First-order design of a reflective viewfinder for adaptive optics ophthalmoscopy

Alfredo Dubra; Yusufu N. Sulai

doi:10.1364/OE.20.026596

First-order design of a reflective viewfinder for adaptive optics ophthalmoscopy

Alfredo Dubra and Yusufu N. Sulai

Optics Express
Vol. 20,
Issue 24,
pp. 26596-26605
(2012)
•https://doi.org/10.1364/OE.20.026596

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Alfredo Dubra and Yusufu N. Sulai, "First-order design of a reflective viewfinder for adaptive optics ophthalmoscopy," Opt. Express 20, 26596-26605 (2012)

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Abstract

Adaptive optics (AO) ophthalmoscopes with small fields of view have limited clinical utility. We propose to address this problem in reflective instruments by incorporating a viewfinder pupil relay designed by considering pupil and image centering and conjugation. Diverting light from an existing pupil optical relay to the viewfinder relay allows switching field of view size. Design methods that meet all four centering and conjugation conditions using either a single concave mirror or with two concave mirrors forming an off-axis afocal telescope are presented. Two different methods for calculating the focal length and orientation of the concave mirrors in the afocal viewfinder relay are introduced. Finally, a 2.2 × viewfinder mode is demonstrated in an AO scanning light ophthalmoscope.

