Abstract

We describe a modified verion of the Hartmann test in which the pattern of the holes is replaced with a circular scanning laser beam. A position-sensitive detector is used to acquire the coordinates of the deflected beam. Significant data are obtained when the Fourier transform of the detector output signals is considered. Application of this test method to the mapping of optical parameters of ophthalmic progressive addition lenses is presented. Prismatic deviation, spherical power, and astigmatism are measured with appropriate accuracy.

© 1994 Optical Society of America

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References

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  1. D. A. Atchison, “Spectacle lens design: a review,” Appl. Opt. 31, 3579–3585 (1992).
    [CrossRef] [PubMed]
  2. B. Bourdoncle, J. P. Chauveau, J. L. Mercier, “Traps in displaying optical performances of a progressive-addition lens,” Appl. Opt. 31, 3586–3593 (1992).
    [CrossRef] [PubMed]
  3. G. H. Guilino, “Design philosophy for progressive addition lenses,” Appl. Opt. 32, 111–117 (1993).
    [CrossRef] [PubMed]
  4. J. C. Wyant, F. D. Smith, “Interferometer for measuring power distribution of ophthalmic lenses,” Appl. Opt. 14, 1607–1612 (1975).
    [CrossRef] [PubMed]
  5. W. Mohr, “Interferometry and progressive lenses,” lecture presented at Gesellschaft fur angewandte Optik (German Society for Applied Optics, Eberbach, 27 May 1988.
  6. D. Malacara, Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 31, 1551–1555 (1992).
    [CrossRef]
  7. F. Francini, M. Macchiarulo, B. Tiribilli, P. K. Buah Bassuah, “Optoelectronic system for displacement and vibration measurements,” Rev. Sci. Instrum. 58, 1678–1681 (1987).
    [CrossRef]
  8. F. Francini, G. Longobardi, P. K. Buah Bassuah, “Automatic inspection with optical position sensors,” Opt. Laser Eng. 16, 49–56(1992).
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1989), Chap. 3, p. 459.

1993 (1)

1992 (4)

D. A. Atchison, “Spectacle lens design: a review,” Appl. Opt. 31, 3579–3585 (1992).
[CrossRef] [PubMed]

B. Bourdoncle, J. P. Chauveau, J. L. Mercier, “Traps in displaying optical performances of a progressive-addition lens,” Appl. Opt. 31, 3586–3593 (1992).
[CrossRef] [PubMed]

D. Malacara, Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 31, 1551–1555 (1992).
[CrossRef]

F. Francini, G. Longobardi, P. K. Buah Bassuah, “Automatic inspection with optical position sensors,” Opt. Laser Eng. 16, 49–56(1992).
[CrossRef]

1987 (1)

F. Francini, M. Macchiarulo, B. Tiribilli, P. K. Buah Bassuah, “Optoelectronic system for displacement and vibration measurements,” Rev. Sci. Instrum. 58, 1678–1681 (1987).
[CrossRef]

1975 (1)

Atchison, D. A.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1989), Chap. 3, p. 459.

Bourdoncle, B.

Buah Bassuah, P. K.

F. Francini, G. Longobardi, P. K. Buah Bassuah, “Automatic inspection with optical position sensors,” Opt. Laser Eng. 16, 49–56(1992).
[CrossRef]

F. Francini, M. Macchiarulo, B. Tiribilli, P. K. Buah Bassuah, “Optoelectronic system for displacement and vibration measurements,” Rev. Sci. Instrum. 58, 1678–1681 (1987).
[CrossRef]

Chauveau, J. P.

Francini, F.

F. Francini, G. Longobardi, P. K. Buah Bassuah, “Automatic inspection with optical position sensors,” Opt. Laser Eng. 16, 49–56(1992).
[CrossRef]

F. Francini, M. Macchiarulo, B. Tiribilli, P. K. Buah Bassuah, “Optoelectronic system for displacement and vibration measurements,” Rev. Sci. Instrum. 58, 1678–1681 (1987).
[CrossRef]

Guilino, G. H.

Longobardi, G.

F. Francini, G. Longobardi, P. K. Buah Bassuah, “Automatic inspection with optical position sensors,” Opt. Laser Eng. 16, 49–56(1992).
[CrossRef]

Macchiarulo, M.

F. Francini, M. Macchiarulo, B. Tiribilli, P. K. Buah Bassuah, “Optoelectronic system for displacement and vibration measurements,” Rev. Sci. Instrum. 58, 1678–1681 (1987).
[CrossRef]

Malacara, D.

D. Malacara, Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 31, 1551–1555 (1992).
[CrossRef]

Malacara, Z.

D. Malacara, Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 31, 1551–1555 (1992).
[CrossRef]

Mercier, J. L.

Mohr, W.

W. Mohr, “Interferometry and progressive lenses,” lecture presented at Gesellschaft fur angewandte Optik (German Society for Applied Optics, Eberbach, 27 May 1988.

Smith, F. D.

Tiribilli, B.

F. Francini, M. Macchiarulo, B. Tiribilli, P. K. Buah Bassuah, “Optoelectronic system for displacement and vibration measurements,” Rev. Sci. Instrum. 58, 1678–1681 (1987).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1989), Chap. 3, p. 459.

