Abstract

In this work, a conical corneal null-screen topographer is presented. The device is designed to adapt to the human morphology of the face and measures the human cornea assuming that its shape is an aspherical surface. The evaluation of the performance of the conical null-screen corneal topographer includes calibration of the device and evaluation and compensation of the distortion introduced by the lens used to acquire the images. For the calibration of the device we perform the evaluation of a spherical reference surface of 7.8 mm radius of curvature and 11 mm in diameter. Here we obtain an rms difference in sagitta between the evaluated surface and the best fitting sphere of about 2.1 μm. We present examples of surface topography measurements on some human corneas. Elevation, sagittal curvature, and meridional curvature maps can be calculated. Other geometrical parameters such as the radius of curvature and the conic constant are obtained. Results of the corneal surface topography were compared with commercial Placido-based corneal topography device.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. M. Kaschke, K. H. Donnerhacke, and M. S. Rill, Optical Devices in Ophthalmology and Optometry. Technology, Design Principles, and Clinical Applications, (Wiley-VCH, 2014).
  2. M. Collins, S. Vincent, and S. Read, “The cornea,” in Handbook of visual optics, Vol. 1, P. Artal, ed. (CRC press, 2017).
  3. W. D. Furlan, “Basic ophthalmic instruments,” in Handbook of visual optics, Vol. 1, P. Artal, ed. (CRC press, 2017).
  4. K. Karnowski, B. J. Kaluzny, M. Szkulmowski, M. Gora, and M. Wojtkowski, “Corneal topography with high-speed swept source OCT in clinical examination,” Biomed. Opt. Express 2(9), 2709–2720 (2011).
    [Crossref]
  5. S. Ortiz, D. Siedlecki, P. Pérez-Merino, N. Chia, A. de Castro, M. Szkulmowski, M. Wojtkowski, and S. Marcos, “Corneal topography from spectral optical coherence tomography (sOCT),” Biomed. Opt. Express 2(12), 3232–3247 (2011).
    [Crossref]
  6. I. Grulkowski, “Anterior segment OCT,” in Handbook of visual optics, Vol. 2, P. Artal, ed. (CRC press, 2017).
  7. W. Tang, M. J. Collins, L. Carney, and B. Davis, “The Accuracy and Precision Performance of Four Videokeratoscopes in Measuring Test Surfaces,” Optom. Vis. Sci. 77(9), 483–491 (2000).
    [Crossref]
  8. R. Díaz-Uribe and M. Campos-García, “Null screen testing of fast convex aspheric surfaces,” Appl. Opt. 39(16), 2670–2677 (2000).
    [Crossref]
  9. M. Campos- García, R. Bolado-Gómez, and R. Díaz-Uribe, “Testing fast aspheric concave surfaces with a cylindrical null screen,” Appl. Opt. 47(6), 849–859 (2008).
    [Crossref]
  10. M. Avendaño-Alejo, V. I. Moreno-Oliva, M. Campos-García, and R. Díaz-Uribe, “Quantitative evaluation of an off-axis parabolic mirror by using a tilted null screen,” Appl. Opt. 48(5), 1008–1015 (2009).
    [Crossref]
  11. M. Campos-García, A. Estrada-Molina, and R. Díaz-Uribe, “New null-screen design for corneal topography,” Proc. SPIE 8011, 801124 (2011).
    [Crossref]
  12. M. Campos-García, C. Cossio-Guerrero, V. I. Moreno-Oliva, and O. Huerta-Carranza, “Surface shape evaluation with a corneal topographer based on a conical null-screen with a novel radial point distribution,” Appl. Opt. 54(17), 5411–5419 (2015).
    [Crossref]
  13. V. E. Armengol-Cruz, M. Campos-García, and C. Cossio-Guerrero, “Evaluation of a human corneal surface with the null-screen method,” Proc. SPIE 10330, 103300Q (2017).
    [Crossref]
  14. A. I. Osorio-Infante, M. Campos-García, and C. Cossio-Guerrero, “Characterization of a conical null-screen corneal topographer,” Proc. SPIE 10330, 103301E (2017).
    [Crossref]
  15. M. Campos-García, V. E. Armengol-Cruz, D. Aguirre Aguirre, and C. Camargo-Fierro, “Obtaining the topography of human corneas with the null-screen testing method,” Proc. SPIE 10692, 1069216 (2018).
    [Crossref]
  16. A. Estrada-Molina, M. Campos-García, and R. Díaz-Uribe, “Sagittal and meridional radii of curvature for a surface with symmetry of revolution by using a null-screen testing method,” Appl. Opt. 52(4), 625–634 (2013).
    [Crossref]
  17. L. Carmona-Paredes and R. Díaz-Uribe, “Geometric analysis of the null screens used for testing convex optical surfaces,” Rev. Mex. Fís. 53, 421–430 (2007).
  18. C. Ricolfe-Viala and A. J. Sánchez-Salmerón, “Lens distortion models evaluation,” Appl. Opt. 49(30), 5914–5928 (2010).
    [Crossref]
  19. P. Arulmozhivarman, L. Praveen Kumar, and A. R. Ganesan, “Measurement of moments for centroid estimation in Shack–Hartmann wavefront sensor—a wavelet-based approach and comparison with other methods,” Optik 117(2), 82–87 (2006).
    [Crossref]

