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Lens Aberrations andophthalmic lens design Gauri S. Shrestha, M.Optom, FIACLE                 LecturerB.P. Koirala Lions C...
IntroductionAn optical defect where rays from a point object donot form a perfect point after passing through opticalsyste...
IntroductionChromatic aberration is caused by thematerial from which the lens is made and iscaused by the material having ...
Chromatic AberrationDispersion (dispersive power)   longitudinal (axial) chromatic aberration of    an optical material: ...
Chromatic AberrationLongitudinal (axial)   Bichrome Test (Red/Green Balance)            Lens                             ...
DefinitionsDispersion is represented with thesymbol ω and called “omega”              nF - nC        ω=              nD - ...
Chromatic AberrationDispersion                                                 C = 656 nm                                 ...
Chromatic AberrationReciprocal of dispersion is the Abbénumber                 1            V=                 ω Low disp...
Chromatic AberrationLongitudinal (axial)                                                     F                            ...
Chromatic Aberration      Transverse (lateral) - lens  yTCAlens = y’C - y’F             yF TCAlens =                      ...
Chromatic Aberration    Transverse (lateral) - prism             εTCAprism =             V                 Gauri S Shresth...
Chromatic AberrationExample 1: What is the chromatic aberration of a+6.00D crown glass lens with an Abbe number of 65?    ...
Chromatic Aberration Example 2: A +5.00D lens has indices of 1.52, 1.53 and 1.54, for the C, D and F Fraunhofer lines resp...
Chromatic AberrationExample #2 continued:ω = 0.0377   V = 26.5 FD   = +0.19 D V                  Gauri S Shrestha, M.Optom...
Reduction of Chromatic     AberrationChromatic aberration cannot beeliminated in an optical elementmade of a single materi...
Reduction of Chromatic       Aberration   Achromatic lenses          r1        r1 ’                                       ...
ExampleWhat is the power of each element of a -2 Dachromatic doublet composed of glassmaterials with Abbé numbers of 60 an...
Reduction of Chromatic       Aberration   Achromatic prisms                                      ε1             ε2        ...
ExampleWhat is the power of each element of a 2∆achromatic doublet prism composed ofglass materials with Abbé numbers of 6...
IntroductionGeometrical optics assumptions Monochromatic light Rays of light involved in image formation  are confined t...
IntroductionIn 1850’s Ludwig von Seidel described 5monochromatic aberrations which affect theimage when the object is far ...
IntroductionSeidel aberrations   third-order (non-paraxial) aberrations        series expansion of sine function, where ...
IntroductionSeidel aberrationsDepends     on lens diameter, object size,   and/or lens positionIndependent     of wavele...
IntroductionMonochromatic aberrations, a.k.a.Seidel aberrations spherical aberration coma oblique astigmatism curvatur...
Spherical AberrationOccurs when a pencil of light is refracted by a large-aperture optical system, which occurs because di...
Spherical Aberration  Longitudinal spherical aberration                                                     Caustic Surfac...
Spherical Aberration  Transverse spherical aberration                                                     Confusion Discap...
Spherical AberrationOnly important for lenses of high power    (+10.00D or more)Controlled by using aspheric surfacesor   ...
Spherical aberrationLarger the pupil size, greater the difference infocusing between two raysDistance in diopters=longitud...
Correction of spherical       aberrationOccluding the periphery of lens by use ofstopsUse of Plano convex lensUse of aplan...
Spherical AberrationCorrection of SA   aspheric surfaces - also reduce oblique    astigmatism and distortion             ...
Correction of ocular    spherical aberrationAnterior corneal surface is flatter peripherally thancentre (aplanatic surface...
ComaOccurs when oblique rays are refracted by a large-aperture optical system. Affects the sharpness ofimage points.Spheri...
ComaFactors that control coma aperture size lens form angle of obliquityComposite image is not circular, butelongated l...
Treatment of Coma..By eliminating the peripheral raysLimiting rays to the axial area of lensBy using the principal axis of...
Oblique AstigmatismOccurs when oblique rays are refracted by a small-aperture system and affects both sharpness of imagepo...
Oblique AstigmatismDefinition Inability of a lens to form a point image of    an oblique point object Interval of Sturm,...
Oblique Astigmatism    Tangential & Sagittal foci and Petzval surface                                  S P                ...
Oblique AstigmatismTangential and Sagittal foci   Teacup & Saucer              Gauri S Shrestha, M.Optom, FIACLE   39
Oblique astigmatismFormation of interval of strum of line foci andcircle of least confusionManagement of Oblique astigmati...
Oblique Astigmatism    Tscherning ellipse        relationship between surface power (front         or back) and back vert...
Curvature of ImageManifests itself as a curved image surface for aflat object surface and primarily affects imagepositionA...
