Abstract

We demonstrate that a modified point diffraction interferometer can be used to measure the power distribution of different kinds of ophthalmic lenses such as spectacles, rigid and soft contact lenses, progressive lenses, etc. The relationship between the shape of the fringes and the power characteristics of the component being tested is simple and makes the design a very convenient and robust tool for inspection or quality control. Some simulations based on the Fresnel approximation are included.

© 2006 Optical Society of America

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References

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  1. R. N. Smartt and W. H. Steel, 'Theory and application of point diffraction interferometers,' Jpn. J. Appl. Phys. 14, 351-356 (1975).
  2. P. Naulleau, K. A. Goldberg, E. Gullikson, and J. Bokor, 'At-wavelength, system-level flare characterization of extreme ultraviolet optical systems,' Appl. Opt. 39, 2941-2947 (2000).
    [CrossRef]
  3. E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
    [CrossRef]
  4. J. S. Goldmeer, D. L. Urban, and Z. Yuan, 'Measurement of gas-phase temperatures in flames with a point diffraction interferometer,' Appl. Opt. 40, 4816-4823 (2001).
    [CrossRef]
  5. C. Koliopoulos, O. Kwon, R. Shagam, J. C. Wyant, and C. R. Hayslett, 'Infrared point diffraction interferometer,' Opt. Lett. 3, 118-120 (1978).
    [CrossRef] [PubMed]
  6. A. K. Aggarwal and S. K. Kaura, 'Further applications of point diffraction interferometer,' J. Opt. (Paris) 17, 135-138 (1986).
    [CrossRef]
  7. Q. Gong and J. M. Geary, 'Modeling point diffraction interferometers,' Opt. Eng. (Bellingham) 35, 351-356 (1996).
    [CrossRef]
  8. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1998), Chap. 8.
  9. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1998), App. III.
  10. J. J. Stamnes, Waves in Focal Regions, Adam Hilger Series on Optics and Optometrics (Hilger, 1986), Chap. 9.

2001

2000

1997

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

1996

Q. Gong and J. M. Geary, 'Modeling point diffraction interferometers,' Opt. Eng. (Bellingham) 35, 351-356 (1996).
[CrossRef]

1986

A. K. Aggarwal and S. K. Kaura, 'Further applications of point diffraction interferometer,' J. Opt. (Paris) 17, 135-138 (1986).
[CrossRef]

1978

1975

R. N. Smartt and W. H. Steel, 'Theory and application of point diffraction interferometers,' Jpn. J. Appl. Phys. 14, 351-356 (1975).

Aggarwal, A. K.

A. K. Aggarwal and S. K. Kaura, 'Further applications of point diffraction interferometer,' J. Opt. (Paris) 17, 135-138 (1986).
[CrossRef]

Batson, P. J.

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

Bokor, J.

P. Naulleau, K. A. Goldberg, E. Gullikson, and J. Bokor, 'At-wavelength, system-level flare characterization of extreme ultraviolet optical systems,' Appl. Opt. 39, 2941-2947 (2000).
[CrossRef]

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1998), Chap. 8.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1998), App. III.

Denham, P. E.

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

Geary, J. M.

Q. Gong and J. M. Geary, 'Modeling point diffraction interferometers,' Opt. Eng. (Bellingham) 35, 351-356 (1996).
[CrossRef]

Goldberg, K. A.

P. Naulleau, K. A. Goldberg, E. Gullikson, and J. Bokor, 'At-wavelength, system-level flare characterization of extreme ultraviolet optical systems,' Appl. Opt. 39, 2941-2947 (2000).
[CrossRef]

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

Goldmeer, J. S.

Gong, Q.

Q. Gong and J. M. Geary, 'Modeling point diffraction interferometers,' Opt. Eng. (Bellingham) 35, 351-356 (1996).
[CrossRef]

Gullikson, E.

Hayslett, C. R.

Kaura, S. K.

A. K. Aggarwal and S. K. Kaura, 'Further applications of point diffraction interferometer,' J. Opt. (Paris) 17, 135-138 (1986).
[CrossRef]

Koliopoulos, C.

Kwon, O.

Lee, S. H.

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

MacDowel, A. A.

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

Medecki, H.

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

Naulleau, P.

Shagam, R.

Smartt, R. N.

R. N. Smartt and W. H. Steel, 'Theory and application of point diffraction interferometers,' Jpn. J. Appl. Phys. 14, 351-356 (1975).

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions, Adam Hilger Series on Optics and Optometrics (Hilger, 1986), Chap. 9.

Steel, W. H.

R. N. Smartt and W. H. Steel, 'Theory and application of point diffraction interferometers,' Jpn. J. Appl. Phys. 14, 351-356 (1975).

Tejnil, E.

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

Urban, D. L.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1998), App. III.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1998), Chap. 8.

Wyant, J. C.

Yuan, Z.

Appl. Opt.

J. Opt. (Paris)

A. K. Aggarwal and S. K. Kaura, 'Further applications of point diffraction interferometer,' J. Opt. (Paris) 17, 135-138 (1986).
[CrossRef]

J. Vac. Sci. Technol. B

E. Tejnil, K. A. Goldberg, S. H. Lee, H. Medecki, P. J. Batson, P. E. Denham, A. A. MacDowel, and J. Bokor, 'At wavelength interferometry for extreme ultraviolet lithography,' J. Vac. Sci. Technol. B 15, 2455-2461 (1997).
[CrossRef]

Jpn. J. Appl. Phys.

