Coma aberration. Lens Design OPTI 517. Prof. Jose Sasian

Transcription

1 Coma aberratio Les Desig OPTI 517

2 Coma 0.5 wave 1.0 wave.0 waves 4.0 waves Spot diagram W W W H,, W 4 H W 131 W H 3 H H cos W 3 W 00 W H cos W H H cos cos 4

3 Coma though focus

4 Cases of zero coma 1 u W131 AA y At y=0, surface is at a image A=0, O axis beam cocetric with ceter of curvature A-bar=0, Off-axis beam cocetric, chief ray goes through the ceter of curvature Aplaatic poits

5 Cases of zero coma

6 Aplaatic-cocetric Cocetric surface A=0 Aplaatic surface u 0

7 Coma as a variatio of magificatio with aperture I 1 u W131 H AA y H,

8 Coma as a variatio of magificatio with aperture II S S m=s /s

9 Sie coditio Coma aberratio ca be cosidered as a variatio of magificatio with respect to the aperture. If the paraxial magificatio is equal to the real ray margial magificatio, the a optical system would be free of coma. Spherical aberratio ca be cosidered as a variatio of the focal legth with the aperture. U U u u' si U si U '

10 Sie coditio O-axis L Sie coditio O Y Y U L' U O h Y Y L L' O h P P P P Optical path legth betwee O ad O is L axis ad does ot deped o Y or Y Optical path legth betwee y ad y is L off-axis = L axis + L - L Lhsi( U) L ' h'si( U') h ' 'si( U') hsi( U) L off-axis That is: OPD has o liear phase errors as a fuctio of field of view! = L axis + h si(u ) - h si(u) u u' si si U U '

11 Imagig a gratig si( U ) m d d si( U ) m d 'si( U ')

12 Cotributio from a aspheric surface W 1 y y 8Ay y-bar chief ray y margial ray

13 Aberratios ad symmetry W W W H,, W 4 H W 131 W 00 3 H cos W 311 H H 3 W 00 W H cos W H H cos cos 4 Coma is a odd aberratio with respect to the stop Natural stop positio to cacel coma by symmetry

14 Structural coefficiets: Thi les (stop at les) D CY BXY AX y S I II S Ж y EX FY III S Ж 1 IV S Ж 0 S V 1 y C L 0 C T 1 A 1 D B 1 1 E C 3 F r r r r c c c c X u u u u m m Y ' ' 1 1 ) 1)( ( 1 x c c c

15 Coma vs Bedig Coma II EX FY Shape factor X

16 Pricipal surface I a aplaat workig at m=0 the equivalet refractig surface is a hemisphere

17 Cassegrai s pricipal surface Sice the equivalet refractig surface i a Cassegrai telescope is a paraboloid the the coma of that Cassegrai is the same of a paraboloid mirror with the same focal legth.

18 Aplaat doublets

19 Kigslake s cemeted aplaat Chromatic correctio Spherical aberratio correctio Coma correctio Still cemeted

20 Cotrol of coma i the presece of a aspheric mirror ear a pupil I the presece of a strog aspheric surface ear the stop or pupil, coma aberratio ca be corrected by movig the surface W 1 y y 8Ay

21 Coma correctio by phatom Origial stop positio stop positio Natural stop positio S y y II S I Optical system Object plae Image plae I the presece of spherical aberratio there is a stop positio for which coma is zero. At that stop positio spherical aberratio might be corrected. The the system becomes aplaatic ad the stop ca be shifted back to its origial positio.

22 The aplaatic member(s) i a family of solutios Doublet Ritchey-Chretie

23 Camera Schmidt Aspheric plate at mirror ceter of curvature A-bar=0 Stop aperture at aspheric plate Note symmetry about mirror CC No spherical aberratio No coma No astigmatism. Aastigmatic over a wide field of view! Satisfies Corady s D-d sum

24 Notes Need to make aplaatic zero-field systems (that are fast). The aligmet becomes easier. Leses for lasers diodes/optical fibers Microscope objectives

25 Sie coditio from optical flux coservatio ad radiace theorem Etedu cosideratios

26 Sie coditio A u ' u si si U U '

27 Optical flux from a Lambertia source AL cos si d AL si si 1 cos Compare with homogeeous source AL d AL AL

28 Optical flux=radiace x throughput 0 0 ' L L T ' ' T L ' 0 0 L ' ' T L L ' L ' 0 0 U ' L ' U U' 0 0 Radiace theorem

29 Sie coditio from optical flux coservatio L ' L ' U U' 0 0 A U A U si ' 'si ' h U h U si ' ' si ' h U h U si ' ' si ' hsi U ' h 'si U ' u ' u si si U U ' Sie coditio

30 Throughput Etedu (area-omega product) A' A' ' T Ж Capacity to trasfer optical flux A 1cos

31 Eve better A' A' ' Homogeeous source A NA Asi Lambertia source

32 Etedu cosideratios are key to desig a optical system Start with the sesor at the ed A 5 5 NA

33 Summary Coma aberratio Coma as a odd aberratio Sie coditio Natural stop positio Aplaatic doublets Zero-field systems