Curvature of Image   Definition    inability of a lens to form a plane image of     a plane object    Image surface is k...
Curvature of ImageDefinition   far-point sphere is the locus of points    conjugate to the fovea as the eye rotates,    w...
Curvature of imageAberration of curvature of image is absent   Image surface (Petzval’s surface)= far point    surface  ...
DistortionOccurs when the magnification of anextended object varies with itsdistance from the optical axis.Distortion affe...
Distortion inability of a lens to form an image of the  same shape as the object when the ratio of the image size to the...
DistortionPupil of the eye acts as a stop behind aspectacle lens pincushion (plus) M.Optom,barrel (minus) 48          Gaur...
DistortionMagnification differences may not beevident with certain objects        plus                                   m...
DistortionMainly a problem for lenses of highpowerAphakesCan be reduced with aspheric lenses            Gauri S Shrestha, ...
Gauri S Shrestha, M.Optom, FIACLE   51
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Aberrations

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Lens aberration and ophthalmic lens design

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Aberrations

  1. 1. Lens Aberrations andophthalmic lens design Gauri S. Shrestha, M.Optom, FIACLE LecturerB.P. Koirala Lions Centre for Ophthalmic Studies
  2. 2. IntroductionAn optical defect where rays from a point object donot form a perfect point after passing through opticalsystemDegrades the optical performance of a lens or prismImperfection of image formation due to severalmechanismsAberroscope-instrument for observing aberration,designed by Tscherning Gauri S Shrestha, M.Optom, FIACLE 2
  3. 3. IntroductionChromatic aberration is caused by thematerial from which the lens is made and iscaused by the material having differentrefractive indices for light of differentwavelengthMonochromatic aberrations occur whenincident light is not confined to paraxial rays Gauri S Shrestha, M.Optom, FIACLE 3
  4. 4. Chromatic AberrationDispersion (dispersive power) longitudinal (axial) chromatic aberration of an optical material: the secondary focal length of the lens is different for each of the monochromatic constituent of light Gauri S Shrestha, M.Optom, FIACLE 4
  5. 5. Chromatic AberrationLongitudinal (axial) Bichrome Test (Red/Green Balance) Lens Retina Gauri S Shrestha, M.Optom, FIACLE 5
  6. 6. DefinitionsDispersion is represented with thesymbol ω and called “omega” nF - nC ω= nD - 1 Gauri S Shrestha, M.Optom, FIACLE 6
  7. 7. Chromatic AberrationDispersion C = 656 nm d = 587 nm F = 486 nm mean dispersion = nF - nC ω= mean refractivity = nd - 1 Gauri S Shrestha, M.Optom, FIACLE 7
  8. 8. Chromatic AberrationReciprocal of dispersion is the Abbénumber 1 V= ω Low dispersion = high Abbé number Glass lenses with V > 50 crown glass Glass lenses with V < 50 flint glass Gauri S Shrestha, M.Optom, FIACLE 8
  9. 9. Chromatic AberrationLongitudinal (axial) F LCA = ωFd = V Gauri S Shrestha, M.Optom, FIACLE 9
  10. 10. Chromatic Aberration Transverse (lateral) - lens yTCAlens = y’C - y’F yF TCAlens = TCA = ω ε 0 V Gauri S Shrestha, M.Optom, FIACLE 10
  11. 11. Chromatic Aberration Transverse (lateral) - prism εTCAprism = V Gauri S Shrestha, M.Optom, FIACLE 11
  12. 12. Chromatic AberrationExample 1: What is the chromatic aberration of a+6.00D crown glass lens with an Abbe number of 65? FD Longitudinal Chromatic Aberration = V 6 = = +0.092 D 65 Gauri S Shrestha, M.Optom, FIACLE 12
  13. 13. Chromatic Aberration Example 2: A +5.00D lens has indices of 1.52, 1.53 and 1.54, for the C, D and F Fraunhofer lines respectively. What is the amount of chromatic aberration? FD Longitudinal Chromatic Aberration = VKnow nF - nC 1.54 – 1.52F = +5.00 ω= = = 0.0377 1.53 – 1.00Find V nD - 1 Gauri S Shrestha, M.Optom, FIACLE 13
  14. 14. Chromatic AberrationExample #2 continued:ω = 0.0377 V = 26.5 FD = +0.19 D V Gauri S Shrestha, M.Optom, FIACLE 14
  15. 15. Reduction of Chromatic AberrationChromatic aberration cannot beeliminated in an optical elementmade of a single materialAchromatic system--two elements(doublet) of different materials thatproduce equal but oppositedispersions Gauri S Shrestha, M.Optom, FIACLE 15