R. N. Smartt and W. H. Steel, 'Theory and application of point diffraction interferometers,' Jpn. J. Appl. Phys. 14, 351-356 (1975).

Opt. Eng. (Bellingham)

Q. Gong and J. M. Geary, 'Modeling point diffraction interferometers,' Opt. Eng. (Bellingham) 35, 351-356 (1996).
[CrossRef]

Opt. Lett.

Other

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1998), Chap. 8.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1998), App. III.

J. J. Stamnes, Waves in Focal Regions, Adam Hilger Series on Optics and Optometrics (Hilger, 1986), Chap. 9.

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Figures (11)

Fig. 1
Fig. 1

(a) Basic scheme for the visualization of the phase produced by a transparent object (TO). (b) Principle of the PDI.

Fig. 2
Fig. 2

Scheme for visualization of the phase produced by an ophthalmic lens.

Fig. 3
Fig. 3

Simulated interferograms for different amounts of defocus: z ( in mm ) = (a) 5, (b) 2, (c) 0.8, (d) 0.5. In all cases a = 7 μ m , t = 0.1 , d = 5 cm , Φ = π 2 .

Fig. 4
Fig. 4

Simulated interferograms of astigmatic wavefronts: (a) z x = 5 mm , z y = 2.5 mm ; (b) z x = 5 mm , z y = 2.5 mm . In all cases a = 7 μ m , t = 0.1 , d = 5 cm , Φ = π 2 .

Fig. 5
Fig. 5

Intensity plots in the x direction for the simulated interferograms of Fig. 3 (solid curves) and in the corresponding “ideal intensity plots” (dashed curves): z ( in mm ) = (a) 5, (b) 2, (c) 0.8, (d) 0.5.

Fig. 6
Fig. 6

(a) Schematic of the simplest experimental setup. (b) Photograph of the experimental device.

Fig. 7
Fig. 7

Basic scheme for calibration of the interferometer.

Fig. 8
Fig. 8

Fit for calibration of the experimental setup: f = 2.5 mm , NA = 0.25 , t = 0.07 , λ = 0.633 μ m .

Fig. 9
Fig. 9

Interferogram for different spectacle lenses. Displacements from the center are due to displacements of the lenses as well as prism effects. (a) positive sphere, (b) negative sphere, (c) positive cylinder, (d) toric.

Fig. 10
Fig. 10

Interferogram for different soft contact lenses in saline solution. Displacements from the center are due to displacements of the lenses as well as prism effects. (a) positive sphere, (b) toric, (c) dehydrated (after one hour exposed to air).

Fig. 11
Fig. 11

Progressive lens. Note the change of sign in defocus from the upper part (far zone) to the lower part (near zone). Astigmatism near the progressive corridor is clearly visible.

Tables (1)

Tables Icon

Table 1 Range of Diopters That Can Be Solved by the HDI for Different Focusing Lenses and Pinhole Diameters a

Equations (11)

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U ( x f , y f ) P ( x f , y f ) exp [ i k 2 ( x f 2 z x + y f 2 z y ) ] ,
P ( x f , y f ) = { 1 if ( x f , y f ) lies inside the geometrically lit region at z = 0 0 elsewhere } .
U ( x , y ) [ 1 t exp ( i Φ ) ] Σ exp [ i k 2 ( x f 2 z x + y f 2 z y ) ] exp { i k 2 d [ ( x x f ) 2 + ( y y f ) 2 ] } d x f d y f + t exp ( i Φ ) P ( x f , y f ) exp [ i k 2 ( x f 2 z x + y f 2 z y ) ] exp { i k 2 d [ ( x x f ) 2 + ( y y f ) 2 ] } d x f d y f ,
[ 1 t exp ( i Φ ) ] a 2 J 1 [ ( a k r ) d ] [ ( a k r ) d ] ,
P ( x , y ) exp ( i Φ ) exp ( i σ ) t d exp [ i k 2 d ( z x x 2 ( d + z x ) + z y y 2 ( d + z y ) ) ] k [ ( d + z x ) ( d + z y ) z x z y ] 1 2 ,
P ( x , y ) = { 1 if ( x , y ) lies inside the geometrically lit region at z = d 0 elsewhere } ,
σ = { π 2 if z x z y > 0 and z x > 0 3 π 2 if z x z y < 0 and z x < 0 π if z x z y < 0 } .
I ( x , y ) a 4 J 1 2 [ ( a k r ) d ] [ ( a k r ) d ] 2 + t 2 d 2 P ( x , y ) k 2 ( d + z x ) ( d + z y ) z x z y + 2 a 2 J 1 ( a k r d ) ( a k r d ) t d P ( x , y ) k [ ( d + z x ) ( d + z y ) z x z y ] 1 2 cos { k 2 d [ z x x 2 ( d + z x ) + z y y 2 ( d + z y ) ] + Φ + σ } .
I ( x , y ) 1 + 1 + 2 cos { k 2 d [ z x x 2 ( d + z x ) + z y y 2 ( d + z y ) ] } .
m z r m 2 λ d 2
P z f 2 ( D )

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