Abstract

Utilizing the measured corneal birefringence from a data set of 150 eyes of 75 human subjects, an algorithm and related computer program, based on Müller-Stokes matrix calculus, were developed in MATLAB for assessing the influence of corneal birefringence on retinal birefringence scanning (RBS) and for converging upon an optical/mechanical design using wave plates (“wave-plate-enhanced RBS”) that allows foveal fixation detection essentially independently of corneal birefringence. The RBS computer model, and in particular the optimization algorithm, were verified with experimental human data using an available monocular RBS-based eye fixation monitor. Fixation detection using wave-plate-enhanced RBS is adaptable to less cooperative subjects, including young children at risk for developing amblyopia.

© 2011 OSA

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2009 (1)

K. Irsch, B. I. Gramatikov, Y. K. Wu, and D. L. Guyton, “Spinning wave plate design for retinal birefringence scanning,” Proc. SPIE 7169, 71691F (2009).
[CrossRef]

2008 (1)

2006 (4)

D. S. Nassif, N. V. Piskun, and D. G. Hunter, “The Pediatric Vision Screener III: detection of strabismus in children,” Arch. Ophthalmol. 124(4), 509–513 (2006).
[CrossRef] [PubMed]

B. I. Gramatikov, O. H. Y. Zalloum, Y. K. Wu, D. G. Hunter, and D. L. Guyton, “Birefringence-based eye fixation monitor with no moving parts,” J. Biomed. Opt. 11(3), 034025 (2006).
[CrossRef] [PubMed]

Q. Zhou, “Retinal scanning laser polarimetry and methods to compensate for corneal birefringence,” Bull. Soc. Belge Ophtalmol. 302(302), 89–106 (2006).
[PubMed]

N. J. Reus, Q. Zhou, and H. G. Lemij, “Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation,” Invest. Ophthalmol. Vis. Sci. 47(9), 3870–3877 (2006).
[CrossRef] [PubMed]

2004 (2)

D. S. Nassif, N. V. Piskun, B. I. Gramatikov, D. L. Guyton, and D. G. Hunter, “Pediatric Vision Screener 2: pilot study in adults,” J. Biomed. Opt. 9(6), 1369–1374 (2004).
[CrossRef] [PubMed]

D. G. Hunter, D. S. Nassif, N. V. Piskun, R. Winsor, B. I. Gramatikov, and D. L. Guyton, “Pediatric Vision Screener 1: instrument design and operation,” J. Biomed. Opt. 9(6), 1363–1368 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (5)

R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43(1), 82–86 (2002).
[PubMed]

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120(7), 901–906 (2002).
[PubMed]

Q. Zhou and R. N. Weinreb, “Individualized compensation of anterior segment birefringence during scanning laser polarimetry,” Invest. Ophthalmol. Vis. Sci. 43(7), 2221–2228 (2002).
[PubMed]

R. W. Knighton and X. R. Huang, “Analytical methods for scanning laser polarimetry,” Opt. Express 10(21), 1179–1189 (2002).
[PubMed]

R. W. Knighton, “Spectral dependence of corneal birefringence at visible wavelengths,” Invest. Ophthalmol. Vis. Sci. 43, E-Abstract 152 (2002).

1999 (2)

1996 (1)

B. C. E. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” Proc. SPIE 2930, 92–101 (1996).
[CrossRef]

1992 (1)

1991 (1)

1988 (1)

1987 (1)

1985 (1)

1979 (1)

R. A. Weale, “Sex, age and the birefringence of the human crystalline lens,” Exp. Eye Res. 29(4), 449–461 (1979).
[CrossRef] [PubMed]

1975 (2)

L. R. Young and D. Sheena, “Survey of eye movement recording methods,” Behav. Res. Meth. Instrum. 7(5), 397–429 (1975).
[CrossRef]

F. A. Bettelheim, “On the optical anisotropy of lens fiber cells,” Exp. Eye Res. 21(3), 231–234 (1975).
[CrossRef] [PubMed]

Bettelheim, F. A.

F. A. Bettelheim, “On the optical anisotropy of lens fiber cells,” Exp. Eye Res. 21(3), 231–234 (1975).
[CrossRef] [PubMed]

Bille, J. F.

B. C. E. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” Proc. SPIE 2930, 92–101 (1996).
[CrossRef]

Bowd, C.

