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Astigmatism Field Curvature Distortion Astigmatism Field Curvature Distortion Lens Design OPTI 517 Prof. Jose Sasian Earliest through focus images T.1. Young, “On the mechanism of the eye,” Phil2. Trans Royal Soc Lond 1801; 91: 23–88 and plates. Prof. Jose Sasian Astigmatism through focus Prof. Jose Sasian Astigmatism 2 2 WH(,) W111 H cos() W 020 W200 H 4 3 22 2 22 3 4 WWHWH040 131 cos( ) 222 cos ( ) WHWHWH220 311 cos( ) 400 Prof. Jose Sasian Anastigmatic • Aplanatic: free from spherical aberration and coma. • Stigmatic ~ pointy • Astigmatism: No pointy • Anastigmatic: No-No pointy = pointy • Anastigmatic: free from spherical aberration, coma, and astigmatism • Aplanatic: coined by John Herschel • Astigmatism: coined by George Airy Prof. Jose Sasian Cases of zero astigmatism 1 2 u WAy222 2 n Prof. Jose Sasian Field behavior 2 2 2 2 2 W (H, ) W222 H cos ( ) W220 H 1 2 u 1122u WAy222 WAy220 Ж P 2 n 42n Prof. Jose Sasian Review of aberrations coefficients 1 WS 040 8 I 1 WS 131 2 II 1 WS 222 2 III 1 WS 220P 4 IV 1 WS 311 2 V 1 WC 020 2 L Prof. Jose Sasian WC111 T Structural coefficients Prof. Jose Sasian Seidel sum for thin lens (stop at lens) n 2 A 1 nn 1 2 S y 4 3 AX 2 BXY CY 2 D I 4 1 22 4n 1 S Жy EX FY B II 2 nn 1 2 SIII Ж 3n 2 C n 2 1 c1 c2 r2 r1 SIV Ж X n c1 c2 r2 r1 n 2 D 2 SV 0 1 m u'u n 1 Y 1 1 m u'u n 1 Cy 2 E L nn 1 nc (n 1)(c1 cx ) CT 0 2n 1 F n Prof. Jose Sasian Thin lens astigmatism 2 SIII Ж When the stop is a the thin lens astigmatism is fixed. Shifting the stop in the presence of spherical aberration or coma Allows changing astigmatism *2 III III2SS II I Prof. Jose Sasian Controlling astigmatism Prof. Jose Sasian 1) Stop position: singlet lens Coma and astigmatism are zero! u 0 *2 SSIII III2 SSSS II I n 1 A 0 Prof. Jose Sasian2 2) Canceling/balancing negative and positive astigmatism Prof. Jose Sasian 3-a) Adding a degree of freedom • In this case one adds a lens which contributes the opposite amount of astigmatism. • The spherical aberration and coma of the new lens are corrected by the system that has the degrees of freedom for such. • New lens hopefully contributes little coma and spherical aberration. Prof. Jose Sasian 3-b) Adding a degree of freedom Ritchey-Chretien I 1.7 waves of astigmatism @ f.3.3 At best surface (Sagittal field surface) Prof. Jose Sasian 3-c) Adding a degree of freedom Ritchey-Chretien II 0.0 waves of astigmatism @ f/1.9 after conic tweak Prof. Jose Sasian 4) Shells near the image plane (or aspheric plate) Prof. Jose Sasian Offner unit magnification relay •Offner relay system: •Three spherical mirrors •Negative unit magnification •No primary aberrations •Ring field concept •Improvement of field with shell Prof. Jose Sasian However; beware of ghosts Prof. Jose Sasian Field curvature 1 22u 1 W220 Ж PA y PC 4 n n 11 nn' Petzval sum: nn''kk11 nnr' 1 For a system of thin lenses: 'k n Prof. Jose Sasian Field curvature interpretation • Assume same glass and consider sag 22 of Petzval surface at a height y: ynny' 2' nr 2 • If the Petzval sum is zero then the lens k has constant thickness across the aperture or across the field. n 1 • Compare with the image displacement S t S caused by a plano parallel plate: n • The conclusion is that Petzval field curvature arises because the overall lens thickness variation across the aperture (in the general case the index of refraction enters as a weight). Prof. Jose Sasian Thickness variation in a telecentric lens Prof. Jose Sasian Four classical ways • 1) A thick meniscus lens can contribute optical power but no field curvature if both surfaces have the same radius. Consider double Gasuss lens. Note the correction for color. • 2) Separated thin lenses: Bulges and constrictions Consider the Cooke triplet and lenses for microlithography. • 3) A field flattener: Fully contributes to Petzval but not to spherical, coma, or astigmatism. Also there is little contribution to optical power. Consider Petzval lens with a field flattener. • 4) New achromat: use to advantage new glass types. 1 'k n Prof. Jose Sasian Four classical ways Use of a thick meniscus lens Use of a field flattener lens Prof. Jose Sasian Four classical ways Creating beam bulges and constrictions Prof. Jose Sasian Four classical ways: Use of glass V-number for flint increases V-number for crown decreases N for crown increases N for flint decreases f a a f b b F a b F=100 mm 1 'k n BK7 BK7-F2 SSKN5-LF5 P=-152 mm P=-139 mm P=-219 mm Prof. Jose Sasian Distortion 2 2 WH(,) W111 H cos() W 020 W200 H 4 3 22 2 22 3 4 WWHWH040 131 cos( ) 222 cos ( ) WHWHWH220 311 cos( ) 400 With respect to chief ray, geometrical or physical centroid W311 H3cos() W511 H5cos() Hh Distortion 100 h Prof. Jose Sasian Distortion Top row, (barrel) distortion:0%, 2.5%, 5% and 10%. Bottom row, (pincushion) distortion 0%, 2.5%, 5% and 10%. Prof. Jose Sasian 1) By Symmetry about the stop or phantom stop Distortion is an odd aberration: It can be cancelled by symmetry About the stop Prof. Jose Sasian 2) Aspheric plate or bending a field flattener Prof. Jose Sasian Exercise: Galilean telescope A plano-convex lens objective with a focal length of about 750-1000 mm. A plano-concave lens for the eyepiece (ocular) with a focal length of about 50 mm. The objective lens was stopped down to an aperture of 12.5 to 25 mm. The field of view is about 15 arc-minutes. The instrument's magnifying power is 15-20. Prof. Jose Sasian.
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