Introduction to aberrations OPTI 518 Lecture 13 Prof. Jose Sasian OPTI 518 Topics • Aspheric surfaces • Stop shifting • Field curve concept Prof. Jose Sasian OPTI 518 Aspheric Surfaces • Meaning not spherical • Conic surfaces: Sphere, prolate ellipsoid, hyperboloid, paraboloid, oblate ellipsoid or spheroid • Cartesian Ovals • Polynomial surfaces • Infinite possibilities for an aspheric surface • Ray tracing for quadric surfaces uses closed formulas; for other surfaces iterative algorithms are used Prof. Jose Sasian OPTI 518 Aspheric surfaces The concept of the sag of a surface 2 cS 4 6 8 10 ZS ASASASAS4 6 8 10 ... 1 1 K ( c2 1 ) 2 S Sxy222 K 2 K is the conic constant K=0, sphere K=-1, parabola C is 1/r where r is the radius of curvature; K is the K<-1, hyperola conic constant (the eccentricity squared); -1<K<0, prolate ellipsoid A’s are aspheric coefficients K>0, oblate ellipsoid Prof. Jose Sasian OPTI 518 Conic surfaces focal properties • Focal points for Ellipsoid case mirrors Hyperboloid case Oblate ellipsoid • Focal points of lenses K n2 Hecht-Zajac Optics Prof. Jose Sasian OPTI 518 Refraction at a spherical surface Aspheric surface description 2 cS 4 6 8 10 ZS ASASASAS4 6 8 10 ... 1 1 K ( c2 1 ) 2 S 1122 2222 22 y x Aicrasphe y 1 x 4 K y Zx 28rr Prof. Jose Sasian OTI 518P Cartesian Ovals ln l'n' Cte . Prof. Jose Sasian OPTI 518 Aspheric cap Aspheric surface The aspheric surface can be thought of as comprising a base sphere and an aspheric cap Cap Spherical base surface Prof. Jose Sasian OPTI 518 Aspheric surface contributions Prof. Jose Sasian OPTI 518 2 1 y Wa220 4 y Prof. Jose Sasian OPTI 518 Stop at aspheric surface 4 2 WHcap , Ayn4 Prof. Jose Sasian OPTI 518 Upon stop shifting 4 2 WHcap , Ayn4 shift shift Prof. Jose Sasian OPTI 518 Aspheric cap contributions New stop y y Old stop Prof. Jose Sasian OPTI 518 Stop shifting 4 2 WHcap , Ayn4 shift shift shift SH yy y 0 y S new old new yyy Prof. Jose Sasian OPTI 518 2 Expansion of shift shift 2 2 2SH S H H shift shift 2 2SH S H H 2 2 2 44SH S H 2 234 24S HH S HH H S HH Prof. Jose Sasian OPTI 518 Aberration function upon stop shifting for an aspheric cap 4 2 WHcap , Ayn4 shift shift 442 Ay44 n 4 Ay n S H 2 42 42 42Ay44 n S H Ay n S H H 2 43 44 4Ay44 n S H H H Ay n S H H 112 12 aaSHaSH 2 82 2 11 1 2 aS23 H H aS H H H aS4 H H 42 8 4 aAyn8 4 Prof. Jose Sasian OPTI 518 Aspheric contributions Prof. Jose Sasian OPTI 518 Aberration function of base sphere and aspheric cap WH ,,, Wspherical H Wcap H Case of an aspherical surface with the stop at the surface: 2221 24u WAyAyn040 4 8 n 222 Sag Sphere A4 x y Prof. Jose Sasian OPTI 518 Stop shifting Prof. Jose Sasian OPTI 518 Stop shifting Prof. Jose Sasian OPTI 518 Stop shifting • How do the aberration coefficients change as we shift the stop? • Used to ease calculations • Most importantly, the formulas give insights • The concept of object shifting Prof. Jose Sasian OPTI 518 Stop shifting parameter Prof. Jose Sasian OPTI 518 Stop shifting formulas Prof. Jose Sasian OPTI 518 Derivation for A Ж Ay11 Ay Ж A22y Ay 0 A12AyAyy 12 yy y A AAAS21 yy AAAS Prof. Jose Sasian OPTI 518 Derivation of new Seidel sums upon stop shifting AASA 2 u SAyI n SSII And similarly for: uu SAAyAASAyII nn uu2 SSIV IV AAy S A y nn 23 SSSSSVV IVIII 33 SSSS III SSSSII II I 2 2 uu SAyASAyIII nn 222u A 2 AAS S A y n 2 SSIII III2 SSSS II I Prof. Jose Sasian OPTI 518 Field focus curve concept 2 w Provides limit for a given wavefront variance. Prof. Jose Sasian OPTI 518 Field focus curve concept Prof. Jose Sasian OPTI 518 Field focus curve concept •Must preserve DOF Prof. Jose Sasian OPTI 518 Summary • Variety in aspheric surfaces • Aspheric surface contributions to fourth- order aberrations • Stop shifting and how aberrations change • The concept of field focus curve Prof. Jose Sasian OPTI 518.