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120(7), 901–906 (2002).
[PubMed]

Burk, R. O. W.

B. C. E. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” Proc. SPIE 2930, 92–101 (1996).
[CrossRef]

Cavuoto, L. A.

Dreher, A. W.

Fischer, J. P.

B. C. E. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” Proc. SPIE 2930, 92–101 (1996).
[CrossRef]

Goelz, S.

B. C. E. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” Proc. SPIE 2930, 92–101 (1996).
[CrossRef]

Gramatikov, B. I.

K. Irsch, B. I. Gramatikov, Y. K. Wu, and D. L. Guyton, “Spinning wave plate design for retinal birefringence scanning,” Proc. SPIE 7169, 71691F (2009).
[CrossRef]

B. I. Gramatikov, O. H. Y. Zalloum, Y. K. Wu, D. G. Hunter, and D. L. Guyton, “Birefringence-based eye fixation monitor with no moving parts,” J. Biomed. Opt. 11(3), 034025 (2006).
[CrossRef] [PubMed]

D. G. Hunter, D. S. Nassif, N. V. Piskun, R. Winsor, B. I. Gramatikov, and D. L. Guyton, “Pediatric Vision Screener 1: instrument design and operation,” J. Biomed. Opt. 9(6), 1363–1368 (2004).
[CrossRef] [PubMed]

D. S. Nassif, N. V. Piskun, B. I. Gramatikov, D. L. Guyton, and D. G. Hunter, “Pediatric Vision Screener 2: pilot study in adults,” J. Biomed. Opt. 9(6), 1369–1374 (2004).
[CrossRef] [PubMed]

Greenfield, D. S.

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120(7), 901–906 (2002).
[PubMed]

Guyton, D. L.

K. Irsch, B. I. Gramatikov, Y. K. Wu, and D. L. Guyton, “Spinning wave plate design for retinal birefringence scanning,” Proc. SPIE 7169, 71691F (2009).
[CrossRef]

B. I. Gramatikov, O. H. Y. Zalloum, Y. K. Wu, D. G. Hunter, and D. L. Guyton, “Birefringence-based eye fixation monitor with no moving parts,” J. Biomed. Opt. 11(3), 034025 (2006).
[CrossRef] [PubMed]

D. S. Nassif, N. V. Piskun, B. I. Gramatikov, D. L. Guyton, and D. G. Hunter, “Pediatric Vision Screener 2: pilot study in adults,” J. Biomed. Opt. 9(6), 1369–1374 (2004).
[CrossRef] [PubMed]

D. G. Hunter, D. S. Nassif, N. V. Piskun, R. Winsor, B. I. Gramatikov, and D. L. Guyton, “Pediatric Vision Screener 1: instrument design and operation,” J. Biomed. Opt. 9(6), 1363–1368 (2004).
[CrossRef] [PubMed]

D. G. Hunter, A. S. Shah, S. Sau, D. Nassif, and D. L. Guyton, “Automated detection of ocular alignment with binocular retinal birefringence scanning,” Appl. Opt. 42(16), 3047–3053 (2003).
[CrossRef] [PubMed]

D. G. Hunter, S. N. Patel, and D. L. Guyton, “Automated detection of foveal fixation by use of retinal birefringence scanning,” Appl. Opt. 38(7), 1273–1279 (1999).
[CrossRef] [PubMed]

D. G. Hunter, J. C. Sandruck, S. Sau, S. N. Patel, and D. L. Guyton, “Mathematical modeling of retinal birefringence scanning,” J. Opt. Soc. Am. A 16(9), 2103–2111 (1999).
[CrossRef] [PubMed]

Huang, X. R.

Hunter, D. G.