Wyant, J. C.

Appl. Opt. (4)

Opt. Eng. (1)

D. Malacara, Z. Malacara, “Testing and centering of lenses by means of a Hartmann test with four holes,” Opt. Eng. 31, 1551–1555 (1992).
[CrossRef]

Opt. Laser Eng. (1)

F. Francini, G. Longobardi, P. K. Buah Bassuah, “Automatic inspection with optical position sensors,” Opt. Laser Eng. 16, 49–56(1992).
[CrossRef]

Rev. Sci. Instrum. (1)

F. Francini, M. Macchiarulo, B. Tiribilli, P. K. Buah Bassuah, “Optoelectronic system for displacement and vibration measurements,” Rev. Sci. Instrum. 58, 1678–1681 (1987).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1989), Chap. 3, p. 459.

W. Mohr, “Interferometry and progressive lenses,” lecture presented at Gesellschaft fur angewandte Optik (German Society for Applied Optics, Eberbach, 27 May 1988.

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Figures (7)

Fig. 1
Fig. 1

Method used for testing a lens element by a circular scanning laser beam.

Fig. 2
Fig. 2

Mechanical movements of the lens with respect to scanning the laser beam. PSD, Position-sensitive detector.

Fig. 3
Fig. 3

Ray deviation and spot coordinates on the detector plane.

Fig. 4
Fig. 4

Plot of the laser beam position on the position-sensitive detector with ρ = 1 mm and L = 100 mm for the following conditions: a, spherical power, E tot = 0; b, astigmatism, ϕ = π/4, E tot = 0; c, astigmatism, ϕ = 3π/4, E tot = 0; c, coma and astigmatism, ϕ = π/2, E tot = 0.5.

Fig. 5
Fig. 5

Map of the astigmatism of a progressive lens in the case of the addition of 3 D. Each ring is spaced 6 deg apart.

Fig. 6
Fig. 6

Map of the prismatic deviation of a progressive lens when 3 D is added.

Fig. 7
Fig. 7

Progression of the lens correction from distant to near vision when 3 D is added. The measurement refers to the geometrical center of the lens.

Equations (28)

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W = P x ξ + P y η + 1 2 S ( ξ 2 + η 2 ) + 1 2 C ( ξ sin ϕ - η cos ϕ ) 2 ,
C = 1 F 1 - 1 F 2 ;
x = ξ - T a x ,
y = η - T a y ,
W / ξ = P x + S ξ + C ( ξ sin ϕ - η cos ϕ ) sin ϕ ,
W / η = P y + S η + C ( ξ sin ϕ - η cos ϕ ) sin ϕ .
ξ ( t ) = ρ cos ω t ,
η ( t ) = ρ sin ω t ,
x ( t ) = ρ cos ( ω t ) - L { P x + S [ ρ cos ( ω t ) ] + C [ ρ cos ( ω t ) sin ϕ - ρ sin ( ω t ) cos ϕ ] sin ϕ } ,
y ( t ) = ρ sin ( ω t ) - L { P y + S [ ρ sin ( ω t ) ] - C [ ρ cos ( ω t ) sin ϕ - ρ sin ( ω t ) cos ϕ ] cos ϕ } .
x ( t ) = a 0 x + a 1 x cos ω t + b 1 x sin ω t + a 2 x cos 2 ω t + b 2 x sin 2 ω t + ,
y ( t ) = a 0 y + a 1 y cos ω t + b 1 y sin ω t + a 2 y cos 2 ω t + b 2 y sin 2 ω t + .
a 0 x = x ( t ) = - L P x ,
a 0 y = y ( t ) = - L P y ,
a 1 x = 2 x ( t ) cos ω t = ρ ( 1 - L S - L C sin 2 ϕ ) ,
b 1 x = 2 x ( t ) sin ω t = ρ L C sin ϕ cos ϕ ,
a 1 y = 2 y ( t ) cos ω t = ρ L C sin ϕ cos ϕ ,
b 1 y = 2 y ( t ) sin ω t = ρ ( 1 - L S - L C cos 2 ϕ ) ,
f ( t ) = 1 / T T / 2 T / 2 f ( t ) d t .
P x = - a 0 x / L ,
P y = - a 0 y / L .
C = [ ( a 1 x - b 1 y ) 2 + ( b 1 x - a 1 y ) 2 ] 1 / 2 ρ L ,
tan 2 ϕ = ( b 1 x + a 1 y ) / ( a 1 x - b 1 y ) .
S = 1 L ρ [ ρ - 1 2 ρ L C - 1 2 ( b 1 y + a 1 x ) ] .
E x 2 = [ x ( t ) - a 0 x - a 1 x cos ω t - b 1 x sin ω t ] 2 ,
E x 2 = x 2 ( t ) - a 0 x 2 - 1 2 a 1 x 2 - 1 2 b 1 x 2 ,
E y 2 = y 2 ( t ) - a 0 y 2 - 1 2 a 1 y 2 - 1 2 b 1 y 2 .
E tot = ( E x 2 + E y 2 ) 1 / 2

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