Abstract

Ophthalmic lenses are generally corrected for oblique astigmatic error or optimized to balance astigmatic and power errors. Distortion is not corrected in these lenses. The nature of the aspheric surface needed to minimize astigmatic error, power error, and distortion in −20-, −14-, and +14-diopter lenses was investigated using the accos V lens design programs. The best correction for the −20- and −14-diopter lenses was obtained by allowing their front and rear surfaces to become deformed ellipsoids of revolution about the minor axis. The +14-diopter front and rear lens surfaces became deformed ellipsoids of revolution about the major and minor axes, respectively. Performance data over the full field of view, corresponding to ±30° of eye rotation, are given.

© 1982 Optical Society of America

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Errata

Milton Katz, "Aspherical surfaces used to minimize oblique astigmatic error, power error, and distortion of some high positive and negative power ophthalmic lenses: erratum," Appl. Opt. 21, 4399_1-4399 (1982)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-21-24-4399_1

References

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  1. M. von Rohr, H. Boegehold, Das Brillenglass als Optisches instrument (Springer, Berlin, 1934), pp. 110–140.
  2. O. Henker, Introduction to the Theory of Spectacles, R. Kanthack, Translator (Jena School of Optics, 1924).
  3. M. Jalie, The Principles of Ophthalmic Lenses (The Association of Dispensing Opticians, London, 1977).
  4. A. G. Bennett, D. F. Edgar, “Spectacle Lens Design and Performance,” a 12-part series of articles in The Optician Part 1 (22July1979); Part 2 (31Aug.1979); Part 3 (28Sept.1979); Part 4 (26Oct.1979); Part 5 (30Nov.1979); Part 6 (25Jan.1980); Part 7 (29Feb.1980); Part 8 (28Nov.1980); Part 9 (25Apr.1980); Part 10 (27June1980); Part 11 (29Aug.1980); Part 12 (10Oct.1980).
  5. E. W. Bechtold, Am. J. Optom. Arch. Am. Acad. Optom. 35, No. 1, (1958).
    [PubMed]
  6. G. A. Fry, Am. J. Optom. Arch. Am. Acad. Optom. 55, No. 4, 238 (1978).
    [CrossRef]
  7. accos V Manual, Scientific Calculations, Inc. (1976).
  8. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 247–262.
  9. R. Kingslake, Lens Design and Fundamentals (Academic, New York, 1978), pp. 19–36.
  10. G. Smith, L. Bailey, “Aspheric Spectacle Lenses—Design and Performance,” The Optician Part 1 (10Apr.1981); Part 2 (8May1981); Part 3 (19June1981).
  11. ANSI Z80.1, Requirements for First Quality Prescription Ophthalmic Lenses (American National Standards Institute, New York, 1979).
  12. A. O. Technical Report, A Discussion of Some Optical and Cosmetic Properties of Cataract Lenses (American Optical Co., Southbridge, Mass.), p. 5.
  13. J. K. Davis, “Spectacle Lenses,” in Refraction and Clinical Optics, A. Safir, Ed. (Harper & Row, Hagerstown, Md., 1980).

1981

G. Smith, L. Bailey, “Aspheric Spectacle Lenses—Design and Performance,” The Optician Part 1 (10Apr.1981); Part 2 (8May1981); Part 3 (19June1981).

1979

A. G. Bennett, D. F. Edgar, “Spectacle Lens Design and Performance,” a 12-part series of articles in The Optician Part 1 (22July1979); Part 2 (31Aug.1979); Part 3 (28Sept.1979); Part 4 (26Oct.1979); Part 5 (30Nov.1979); Part 6 (25Jan.1980); Part 7 (29Feb.1980); Part 8 (28Nov.1980); Part 9 (25Apr.1980); Part 10 (27June1980); Part 11 (29Aug.1980); Part 12 (10Oct.1980).

1978

G. A. Fry, Am. J. Optom. Arch. Am. Acad. Optom. 55, No. 4, 238 (1978).
[CrossRef]

1958

E. W. Bechtold, Am. J. Optom. Arch. Am. Acad. Optom. 35, No. 1, (1958).
[PubMed]

Bailey, L.

G. Smith, L. Bailey, “Aspheric Spectacle Lenses—Design and Performance,” The Optician Part 1 (10Apr.1981); Part 2 (8May1981); Part 3 (19June1981).