D. S. Nassif, N. V. Piskun, and D. G. Hunter, “The Pediatric Vision Screener III: detection of strabismus in children,” Arch. Ophthalmol. 124(4), 509–513 (2006).
[CrossRef] [PubMed]

B. I. Gramatikov, O. H. Y. Zalloum, Y. K. Wu, D. G. Hunter, and D. L. Guyton, “Birefringence-based eye fixation monitor with no moving parts,” J. Biomed. Opt. 11(3), 034025 (2006).
[CrossRef] [PubMed]

D. S. Nassif, N. V. Piskun, B. I. Gramatikov, D. L. Guyton, and D. G. Hunter, “Pediatric Vision Screener 2: pilot study in adults,” J. Biomed. Opt. 9(6), 1369–1374 (2004).
[CrossRef] [PubMed]

D. G. Hunter, D. S. Nassif, N. V. Piskun, R. Winsor, B. I. Gramatikov, and D. L. Guyton, “Pediatric Vision Screener 1: instrument design and operation,” J. Biomed. Opt. 9(6), 1363–1368 (2004).
[CrossRef] [PubMed]

D. G. Hunter, A. S. Shah, S. Sau, D. Nassif, and D. L. Guyton, “Automated detection of ocular alignment with binocular retinal birefringence scanning,” Appl. Opt. 42(16), 3047–3053 (2003).
[CrossRef] [PubMed]

D. G. Hunter, S. N. Patel, and D. L. Guyton, “Automated detection of foveal fixation by use of retinal birefringence scanning,” Appl. Opt. 38(7), 1273–1279 (1999).
[CrossRef] [PubMed]

D. G. Hunter, J. C. Sandruck, S. Sau, S. N. Patel, and D. L. Guyton, “Mathematical modeling of retinal birefringence scanning,” J. Opt. Soc. Am. A 16(9), 2103–2111 (1999).
[CrossRef] [PubMed]

Irsch, K.

K. Irsch, B. I. Gramatikov, Y. K. Wu, and D. L. Guyton, “Spinning wave plate design for retinal birefringence scanning,” Proc. SPIE 7169, 71691F (2009).
[CrossRef]

klein Brink, H. B.

Knighton, R. W.

R. W. Knighton, X. R. Huang, and L. A. Cavuoto, “Corneal birefringence mapped by scanning laser polarimetry,” Opt. Express 16(18), 13738–13751 (2008).
[CrossRef] [PubMed]

R. W. Knighton, “Spectral dependence of corneal birefringence at visible wavelengths,” Invest. Ophthalmol. Vis. Sci. 43, E-Abstract 152 (2002).

R. W. Knighton and X. R. Huang, “Analytical methods for scanning laser polarimetry,” Opt. Express 10(21), 1179–1189 (2002).
[PubMed]

R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43(1), 82–86 (2002).
[PubMed]

Lemij, H. G.

N. J. Reus, Q. Zhou, and H. G. Lemij, “Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation,” Invest. Ophthalmol. Vis. Sci. 47(9), 3870–3877 (2006).
[CrossRef] [PubMed]

Nassif, D.

Nassif, D. S.

D. S. Nassif, N. V. Piskun, and D. G. Hunter, “The Pediatric Vision Screener III: detection of strabismus in children,” Arch. Ophthalmol. 124(4), 509–513 (2006).
[CrossRef] [PubMed]

D. S. Nassif, N. V. Piskun, B. I. Gramatikov, D. L. Guyton, and D. G. Hunter, “Pediatric Vision Screener 2: pilot study in adults,” J. Biomed. Opt. 9(6), 1369–1374 (2004).
[CrossRef] [PubMed]

D. G. Hunter, D. S. Nassif, N. V. Piskun, R. Winsor, B. I. Gramatikov, and D. L. Guyton, “Pediatric Vision Screener 1: instrument design and operation,” J. Biomed. Opt. 9(6), 1363–1368 (2004).
[CrossRef] [PubMed]

Patel, S. N.

Pelz, B. C. E.

B. C. E. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” Proc. SPIE 2930, 92–101 (1996).
[CrossRef]

Piskun, N. V.

D. S. Nassif, N. V. Piskun, and D. G. Hunter, “The Pediatric Vision Screener III: detection of strabismus in children,” Arch. Ophthalmol. 124(4), 509–513 (2006).
[CrossRef] [PubMed]

D. S. Nassif, N. V. Piskun, B. I. Gramatikov, D. L. Guyton, and D. G. Hunter, “Pediatric Vision Screener 2: pilot study in adults,” J. Biomed. Opt. 9(6), 1369–1374 (2004).
[CrossRef] [PubMed]

D. G. Hunter, D. S. Nassif, N. V. Piskun, R. Winsor, B. I. Gramatikov, and D. L. Guyton, “Pediatric Vision Screener 1: instrument design and operation,” J. Biomed. Opt. 9(6), 1363–1368 (2004).
[CrossRef] [PubMed]

Reiter, K.

