Introductions to aberrations OPTI 517

Lecture 11

Prof. Jose Sasian OPTI 518 Spherical aberration

Prof. Jose Sasian OPTI 518 Meridional and sagittal ray fans

Prof. Jose Sasian OPTI 518 Spherical aberration 0.25 wave f/10; f=100 mm; wave=0.0005 mm

Prof. Jose Sasian OPTI 518 Spherical aberration 0.5 wave f/10; f=100 mm; wave=0.0005 mm

Prof. Jose Sasian OPTI 518 Spherical aberration 1 wave f/10; f=100 mm; wave=0.0005 mm

Prof. Jose Sasian OPTI 518 Spherical aberration is uniform over the field of view

  2 W040   

Wavefront Spots

Prof. Jose Sasian OPTI 518 Interferometric representation

5 waves

Prof. Jose Sasian OPTI 518 Cases of zero spherical aberration from a spherical surface    2 1 2  u  W040   W040  SI S I   A y  8  n  y  0 A  0 u / n  u'/ n u / n  0

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

Prof. Jose Sasian OPTI 518 Surface at image y  0

Prof. Jose Sasian OPTI 518 Concentric surface A  0

Prof. Jose Sasian OPTI 518 Aplanatic points of a spherical surface 1 1 u / n u'/ n  u / n  0    0 n's' ns n' n n'n   s' s r n'n S  r n n'n S' r n' S  2.5r S' 5/ 3 r n 1.5

Prof. Jose Sasian OPTI 518 Diffraction images

Two waves of spherical aberration Prof. Jose Sasian OPTI 518 Coma aberration

Prof. Jose Sasian OPTI 518 Meridional and sagittal ray fans

Prof. Jose Sasian OPTI 518 Roland Shack’s notes Prof. Jose Sasian OPTI 518 Coma zonal diagrams

Roland Shack’s notes Prof. Jose Sasian OPTI 518 Coma zonal diagrams

Prof. Jose Sasian OPTI 518 Spot diagrams through focus

Roland Shack’s notes Prof. Jose Sasian OPTI 518 Positive coma over the field of view

Roland Shack’s notes Prof. Jose Sasian OPTI 518 Caustic sheets

Prof. Jose Sasian OPTI 518 Coma aberration 0.25 wave f/10; f=100 mm; wave=0.0005 mm

Prof. Jose Sasian OPTI 518 Coma aberration 0.5 wave f/10; f=100 mm; wave=0.0005 mm

Prof. Jose Sasian OPTI 518 Coma aberration 1.0 wave f/10; f=100 mm; wave=0.0005 mm

Prof. Jose Sasian OPTI 518 Coma varies linearly over the field of view     W131 H    

Prof. Jose Sasian OPTI 518 Interferometric representation

5 waves

Prof. Jose Sasian OPTI 518 Cases of zero coma aberration from a spherical surface   1    W  S  u  W131 H    131 II SII   AAy  2  n  y  0 A  0 A  0 u / n  u'/ n u / n  0

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 Prof. Jose Sasian OPTI 518 Concentric surface with stop or pupils A  0

Prof. Jose Sasian OPTI 518 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Uu ' '

The first-order magnification is equal to the real marginal ray magnification

Prof. Jose Sasian OPTI 518 U U’

Prof. Jose Sasian OPTI 518 Diffraction images

2 waves 4 waves

Prof. Jose Sasian OPTI 518 Geometrical and diffraction

Prof. Jose Sasian OPTI 518 Coma

Two waves of coma through focus

Prof. Jose Sasian OPTI 518 Astigmatism aberration

Prof. Jose Sasian OPTI 518 Meridional and sagittal ray fans

Prof. Jose Sasian OPTI 518 Astigmatism

Roland Shack’s notes Prof. Jose Sasian OPTI 518 Astigmatism

Roland Shack’s notes Prof. Jose Sasian OPTI 518 Spots through focus

Prof. Jose Sasian Roland Shack’s notes OPTI 518 Quadratic (radial) Astigmatism

Prof. Jose Sasian Theoretical behavior OPTI 518 Medial focus

Prof. Jose Sasian Roland Shack’s notes OPTI 518 Astigmatism aberration 0. 25 wave f/10; f=100 mm; wave=0.0005 mm