2018 (1)

M. Campos-García, V. E. Armengol-Cruz, D. Aguirre Aguirre, and C. Camargo-Fierro, “Obtaining the topography of human corneas with the null-screen testing method,” Proc. SPIE 10692, 1069216 (2018).
[Crossref]

2017 (2)

V. E. Armengol-Cruz, M. Campos-García, and C. Cossio-Guerrero, “Evaluation of a human corneal surface with the null-screen method,” Proc. SPIE 10330, 103300Q (2017).
[Crossref]

A. I. Osorio-Infante, M. Campos-García, and C. Cossio-Guerrero, “Characterization of a conical null-screen corneal topographer,” Proc. SPIE 10330, 103301E (2017).
[Crossref]

2015 (1)

2013 (1)

2011 (3)

2010 (1)

2009 (1)

2008 (1)

2007 (1)

L. Carmona-Paredes and R. Díaz-Uribe, “Geometric analysis of the null screens used for testing convex optical surfaces,” Rev. Mex. Fís. 53, 421–430 (2007).

2006 (1)

P. Arulmozhivarman, L. Praveen Kumar, and A. R. Ganesan, “Measurement of moments for centroid estimation in Shack–Hartmann wavefront sensor—a wavelet-based approach and comparison with other methods,” Optik 117(2), 82–87 (2006).
[Crossref]

2000 (2)

W. Tang, M. J. Collins, L. Carney, and B. Davis, “The Accuracy and Precision Performance of Four Videokeratoscopes in Measuring Test Surfaces,” Optom. Vis. Sci. 77(9), 483–491 (2000).
[Crossref]

R. Díaz-Uribe and M. Campos-García, “Null screen testing of fast convex aspheric surfaces,” Appl. Opt. 39(16), 2670–2677 (2000).
[Crossref]

Aguirre Aguirre, D.

M. Campos-García, V. E. Armengol-Cruz, D. Aguirre Aguirre, and C. Camargo-Fierro, “Obtaining the topography of human corneas with the null-screen testing method,” Proc. SPIE 10692, 1069216 (2018).
[Crossref]

Armengol-Cruz, V. E.

M. Campos-García, V. E. Armengol-Cruz, D. Aguirre Aguirre, and C. Camargo-Fierro, “Obtaining the topography of human corneas with the null-screen testing method,” Proc. SPIE 10692, 1069216 (2018).
[Crossref]

V. E. Armengol-Cruz, M. Campos-García, and C. Cossio-Guerrero, “Evaluation of a human corneal surface with the null-screen method,” Proc. SPIE 10330, 103300Q (2017).
[Crossref]

Arulmozhivarman, P.

P. Arulmozhivarman, L. Praveen Kumar, and A. R. Ganesan, “Measurement of moments for centroid estimation in Shack–Hartmann wavefront sensor—a wavelet-based approach and comparison with other methods,” Optik 117(2), 82–87 (2006).
[Crossref]

Avendaño-Alejo, M.

Bolado-Gómez, R.

Camargo-Fierro, C.

M. Campos-García, V. E. Armengol-Cruz, D. Aguirre Aguirre, and C. Camargo-Fierro, “Obtaining the topography of human corneas with the null-screen testing method,” Proc. SPIE 10692, 1069216 (2018).
[Crossref]

Campos- García, M.

Campos-García, M.