  16. 16. Reduction of Chromatic Aberration Achromatic lenses r1 r1 ’ FTOTAL = F1 + F2crownflint F1 F2 r1’ = -r1 --- +--- = 0 V1 V2 r2 r 2’ Gauri S Shrestha, M.Optom, FIACLE 16
  17. 17. ExampleWhat is the power of each element of a -2 Dachromatic doublet composed of glassmaterials with Abbé numbers of 60 and 40,respectively? V1 F1 = F TOTAL V1 - V 2 60 (-2) = -6 D F1 = 60 – 40 V2 40 F2 = F TOTAL = (-2) = +4 D V1 – V 2 60 - 40
  18. 18. Reduction of Chromatic Aberration Achromatic prisms ε1 ε2 =crown V1 V2flint ε = ε 1- ε 2 Gauri S Shrestha, M.Optom, FIACLE 18
  19. 19. ExampleWhat is the power of each element of a 2∆achromatic doublet prism composed ofglass materials with Abbé numbers of 60and 40, respectively? V1 ε1 = εTOTAL V1 - V 2 ε1 = 60 (2) = 6 p.d. 60 - 40 V2 40 ε2 = εTOTAL = (2) = 4 p.d. V1 - V 2 60 - 40
  20. 20. IntroductionGeometrical optics assumptions Monochromatic light Rays of light involved in image formation are confined to a small cylindrical region immediately surrounding the optical axis (paraxial region) Gauri S Shrestha, M.Optom, FIACLE 20
  21. 21. IntroductionIn 1850’s Ludwig von Seidel described 5monochromatic aberrations which affect theimage when the object is far enough off axisor the area of the lens used is far enoughfrom the axis Gauri S Shrestha, M.Optom, FIACLE 21
  22. 22. IntroductionSeidel aberrations third-order (non-paraxial) aberrations  series expansion of sine function, where angle α is in radians: α3 α5 α7 1st order: sin α = α - + - + … ± 10 deg 3! 5! 7! 3rd order: ± 23 deg Gauri S Shrestha, M.Optom, FIACLE 22
  23. 23. IntroductionSeidel aberrationsDepends on lens diameter, object size, and/or lens positionIndependent of wavelengthFull correction of one aberration requires correction of all previous aberrations Gauri S Shrestha, M.Optom, FIACLE 23
  24. 24. IntroductionMonochromatic aberrations, a.k.a.Seidel aberrations spherical aberration coma oblique astigmatism curvature of image distortion Gauri S Shrestha, M.Optom, FIACLE 24
  25. 25. Spherical AberrationOccurs when a pencil of light is refracted by a large-aperture optical system, which occurs because different zones of the aperture have different focal lengths. Gauri S Shrestha, M.Optom, FIACLE 25
  26. 26. Spherical Aberration Longitudinal spherical aberration Caustic Surfaceaperture LSA LSA increases with the square of aperture Gauri S Shrestha, M.Optom, FIACLE 26
  27. 27. Spherical Aberration Transverse spherical aberration Confusion Discaperture TSA TSA increases with the cube of the aperture Gauri S Shrestha, M.Optom, FIACLE 27
  28. 28. Spherical AberrationOnly important for lenses of high power (+10.00D or more)Controlled by using aspheric surfacesor using a crossed lensCrossed lens -- front surface power isgreater than the back surface power bya factor of 6 Gauri S Shrestha, M.Optom, FIACLE 28
  29. 29. Spherical aberrationLarger the pupil size, greater the difference infocusing between two raysDistance in diopters=longitudinal sphericalaberration+ve sph aberration= when peripheral rays arerefracted more than paraxial-ve =when peripheral rays are refracted lessthan paraxial.Relaxed human eye-small amount of +ve sphaberration(upto 1D for pupil of 8mm diameter) Gauri S Shrestha, M.Optom, FIACLE 29
  30. 30. Correction of spherical aberrationOccluding the periphery of lens by use ofstopsUse of Plano convex lensUse of aplanatic surfaces( peripheralcurvature less than central curvature)Use of doublet principal lens and a weakerlens of different refractive index cementedtogetherUse of aspheric lenses Gauri S Shrestha, M.Optom, FIACLE 30
  31. 31. Spherical AberrationCorrection of SA aspheric surfaces - also reduce oblique astigmatism and distortion Gauri S Shrestha, M.Optom, FIACLE 31
  32. 32. Correction of ocular spherical aberrationAnterior corneal surface is flatter peripherally thancentre (aplanatic surface)Nucleus of the lens has higher refractive indexthan the lens cortexIris acts as stop to reduce spherical aberrationPupil eliminates the marginal raysRetinal cones are much more sensitive to paraxialrays than oblique/peripheral rays Gauri S Shrestha, M.Optom, FIACLE 32
  33. 33. ComaOccurs when oblique rays are refracted by a large-aperture optical system. Affects the sharpness ofimage points.Spherical aberration occurs for beams of lightparallel to the optic axis; coma occurs for obliquebeamsRarely a problem with spectacle lenses the limiting effect ofthe pupil Gauri S Shrestha, M.Optom, FIACLE 33
