Introductions to aberrations OPTI 517

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1 Introductions to aberrations OPTI 517 Lecture 11

2 Spherical aberration

3 Meridional and sagittal ray fans

4 Spherical aberration 0.25 wave f/10; f=100 mm; wave= mm

5 Spherical aberration 0.5 wave f/10; f=100 mm; wave= mm

6 Spherical aberration 1 wave f/10; f=100 mm; wave= mm

7 Spherical aberration is uniform over the field of view W Wavefront Spots

8 Interferometric representation 5 waves

9 Cases of zero spherical aberration W from a spherical surface W y 0 A S I u A y n S I 2 u/ n u'/ n' u/ n0 y=0 the aperture is zero or the surface is at an image A=0 the surface is concentric with the Gaussian image point on axis u /n-u/n=0 the conjugates are at the aplanatic points Aplanatic means free from error; freedom from spherical aberration and coma

10 Surface at image y 0

11 Concentric surface A 0

12 Aplanatic points of a spherical surface / ' 2.5 ' ' ' ' ' ' ' 0 1 ' ' 1 n r S r S n n n r S n n n r S r n n s n s n ns s n 0 / / ' / n u n u n u

13 Diffraction images Two waves of spherical aberration

14 Coma aberration

15 Meridional and sagittal ray fans

16 Roland Shack s notes

17 Coma zonal diagrams

18 Spot diagrams through focus Roland Shack s notes

19 Coma zonal diagrams Roland Shack s notes

20 Positive coma over the field of view Roland Shack s notes

21 Caustic sheets

22 Coma aberration 0.25 wave f/10; f=100 mm; wave= mm

23 Coma aberration 0.5 wave f/10; f=100 mm; wave= mm

24 Coma aberration 1.0 wave f/10; f=100 mm; wave= mm

25 Coma varies linearly over the field W 131 of view H

26 Interferometric representation 5 waves

27 Cases of zero coma aberration from a spherical surface W 131 H y 0 A 0 A W S II S II u/ n u'/ n' u/ n0 u AAy n y=0 the aperture is zero or the surface is at an image A=0 the surface is concentric with the Gaussian image point on axis Abar=0 surface is concentric with stop or pupils u /n-u/n=0 the conjugates are at the aplanatic points Aplanatic means free from error; freedom from spherical aberration and coma

28 Concentric surface with stop or pupils A 0

29 Sine condition In the absence of spherical aberration there are no linear phase errors that depend on the field of view if the sine condition is met: sin U u sin U' u' The first-order magnification is equal to the real marginal ray magnification

30 U U

31 Diffraction images 2 waves 4 waves

32 Geometrical and diffraction

33 Coma Two waves of coma through focus

34 Astigmatism aberration

35 Meridional and sagittal ray fans

36 Astigmatism Roland Shack s notes

37 Astigmatism Roland Shack s notes

38 Spots through focus Roland Shack s notes

39 Quadratic (radial) Astigmatism Theoretical behavior

40 Medial focus Roland Shack s notes

41 Astigmatism aberration wave f/10; f=100 mm; wave= mm

42 Astigmatism aberration 0. 5 wave f/10; f=100 mm; wave= mm

43 Astigmatism aberration 1.0 wave f/10; f=100 mm; wave= mm

44 Astigmatism varies as the square of the field of view W 222 H 2

45 Astigmatism Roland Shack s notes

46 Interferometric representation 5 waves

47 Cases of zero astigmatism aberration from a spherical surface W 222 H 2 y A W S III u/ n u'/ n' u/ n0 u A y n S III 2 y=0 the aperture is zero or the surface is at an image Abar=0 surface is concentric with stop or pupils u /n-u/n=0 the conjugates are at the aplanatic points Aplanatic means free from error; freedom from spherical aberration and coma. Aplanatic spherical surface is also anastigmatic Anastigmatic: free from spherical, coma and astigmatism 1 2

48 Two waves of astigmatism

49 The field curves t s W u A y 2 n 1 u 4 n 2 2 W220 Ж P A y Tangential Sagittal Petzval Gaussian

50 Field curves by an optical design program

51 Eye astigmatism

52 Diffraction images Roland Shack s notes

53 Field curvature W 220 H H

54 Field curvature varies as the square of the field of view W 220 H H

55 Meridional and sagittal ray fans

56 Field curvature 1 4 u n P C 2 2 W220 Ж PA y 1 n Petzval sum: k 1 1 n' n n' ' n i1 n' nr k k 1 1 For a system of thin lenses In air: 1 ' k k i n i1 i

57 Petzval field curvature interpretation For a single lens Petzval nnr ' nr ' nr ' n' r r 2 1 n' n n' 1 n' 1 n' i Multiply by 2 h 2 or 2 2 h n' 11 1 h n' 1 t 2 Petzval n' r1 r2 2 n' h is a given height; t is the lens sag or thickness at height h Then h 2 2 Petzval Is the sag of the Petzval field curvature and is the image displacement by a parallel plate of thickness t. n'1 t n' Thus Petzval field curvature can be interpreted as the image shift due to a parallel plate of varying thickness t.

58 Petzval field curvature interpretation t h 2 2 Petzval h t t 2 t 1 Stop Telecentric lens case Field flattener case

59 Petzval field curvature: Stop at center of curvature

60 Petzval radius for a lens 1 ' k n R=t= F=100 mm Petzval radius= =nf Bk7 glass

61 Interferometric representation 5 waves

62 Field curves vertex curvature 2 W020 yi z 2 2 n' W 2 2 nu ' ' Ж 2z 1 4 n' W020 y Ж 2 2 I n ' 3 Ct 4 2 W W Ж 2 n' Cm 4 2 W W Ж n' 1 Cs 4 W W 2 Ж 2 n' CP 4 W 2 220P Ж 220P P P

W 311 Distortion H H H W 311 1 2 S V A u

63 W 311 Distortion H H H W S V A u A n 2 2 SV Ж P A y 1 n 2 SV A A y Ж Ay yp 2

64 Distortion 2.5%, 5% and 10%

65 Distortion Distortion Y y y 100

66 Interferometric representation

67 Geometrical imaging with aberrations Spot diagram concept applied to an extended object

68 Parity of the aberrations The aberrations can be classified as even and odd aberrations. Spherical aberration, astigmatism, field curvature, and longitudinal color are even aberrations. Coma, distortion, and transverse color are odd aberrations. The parity is found by observation of the algebraic power s parity of the field and aperture vectors in the aberration coefficients. The odd aberrations have the important property that in a symmetrical system they Cancel (fourth-order), each half contributes the same amount of aberration but with opposite algebraic sign. The symmetry is about the aperture stop. In comparison in a symmetrical system the even aberrations from each half of the system add, rather than cancel

70 Summary Discussion of the primary aberrations Use of several types of plots Main point is to gain understanding and familiarity Must be able to recognize the aberrations under a variety of representations. Must be able to appreciate how the ideal image degrades in the presence of aberration

Advanced Lens Design

Advanced Lens Design Lecture 3: Aberrations I 214-11-4 Herbert Gross Winter term 214 www.iap.uni-jena.de 2 Preliminary Schedule 1 21.1. Basics Paraxial optics, imaging, Zemax handling 2 28.1. Optical systems