Reus, N. J.

N. J. Reus, Q. Zhou, and H. G. Lemij, “Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation,” Invest. Ophthalmol. Vis. Sci. 47(9), 3870–3877 (2006).
[CrossRef] [PubMed]

Sandruck, J. C.

Sau, S.

Shah, A. S.

Sheena, D.

L. R. Young and D. Sheena, “Survey of eye movement recording methods,” Behav. Res. Meth. Instrum. 7(5), 397–429 (1975).
[CrossRef]

van Blokland, G. J.

Verhelst, S. C.

Weale, R. A.

R. A. Weale, “Sex, age and the birefringence of the human crystalline lens,” Exp. Eye Res. 29(4), 449–461 (1979).
[CrossRef] [PubMed]

Weinreb, R. N.

Q. Zhou and R. N. Weinreb, “Individualized compensation of anterior segment birefringence during scanning laser polarimetry,” Invest. Ophthalmol. Vis. Sci. 43(7), 2221–2228 (2002).
[PubMed]

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120(7), 901–906 (2002).
[PubMed]

A. W. Dreher, K. Reiter, and R. N. Weinreb, “Spatially resolved birefringence of the retinal nerve fiber layer assessed with a retinal laser ellipsometer,” Appl. Opt. 31(19), 3730–3735 (1992).
[CrossRef] [PubMed]

Weschenmoser, C.

B. C. E. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” Proc. SPIE 2930, 92–101 (1996).
[CrossRef]

Winsor, R.

D. G. Hunter, D. S. Nassif, N. V. Piskun, R. Winsor, B. I. Gramatikov, and D. L. Guyton, “Pediatric Vision Screener 1: instrument design and operation,” J. Biomed. Opt. 9(6), 1363–1368 (2004).
[CrossRef] [PubMed]

Wu, Y. K.

K. Irsch, B. I. Gramatikov, Y. K. Wu, and D. L. Guyton, “Spinning wave plate design for retinal birefringence scanning,” Proc. SPIE 7169, 71691F (2009).
[CrossRef]

B. I. Gramatikov, O. H. Y. Zalloum, Y. K. Wu, D. G. Hunter, and D. L. Guyton, “Birefringence-based eye fixation monitor with no moving parts,” J. Biomed. Opt. 11(3), 034025 (2006).
[CrossRef] [PubMed]

Young, L. R.

L. R. Young and D. Sheena, “Survey of eye movement recording methods,” Behav. Res. Meth. Instrum. 7(5), 397–429 (1975).
[CrossRef]

Zalloum, O. H. Y.

B. I. Gramatikov, O. H. Y. Zalloum, Y. K. Wu, D. G. Hunter, and D. L. Guyton, “Birefringence-based eye fixation monitor with no moving parts,” J. Biomed. Opt. 11(3), 034025 (2006).
[CrossRef] [PubMed]

Zangwill, L. M.

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120(7), 901–906 (2002).
[PubMed]

Zhou, Q.

N. J. Reus, Q. Zhou, and H. G. Lemij, “Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation,” Invest. Ophthalmol. Vis. Sci. 47(9), 3870–3877 (2006).
[CrossRef] [PubMed]

Q. Zhou, “Retinal scanning laser polarimetry and methods to compensate for corneal birefringence,” Bull. Soc. Belge Ophtalmol. 302(302), 89–106 (2006).
[PubMed]

Q. Zhou and R. N. Weinreb, “Individualized compensation of anterior segment birefringence during scanning laser polarimetry,” Invest. Ophthalmol. Vis. Sci. 43(7), 2221–2228 (2002).
[PubMed]

Appl. Opt. (3)

Arch. Ophthalmol. (2)

D. S. Nassif, N. V. Piskun, and D. G. Hunter, “The Pediatric Vision Screener III: detection of strabismus in children,” Arch. Ophthalmol. 124(4), 509–513 (2006).
[CrossRef] [PubMed]

R. N. Weinreb, C. Bowd, D. S. Greenfield, and L. M. Zangwill, “Measurement of the magnitude and axis of corneal polarization with scanning laser polarimetry,” Arch. Ophthalmol. 120(7), 901–906 (2002).
[PubMed]

Behav. Res. Meth. Instrum. (1)

