Abstract

This paper presents a new echelette optical low-pass filter that serves as a Bangerter filter (BF) for diagnosis and treatment of amblyopia and diplopia. Theoretical analysis and experimental measurements showed that echelette BFs have several advantages over the modern BFs used in medicine. Four echelette BFs with different grating periods and one BF were manufactured, and image blurring in an optical visual system with an echelette BF was experimentally investigated. The experimentally measured modulation transfer function and line spread function demonstrated definite image blurring (line expansion) that is inversely proportional to the width of the grating period. The results of measurements of the angular resolution of the optical system with an echelette BF coincide well with the results obtained by theory.

© 2013 Optical Society of America

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References

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  1. A. Davies and Ph. Fennessy, Digital Imaging for Photographers, 4th ed. (Focal, 2001).
  2. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).
  3. B. R. de Zárate and J. Tejedor, “Current concepts in the management of amblyopia,” Clin. Ophthalmol. 1, 403–414 (2007).
  4. K. A. Arnoldi, “Current recommendations for amblyopia treatment,” Am. Orthoptic J. 57, 60–67 (2007).
    [CrossRef]
  5. G. Pérez, S. M. Archer, and P. Artal, “Optical characterization of Bangerter foils,” Investig. Ophthalmol. Vis. Sci. 51, 609–613 (2010).
    [CrossRef]
  6. R. Malhotra, S.-Y. Then, A. Richards, and E. Cheek, “The effect of Bangerter occlusion foils on blepharospasm and hemifacial spasm in occlusion-positive and occlusion-negative patients,” Open Ophthalmol J. 4, 1 (2010).
  7. C. Faucher and D. de Guise, “Spasm of the near reflex triggered by disruption of normal binocular vision,” Optom. Vis. Sci. 81, 178–181 (2004).
    [CrossRef]
  8. R. P. Rutstein and G. E. Quinn, “A randomized trial of full-time Bangerter filters versus part-time daily patching for the treatment of moderate amblyopia in children,” http://ichgcp.net/clinical-trials-registry/research/index/NCT00525174 .
  9. R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
    [CrossRef]
  10. R. L. Townsend, “Spatial-frequency filter for a Kell-type color camera,” Appl. Opt. 11, 2463–2472 (1972).
    [CrossRef]
  11. M. Mino and Y. Okano, “Optical low-pass filter for a single vidicon color television camera,” J. SMPTE 81, 282–284 (1972).
    [CrossRef]
  12. P. Ewart, “Optics: the science of light 2nd year Physics FHS A2,” http://www2.physics.ox.ac.uk/sites/default/files/201119/optic_lectures_2012_pdf_11269.pdf15 .
  13. M. Kato, Y. Nakayama, and T. Suzuki, “Speckle reduction in holography with a spatially incoherent source,” Appl. Opt. 14, 1093–1099 (1975).
    [CrossRef]
  14. M. Born and E. Wolf, Principles of Optics (Pergamon, 1989).
  15. Y. Borodin, V. Petrov, and A. Lapchuk, “Optical low-pass filter for diagnosis and treatment of amblyopia and diplopia,” Ukraine Patent No. 76127 (December25, 2012).

2010 (3)

G. Pérez, S. M. Archer, and P. Artal, “Optical characterization of Bangerter foils,” Investig. Ophthalmol. Vis. Sci. 51, 609–613 (2010).
[CrossRef]

R. Malhotra, S.-Y. Then, A. Richards, and E. Cheek, “The effect of Bangerter occlusion foils on blepharospasm and hemifacial spasm in occlusion-positive and occlusion-negative patients,” Open Ophthalmol J. 4, 1 (2010).

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

2007 (2)

B. R. de Zárate and J. Tejedor, “Current concepts in the management of amblyopia,” Clin. Ophthalmol. 1, 403–414 (2007).

K. A. Arnoldi, “Current recommendations for amblyopia treatment,” Am. Orthoptic J. 57, 60–67 (2007).
[CrossRef]

2004 (1)

C. Faucher and D. de Guise, “Spasm of the near reflex triggered by disruption of normal binocular vision,” Optom. Vis. Sci. 81, 178–181 (2004).
[CrossRef]

1975 (1)

1972 (2)

M. Mino and Y. Okano, “Optical low-pass filter for a single vidicon color television camera,” J. SMPTE 81, 282–284 (1972).
[CrossRef]

R. L. Townsend, “Spatial-frequency filter for a Kell-type color camera,” Appl. Opt. 11, 2463–2472 (1972).
[CrossRef]

Archer, S. M.

G. Pérez, S. M. Archer, and P. Artal, “Optical characterization of Bangerter foils,” Investig. Ophthalmol. Vis. Sci. 51, 609–613 (2010).
[CrossRef]

Arnoldi, K. A.

K. A. Arnoldi, “Current recommendations for amblyopia treatment,” Am. Orthoptic J. 57, 60–67 (2007).
[CrossRef]

Artal, P.

G. Pérez, S. M. Archer, and P. Artal, “Optical characterization of Bangerter foils,” Investig. Ophthalmol. Vis. Sci. 51, 609–613 (2010).
[CrossRef]

Beck, R. W.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Bonsall, D. J.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1989).