M. Campos-García, V. E. Armengol-Cruz, D. Aguirre Aguirre, and C. Camargo-Fierro, “Obtaining the topography of human corneas with the null-screen testing method,” Proc. SPIE 10692, 1069216 (2018).
[Crossref]

A. I. Osorio-Infante, M. Campos-García, and C. Cossio-Guerrero, “Characterization of a conical null-screen corneal topographer,” Proc. SPIE 10330, 103301E (2017).
[Crossref]

V. E. Armengol-Cruz, M. Campos-García, and C. Cossio-Guerrero, “Evaluation of a human corneal surface with the null-screen method,” Proc. SPIE 10330, 103300Q (2017).
[Crossref]

M. Campos-García, C. Cossio-Guerrero, V. I. Moreno-Oliva, and O. Huerta-Carranza, “Surface shape evaluation with a corneal topographer based on a conical null-screen with a novel radial point distribution,” Appl. Opt. 54(17), 5411–5419 (2015).
[Crossref]

A. Estrada-Molina, M. Campos-García, and R. Díaz-Uribe, “Sagittal and meridional radii of curvature for a surface with symmetry of revolution by using a null-screen testing method,” Appl. Opt. 52(4), 625–634 (2013).
[Crossref]

M. Campos-García, A. Estrada-Molina, and R. Díaz-Uribe, “New null-screen design for corneal topography,” Proc. SPIE 8011, 801124 (2011).
[Crossref]

M. Avendaño-Alejo, V. I. Moreno-Oliva, M. Campos-García, and R. Díaz-Uribe, “Quantitative evaluation of an off-axis parabolic mirror by using a tilted null screen,” Appl. Opt. 48(5), 1008–1015 (2009).
[Crossref]

R. Díaz-Uribe and M. Campos-García, “Null screen testing of fast convex aspheric surfaces,” Appl. Opt. 39(16), 2670–2677 (2000).
[Crossref]

Carmona-Paredes, L.

L. Carmona-Paredes and R. Díaz-Uribe, “Geometric analysis of the null screens used for testing convex optical surfaces,” Rev. Mex. Fís. 53, 421–430 (2007).

Carney, L.

W. Tang, M. J. Collins, L. Carney, and B. Davis, “The Accuracy and Precision Performance of Four Videokeratoscopes in Measuring Test Surfaces,” Optom. Vis. Sci. 77(9), 483–491 (2000).
[Crossref]

Chia, N.

Collins, M.

M. Collins, S. Vincent, and S. Read, “The cornea,” in Handbook of visual optics, Vol. 1, P. Artal, ed. (CRC press, 2017).

Collins, M. J.

W. Tang, M. J. Collins, L. Carney, and B. Davis, “The Accuracy and Precision Performance of Four Videokeratoscopes in Measuring Test Surfaces,” Optom. Vis. Sci. 77(9), 483–491 (2000).
[Crossref]

Cossio-Guerrero, C.

V. E. Armengol-Cruz, M. Campos-García, and C. Cossio-Guerrero, “Evaluation of a human corneal surface with the null-screen method,” Proc. SPIE 10330, 103300Q (2017).
[Crossref]

A. I. Osorio-Infante, M. Campos-García, and C. Cossio-Guerrero, “Characterization of a conical null-screen corneal topographer,” Proc. SPIE 10330, 103301E (2017).
[Crossref]

M. Campos-García, C. Cossio-Guerrero, V. I. Moreno-Oliva, and O. Huerta-Carranza, “Surface shape evaluation with a corneal topographer based on a conical null-screen with a novel radial point distribution,” Appl. Opt. 54(17), 5411–5419 (2015).
[Crossref]

Davis, B.

W. Tang, M. J. Collins, L. Carney, and B. Davis, “The Accuracy and Precision Performance of Four Videokeratoscopes in Measuring Test Surfaces,” Optom. Vis. Sci. 77(9), 483–491 (2000).
[Crossref]

de Castro, A.

Díaz-Uribe, R.

Donnerhacke, K. H.

M. Kaschke, K. H. Donnerhacke, and M. S. Rill, Optical Devices in Ophthalmology and Optometry. Technology, Design Principles, and Clinical Applications, (Wiley-VCH, 2014).

Estrada-Molina, A.

Furlan, W. D.

W. D. Furlan, “Basic ophthalmic instruments,” in Handbook of visual optics, Vol. 1, P. Artal, ed. (CRC press, 2017).

Ganesan, A. R.

P. Arulmozhivarman, L. Praveen Kumar, and A. R. Ganesan, “Measurement of moments for centroid estimation in Shack–Hartmann wavefront sensor—a wavelet-based approach and comparison with other methods,” Optik 117(2), 82–87 (2006).
[Crossref]

Gora, M.

Grulkowski, I.

I. Grulkowski, “Anterior segment OCT,” in Handbook of visual optics, Vol. 2, P. Artal, ed. (CRC press, 2017).

Huerta-Carranza, O.