L. R. Young and D. Sheena, “Survey of eye movement recording methods,” Behav. Res. Meth. Instrum. 7(5), 397–429 (1975).
[CrossRef]

Bull. Soc. Belge Ophtalmol. (1)

Q. Zhou, “Retinal scanning laser polarimetry and methods to compensate for corneal birefringence,” Bull. Soc. Belge Ophtalmol. 302(302), 89–106 (2006).
[PubMed]

Exp. Eye Res. (2)

F. A. Bettelheim, “On the optical anisotropy of lens fiber cells,” Exp. Eye Res. 21(3), 231–234 (1975).
[CrossRef] [PubMed]

R. A. Weale, “Sex, age and the birefringence of the human crystalline lens,” Exp. Eye Res. 29(4), 449–461 (1979).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. (4)

Q. Zhou and R. N. Weinreb, “Individualized compensation of anterior segment birefringence during scanning laser polarimetry,” Invest. Ophthalmol. Vis. Sci. 43(7), 2221–2228 (2002).
[PubMed]

R. W. Knighton, “Spectral dependence of corneal birefringence at visible wavelengths,” Invest. Ophthalmol. Vis. Sci. 43, E-Abstract 152 (2002).

N. J. Reus, Q. Zhou, and H. G. Lemij, “Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation,” Invest. Ophthalmol. Vis. Sci. 47(9), 3870–3877 (2006).
[CrossRef] [PubMed]

R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43(1), 82–86 (2002).
[PubMed]

J. Biomed. Opt. (3)

B. I. Gramatikov, O. H. Y. Zalloum, Y. K. Wu, D. G. Hunter, and D. L. Guyton, “Birefringence-based eye fixation monitor with no moving parts,” J. Biomed. Opt. 11(3), 034025 (2006).
[CrossRef] [PubMed]

D. S. Nassif, N. V. Piskun, B. I. Gramatikov, D. L. Guyton, and D. G. Hunter, “Pediatric Vision Screener 2: pilot study in adults,” J. Biomed. Opt. 9(6), 1369–1374 (2004).
[CrossRef] [PubMed]

D. G. Hunter, D. S. Nassif, N. V. Piskun, R. Winsor, B. I. Gramatikov, and D. L. Guyton, “Pediatric Vision Screener 1: instrument design and operation,” J. Biomed. Opt. 9(6), 1363–1368 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (5)

Opt. Express (2)

Proc. SPIE (2)

K. Irsch, B. I. Gramatikov, Y. K. Wu, and D. L. Guyton, “Spinning wave plate design for retinal birefringence scanning,” Proc. SPIE 7169, 71691F (2009).
[CrossRef]

B. C. E. Pelz, C. Weschenmoser, S. Goelz, J. P. Fischer, R. O. W. Burk, and J. F. Bille, “In vivo measurement of the retinal birefringence with regard on corneal effects using an electro-optical ellipsometer,” Proc. SPIE 2930, 92–101 (1996).
[CrossRef]

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E. Collet, Polarized Light, Fundamentals and Applications (Marcel Dekker, New York, 1993).

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Figures (5)

Fig. 1
Fig. 1

(a) RBS signal strength at 2f (in relative power units) as a function of corneal retardance (CR) and corneal azimuth (CA) during simulated central fixation with computer model of the RBS design implemented into the eye fixation monitor used for model validation purposes (see Subsection 2.3). (b) Contour plot of (a), with contours plotted only up to a signal strength of 0.4. Eyes that fall within the white regions (where the signal is above the threshold of 0.4) will yield strong enough signals for reliable detection, and eyes in the colored regions will not. Please note the different scales on the color bar. Right eyes (and mirrored left eyes) are indicated as circles and left eyes (and mirrored right eyes) as crosses.