Borodin, Y.

Y. Borodin, V. Petrov, and A. Lapchuk, “Optical low-pass filter for diagnosis and treatment of amblyopia and diplopia,” Ukraine Patent No. 76127 (December25, 2012).

Cheek, E.

R. Malhotra, S.-Y. Then, A. Richards, and E. Cheek, “The effect of Bangerter occlusion foils on blepharospasm and hemifacial spasm in occlusion-positive and occlusion-negative patients,” Open Ophthalmol J. 4, 1 (2010).

Cotter, S. A.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Crouch, E. R.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Davies, A.

A. Davies and Ph. Fennessy, Digital Imaging for Photographers, 4th ed. (Focal, 2001).

de Guise, D.

C. Faucher and D. de Guise, “Spasm of the near reflex triggered by disruption of normal binocular vision,” Optom. Vis. Sci. 81, 178–181 (2004).
[CrossRef]

de Zárate, B. R.

B. R. de Zárate and J. Tejedor, “Current concepts in the management of amblyopia,” Clin. Ophthalmol. 1, 403–414 (2007).

Faucher, C.

C. Faucher and D. de Guise, “Spasm of the near reflex triggered by disruption of normal binocular vision,” Optom. Vis. Sci. 81, 178–181 (2004).
[CrossRef]

Fennessy, Ph.

A. Davies and Ph. Fennessy, Digital Imaging for Photographers, 4th ed. (Focal, 2001).

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).

Holmes, J. M.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Hoover, D. L.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Kato, M.

Lapchuk, A.

Y. Borodin, V. Petrov, and A. Lapchuk, “Optical low-pass filter for diagnosis and treatment of amblyopia and diplopia,” Ukraine Patent No. 76127 (December25, 2012).

Lazar, E. L.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Leske, D. A.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Lorenzana, I. J.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Malhotra, R.

R. Malhotra, S.-Y. Then, A. Richards, and E. Cheek, “The effect of Bangerter occlusion foils on blepharospasm and hemifacial spasm in occlusion-positive and occlusion-negative patients,” Open Ophthalmol J. 4, 1 (2010).

Mino, M.

M. Mino and Y. Okano, “Optical low-pass filter for a single vidicon color television camera,” J. SMPTE 81, 282–284 (1972).
[CrossRef]

Nakayama, Y.

Okano, Y.

M. Mino and Y. Okano, “Optical low-pass filter for a single vidicon color television camera,” J. SMPTE 81, 282–284 (1972).
[CrossRef]

Pérez, G.

G. Pérez, S. M. Archer, and P. Artal, “Optical characterization of Bangerter foils,” Investig. Ophthalmol. Vis. Sci. 51, 609–613 (2010).
[CrossRef]

Petrov, V.

Y. Borodin, V. Petrov, and A. Lapchuk, “Optical low-pass filter for diagnosis and treatment of amblyopia and diplopia,” Ukraine Patent No. 76127 (December25, 2012).

Quinn, G. E.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Repka, M. X.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Richards, A.

R. Malhotra, S.-Y. Then, A. Richards, and E. Cheek, “The effect of Bangerter occlusion foils on blepharospasm and hemifacial spasm in occlusion-positive and occlusion-negative patients,” Open Ophthalmol J. 4, 1 (2010).

Rutstein, R. P.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Suh, D. W.

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Suzuki, T.

Tejedor, J.

B. R. de Zárate and J. Tejedor, “Current concepts in the management of amblyopia,” Clin. Ophthalmol. 1, 403–414 (2007).

Then, S.-Y.

R. Malhotra, S.-Y. Then, A. Richards, and E. Cheek, “The effect of Bangerter occlusion foils on blepharospasm and hemifacial spasm in occlusion-positive and occlusion-negative patients,” Open Ophthalmol J. 4, 1 (2010).

Townsend, R. L.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1989).

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).

Am. Orthoptic J. (1)

K. A. Arnoldi, “Current recommendations for amblyopia treatment,” Am. Orthoptic J. 57, 60–67 (2007).
[CrossRef]

Appl. Opt. (2)

Clin. Ophthalmol. (1)

B. R. de Zárate and J. Tejedor, “Current concepts in the management of amblyopia,” Clin. Ophthalmol. 1, 403–414 (2007).

Investig. Ophthalmol. Vis. Sci. (1)

G. Pérez, S. M. Archer, and P. Artal, “Optical characterization of Bangerter foils,” Investig. Ophthalmol. Vis. Sci. 51, 609–613 (2010).
[CrossRef]

J. SMPTE (1)

M. Mino and Y. Okano, “Optical low-pass filter for a single vidicon color television camera,” J. SMPTE 81, 282–284 (1972).
[CrossRef]

Open Ophthalmol J. (1)

R. Malhotra, S.-Y. Then, A. Richards, and E. Cheek, “The effect of Bangerter occlusion foils on blepharospasm and hemifacial spasm in occlusion-positive and occlusion-negative patients,” Open Ophthalmol J. 4, 1 (2010).