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References

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Y. Zhang, J. T. Rha, R. S. Jonnal, and D. T. Miller, “Adaptive optics parallel spectral domain optical coherence tomography for imaging the living retina,” Opt. Express 13(12), 4792–4811 (2005).
[Crossref] [PubMed]
Y. Zhang, S. Poonja, and A. Roorda, “MEMS-based adaptive optics scanning laser ophthalmoscopy,” Opt. Lett. 31(9), 1268–1270 (2006).
[Crossref] [PubMed]
Y. Zhang, B. Cense, J. Rha, R. S. Jonnal, W. Gao, R. J. Zawadzki, J. S. Werner, S. Jones, S. Olivier, and D. T. Miller, “High-speed volumetric imaging of cone photoreceptors with adaptive optics spectral-domain optical coherence tomography,” Opt. Express 14(10), 4380–4394 (2006).
[Crossref] [PubMed]
S. A. Burns, R. Tumbar, A. E. Elsner, D. Ferguson, and D. X. Hammer, “Large-field-of-view, modular, stabilized, adaptive-optics-based scanning laser ophthalmoscope,” J. Opt. Soc. Am. A 24(5), 1313–1326 (2007).
[Crossref] [PubMed]
K. M. Ivers, C. Li, N. Patel, N. Sredar, X. Luo, H. Queener, R. S. Harwerth, and J. Porter, “Reproducibility of measuring lamina cribrosa pore geometry in human and nonhuman primates with in vivo adaptive optics imaging,” Invest. Ophthalmol. Vis. Sci. 52(8), 5473–5480 (2011).
[Crossref] [PubMed]
A. Dubra, Y. Sulai, J. L. Norris, R. F. Cooper, A. M. Dubis, D. R. Williams, and J. Carroll, “Non-invasive imaging of the human rod photoreceptor mosaic using a confocal adaptive optics scanning ophthalmoscope,” Biomed. Opt. Express 2(7), 1864–1876 (2011).
[Crossref] [PubMed]
R. F. Cooper, A. M. Dubis, A. Pavaskar, J. Rha, A. Dubra, and J. Carroll, “Spatial and temporal variation of rod photoreceptor reflectance in the human retina,” Biomed. Opt. Express 2(9), 2577–2589 (2011).
[Crossref] [PubMed]
E. W. Dees, A. Dubra, and R. C. Baraas, “Variability in parafoveal cone mosaic in normal trichromatic individuals,” Biomed. Opt. Express 2(5), 1351–1358 (2011).
[Crossref] [PubMed]
P. Bedggood and A. Metha, “Variability in bleach kinetics and amount of photopigment between individual foveal cones,” Invest. Ophthalmol. Vis. Sci. 53(7), 3673–3681 (2012).
[Crossref] [PubMed]
T. Yamaguchi, N. Nakazawa, K. Bessho, Y. Kitaguchi, N. Maeda, T. Fujikado, and T. Mihashi, “Adaptive optics fundus camera using a liquid crystal phase modulator,” Opt. Rev. 15(3), 173–180 (2008).
[Crossref]
K. Nozato and K. Miyata, “Adaptive optics apparatus, adaptive optics method, and imaging apparatus,” US Patent 2011/0116044 A1 (May 19 2011).
I. Audo, M. El Sanharawi, C. Vignal-Clermont, A. Villa, A. Morin, J. Conrath, D. Fompeydie, J. A. Sahel, K. Gocho-Nakashima, O. Goureau, and M. Paques, “Foveal damage in habitual poppers users,” Arch. Ophthalmol. 129(6), 703–708 (2011).
[Crossref] [PubMed]
F. Felberer, J.-S. Kroisamer, C. K. Hitzenberger, and M. Pircher, “Lens based adaptive optics scanning laser ophthalmoscope,” Opt. Express 20(16), 17297–17310 (2012).
[Crossref]
J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14(11), 2884–2892 (1997).
[Crossref] [PubMed]
A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]
B. Hermann, E. J. Fernández, A. Unterhuber, H. Sattmann, A. F. Fercher, W. Drexler, P. M. Prieto, and P. Artal, “Adaptive-optics ultrahigh-resolution optical coherence tomography,” Opt. Lett. 29(18), 2142–2144 (2004).
[Crossref] [PubMed]
A. Dubra and Y. Sulai, “Reflective afocal broadband adaptive optics scanning ophthalmoscope,” Biomed. Opt. Express 2(6), 1757–1768 (2011).
[Crossref] [PubMed]
A. Gómez-Vieyra, A. Dubra, D. Malacara-Hernández, and D. R. Williams, “First-order design of off-axis reflective ophthalmic adaptive optics systems using afocal telescopes,” Opt. Express 17(21), 18906–18919 (2009).
[Crossref] [PubMed]
F. C. Delori, R. H. Webb, D. H. Sliney, and American National Standards Institute, “Maximum permissible exposures for ocular safety (ANSI 2000), with emphasis on ophthalmic devices,” J. Opt. Soc. Am. A 24(5), 1250–1265 (2007).
[Crossref] [PubMed]
ANSI, “American National Standard for safe use of lasers in research, development or testing (ANSI z136.8-2012),” (The Laser Institute of America, 2012).
A. Dubra and Z. Harvey, “Registration of 2d images from fast scanning ophthalmic instruments,” in The 4th International Workshop on Biomedical Image Registration (2010)
P. Bedggood, M. Daaboul, R. Ashman, G. Smith, and A. Metha, “Characteristics of the human isoplanatic patch and implications for adaptive optics retinal imaging,” J. Biomed. Opt. 13(2), 024008 (2008).
[Crossref] [PubMed]
W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond., B 112(778), 428–450 (1933).
[Crossref]

2012 (2)

P. Bedggood and A. Metha, “Variability in bleach kinetics and amount of photopigment between individual foveal cones,” Invest. Ophthalmol. Vis. Sci. 53(7), 3673–3681 (2012).
[Crossref] [PubMed]

F. Felberer, J.-S. Kroisamer, C. K. Hitzenberger, and M. Pircher, “Lens based adaptive optics scanning laser ophthalmoscope,” Opt. Express 20(16), 17297–17310 (2012).
[Crossref]

2011 (6)

I. Audo, M. El Sanharawi, C. Vignal-Clermont, A. Villa, A. Morin, J. Conrath, D. Fompeydie, J. A. Sahel, K. Gocho-Nakashima, O. Goureau, and M. Paques, “Foveal damage in habitual poppers users,” Arch. Ophthalmol. 129(6), 703–708 (2011).
[Crossref] [PubMed]

A. Dubra and Y. Sulai, “Reflective afocal broadband adaptive optics scanning ophthalmoscope,” Biomed. Opt. Express 2(6), 1757–1768 (2011).
[Crossref] [PubMed]