Kaluzny, B. J.

Karnowski, K.

Kaschke, M.

M. Kaschke, K. H. Donnerhacke, and M. S. Rill, Optical Devices in Ophthalmology and Optometry. Technology, Design Principles, and Clinical Applications, (Wiley-VCH, 2014).

Marcos, S.

Moreno-Oliva, V. I.

Ortiz, S.

Osorio-Infante, A. I.

A. I. Osorio-Infante, M. Campos-García, and C. Cossio-Guerrero, “Characterization of a conical null-screen corneal topographer,” Proc. SPIE 10330, 103301E (2017).
[Crossref]

Pérez-Merino, P.

Praveen Kumar, L.

P. Arulmozhivarman, L. Praveen Kumar, and A. R. Ganesan, “Measurement of moments for centroid estimation in Shack–Hartmann wavefront sensor—a wavelet-based approach and comparison with other methods,” Optik 117(2), 82–87 (2006).
[Crossref]

Read, S.

M. Collins, S. Vincent, and S. Read, “The cornea,” in Handbook of visual optics, Vol. 1, P. Artal, ed. (CRC press, 2017).

Ricolfe-Viala, C.

Rill, M. S.

M. Kaschke, K. H. Donnerhacke, and M. S. Rill, Optical Devices in Ophthalmology and Optometry. Technology, Design Principles, and Clinical Applications, (Wiley-VCH, 2014).

Sánchez-Salmerón, A. J.

Siedlecki, D.

Szkulmowski, M.

Tang, W.

W. Tang, M. J. Collins, L. Carney, and B. Davis, “The Accuracy and Precision Performance of Four Videokeratoscopes in Measuring Test Surfaces,” Optom. Vis. Sci. 77(9), 483–491 (2000).
[Crossref]

Vincent, S.

M. Collins, S. Vincent, and S. Read, “The cornea,” in Handbook of visual optics, Vol. 1, P. Artal, ed. (CRC press, 2017).

Wojtkowski, M.

Appl. Opt. (6)

Biomed. Opt. Express (2)

Optik (1)

P. Arulmozhivarman, L. Praveen Kumar, and A. R. Ganesan, “Measurement of moments for centroid estimation in Shack–Hartmann wavefront sensor—a wavelet-based approach and comparison with other methods,” Optik 117(2), 82–87 (2006).
[Crossref]

Optom. Vis. Sci. (1)

W. Tang, M. J. Collins, L. Carney, and B. Davis, “The Accuracy and Precision Performance of Four Videokeratoscopes in Measuring Test Surfaces,” Optom. Vis. Sci. 77(9), 483–491 (2000).
[Crossref]

Proc. SPIE (4)

M. Campos-García, A. Estrada-Molina, and R. Díaz-Uribe, “New null-screen design for corneal topography,” Proc. SPIE 8011, 801124 (2011).
[Crossref]

V. E. Armengol-Cruz, M. Campos-García, and C. Cossio-Guerrero, “Evaluation of a human corneal surface with the null-screen method,” Proc. SPIE 10330, 103300Q (2017).
[Crossref]

A. I. Osorio-Infante, M. Campos-García, and C. Cossio-Guerrero, “Characterization of a conical null-screen corneal topographer,” Proc. SPIE 10330, 103301E (2017).
[Crossref]

M. Campos-García, V. E. Armengol-Cruz, D. Aguirre Aguirre, and C. Camargo-Fierro, “Obtaining the topography of human corneas with the null-screen testing method,” Proc. SPIE 10692, 1069216 (2018).
[Crossref]

Rev. Mex. Fís. (1)

L. Carmona-Paredes and R. Díaz-Uribe, “Geometric analysis of the null screens used for testing convex optical surfaces,” Rev. Mex. Fís. 53, 421–430 (2007).

Other (4)

M. Kaschke, K. H. Donnerhacke, and M. S. Rill, Optical Devices in Ophthalmology and Optometry. Technology, Design Principles, and Clinical Applications, (Wiley-VCH, 2014).

M. Collins, S. Vincent, and S. Read, “The cornea,” in Handbook of visual optics, Vol. 1, P. Artal, ed. (CRC press, 2017).

