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Aspheric Lenses Aspheric Lenses Aspheric Lenses Aspheric Lenses Brief outline of spectacle lens design Effect of lens is +4.00. +4.00 plano-convex 2 What do we mean by “power” for a single vision lens? Aspheric Lenses Brief outline of spectacle lens design 30° Effect of lens is +4.25/+1.00. +4.00 plano-convex 3 Power is seen to vary with the zone of lens in use Aspheric Lenses Brief outline of spectacle lens design 30° tangential refraction +4.00 plano-convex tangential power = +5.25 Effect of lens is +4.25/+1.00. 4 Aspheric Lenses Brief outline of spectacle lens design 30° sagittal refraction +4.00 plano-convex sagittal power = +4.25 Effect of lens is +4.25/+1.00. 5 Aspheric Lenses Brief outline of spectacle lens design +4.00 +4.00 6 Aspheric Lenses Brief outline of spectacle lens design +4.00 +4.00/+0.25 7 Aspheric Lenses Brief outline of spectacle lens design +4.00 +4.00/+0.75 8 Aspheric Lenses Brief outline of spectacle lens design +4.12/+1.00 ray-tracing software FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers 6.00 4.00 2.00 oblique vertex sphere powers sphere 0.00 5 0 40 35 30 25 20 15 10 +4.00 single vision lens ocular rotation in degrees 9 Aspheric Lenses Brief outline of spectacle lens design ray-tracing software 400 FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere 300 powers 6.00 4.00200 2.00 oblique vertex sphere powers sphere 0.00 0 10 5 0 40 35 30 25 20 15 10 ocular rotation in degrees +4.00 single vision lens 00 +3.0 +4.0 +5.0 Field diagram 10 Aspheric Lenses Brief outline of spectacle lens design ray-tracing software 25 20 15 10 5 0 5 10 15 20 25 25 20 FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique1.00 vertex sphere 15 0.75 powers0.50 10 0.25 6.00 5 0 4.00 . 5 2.00 oblique vertex 10 powers sphere 0.00 5 0 40 35 30 25 20 15 10 15 ocular rotation in degrees +4.00 single vision lens 20 25 Iso-cylinder plot 11 Aspheric Lenses Brief outline of spectacle lens design 25 20 15 10 5 0 5 10 15 20 25 25 20 1.00 0.75 15 0.50 10 FIELD DIAGRAMS0.25 FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere 5 powers 6.00 0 4.00 . 2.00 oblique vertex sphere powers sphere 0.00 5 0 5 40 35 30 25 20 15 10 ocular rotation in degrees 10 15 20 25 +4.00 single vision lens Iso-cylinder plot 12 Aspheric Lenses Brief outline of spectacle lens design ocular rotation (mm) +4.25/+1.00 S 20400 MOP 15300 T 30° +5.25 10200 +4.25 105 0 000 +3.0 +4.0 +5.0 power +4.00 FIELD DIAGRAM plano-convex 13 Off-axis performance of a single vision lens Aspheric Lenses Brief outline of spectacle lens design ocular rotation T & S 400 300 200 100 00 +3.0 +4.0 +5.0 oblique powers IDEAL LENS 14 Off-axis performance of a single vision lens Aspheric Lenses Brief outline of spectacle lens design ocular rotation T & S 400 300 200 100 +10.00 00 +3.0 +4.0 +5.0 oblique powers POINT FOCAL LENS von Rohr (C. Zeiss) 1910 15 Off-axis performance of a single vision lens Aspheric Lenses Brief outline of spectacle lens design ocular rotation S T 400 300 200 100 +7.75 00 +3.0 +4.0 +5.0 oblique powers PERCIVAL LENS Tillyer (AO) 1917 16 Off-axis performance of a single vision lens Aspheric Lenses Brief outline of spectacle lens design S T 400 300 200 100 +8.25 00 +3.0 +4.0 +5.0 MIN. T-ERROR FORM Davis (AO) 1967 17 Off-axis performance of a single vision lens Aspheric Lenses Brief outline of spectacle lens design S T T & S S T 400 400 400 300 300 300 200 200 200 100 100 100 00 00 00 +3.0 +4.0 +5.0 +3.0 +4.0 +5.0 +3.0 +4.0 +5.0 MIN. T-ERROR FORM POINT FOCAL LENS PERCIVAL LENS 18 Off-axis performance of a single vision lens Aspheric Lenses T & S pow ast 400 400 300 300 200 200 100 100 00 00 +3.0 +4.0 +5.0 -1.0 0.0 +1.0 POINT FOCAL LENS Astigmatism & Power Error S T pow ast 400 400 300 300 200 200 100 100 00 00 +3.0 +4.0 +5.0 -1.0 0.0 +1.0 PERCIVAL LENS Astigmatism & Power Error 19 Aspheric Lenses Back (F ) curve 2 -23.00 boundary values +9.25 +4.25 -9.25-50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 +5 +10 Lens power (F) -5 Ostwalt form -10 V D alt tw Os -15 V D -20 ton las Wol +17.00 -25 -22.00 -30 Wollaston form Tscherning’s Ellipse Minimum T-Error forms 20 Aspheric Lenses Lens surfaces 21 Aspheric Lenses Lens surfaces sphere ellipsoid Tscherning assumed the No restriction due to the use of spherical surfaces form with aspherical surfaces 22 Aspheric Lenses Lens surfaces - the conicoids sphericalspherecircle surface ellipsoidalellipsoidellipse surface 23 Aspheric Lenses Lens surfaces - the conicoids paraboloidalparabola surface hyperboloidalhyperbola surface 24 Aspheric Lenses Lens surfaces - the conicoids produced by rotation of conic sections y paraboloid prolate ellipsoid +10.00 oblate x ellipsoid 1000(n – 1) z F0 = r0 r0 sphere hyperboloid p represents the eccentricity 2 2 2 equation to a conicoidal surface - x +y + pz –2r0z = 0 25 Aspheric Lenses Lens surfaces - the conicoids produced by rotation of conic sections ellipsoid 2 2 2 equation to a conicoidal surface - x +y + pz –2r0z = 0 26 Aspheric Lenses Lens surfaces - the conicoids y ellipsoid 1 > p > 0 b z r0 a a2 –b2 “eccentricity” e = a2 sphere p = 1 b2 p = (1 – e2) p = a2 p = (1 + K) 2 2 2 equation to a conicoidal surface - x +y + pz –2r0z = 0 27 Aspheric Lenses Lens surfaces - the conicoids y ellipsoid 1 > p > 0 b z r0 a pp= =1 p0.9=p 0.8=p 0.7=p 0.6= 0.5 2 2 2 equation to a conicoidal surface - x + y + pz –2r0z = 0 28 Aspheric Lenses What does an aspherical surface do ? 29 Aspheric Lenses Lens surfaces - the conicoids produced by rotation of conic sections +10.00 +10.00 +10.00 C sphere 30 Aspheric Lenses Lens surfaces - the conicoids produced by rotation of conic sections +9.00 +10.00 sphere hyperboloid 31 Aspheric Lenses Lens surfaces - the conicoids +9.75 +10.00 sphere hyperboloid 32 Aspheric Lenses What does an aspherical surface do ? An aspherical surface is astigmatic. refracted pencil is astigmatic no astigmatism spherical front surface ellipsoidal front surface = oblique astigmatism no oblique astigmatism The lens designer uses the surface astigmatism to neutralize the astigmatism of oblique incidence. 33 Aspheric Lenses Back (F2) curve +4.25 -9.25 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 +5 +10 Lens power (F) -5 Ostwalt form -10 -15 -20 -25 -30 Tscherning’s Ellipse Minimum T-Error forms 34 Aspheric Lenses -5.00 D lenses in minimum tangential-error forms +4.25 0 +2.00 -9.25 p = 1 -5.00 p = - 4.8 -7.00 p = +0.39 (spherical) (hyperboloid) (ellipsoidal) Ostwalt Min. T-error form +6.00 +10.00 +17.06 -11.00 p = +1.27 -15.00 p = +1.16 -22.06 p = 1 (ellipsoidal) (ellipsoidal) (spherical) Wollaston Min.T-Error form 35 Aspheric Lenses +4.00 D lenses in minimum tangential-error forms 0.5 0.5 +8.11 p = 1 +5.42 p = -1.75 +3.95 p = -10.3 (spherical) (hyperboloid) (hyperboloid) -4.30 -1.50 0 4.3 60 3.8 60 n = 1.50 n = 1.50 n = 1.50 Ostwalt Min. T-error form Typical low-power aspheric lens 0.5 0.5 0.5 +5.44 p = -3.95 +5.45 p = -5.75 +5.45 p = -7.90 (hyperboloid) (hyperboloid) (hyperboloid) -1.50 -1.50 -1.50 3.2 60 2.9 60 2.6 60 n = 1.60 n = 1.67 n = 1.74 Typical low-power aspheric lens Typical low-power aspheric lens Typical low-power aspheric lens 36 Aspheric Lenses Mechanical performance of lenses -4.00D plastics aspheric lenses at 40 1.498 1.532 1.586 1.60 1.66 1.74 3.6mm 2.5mm 2.9mm 2.5mm 2.4mm 2.3mm 2.0 1.0 1.5 1.2 1.2 1.2 40mm mm mm mm mm mm 40mm 4.7 g 3.12.4 g 3.3 g 3.1 g 3.2 g 3.2 g Aspheric Lenses Higher order aspherical surfaces 2 2 The equation to a conic section, y = 2roz - pz , can be written in the form y2 z = 2 2 ½ r0 + { r0 - p y } Expanding by the binomial theorem produces the series : y2 1.p y4 1.3.p2 y6 1.3.5.p3 y8 z = + + + + …… 2. 3 3. 5 4. 7 2r0 2 2!.r0 2 3!.r0 2 4!.r0 This can be written in the form : z = Ay2 + B y4 +Cy6 + Dy8 + Ey10 + …… 2. 3 where, A = 1/2r0, B = 1.p/2 2!.r0 , etc. A series of this form is called a polynomial equation.
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