K. M. Ivers, C. Li, N. Patel, N. Sredar, X. Luo, H. Queener, R. S. Harwerth, and J. Porter, “Reproducibility of measuring lamina cribrosa pore geometry in human and nonhuman primates with in vivo adaptive optics imaging,” Invest. Ophthalmol. Vis. Sci. 52(8), 5473–5480 (2011).
[Crossref] [PubMed]

A. Dubra, Y. Sulai, J. L. Norris, R. F. Cooper, A. M. Dubis, D. R. Williams, and J. Carroll, “Non-invasive imaging of the human rod photoreceptor mosaic using a confocal adaptive optics scanning ophthalmoscope,” Biomed. Opt. Express 2(7), 1864–1876 (2011).
[Crossref] [PubMed]

R. F. Cooper, A. M. Dubis, A. Pavaskar, J. Rha, A. Dubra, and J. Carroll, “Spatial and temporal variation of rod photoreceptor reflectance in the human retina,” Biomed. Opt. Express 2(9), 2577–2589 (2011).
[Crossref] [PubMed]

E. W. Dees, A. Dubra, and R. C. Baraas, “Variability in parafoveal cone mosaic in normal trichromatic individuals,” Biomed. Opt. Express 2(5), 1351–1358 (2011).
[Crossref] [PubMed]

2009 (1)

A. Gómez-Vieyra, A. Dubra, D. Malacara-Hernández, and D. R. Williams, “First-order design of off-axis reflective ophthalmic adaptive optics systems using afocal telescopes,” Opt. Express 17(21), 18906–18919 (2009).
[Crossref] [PubMed]

2008 (2)

T. Yamaguchi, N. Nakazawa, K. Bessho, Y. Kitaguchi, N. Maeda, T. Fujikado, and T. Mihashi, “Adaptive optics fundus camera using a liquid crystal phase modulator,” Opt. Rev. 15(3), 173–180 (2008).
[Crossref]

P. Bedggood, M. Daaboul, R. Ashman, G. Smith, and A. Metha, “Characteristics of the human isoplanatic patch and implications for adaptive optics retinal imaging,” J. Biomed. Opt. 13(2), 024008 (2008).
[Crossref] [PubMed]

1933 (1)

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond., B 112(778), 428–450 (1933).
[Crossref]

Artal, P.

Ashman, R.

Audo, I.

Baraas, R. C.

E. W. Dees, A. Dubra, and R. C. Baraas, “Variability in parafoveal cone mosaic in normal trichromatic individuals,” Biomed. Opt. Express 2(5), 1351–1358 (2011).
[Crossref] [PubMed]

Bedggood, P.

P. Bedggood and A. Metha, “Variability in bleach kinetics and amount of photopigment between individual foveal cones,” Invest. Ophthalmol. Vis. Sci. 53(7), 3673–3681 (2012).
[Crossref] [PubMed]

Bessho, K.

Burns, S. A.

Campbell, M. C. W.

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]

Carroll, J.

Cense, B.

Conrath, J.

Cooper, R. F.

Crawford, B. H.

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond., B 112(778), 428–450 (1933).
[Crossref]

Daaboul, M.

Dees, E. W.

E. W. Dees, A. Dubra, and R. C. Baraas, “Variability in parafoveal cone mosaic in normal trichromatic individuals,” Biomed. Opt. Express 2(5), 1351–1358 (2011).
[Crossref] [PubMed]

Delori, F. C.

Donnelly Iii, W.

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]

Drexler, W.

Dubis, A. M.

Dubra, A.

E. W. Dees, A. Dubra, and R. C. Baraas, “Variability in parafoveal cone mosaic in normal trichromatic individuals,” Biomed. Opt. Express 2(5), 1351–1358 (2011).
[Crossref] [PubMed]

A. Dubra and Y. Sulai, “Reflective afocal broadband adaptive optics scanning ophthalmoscope,” Biomed. Opt. Express 2(6), 1757–1768 (2011).
[Crossref] [PubMed]

El Sanharawi, M.

Elsner, A. E.

Felberer, F.

F. Felberer, J.-S. Kroisamer, C. K. Hitzenberger, and M. Pircher, “Lens based adaptive optics scanning laser ophthalmoscope,” Opt. Express 20(16), 17297–17310 (2012).
[Crossref]

Fercher, A. F.