Ophthalmology (1)

R. P. Rutstein, G. E. Quinn, E. L. Lazar, R. W. Beck, D. J. Bonsall, S. A. Cotter, E. R. Crouch, J. M. Holmes, D. L. Hoover, D. A. Leske, I. J. Lorenzana, M. X. Repka, and D. W. Suh, “A randomized trial comparing Bangerter filters and patching for the treatment of moderate amblyopia in children,” Ophthalmology 117, 998–1004.e6 (2010).
[CrossRef]

Optom. Vis. Sci. (1)

C. Faucher and D. de Guise, “Spasm of the near reflex triggered by disruption of normal binocular vision,” Optom. Vis. Sci. 81, 178–181 (2004).
[CrossRef]

Other (6)

R. P. Rutstein and G. E. Quinn, “A randomized trial of full-time Bangerter filters versus part-time daily patching for the treatment of moderate amblyopia in children,” http://ichgcp.net/clinical-trials-registry/research/index/NCT00525174 .

A. Davies and Ph. Fennessy, Digital Imaging for Photographers, 4th ed. (Focal, 2001).

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice-Hall, 2002).

P. Ewart, “Optics: the science of light 2nd year Physics FHS A2,” http://www2.physics.ox.ac.uk/sites/default/files/201119/optic_lectures_2012_pdf_11269.pdf15 .

M. Born and E. Wolf, Principles of Optics (Pergamon, 1989).

Y. Borodin, V. Petrov, and A. Lapchuk, “Optical low-pass filter for diagnosis and treatment of amblyopia and diplopia,” Ukraine Patent No. 76127 (December25, 2012).

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Figures (18)

Fig. 1.
Fig. 1.

Optical scheme of the eye with spectacles and a low-pass filter on the spectacle lens surface.

Fig. 2.
Fig. 2.

Meander-type two-level diffraction grating.

Fig. 3.
Fig. 3.

Calculated point spread function of eye (ideal eye model) seeing through a diffraction grating (meander with period T = 0.7 mm and relief depth h = 10 μm ) obtained in white light by green eye receptors (by eye cones): pupil diameter d = 2.1 mm , eye diameter D = 24 mm .

Fig. 4.
Fig. 4.

Calculated point spread function of the eye (ideal eye model) seeing through slit of width W = 0.7 mm in monochrome light with λ = 0.532 μm .

Fig. 5.
Fig. 5.

Echelette grating.

Fig. 6.
Fig. 6.

Calculated line spread function (LSF) of the eye (ideal eye model) seeing through the echelette grating in coherent light.

Fig. 7.
Fig. 7.

Calculated LSF of the eye (ideal eye model) seeing through echelette grating for white light with averaging considering the green cone sensitivity of the eye: eye pupil diameter d = 2.1 mm ; eye diameter D = 24 mm .

Fig. 8.
Fig. 8.

Stair-type echelette grating.

Fig. 9.
Fig. 9.

Echelette BF structure on one transparent plate.

Fig. 10.
Fig. 10.

Echelette-type BF structure on two transparent plates.

Fig. 11.
Fig. 11.

Point spread function of optical system of eye with echelette-type BF.

Fig. 12.
Fig. 12.

MTFs of digital photographic camera with echelette-type BF.

Fig. 13.
Fig. 13.

Siemens stars photographed through echelette-type BFs with different periods T (mm).

Fig. 14.
Fig. 14.

Snellen chart photographed through echelette-type BFs with different grating periods T (mm).

Fig. 15.
Fig. 15.

Setup for measuring angular visual acuity with echelette-type BF.

Fig. 16.
Fig. 16.

Photograph of thin line taken without filter (top) and LSF (bottom).

Fig. 17.
Fig. 17.

Photograph of thin line taken with echelette BF with period T = 0.6 mm (top) and LSF (bottom).

Fig. 18.
Fig. 18.

Photograph of thin line taken by digital camera with OLPF based on meander-type grating (see Fig. 2) with period T = 0.8 mm , h = 0.1 mm (top) and LSF (bottom).

Tables (2)

Tables Icon

Table 1. Snellen Table and Echelette Period

Tables Icon

Table 2. Theoretical and Actual Angular Visual Acuity with Echelette BF

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

s · 2 λ / T 1 T 1
δ ϕ = m · δ λ / T ,
m ( n 1 ) h / λ ,
m δ λ T ( n 1 ) h λ δ λ T ( n 1 ) h T * 0.1 λ T
T = 1.22 λ / α .
D = 1.22 λ / α ,
h ( x , y ) = i = 1 Δ h * θ ( i n T ) + m = 1 Δ h * θ ( y m T ) ,
T ( x , y ) = exp j 2 π λ ( n 1 ) ( i = 1 Δ h * θ ( i n T ) ) exp j 2 π λ ( n 1 ) ( m = 1 Δ h * θ ( y m T ) ) = T 1 ( x ) * T 2 ( y ) .
I ( x , y ) I 0 sinc 2 ( π T λ F c x ) sinc 2 ( π T λ c F y ) ,

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