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.