Overview of Aberrations

Transcription

1 Overview of Aberratios Les Desig OPTI 57

2 Aberratio From the Lati, aberrare, to wader from; Lati, ab, away, errare, to wader. Symmetry properties

3 Overview of Aberratios (Departures from ideal behavior) Basic reasoig Wave aberratio fuctio Aberratio coefficiets Commets Aspheric cotributios Stop shift Bedig a les

4 Wavefrot

5 Basic reasoig Ideally wavefrots ad rays coverge to Gaussia image poits. This implies that ideally wavefrots must be spherical ad rays must be homocetric.

6 Basic reasoig Actual image degradatio by a optical system implies that the colliear trasformatio ca ot model accurately imagig. I the wave picture for light propagatio we otice that wavefrots must be deformed from the ideal spherical shape. Wavefrot deformatio is determied by the use of a referece sphere with ceter at the Gaussia image poit ad passig by the exit pupil o-axis poit. Referece sphere Referece sphere is cetered at Gaussia image poit Deformed wavefrot Image plae Exit pupil

7 Basic reasoig A axially symmetric system ca oly have a axially symmetric wavefrot deformatio for a object poit o-axis. I its simplest form this deformatio ca be quadratic or quartic with respect to the aperture. If the referece sphere is cetered i the Gaussia image poit the the quadratic deformatio ca ot be preset for the desig wavelegth.

8 Basic reasoig For a object poit that is off-axis the axial symmetry of the beam is lost ad is reduced to plae symmetry. Therefore for that off-axis beam the wavefrot deformatio ca have axial, plae, or double plae symmetry.

9 Basic reasoig The simplest plae symmetric wavefrot deformatio shapes represet the primary aberratios. These are: Spherical aberratio Axially symmetric Coma Plae symmetric Astigmatism Double plae symmetric Field curvature Axially symmetric Distortio Plae symmetric Logitudial Axially symmetric chromatic Lateral Plae symmetric chromatic

10 Aberratio forms: symmetry cosideratios Distortio Focus Field curvature Focus Astigmatism Spherical aberratio Coma O-axis Spherical aberratio Off-axis

11 Wave aberratio fuctio The wave aberratio fuctio is a fuctio of the field H ad aperture vectors. Because this fuctio represets a scalar, which is the wavefrot deformatio at the exit pupil, it depeds o the dot product of the field ad aperture vectors. The assumed axial symmetry leads to a select set of terms. W W W... W H,, W H H 4 k l m, W k, l, m H cos j, m, W 3 00 W 3 H cos W 3 H H 3 W 00 W H cos W 400 H cos cos H 4 H

12 Wave aberratio fuctio The field vector has its foot at the ceter of the image plae ad the aperture vector has its foot at the ceter of the exit pupil. Both are ormalized Aperture ad field vectors Aperture vector Field vector H Optical axis Exit pupil Image plae

13 Wave aberratio fuctio Note that defocus W00 ad the chage of scale W terms are ot eeded because Gaussia optics accurately predict the locatio ad size of the image. The pisto terms W00 ad W400 represet a costat phase chage that does ot degrade the image.

14 Summary of primary aberratios

15 W W W W W Aberratio coefficiets 040 S S I A y I 8 4 u S 3 S II AAy II S III A y S III SIV Ж P 0 S IV A 3 S V u u u SV Ж PA y A SV AA y Ж AyyP

16 Aberratio coefficiets W 00 C L W C T C L Ay C T Ay

17 Aberratio coefficiets A u yc i A Ж uy uy u yc c r i P c / F d C

18 Aberratio coefficiets Ж is the Lagrage ivariat. c is the surface curvature, is the umber or reciprocal dispersive power. All with the margial ad chief ray paraxial ray traces!!! Les optimizatio started!!!

19 Commets o aberratios Third-order or fourth-order? A well corrected system has its third-order aberratios almost zero Aberratio cacellatio is the mai mechaism for image correctio Presetig to the optimizatio routie a system with its third-order aberratios corrected is a good startig poit Some simple systems are desiged by formulas that relate third-order aberratios Note symmetry i third-order aberratio coefficiets Wave aberratios seem to be simpler to uderstad tha trasverse ray aberratios

20 Example

21 Example

22 Summary of aberratios

23 Aspheric surfaces Z S cs ( K ) c S A S 4 4 A S 6 6 A S 8 8 A 0 S 0... S x y C is /r where r is the radius of curvature; K is the coic costat; A s are aspheric coefficiets Aspheric cotributio ca be thought of as a cap to the spherical part

24 Aspheric cotributios I I S a 0 S IV 0 C L II y S a y 3 V y S a y 0 C T III y S a y y c a 4 3 y A a 4 4 8

25 Aspheric cotributios II

26 Aspheric cotributios III Whe the stop is at the aspheric surface oly spherical aberratio is cotributed give that all the beams see the same portio of the surface Whe the stop is away from the surface, differet field beams pass through differet parts of the aspheric surface ad other aberratios are cotributed

27 Stop Shiftig Optical axis Exit pupil Image plae Stop shift is a chage i the locatio of the aperture stop alog the axis Stop shift does ot chage the f/# Stop shift select a differet portio of the wavefrot fro off-axis beams

28 Stop shiftig

29 Stop shiftig

30 Stop Shift S I 0 y S y S II S I III S IV S V y y S II y y 0 y y C L 0 y C y T C L S I y y y y S IV 3SIII 3 SII SI 3

31 Wave coefficiets i terms of Seidel sums W W W S I S II S III W0 SIII S 4 W 3 S V IV

32 The ratio y y Ca be calculated at ay plae i the optical system S u u y y A A u y A ew old ew old ew old S is the stop shiftig parameter

33 Structural coefficiets S 4 I y 4 p 3 I C L y p L S Жy II p II C T Ж T S III Ж III S S IV V Ж IV Ж y p 3 V y p Margial ray height at the pricipal plaes

34 Structural coefficiets: Thi les (stop at les) D CY BXY AX y S I II S Жy EX FY III S Ж IV S Ж 0 S V L C y 0 C T A D 4 B E C 3 F r r r r c c c c X u u u u m m Y ' ' ) )( ( x c c c Surface optical power

35 Bedig a les Maitais the optical power Chages the optical shape Meiscus, plaocovex, doublecovex, etc. Shape factor X c c c c r r r r

36 Usig a les desig program Must be able to iterpret correctly the iformatio displayed by the program I some istaces the program is right but we thik it is wrog. So we must carefully review our assumptios Whe there is disagreemet betwee you a the program, there is a opportuity to lear Verify that the program is modelig what you wat Check ad double check You must feel comfortable whe usig a program. Read the maual Play with the program to verify that it does what you thik it does Must reach the poit whe it is actually fu to use the program

37 Summary Review of aberratios Aspheric surfaces Stop shiftig Aberratio coefficiets Usig a les desig program Next class derivatio of coefficiets

38 Mode matchig cocept Same mode diameter Same amplitude distributio Same phase distributio Same polarizatio Same x,y,z positio Same agular positio

39 Fiber couplig efficiecy z overlap itegral x xdx m m m x m x dx z z Herwig Kogelik