Bechtold, E. W.

E. W. Bechtold, Am. J. Optom. Arch. Am. Acad. Optom. 35, No. 1, (1958).
[PubMed]

Bennett, A. G.

A. G. Bennett, D. F. Edgar, “Spectacle Lens Design and Performance,” a 12-part series of articles in The Optician Part 1 (22July1979); Part 2 (31Aug.1979); Part 3 (28Sept.1979); Part 4 (26Oct.1979); Part 5 (30Nov.1979); Part 6 (25Jan.1980); Part 7 (29Feb.1980); Part 8 (28Nov.1980); Part 9 (25Apr.1980); Part 10 (27June1980); Part 11 (29Aug.1980); Part 12 (10Oct.1980).

Boegehold, H.

M. von Rohr, H. Boegehold, Das Brillenglass als Optisches instrument (Springer, Berlin, 1934), pp. 110–140.

Davis, J. K.

J. K. Davis, “Spectacle Lenses,” in Refraction and Clinical Optics, A. Safir, Ed. (Harper & Row, Hagerstown, Md., 1980).

Edgar, D. F.

A. G. Bennett, D. F. Edgar, “Spectacle Lens Design and Performance,” a 12-part series of articles in The Optician Part 1 (22July1979); Part 2 (31Aug.1979); Part 3 (28Sept.1979); Part 4 (26Oct.1979); Part 5 (30Nov.1979); Part 6 (25Jan.1980); Part 7 (29Feb.1980); Part 8 (28Nov.1980); Part 9 (25Apr.1980); Part 10 (27June1980); Part 11 (29Aug.1980); Part 12 (10Oct.1980).

Fry, G. A.

G. A. Fry, Am. J. Optom. Arch. Am. Acad. Optom. 55, No. 4, 238 (1978).
[CrossRef]

Henker, O.

O. Henker, Introduction to the Theory of Spectacles, R. Kanthack, Translator (Jena School of Optics, 1924).

Jalie, M.

M. Jalie, The Principles of Ophthalmic Lenses (The Association of Dispensing Opticians, London, 1977).

Kingslake, R.

R. Kingslake, Lens Design and Fundamentals (Academic, New York, 1978), pp. 19–36.

Smith, G.

G. Smith, L. Bailey, “Aspheric Spectacle Lenses—Design and Performance,” The Optician Part 1 (10Apr.1981); Part 2 (8May1981); Part 3 (19June1981).

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 247–262.

von Rohr, M.

M. von Rohr, H. Boegehold, Das Brillenglass als Optisches instrument (Springer, Berlin, 1934), pp. 110–140.

Am. J. Optom. Arch. Am. Acad. Optom.

E. W. Bechtold, Am. J. Optom. Arch. Am. Acad. Optom. 35, No. 1, (1958).
[PubMed]

G. A. Fry, Am. J. Optom. Arch. Am. Acad. Optom. 55, No. 4, 238 (1978).
[CrossRef]

The Optician Part 1

G. Smith, L. Bailey, “Aspheric Spectacle Lenses—Design and Performance,” The Optician Part 1 (10Apr.1981); Part 2 (8May1981); Part 3 (19June1981).

A. G. Bennett, D. F. Edgar, “Spectacle Lens Design and Performance,” a 12-part series of articles in The Optician Part 1 (22July1979); Part 2 (31Aug.1979); Part 3 (28Sept.1979); Part 4 (26Oct.1979); Part 5 (30Nov.1979); Part 6 (25Jan.1980); Part 7 (29Feb.1980); Part 8 (28Nov.1980); Part 9 (25Apr.1980); Part 10 (27June1980); Part 11 (29Aug.1980); Part 12 (10Oct.1980).

Other

M. von Rohr, H. Boegehold, Das Brillenglass als Optisches instrument (Springer, Berlin, 1934), pp. 110–140.

O. Henker, Introduction to the Theory of Spectacles, R. Kanthack, Translator (Jena School of Optics, 1924).

M. Jalie, The Principles of Ophthalmic Lenses (The Association of Dispensing Opticians, London, 1977).

ANSI Z80.1, Requirements for First Quality Prescription Ophthalmic Lenses (American National Standards Institute, New York, 1979).

A. O. Technical Report, A Discussion of Some Optical and Cosmetic Properties of Cataract Lenses (American Optical Co., Southbridge, Mass.), p. 5.