Prof. Jose Sasian OPTI 518 Astigmatism aberration 0. 5 wave f/10; f=100 mm; wave=0.0005 mm

Prof. Jose Sasian OPTI 518 Astigmatism aberration 1.0 wave f/10; f=100 mm; wave=0.0005 mm

Prof. Jose Sasian OPTI 518 Astigmatism varies as the square of the field of view

  2 W222 H  

Prof. Jose Sasian OPTI 518 Astigmatism

Prof. Jose Sasian Roland Shack’s notes OPTI 518 Interferometric representation

5 waves

Prof. Jose Sasian OPTI 518 Cases of zero astigmatism aberration from a spherical surface

  2 1 2  u  W H   W222  S III S III   A y  222 2  n  y  0 A  0 u / n  u'/ n u / n  0

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; fredom from spherical aberration and coma

Aplanatic surface is also anastigmtaic Prof. Jose Sasian OPTI 518 Two waves of astigmatism

Prof. Jose Sasian OPTI 518 The field curves

s t

Tangential 1 2 u WAy222   Sagittal 2 n Petzval 1 22u Gaussian W220 Ж PAy   4 n

Prof. Jose Sasian OPTI 518 Field curves by an optical design program

Prof. Jose Sasian OPTI 518 Eye astigmatism

Prof. Jose Sasian OPTI 518 Diffraction images

Prof. Jose Sasian Roland Shack’s notes OPTI 518 Field curvature     W220 H  H   

Prof. Jose Sasian OPTI 518 Field curvature varies as the square of the field of view

    W220 H  H   

Prof. Jose Sasian OPTI 518 Meridional and sagittal ray fans

Prof. Jose Sasian OPTI 518 Field curvature

1 22u   1 W220 Ж PA    y PC  4 n  n

11 nn' Petzval sum:  nn''kk11 nnr'

1  For a system of thin lenses:   'k n

Prof. Jose Sasian OPTI 518 Petzval field curvature interpretation

1 2 n'n n'1 n'1 n'1 1 1  For a single lens         Petzval i1 n'nr n'r1 n'r2 n'  r1 r2 

h2 h2 n'1 1 1  h2 n'1 Multiply by or      t 2 n'  r r  2 n' 2 Petzval  1 2 

h is a given height; t is the lens sag or thickness at height h

h2 Then Is the sag of the Petzval field curvature and n'1 2 t Petzval n' is the image displacement by a parallel plate of thickness t.

Thus Petzval field curvature can be interpreted as the image shift due to a “parallel plate” of varying thickness t. Prof. Jose Sasian OPTI 518 Petzval field curvature interpretation

h2 2 t Petzval

h

t

t2

t1

Telecentric lens case Stop Field flattener case

Prof. Jose Sasian OPTI 518 Petzval field curvature: Stop at center of curvature

Prof. Jose Sasian OPTI 518 Petzval radius for a lens

1  R=t=51.852239  F=100 mm '  n Petzval radius=151.852239=nf k Bk7 glass

Prof. Jose Sasian OPTI 518 Interferometric representation

5 waves

Prof. Jose Sasian OPTI 518 Field curves vertex curvature

W y 2 znWW22'20 I   nu''22Ж 220 222 13 CWWtP4 2 220  222 Ж 2 1 CWW4   mPЖ 2 220 222 11 CWWsP4 2 220  222 Ж 2 1 CW4 PPЖ 2 220

Prof. Jose Sasian OPTI 518 Distortion     W311 H  H H  

A  u  S Ж 22PAy   1 V    W  S A  n  311 2 V  2 1  SAAyV   2 Ж Ay yP  n 

Prof. Jose Sasian OPTI 518 Distortion

2.5%, 5% and 10%

Prof. Jose Sasian OPTI 518 Distortion

Y  y Distortion  100 y

Prof. Jose Sasian OPTI 518 Interferometric representation

Prof. Jose Sasian OPTI 518 Geometrical imaging with aberrations

Spot diagram concept applied to an extended object

Prof. Jose Sasian OPTI 518 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

Prof. Jose Sasian OPTI 518 Prof. Jose Sasian OPTI 518 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

Prof. Jose Sasian OPTI 518