Summary of formulas Summary of optical systems

Transcription

1 Summar of formulas Summar of optical sstems Les Desig OPTI 57

2 Imagig: cetral projectio X' Y' Z' a X b Y c Z d axbyczd a X b Y c Z d axbyczd a X byczd axbyczd Colliear trasformatio Newtoia equatios Gaussia equatios Cardial poits. m m Z \ f' Z' Z' f' Z f f Z Z' f' m f m

3 Optical sstem coceptual model

4 Wave aberratio fuctio W( H, ) W W Hcos( ) W W H W W H cos( ) W H cos ( ) W H W H cos( ) W H

5

6 Chromatic coefficiets For a sstem of j surfaces For a sstem of thi leses i air j W A j j / j i j W i i j W 00 j j j A i / j W 00 i i

7 Aspheric cotributios a W C L a W 3 a W C T a W c a 4 3 A a W a

8 Stop Shiftig S I S 0 II S I S III S IV S II 0 S I S V C L 0 C T C L S IV 3SIII 3 SII SI 3

9 Structural coefficiets

10 Structural coefficiets: Thi les (stop at les) D CY BXY AX S I II S Ж EX FY III S Ж IV S Ж 0 S V L C 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

11 Miscellaeous Petzval sum: ' k ' k ' r ' For a sstem of thi leses i air: ' k Distortio H h 00 h

12 Miscellaeous Coddigto equatios ' s' s 'cos I' cos I 'cos I' t' R s cos I ' cos I' cos I t R t Sie coditio u u' si U si U '

13 Some agular quatities The memoic 345 Idex of air ~.0003 Oe arc-miute ~ Oe arc secod ~ degrees ~/4 Oe arc miute ~health ee resolutio Half degree ~Su, Moo agular subted +/- 3.4 degrees FOV of 35 mm camera with 50 mm les.

14 Magi mirror Iveted i 876 b Alphose Magi i Frace Actuall described b Newto i his descriptio about makig the mirrors for his celebrated telescope Mirror surface A Magi mirror uses a les with oe surface coated to be a mirror. Magi mirrors are used to reflect light from the light sources i lighthouses without the problem of tarishig due to the salt eviromet. Magi mirrors are variable aberratio geerators for a give optical power. The have ver useful aberratio correctig properties. Both moo-chromatic ad chromatic.

15 Telescopes Objectives Achromatic ad aplaatic doublet Apochromatic ad aplaatic doublet/triplet Schupma medial sigle glass objective

16 Review of telescopes Cassegrai Mersee Schmidt camera Maksutov Houghto Paul-Baker Offer rela Meiel s two stage optics

17 Cassegrai tpe True Cassegrai Ritche-Chretie: aplaatic Dall-Kirkham: spherical secodar Pressma-Carmichel; spherical primar Olivier Guo (o diffractio rigs)

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

19 Maksutov: Meiscus les Strog meiscus shape corrects spherical aberratio Coma b the positio of the stop ad meiscus les Chromatic chage of focus b the meiscus les thickess Sigle glass achromat j W 00 i i

20 Houghto: earl afocal doublet Same glass doublet Several solutios Correctio for spherical aberratio, coma, ad chromatic aberratios Correctio for astigmatism All spherical surfaces

21 Merssee afocal sstem Aastigmatic Cofocal paraboloids

22 Image ad Pupil Aberratio relatioships

23 Paul-Baker sstem Aastigmatic-Flat field Aastigmatic Parabolic primar Spherical secodar ad tertiar Curved field Tertiar CC at secodar Aastigmatic, Flat field Parabolic primar Elliptical secodar Spherical tertiar Tertiar CC at secodar

24 Meiel s two stage optics cocept (985) Large Deploable Reflector Secod stage corrects for errors of first stage; fourth mirror is at the exit pupil.

25 Aplaatic, Aastigmatic, Flat-field, Orthoscopic (free from distortio, rectiliear, JS 987) Spherical primar telescope. The quaterar mirror is ear the exit pupil. Spherical aberratio ad Coma are the corrected with a sigle aspheric surface. The Petzval sum is zero. If more aspheric surfaces are allowed the more aberratios ca be corrected.