Fig. 2
Fig. 2

Top view of opto-mechanical layout of the RBS system of the monocular eye fixation monitor, with added holder for optional inclusion of a wave plate (WP) by means of a rotary mount (RM). A 785 nm laser diode (LD1) produces linearly vertical polarized light, which is deflected by a gold mirror (GM) through a 100 mm f.l. biconvex lens (L1) and a non-polarizing beam splitter (NPBS). The light is then reflected by a polarizing beam splitter (PBS) into a scanning unit, which consists of two plane gold mirrors (M1 and M2). As the mirrors are spun (f = 40 Hz) by a motor (not shown), the stationary beam is converted into a circular scan, pivoting about the center of a stationary 30 mm exit pupil at the subject's eye overfilling the subject's pupil. The scanned circle of light seen by the subject subtends an angle of approximately 3° at the subject's eye (not shown). By the eye's own optics, the beam is focused on the retina, and a portion of this light reflected from the ocular fundus follows the same path back out of the eye. The PBS separates the polarization-altered light into two orthogonal components. The horizontal polarization component is transmitted, passes through a 100 mm f.l. biconvex lens (L2) and a bandpass filter (780 ± 8) nm (F1) with a full width half maximum (FWHM) of (30 ± 8) nm, before finally reaching one of the two photodetectors (PD1). The vertical polarization component is reflected by the polarizing beam splitter (PBS), and part of the vertically polarized light is directed by the NPBS towards the second photodetector (PD2) after passing through another biconvex lens (L3) and bandpass filter (F2) with the same properties. The electronically balanced outputs of the pair of photodetectors are subtracted, yielding the differential polarization signal (S1 signal).

Fig. 3
Fig. 3

Normalized standard deviation of RBS signal strengths of the “right” eyes in the Knighton/Gramatikov data set as a function of retardance and azimuth (fast axis orientation) of the double-pass wave plate. (a) Both retarder properties were varied with an incremental resolution of 10° (i.e. 22 nm for the retardance). (b) Retardance and azimuth of the wave plate were varied with an incremental resolution of 1° (i.e. 2 nm at 785 nm wavelength) and 2° respectively, within the best range of minimal normalized standard deviation from (a).

Fig. 4
Fig. 4

(a) RBS signal strength at 2f (in relative power units) as a function of CR and CA during simulated central fixation with computer model of the RBS design implemented into the monocular eye fixation monitor after adding a double-pass 61° (133 nm) wave plate with fixed azimuth of 144°. (b) Contour plot of (a), with contours plotted only up to a signal strength of 0.4. Eyes that fall within the white regions (where the signal is above the threshold of 0.4) will yield strong enough signals for reliable detection, and eyes in the colored regions will not. Please note the different scales on the color bar. Right eyes (and mirrored left eyes) are indicated as circles and left eyes (and mirrored right eyes) as crosses.

Fig. 5
Fig. 5

(a) RBS signal strength at 2f (in relative power units) as a function of CR and CA during simulated central fixation with computer model of the monocular RBS-based eye fixation monitor after adding a double-pass 61° (133 nm) wave plate with fixed azimuth of 66°. (b) RBS signal strength at 2f (in relative power units) plotted as a function of fast axis orientation of the added 61° (133 nm) wave plate, for a given pair of right eye corneal retardance and azimuth (CR = 33.7 nm, CA = 77°) during simulated central fixation with computer model of the monocular RBS-based eye fixation monitor.

Tables (3)

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Table 1 Measured corneal retardance (CR) and corneal azimuth (CA) for studied right eyes

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Table 2 Predicted RBS signal strength in relative power units during simulated central fixation with computer model of monocular eye fixation monitor for studied right eyes a

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Table 3 Measured RBS signal strength of right eyes of the subjects (in relative power units) a

Equations (7)

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S o u t = M c o r n e a ( o u t ) ( C R , C A ) M r e t i n a ( o u t ) ( δ r , θ r ) M f u n d u s M r e t i n a ( i n ) ( δ r , θ r ) M c o r n e a ( i n ) ( C R , C A ) S i n .
θ r = tan 1 ( R sin ( φ ) + y r e t R cos ( φ ) + x r e t ) + 90 °
δ r = ( i = 1 2 e r τ i ) ( i = 3 5 ( 1 e r τ i ) )
M f u n d u s = ( 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ) .
CA = CSA + 90 ° ,
S o u t = M W P ( o u t ) ( δ W P , θ W P ) M c o r n e a ( o u t ) ( C R , C A ) M r e t i n a ( o u t ) ( δ r , θ r ) M f u n d u s M r e t i n a ( i n ) ( δ r , θ r ) M c o r n e a ( i n ) ( C R , C A ) M W P ( i n ) ( δ W P , θ W P ) S i n .
cos δ T = cos δ R cos δ C sin δ R sin δ C cos 2 ( θ R θ C )

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