Brief outline of spectacle lens design

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2 Brief outline of spectacle lens design Effect of lens is plano-convex 2 What do we mean by power for a single vision lens?

Brief outline of spectacle lens design 30 Effect of lens is +4.25/+1.00.

3 Brief outline of spectacle lens design 30 Effect of lens is +4.25/ plano-convex 3 Power is seen to vary with the zone of lens in use

$Brief outline of spectacle lens design 30 tangential refraction +4.$

4 Brief outline of spectacle lens design 30 tangential refraction plano-convex tangential power = Effect of lens is +4.25/

5 Brief outline of spectacle lens design 30 sagittal refraction plano-convex sagittal power = Effect of lens is +4.25/

6 Brief outline of spectacle lens design

7 Brief outline of spectacle lens design /

8 Brief outline of spectacle lens design /

9 5 0 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 single vision lens oblique vertex sphere powers ocular rotation in degrees 9

10 5 0 Aspheric Lenses Brief outline of spectacle lens design ray-tracing software 40 0 FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere powers single vision lens oblique vertex sphere powers ocular rotation in degrees Field diagram 10

11 5 0 Aspheric Lenses Brief outline of spectacle lens design ray-tracing software single vision lens FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique 1.00 vertex sphere powers oblique vertex sphere powers ocular rotation in degrees Iso-cylinder plot 11

5 0 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 0.

12 5 0 Aspheric Lenses Brief outline of spectacle lens design FIELD DIAGRAMS FOR SPECTACLE LENSES Tangential & sagittal oblique vertex sphere 5 powers oblique vertex sphere powers ocular rotation in degrees single vision lens 25 Iso-cylinder plot 12

13 Brief outline of spectacle lens design ocular rotation +4.25/ (mm) S MOP T plano-convex FIELD DIAGRAM power 13 Off-axis performance of a single vision lens

14 Brief outline of spectacle lens design ocular rotation 40 0 T & S IDEAL LENS oblique powers 14 Off-axis performance of a single vision lens

15 Brief outline of spectacle lens design ocular rotation 40 0 T & S oblique powers POINT FOCAL LENS von Rohr (C. Zeiss) Off-axis performance of a single vision lens

16 Brief outline of spectacle lens design ocular rotation 40 0 S T PERCIVAL LENS Tillyer (AO) 1917 oblique powers 16 Off-axis performance of a single vision lens

17 Brief outline of spectacle lens design 40 0 S T MIN. T-ERROR FORM Davis (AO) Off-axis performance of a single vision lens

18 Brief outline of spectacle lens design 40 0 S T 40 0 T & S 40 0 S T MIN. T-ERROR FORM POINT FOCAL LENS PERCIVAL LENS 18 Off-axis performance of a single vision lens

19 40 0 T & S 40 0 pow ast POINT FOCAL LENS Astigmatism & Power Error 40 0 S T 40 0 pow ast PERCIVAL LENS Astigmatism & Power Error

20 Back curve (F 2 ) boundary values Lens power (F) Ostwalt form Ostwalt DV Wollaston DV Wollaston form Tscherning s Ellipse Minimum T-Error forms 20

21 Lens surfaces 21

22 Lens surfaces sphere Tscherning assumed the use of spherical surfaces ellipsoid No restriction due to the form with aspherical surfaces 22

23 Lens surfaces - the conicoids spherical sphere circle surface 23 ellipsoidal ellipsoid ellipse surface

24 Lens surfaces - the conicoids paraboloidal parabola surface 24 hyperboloidal hyperbolasurface

25 Lens surfaces - the conicoids produced by rotation of conic sections y paraboloid prolate ellipsoid oblate x ellipsoid F 0 = 1000(n 1) r 0 z r 0 sphere hyperboloid p represents the eccentricity equation to a conicoidal surface - x 2 +y 2 + pz 2 2r 0 z = 0 25

26 Lens surfaces - the conicoids produced by rotation of conic sections ellipsoid equation to a conicoidal surface - x 2 +y 2 + pz 2 2r 0 z = 0 26

27 Lens surfaces - the conicoids y ellipsoid 1 > p > 0 b r 0 a z eccentricity e = p = (1 e 2 ) a 2 b 2 a 2 sphere p = 1 p = b 2 a 2 p = (1 + K) equation to a conicoidal surface - x 2 +y 2 + pz 2 2r 0 z = 0 27