Ferguson, D.

Fernández, E. J.

Fompeydie, D.

Fujikado, T.

Gao, W.

Gocho-Nakashima, K.

Gómez-Vieyra, A.

Goureau, O.

Hammer, D. X.

Harwerth, R. S.

Hebert, T. J.

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]

Hermann, B.

Hitzenberger, C. K.

F. Felberer, J.-S. Kroisamer, C. K. Hitzenberger, and M. Pircher, “Lens based adaptive optics scanning laser ophthalmoscope,” Opt. Express 20(16), 17297–17310 (2012).
[Crossref]

Ivers, K. M.

Jones, S.

Jonnal, R. S.

Kitaguchi, Y.

Kroisamer, J.-S.

F. Felberer, J.-S. Kroisamer, C. K. Hitzenberger, and M. Pircher, “Lens based adaptive optics scanning laser ophthalmoscope,” Opt. Express 20(16), 17297–17310 (2012).
[Crossref]

Li, C.

Liang, J.

J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14(11), 2884–2892 (1997).
[Crossref] [PubMed]

Luo, X.

Maeda, N.

Malacara-Hernández, D.

Metha, A.

P. Bedggood and A. Metha, “Variability in bleach kinetics and amount of photopigment between individual foveal cones,” Invest. Ophthalmol. Vis. Sci. 53(7), 3673–3681 (2012).
[Crossref] [PubMed]

Mihashi, T.

Miller, D. T.

J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14(11), 2884–2892 (1997).
[Crossref] [PubMed]

Morin, A.

Nakazawa, N.

Norris, J. L.

Olivier, S.

Paques, M.

Patel, N.

Pavaskar, A.

Pircher, M.

F. Felberer, J.-S. Kroisamer, C. K. Hitzenberger, and M. Pircher, “Lens based adaptive optics scanning laser ophthalmoscope,” Opt. Express 20(16), 17297–17310 (2012).
[Crossref]

Poonja, S.

Y. Zhang, S. Poonja, and A. Roorda, “MEMS-based adaptive optics scanning laser ophthalmoscopy,” Opt. Lett. 31(9), 1268–1270 (2006).
[Crossref] [PubMed]

Porter, J.

Prieto, P. M.

Queener, H.

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]

Rha, J.

Rha, J. T.

Romero-Borja, F.

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]

Roorda, A.

Y. Zhang, S. Poonja, and A. Roorda, “MEMS-based adaptive optics scanning laser ophthalmoscopy,” Opt. Lett. 31(9), 1268–1270 (2006).
[Crossref] [PubMed]

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]

Sahel, J. A.

Sattmann, H.

Sliney, D. H.

Smith, G.

Sredar, N.

Stiles, W. S.

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond., B 112(778), 428–450 (1933).
[Crossref]

Sulai, Y.

A. Dubra and Y. Sulai, “Reflective afocal broadband adaptive optics scanning ophthalmoscope,” Biomed. Opt. Express 2(6), 1757–1768 (2011).
[Crossref] [PubMed]

Tumbar, R.

Unterhuber, A.

Vignal-Clermont, C.

Villa, A.

Webb, R. H.

Werner, J. S.

Williams, D. R.

J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14(11), 2884–2892 (1997).
[Crossref] [PubMed]

Yamaguchi, T.

Zawadzki, R. J.

Zhang, Y.

Y. Zhang, S. Poonja, and A. Roorda, “MEMS-based adaptive optics scanning laser ophthalmoscopy,” Opt. Lett. 31(9), 1268–1270 (2006).
[Crossref] [PubMed]

Arch. Ophthalmol. (1)

Biomed. Opt. Express (4)

A. Dubra and Y. Sulai, “Reflective afocal broadband adaptive optics scanning ophthalmoscope,” Biomed. Opt. Express 2(6), 1757–1768 (2011).
[Crossref] [PubMed]

E. W. Dees, A. Dubra, and R. C. Baraas, “Variability in parafoveal cone mosaic in normal trichromatic individuals,” Biomed. Opt. Express 2(5), 1351–1358 (2011).
[Crossref] [PubMed]

