases stop at lens

31 Thin lens special cases stop at lens

32 Thin lens special cases stop at lens For double convex lens (CX) For double concave lens (CC)

33 Thin lens special cases stop at lens

34 Thin lens special cases stop at lens

35 Achromatic doublet Two thin lenses in contact The stop is at the doublet y y Y Y Y Y

36 Achromatic doublet Correction for chromatic change of focus L 2 k k ypk, i0 yp L, k L L 1 L For an achromatic doublet: L 0

37 Achromatic doublet Correction for spherical aberration I 3 4 k k ypk, i0 yp Ik, I A X BXYCY D AX BXY CY D For a given conjugate factor Y, spherical aberration is a function Of the shape factors X 1 and X 2. For a constant value of spherical aberration we obtain a hyperbola as a function of X1 and X2.

38 Achromatic doublet Correction for coma aberration 2 k 2 k ypk, II II, k Sk I, k i0 yp II E X FY E X FY For a given conjugate factor Y and a constant amount of coma the graph of X1 and X2 is a straight line.

39 Achromatic doublet Astigmatism aberration k k 2 III III, k 2Sk II, k Sk I, k i0 1 1 III 1 2 Astigmatism is independent of the relative lens powers, shape factors, or conjugate factors.

40 Achromatic doublet Field curvature aberration IV k k i0 IV, k IV n n n For an achromatic doublet there is no field curvature if n IV 0

41 Achromatic doublet Distortion and chromatic change of magnification 2 k y P 2 3 V V, k Sk IV, k 3 III, k 3Sk II, k S k I, k i0 y Pk, k S T T, k k L, k i0 V T 0 0

42 Cemented achromatic doublet c n11 2n2 1 X X 1 X 1 c X11 1 X2 1 2 n 1 n 1 X 1 1 n n n n For achromat For a cemented achromatic lens the graph of X1 and X2 is a straight line.

43 Crown in front: BK7 and F8

44 Flint in front: BK7 and F8

45 Cemented achromatic doublet

46 Cemented doublet solutions Crown in front Flint in front

47 Lister objective

48 Lister objective Two achromatic doublets that are spaced Telecentric in image space Normalized system Ж 1 ya 1 ua 1 IA 0 0 IB

49 Lister objective The aperture stop is at the first lens. The system is telecentric B 1 y A B 1 1 y B

50 Lister objective

51 Condition for zero coma 2 k 2 k ypk, II II, k Sk I, k i0 yp y y II A A IIA B B IIB IB II yb IIA yb IIB 1 0 IIA y 2 B 1 y B 2 IIB

52 Condition for zero astigmatism k k 2 III III, k 2Sk II, k Sk I, k i0 1 y 0 III A B B IIB y y III B B IIB S k y k P, k P, k 2Ж y 2 yb yb IIB 0 2 yb 1 IIB 2 yb IIB yb yb2 yb IIA 2 1 y B

53 Lister Objective Choose: IIB IIA 2 y y B 1 y B B 2 2 yb 12y y y y B A IIA IIB 2 2 B B B y B 2 y 1 y B B 2

54 Ray diffractive law (1D)

55 Grating linear phase change m nsin I' nsin I d m ynsin I' y ynsin I y d

56 Diffractive optics high-index model 1/d

57 Diffractive optics high-index model 1/d

58 Diffractive lens (n very X=0) I II III 2 3Y 1 2Y 1 A=0 B=0 C=3 D=1 E=0 F=2 IV V L T diffractive 0

59 Mirror Systems S ypyp s s' 2Ж Y 1 s2n Y 1 s' 2 n'

60 Two mirror afocal system

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64 Two mirror systems

65 Merssene afocal system Anastigmatic Confocal paraboloids

66 Paul-Baker system Anastigmatic-Flat field Anastigmatic Parabolic primary Spherical secondary and tertiary Curved field Tertiary CC at secondary Anastigmatic, Flat field Parabolic primary Elliptical secondary Spherical tertiary Tertiary CC at secondary

67 Meinel s two stage optics concept (1985) Large Deployable Reflector Second stage corrects for errors of first stage; fourth mirror is at the exit pupil.

68 Aplanatic, Anastigmatic, Flat-field, Orthoscopic (free from distortion, rectilinear, JS 1987) Spherical primary telescope. The quaternary mirror is near the exit pupil. Spherical aberration and Coma are then corrected with a single aspheric surface. The Petzval sum is zero. If more aspheric surfaces are allowed then more aberrations can be corrected.

69 Summary Structural coefficients Basic treatment Analysis of simple systems