W. D. Furlan, “Basic ophthalmic instruments,” in Handbook of visual optics, Vol. 1, P. Artal, ed. (CRC press, 2017).

I. Grulkowski, “Anterior segment OCT,” in Handbook of visual optics, Vol. 2, P. Artal, ed. (CRC press, 2017).

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Figures (10)

Fig. 1.
Fig. 1. Null-screen testing configuration.
Fig. 2.
Fig. 2. Null-screen design parameters.
Fig. 3.
Fig. 3. Normal evaluation.
Fig. 4.
Fig. 4. a) Flat-printed conical null-screen with drop shaped targets, b) Conical corneal topographer targets.
Fig. 5.
Fig. 5. a) The resultant image of the null-screen targets after reflection on the reference surface, b) processed image.
Fig. 6.
Fig. 6. Elevation map for the reference surface.
Fig. 7.
Fig. 7. The resultant image of the null-screen targets after reflection, and their corresponding binarized image. S1: left cornea: a) and b), right cornea: c) and d). S2: left cornea: e) and f), right cornea: g) and h).
Fig. 8.
Fig. 8. Elevation maps: a) left cornea S1, b) right cornea S1, c) left cornea S2, d) right cornea S2.
Fig. 9.
Fig. 9. Axial curvature maps: a) left cornea S1, b) right cornea S1, c) left cornea S2, d) right cornea S2.
Fig. 10.
Fig. 10. Tangential curvature maps: a) left cornea S1, b) right cornea S1, c) left cornea S2, d) right cornea S2.

Tables (4)

Tables Icon

Table 1. Conical null-screen design parameters.

Tables Icon

Table 2. Parameters resulting from least squares fitting of sagitta data.

Tables Icon

Table 3. Parameters resulting from least squares fitting of corneal surfaces.

Tables Icon

Table 4. Comparison of the geometrical parameters of corneas.

Equations (19)

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

z = c ρ 2 1 + ( 1 Q c 2 ρ 2 ) 1 / 1 2 2 ,
ρ 2 = F ρ 1 , z 2 = F a ( b + e ) ,
F = a { Q ( b + e ) + r } [ ( a r ) 2 ( b + e ) ρ 1 2 { Q ( b + e ) + 2 r } ] 1 / 1 2 2 Q a 2 + ρ 1 2 .
ρ 3 = s { α ( z 2 + e + h ) + ρ 2 } α h + s , z 3 = h ( α z 2 + ρ 2 ) s ( e + h ) α h + s ,
α = ρ 1 ρ 2 2 ρ 3 ( Q z 2 r ) 2 + 2 a ρ 2 ( Q z 2 r ) a ρ 2 2 a ( Q z 2 r ) 2 2 ρ 1 ρ 2 ( Q z 2 r ) .
d = a D b + e + β ,
β = r Q [ 1 ( 1 Q D 2 4 r 2 ) 1 / 1 2 2 ] .
X = R C o s ( s θ / l ) , Y = R S i n ( s θ / l ) ,
R = { ρ 3 2 + ( z 3 h e ) 2 } 1 / 1 2 2 , l = ( s + h ) 1 / 2 ,
N = R I | R I | = ( n x , n y , n z )
R = ( x 1 , y 1 , a ) ( x 1 2 + y 1 2 + a 2 ) 1 / 1 2 2 .
I = ( x s x 3 , y s y 3 , z s z 3 ) [ ( x s x 3 ) 2 + ( y s y 3 ) 2 + ( z s z 3 ) 2 ] 1 / 1 2 2 .
z z i = P i P f ( n x n z d x + n y n z d y ) ,
z = r { r 2 Q [ ( x x o ) 2 + ( y y o ) 2 ] } 1 / 1 2 2 Q + A ( x x o ) + B ( y y o ) + z o
k a x i = x n x n z + y n y n z ( x 2 + y 2 ) 1 / 2 [ x 2 + y 2 + ( x n x n z + y n y n z ) 2 ] .
k t a n = k a x i + k f i t ( x 2 + y 2 ) [ r f i t 2 + k f i t ( x 2 + y 2 ) ] 3 / 3 2 2 ,
η ( n x n z ) 2 + ( n y n z ) 2 = x 2 + y 2 { r f i t 2 ( k f i t + 1 ) ( x 2 + y 2 ) } 1 / 2 ,
x 1 = M x o + E ( x o 2 + y o 2 ) x o , y 1 = M y o + E ( x o 2 + y o 2 ) y o ,
x c = i = 1 N j = 1 M x i , j I i , j / i = 1 N j = 1 M x i , j I i , j i = 1 N j = 1 M I i , j i = 1 N j = 1 M I i , j , y c = i = 1 N j = 1 M y i , j I i , j / i = 1 N j = 1 M y i , j I i , j i = 1 N j = 1 M I i , j i = 1 N j = 1 M I i , j ,

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