Invest. Ophthalmol. Vis. Sci. (2)

P. Bedggood and A. Metha, “Variability in bleach kinetics and amount of photopigment between individual foveal cones,” Invest. Ophthalmol. Vis. Sci. 53(7), 3673–3681 (2012).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

J. Opt. Soc. Am. A (3)

J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14(11), 2884–2892 (1997).
[Crossref] [PubMed]

Opt. Express (5)

A. Roorda, F. Romero-Borja, W. Donnelly Iii, H. Queener, T. J. Hebert, and M. C. W. Campbell, “Adaptive optics scanning laser ophthalmoscopy,” Opt. Express 10(9), 405–412 (2002).
[PubMed]

F. Felberer, J.-S. Kroisamer, C. K. Hitzenberger, and M. Pircher, “Lens based adaptive optics scanning laser ophthalmoscope,” Opt. Express 20(16), 17297–17310 (2012).
[Crossref]

Opt. Lett. (2)

Y. Zhang, S. Poonja, and A. Roorda, “MEMS-based adaptive optics scanning laser ophthalmoscopy,” Opt. Lett. 31(9), 1268–1270 (2006).
[Crossref] [PubMed]

Opt. Rev. (1)

Proc. R. Soc. Lond., B (1)

W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond., B 112(778), 428–450 (1933).
[Crossref]

Other (3)

K. Nozato and K. Miyata, “Adaptive optics apparatus, adaptive optics method, and imaging apparatus,” US Patent 2011/0116044 A1 (May 19 2011).

ANSI, “American National Standard for safe use of lasers in research, development or testing (ANSI z136.8-2012),” (The Laser Institute of America, 2012).

A. Dubra and Z. Harvey, “Registration of 2d images from fast scanning ophthalmic instruments,” in The 4th International Workshop on Biomedical Image Registration (2010)

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Fig. 1

Pupil relay formed by a single concave mirror with focal length f. The mirror is a distance a from the entrance pupil, while the exit pupil is at a distance a f / (a - f). P₀ and P_f are the initial and final vergences of the imaging beam.

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Fig. 2

Vectors used to describe the optical axis of an off-axis reflective afocal telescope formed by two concave mirrors (M₁ and M₂), projected on the x-y plane.

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Fig. 3

Focal lengths of the concave mirrors required to achieve a given viewfinder relay magnification Mθ calculated using the numerical approach described in section 2.2.1.

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Fig. 4

AOSLO diagram [17], illustrating how the change between the high-magnification and viewfinder mode was implemented. In the later, a spherical mirror (sph 6’) and a fold mirror are positioned using magnetic mounts. This arrangement bypasses the afocal telescope formed by spherical mirror 5 and 6.

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Fig. 5

AOSLO and fundus images of subjects JC_0832 (A-E) and JC_0007 (F-J). The left and central columns show 1.75° and 2.2 × 1.75° (viewfinder mode) FOV AOSLO images, respectively, of the fovea and the optic disc. The retinal location and extent of the AOSLO images are indicated on the fundus images (right) through the red contours. All scale bars are 1° across.

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Equations (11)

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

P_{f} = \frac{(f - a) (P_{0} (f - a) + 1)}{f^{2}},

a = \frac{M + 1}{P_{0} - M^{2} P_{f}} .

a = \frac{M^{θ} (M_{0} + M^{θ})}{{(M^{θ})}^{2} P_{0} - M_{0}^{2} P_{f}} .

f = \frac{a M_{0}}{M_{0} + M^{θ}},

\begin{array}{l} v_{1} = f_{1} [1, 0, 0], \\ v_{2} = - (f_{1} + f_{2}) [\cos (2 I_{1 xy}), \sin (2 I_{1 xy}), 0], \\ v_{3} = f_{2} [\cos (2 I_{2z}) \cos (2 I_{2xy} - 2 I_{1xy}), - \cos (2 I_{2z}) \sin (2 I_{2xy} - 2 I_{1 xy}), \sin (2 I_{2z})] . \end{array}