28 Lens surfaces - the conicoids y ellipsoid 1 > p > 0 b r 0 a p = p = p = p 0.8 = p 0.7 = 0.6 p = 0.5 z equation to a conicoidal surface - x 2 + y 2 + pz 2 2r 0 z = 0 28

29 What does an aspherical surface do? 29

30 Lens surfaces - the conicoids produced by rotation of conic sections C sphere 30

31 Lens surfaces - the conicoids produced by rotation of conic sections sphere hyperboloid 31

32 Lens surfaces - the conicoids sphere hyperboloid 32

$refracted pencil is astigmatic no$ oblique astigmatism ellipsoidal front

33 What does an aspherical surface do? An aspherical surface is astigmatic. refracted pencil is astigmatic no astigmatism spherical front surface = oblique astigmatism ellipsoidal front surface no oblique astigmatism The lens designer uses the surface astigmatism to neutralize the astigmatism of oblique incidence. 33

34 Back curve (F 2 ) Lens power (F) Ostwalt form Tscherning s Ellipse Minimum T-Error forms 34

35 -5.00 D lenses in minimum tangential-error forms p = 1 (spherical) p = (hyperboloid) p = (ellipsoidal) Ostwalt Min. T-error form p = (ellipsoidal) p = (ellipsoidal) p = 1 (spherical) Wollaston Min.T-Error form 35

36 +4.00 D lenses in minimum tangential-error forms p = 1 (spherical) p = (hyperboloid) p = (hyperboloid) n = 1.50 n = 1.50 n = 1.50 Ostwalt Min. T-error form Typical low-power aspheric lens p = (hyperboloid) p = (hyperboloid) p = (hyperboloid) 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

37 Mechanical performance of lenses -4.00D plastics aspheric lenses at mm 2.5mm 2.9mm 2.5mm 2.4mm 2.3mm 40mm 2.0 mm 1.0 mm 1.5 mm 1.2 mm 1.2 mm mm 4.7 g g 3.3 g 3.1 g 3.2 g 3.2 g

38 Higher order aspherical surfaces The equation to a conic section, y 2 = 2r o z - pz 2, can be written in the form z = y 2 r 0 + { r 02 - p y 2 } ½ Expanding by the binomial theorem produces the series : z = y 2 2r p y p2 y !.r !.r p 3 y !.r This can be written in the form : z = Ay 2 + B y 4 +Cy 6 + Dy 8 + Ey 10 + where, A = 1/2r 0, B = 1.p/2 2. 2!.r 03, etc. A series of this form is called a polynomial equation.

Essilor Omega Zeiss Aphal Rodenstock Perfastar Sola Hi-Drop z

39 Lens Surfaces - higher order aspherics Convex surface is a deformed conicoid US Patent Jun AO Fulvue Essilor Omega Zeiss Aphal Rodenstock Perfastar Sola Hi-Drop z = A 2 y 2 + A 3 y 3 +A 4 y 4 + A 5 y 5 + A 6 y 6 + A 7 y 7 + A 8 y 8 +.

40 Design Aspheric of Aspheric Lenses Lenses Stylis Lineas Nulux EP SeeMax AP Cosmolit Hypal Aspheo

41 Atoric spectacle lenses oblate elliptical section p = +3.0 oblate elliptical section p = / x 90

42 Bi-aspheric spectacle lenses? aspherical atoroidal aspherical aspherical spherical prescriptions astigmatic prescriptions -4.00/-2.00 x 180

43 Changes in vertex distance -6mm -6mm 40 0 pow ast 40 0 pow ast 40 0 pow ast aspheric lens power error & astigmatism at CRD 27mm aspheric lens power error & astigmatism at CRD 21mm Freeform aspheric lens power error & astigmatism at CRD 21mm

44 Thank you for your kind attention! Mo Jalie Ulster University Coleraine UK

Chapter 3: LENS FORM Sphere

Chapter 3: LENS FORM Sphere It can be helpful to think of very basic lens forms in terms of prisms. Recall, as light passes through a prism it is refracted toward the prism base. Minus lenses therefore