J. K. Davis, “Spectacle Lenses,” in Refraction and Clinical Optics, A. Safir, Ed. (Harper & Row, Hagerstown, Md., 1980).

accos V Manual, Scientific Calculations, Inc. (1976).

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 247–262.

R. Kingslake, Lens Design and Fundamentals (Academic, New York, 1978), pp. 19–36.

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Figures (5)

Fig. 1
Fig. 1

Optical geometry of a positive ophthalmic lens. The center of rotation of the eye is at R. This represents the location of the aperture stop for the lens. Rotation of the eye through the angle θ′ dictates the slope of the chief ray in image space and the position of the image point Q′. The slope θ of the chief ray in object space is found by tracing the chief ray backward through the lens. The slope θ varies with the lens bending. The position of the paraxial image point q′ is found by taking the paraxial edge ray with slope θ through the second principal point H′. There is no bending for spherically surfaced lenses that will produce an object space chief ray slope angle θ that will cause q′ to coincide with Q′. The required chief ray angle θe is given by the slope of ray HQ′ (broken line). The design goal is to find lens surfaces that will refract an incident ray with slope θe through the center of the aperture stop (θ′ = 30°) to the point Q′ and also shift the s′ and t′ focuses to coincide at I on the far point sphere.

Fig. 2
Fig. 2

Trigometrically traced thick ophthalmic lenses corrected for astigmatic errors (point focal) are indicated by the unbroken line. A shallow (Ostwalt) form and a steep (Wollaston) form can be found for each vertex power between +6.6 and −24.6 diopters. Lenses of power greater than +6.6 diopters cannot be made point focal. The broken line indicates bendings at which these lenses exhibit minimal astigmatism. Distortion cannot be corrected for any lens power. However, the dot–dash line indicates bendings at which distortion is minimal. All the computations were made for spherically surfaced lenses made of ophthalmic crown glass and a vertex distance VR = 27 mm. Lens center thicknesses ranged from 0.5 to 9.0 mm for high minus to high plus lenses.

Fig. 3
Fig. 3

Astigmatism (OAE), power error (MOE), and distortion of −20-diopter lenses: (A) Ostwalt form; (B) Wollaston form; (C) minimum distortion form; (D) aspheric form A; (E) aspheric form B.

Fig. 4
Fig. 4

Astigmatism (OAE), power error (MOE), and distortion of −14-diopter lenses: (A) Ostwalt form; (B) Wollaston form; (C) minimum distortion form; (D) aspheric form.

Fig. 5
Fig. 5

Astigmatism (OAE), power error (MOE), and distortion of +14-diopter lenses: (A) minimum astigmatic form; (B) minimum distortion form; (C) aspheric form.

Tables (16)

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Table I Data for −20-Diopter Lenses

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Table II Oblique Astigmatism at Fractional Field Angles of −20-Dlopter Lenses

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Table III Power Error at Fractional Field Angles of −20-Diopter Lenses

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Table IV Distortion at Fractional Field Angles of −20-Diopter Lenses

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Table V Summary of Aberrations vs Field angles of −20-Diopter Aspheric Lenses

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Table VI Surface Profiles of −20-Diopter Aspherics

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Table VII Data for −14-Diopter Lenses

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Table VIII Oblique Astigmatism at Fractional Field Angles for −14-Diopter Lenses

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Table IX Power Error at Fractional Field Angles for −14-Diopter Lenses

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Table X Distortion at Fractional Field Angles for −14-Diopter Lenses

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Table XI Profiles of −14-Diopter Aspheric Lens Surfaces

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Table XII Data for +14-Diopter Lenses

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Table XIII Oblique Astigmatism at Fractional Field Angles of +14-Diopter Lenses

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Table XIV Mean Oblique Error at Fractional Field Angles of +14-Diopter Lenses

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Table XV Distortion at Fractional Field Angles of +14-Diopter Lenses

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Table XVI Surface Profile of +14-Diopter Aspheric Lens

Equations (2)

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MOE = F t + F s 2 - F .
Z = c ρ 2 / [ 1 + 1 - ( κ + 1 ) c 2 ρ 2 ] + d ρ 4 + e ρ 6 + f ρ 8 + g ρ 10 , ρ 2 = x 2 + y 2 .

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