\begin{array}{l} v'_{1} = f'_{1} [1, 0, 0], \\ v'_{2} = - (f'_{1} + f'_{2}) [\cos (2 I'_{1xy}) \cos (2 I'_{1z}), \sin (2 I'_{1xy}) \cos (2 I'_{1z}), \sin (2 I'_{1z})], \\ v'_{3} = f'_{2} [\cos (2 I'_{2 z}) \cos (2 I'_{2xy} - 2 I'_{1xy}), - \cos (2 I'_{2z}) \sin (2 I'_{2xy} - 2 I'_{1xy}), \sin (2 I'_{2 z})] . \end{array}

\begin{matrix} \frac{v_{1}}{f_{1}} = \frac{v'_{1}}{f'_{1}}, \\ \frac{v_{3}}{f_{2}} = \frac{v'_{3}}{f'_{2}}, \\ v_{1} + v_{2} + v_{3} = v'_{1} + v'_{2} + v'_{3} . \end{matrix}

\begin{array}{l} I'_{2 z} = I_{2 z}, \\ I'_{2xy} - I'_{1xy} = I_{2xy} - I_{1xy}, \\ v'_{2} - v_{1} (1 - \frac{f'_{1}}{f_{1}}) = v_{2} + v_{3} (1 - \frac{f'_{2}}{f_{2}}) . \end{array}

M^{θ} = \frac{f_{2} f'_{1}}{f_{1} f'_{2}} .

\begin{array}{l} I'_{2 z} = I_{2 z}, \\ I'_{2 x y} - I'_{1 x y} = I_{2 x y} - I_{1 x y}, \\ f'_{2} (0.0037056 - 0.5 I'_{1 z}^{2} + I'_{1 x y} (I'_{1 z}^{2} - 0.5)) - 0.16123 = 0, \\ f'_{2} (0.0055145 + I'_{1 x y} (I'_{1 z}^{2} - 0.5)) + 3.0508 = 0, \\ f'_{2} (0.064532 - 4.42 I'_{1 z}^{2}) - 64.5323 = 0, \end{array}

\begin{array}{l} I'_{1 x y} = 1.056 º, \\ I'_{1 z} = 0.179 º, \\ I'_{2 x y} = 2.456 º, \\ I'_{2 z} = 1.85 º, \\ f'_{2} = 823.7 mm, \\ f'_{1} = 2.2 \frac{f_{1}}{f_{2} f'_{2}} = 996.7 mm . \end{array}

Abstract

References

2012 (2)

2011 (6)

2009 (1)

2008 (2)

2007 (2)

2006 (2)

2005 (1)

2004 (1)

2002 (1)

1997 (1)

1933 (1)

Artal, P.

Ashman, R.

Audo, I.

Baraas, R. C.

Bedggood, P.

Bessho, K.

Burns, S. A.

Campbell, M. C. W.

Carroll, J.

Cense, B.

Conrath, J.

Cooper, R. F.

Crawford, B. H.

Daaboul, M.

Dees, E. W.

Delori, F. C.

Donnelly Iii, W.

Drexler, W.

Dubis, A. M.

Dubra, A.

El Sanharawi, M.

Elsner, A. E.

Felberer, F.

Fercher, A. F.

Ferguson, D.

Fernández, E. J.

Fompeydie, D.

Fujikado, T.

Gao, W.

Gocho-Nakashima, K.

Gómez-Vieyra, A.

Goureau, O.

Hammer, D. X.

Harwerth, R. S.

Hebert, T. J.

Hermann, B.

Hitzenberger, C. K.

Ivers, K. M.

Jones, S.

Jonnal, R. S.

Kitaguchi, Y.

Kroisamer, J.-S.

Li, C.

Liang, J.

Luo, X.

Maeda, N.

Malacara-Hernández, D.

Metha, A.

Mihashi, T.

Miller, D. T.

Morin, A.

Nakazawa, N.

Norris, J. L.

Olivier, S.

Paques, M.

Patel, N.

Pavaskar, A.

Pircher, M.

Poonja, S.

Porter, J.

Prieto, P. M.

Queener, H.

Rha, J.

Rha, J. T.

Romero-Borja, F.

Roorda, A.

Sahel, J. A.