Astigmatism Field Curvature Distortio Les Desig OPTI 57
. Phil Earliest through focus images.t. Youg, O the mechaism of the eye, Tras Royal Soc Lod 80; 9: 3 88 ad plates.
Astigmatism through focus
Astigmatism W( H, ) W Hcos( ) W W H 00 00 4 3 3 W W H cos( ) W H cos ( ) W H W H cos( ) W H 040 3 0 3 400 4
Aastigmatic Aplaatic: free from spherical aberratio ad coma. Stigmatic ~ poity Astigmatism: No poity Aastigmatic: No-No poity = poity Aastigmatic: free from spherical aberratio, coma, ad astigmatism Aplaatic: coied by Joh Herschel Astigmatism: coied by George Airy
Cases of zero astigmatism u W A y
W Field behavior ( H, ) W H cos ( ) W 0H u W A y u 4 W0 A y Ж P
Review of aberratios coefficiets 040 3 0 3 00 8 4 I II III P IV V L T W S W S W S W S W S W C W C
Structural coefficiets
Seidel sum for thi les (stop at les) D CY BXY AX y S I 3 4 4 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
Thi les astigmatism SIII Ж Whe the stop is a the thi les astigmatism is fixed. Shiftig the stop i the presece of spherical aberratio or coma Allows chagig astigmatism S S * III III II I
Cotrollig astigmatism
) Stop positio: siglet les A u 0 Coma ad astigmatism are zero! 0 S S SS S S * III III II I
) Cacelig/balacig egative ad positive astigmatism
3-a) Addig a degree of freedom I this case oe adds a les which cotributes the opposite amout of astigmatism. The spherical aberratio ad coma of the ew les are corrected by the system that has the degrees of freedom for such. New les hopefully cotributes little coma ad spherical aberratio.
3-b) Addig a degree of freedom Ritchey-Chretie I.7 waves of astigmatism @ f.3.3 At best surface (Sagittal field surface)
3-c) Addig a degree of freedom Ritchey-Chretie II 0.0 waves of astigmatism @ f/.9 after coic tweak
4) Shells ear the image plae (or aspheric plate)
Offer uit magificatio relay Offer relay system: Three spherical mirrors Negative uit magificatio No primary aberratios Rig field cocept Improvemet of field with shell
However; beware of ghosts
Field curvature u P C k W0 Ж PA y 4 i i Petzval sum: k ' ' ' i ' r i For a system of thi leses: ' k i i i k is the umber of surfaces i the system r is the surface vertex radius of curvature ρ is the object surface radius of curvature ρ is the image surface radius of curvature
Field curvature iterpretatio Assume same glass ad cosider sag of Petzval surface at a height y: If the Petzval sum is zero the the les has costat thickess across the aperture or across the field. Compare with the image displacemet S caused by a plao parallel plate: y ' y ' r k S t The coclusio is that Petzval field curvature arises because the overall les thickess variatio across the aperture (i the geeral case the idex of refractio eters as a weight).
Thickess variatio i a telecetric les
Four classical ways ) A thick meiscus les ca cotribute optical power but o field curvature if both surfaces have the same radius. Cosider double Gasuss les. Note the correctio for color. ) Separated thi leses: Bulges ad costrictios Cosider the Cooke triplet ad leses for microlithography. 3) A field flatteer: Fully cotributes to Petzval but ot to spherical, coma, or astigmatism. Also there is little cotributio to optical power. Cosider Petzval les with a field flatteer. 4) New achromat: use to advatage ew glass types. ' k
Four classical ways Use of a thick meiscus les Use of a field flatteer les
Four classical ways Creatig beam bulges ad costrictios
Four classical ways: Use of glass V-umber for flit icreases V-umber for crow decreases N for crow icreases N for flit decreases f a a f b b F a b F=00 mm BK7 P=-5 mm BK7-F P=-39 mm SSKN5-LF5 P=-9 mm ' k
Distortio W( H, ) W Hcos( ) W W H 00 00 4 3 3 W W H cos( ) W H cos ( ) W H W H cos( ) W H 040 3 0 3 400 4 With respect to chief ray, geometrical or physical cetroid W3 H3cos() W5 H5cos() Distortio H h h 00
Distortio Top row, (barrel) distortio:0%,.5%, 5% ad 0%. Bottom row, (picushio) distortio 0%,.5%, 5% ad 0%.
) By Symmetry about the stop or phatom stop Distortio is a odd aberratio: It ca be cacelled by symmetry About the stop
) Aspheric plate or bedig a field flatteer
Exercise: Galilea telescope A plao-covex les objective with a focal legth of about 750-000 mm. A plao-cocave les for the eyepiece (ocular) with a focal legth of about 50 mm. The objective les was stopped dow to a aperture of.5 to 5 mm. The field of view is about 5 arc-miutes. The istrumet's magifyig power is 5-0.