  34. 34. ComaFactors that control coma aperture size lens form angle of obliquityComposite image is not circular, butelongated like coma or comet Gauri S Shrestha, M.Optom, FIACLE 34
  35. 35. Treatment of Coma..By eliminating the peripheral raysLimiting rays to the axial area of lensBy using the principal axis of lens ratherthan subsidiary axis Gauri S Shrestha, M.Optom, FIACLE 35
  36. 36. Oblique AstigmatismOccurs when oblique rays are refracted by a small-aperture system and affects both sharpness of imagepoints and image position.A.K.A. radial astigmatism; marginal astigmatismAstigmatic form for off axis object pointsAffects both sharpness of image points and image positionInability of lens to form a point image of an oblique pointobject (toric effect) Gauri S Shrestha, M.Optom, FIACLE 36
  37. 37. Oblique AstigmatismDefinition Inability of a lens to form a point image of an oblique point object Interval of Sturm, 2 line foci and the circle of least confusion Gauri S Shrestha, M.Optom, FIACLE 37
  38. 38. Oblique Astigmatism Tangential & Sagittal foci and Petzval surface S P T PT = 3 PS ST PS = 2When lens forms an image of a plane object, theimage lies along a curved surface=Petzval surface Gauri S Shrestha, M.Optom, FIACLE 38
  39. 39. Oblique AstigmatismTangential and Sagittal foci Teacup & Saucer Gauri S Shrestha, M.Optom, FIACLE 39
  40. 40. Oblique astigmatismFormation of interval of strum of line foci andcircle of least confusionManagement of Oblique astigmatism- Restricting the aperture of lenses Use of meniscus lenses than biconvex/biconcave Orientation of lens such that incident light is parallel to the principal axis Gauri S Shrestha, M.Optom, FIACLE 40
  41. 41. Oblique Astigmatism Tscherning ellipse  relationship between surface power (front or back) and back vertex power of a thin lens for which oblique astigmatism is eliminated F + F2 = -13.85 -- √ 30 – 2.87F – 0.182F2 2 Above equation determines the back surface power, F2, for a given lens power F for which there is no oblique astigmatismLimit= +7.25 to -23.00D Gauri S Shrestha, M.Optom, FIACLE 41
  42. 42. Curvature of ImageManifests itself as a curved image surface for aflat object surface and primarily affects imagepositionAffects image positionTreatment-the curvature of retina compensates for curvatureof field Gauri S Shrestha, M.Optom, FIACLE 42
  43. 43. Curvature of Image Definition  inability of a lens to form a plane image of a plane object  Image surface is known as Petzval’s surface n = index of refraction of lensrPETZVAL = -nf´ f´ = 2° focal length of the lens Gauri S Shrestha, M.Optom, FIACLE 43
  44. 44. Curvature of ImageDefinition far-point sphere is the locus of points conjugate to the fovea as the eye rotates, where rFPS = s - f’ plus lens minus lens Gauri S Shrestha, M.Optom, FIACLE 44
  45. 45. Curvature of imageAberration of curvature of image is absent Image surface (Petzval’s surface)= far point surface rFPS = s - f’= 0.027-f’ -nf’ = 0.027-f’ or f’ = 0.027/(1-n)For any lens whose power is other than -19.37Dfor COR= 27mm, little can be done to cause thePetzval surface of the lens to correspond to the farpoint sphere of the eye in the absence of obliqueastigmatism Gauri S Shrestha, M.Optom, FIACLE 45
  46. 46. DistortionOccurs when the magnification of anextended object varies with itsdistance from the optical axis.Distortion affects image shape andlateral position, but not image clarity Gauri S Shrestha, M.Optom, FIACLE 46
  47. 47. Distortion inability of a lens to form an image of the same shape as the object when the ratio of the image size to the object size has a constant value for all object sizes, no distortion exits and the condition of orthoscopy exits Gauri S Shrestha, M.Optom, FIACLE 47
  48. 48. DistortionPupil of the eye acts as a stop behind aspectacle lens pincushion (plus) M.Optom,barrel (minus) 48 Gauri S Shrestha, FIACLE
  49. 49. DistortionMagnification differences may not beevident with certain objects plus minus Gauri S Shrestha, M.Optom, FIACLE 49
  50. 50. DistortionMainly a problem for lenses of highpowerAphakesCan be reduced with aspheric lenses Gauri S Shrestha, M.Optom, FIACLE 50
  51. 51. Gauri S Shrestha, M.Optom, FIACLE 51

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