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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 5, Iss. 14 — Nov. 16, 2010
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Dual electro-optical modulator polarimeter based on adaptive optics scanning laser ophthalmoscope

Hongxin Song, Xiaofeng Qi, Weiyao Zou, Zhangyi Zhong, and Stephen A. Burns  »View Author Affiliations


Optics Express, Vol. 18, Issue 21, pp. 21892-21904 (2010)
http://dx.doi.org/10.1364/OE.18.021892


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Abstract

We constructed a high speed and high-resolution Stokes vector retinal imaging polarimeter with dual electro-optical modulators based on adaptive optics scanning laser ophthalmoscope. By varying the voltages on the EO crystals line by line, we were able to measure over 500,000 Stokes vectors per second. We used this system in three human subjects demonstrating the capability of the system to be employed in vivo. The high speed effectively decreases the adverse impact of eye motion induced errors in polarization calculations, improving the contrast of retinal structures based on their polarization properties.

© 2010 OSA

1. Introduction

The polarization state of light scattered from tissue is controlled by both the properties of the medium through which the light travels to and from the tissue and by the structural and optical properties of the tissue itself. The human eye, for example, has complex polarization properties that vary as light traverses the eye from the cornea to the retina. An approximately fixed retardation was found at the central area of the cornea, although there are spatial variations [1

1. L. J. Bour, “Polarized Light and the Eye,” Visual Optics and Instrumentation1, (1991).

4

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

]. The crystalline lens has a lamellar organization of lenticular cells, but unlike the cornea, does not contribute substantially to the total optical retardation of the eye [2

2. G. J. Van Blokland and S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4(1), 82–90 (1987). [PubMed]

,5

5. L. J. Bour and N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21(9), 1413–1421 (1981). [PubMed]

]. The retinal nerve fiber layer (RNFL) is composed of the ganglion cell axons and exhibits birefringence arising from the organization of microtubules [5

5. L. J. Bour and N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21(9), 1413–1421 (1981). [PubMed]

10

10. G. J. van Blokland, “Ellipsometry of the human retina in vivo: preservation of polarization,” J. Opt. Soc. Am. A 2(1), 72–75 (1985). [PubMed]

] as do the Henle fibers [11

11. H. B. Brink and G. J. van Blokland, “Birefringence of the human foveal area assessed in vivo with Mueller-matrix ellipsometry,” J. Opt. Soc. Am. A 5(1), 49–57 (1988). [PubMed]

14

14. D. A. VanNasdale, A. E. Elsner, A. Weber, M. Miura, and B. P. Haggerty, “Determination of foveal location using scanning laser polarimetry,” J. Vis. 9(3), 21, 1–17 (2009). [PubMed]

].

2. Method

2.1 Apparatus

We modified the Indiana adaptive optics SLO [42

42. 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).

] as shown in Fig. 1
Fig. 1 Schematic of the AOSLO polarimeter. Channel A with dual LiNbO3 crystals (CR1 and CR2) is for polarization imaging. Channel B is used to calibrate the dual crystals in Channel A.
. A flip mirror (FM1) is introduced into the detection channel after the confocal apertures. By inserting or removing this mirror, we can rapidly switch between regular retinal imaging and polarization imaging. A lens (f = 30 mm) collimates and shrinks the beam diameter to 1.5 mm. A second flip mirror (FM2) is used to switch between channel A and channel B. Channel A is the high speed channel, consisting of two electro-optical crystals (Lithium Niobate, LiNbO3) and a polarizer (Corning PolarCor) followed by a detector (APD Perkins Elmer). The fast axis of the first and second crystal and the polarizer was 0, 45, and 90 degrees relative to the table plane respectively. The apertures of the two crystals are both 2 mm. Channel B is the slower, waveplate based system, which consists of a rotatable high quality quarter wave plate, a polarizer and a detector. This channel was used for calibrating the polarization properties of channel A.

2.2 Device calibration

2.2.1 Calibration of the EO crystals based on ideal Mueller matrix

The polarization state of a light beam can be described by a four-element column vector, [S0S1S2S3]T, known as a Stokes vector [43

43. W. A. Shurcliff, “Polarized Light: Production and Use,” Harvard U. Press (1962).

], where S0 represents the total intensity of the light, S1 the difference between horizontal and vertical linear components, S2 the difference between + 45° and −45° linear components, and S3 the difference between right and left circular components. The degree of polarization (DOP) [44

44. R. A. Chipman, “Polarimetry,” Handbook of Optics2, 22.21–22.37 (1995).

] is the proportion of light that is polarized, while the degree of depolarization (DODP) is 1-DOP.

The retardation of an optical element can be described by a Mueller matrix [44

44. R. A. Chipman, “Polarimetry,” Handbook of Optics2, 22.21–22.37 (1995).

]. Therefore the theoretical Mueller matrix of the LiNbO3 crystals can be written as
M=[10000cos22θ+sin22θcosσsin2θcos2θ(1cosσ)sin2θsinσ0sin2θcos2θ(1cosσ)sin22θ+cos22θcosσcos2θsinσ0sin2θsinσcos2θsinσcosσ]
(1)
where θ is the angle of the fast axis of the crystal and σ is its birefringence. If the half-wave voltage of the crystal is Vπ, the birefringence σ when voltage V is applied is

σ=VπVπ
(2)

If the Stokes vector of light going into Channel A is [S0, S1, S2, S3]T, then the light coming out Sout = [S0, S1, S2, S3]T can be expressed as
[S0'S1'S2'S3']=LP(90)CR2(45)CR1(0)[S0S1S2S3]
(3)
where LP (90) is the Mueller matrix of polarizer at 90 degrees, CR2 (45) and CR1 (0) are the Mueller matrix of the two crystals with fast axis at 45° and 0° respectively. S0 is the only quantity of the outgoing light that we can measure and thus we need to make a series of measurements that vary S0.

After expanding Eq. (3) and substituting Eq. (2) for σ and solving for S0 we have
S0'=S0S1Cos(V2πVπ2)S2Sin(V1πVπ1)Sin(V2πVπ2)+S3Sin(V2πVπ2)Cos(V1πVπ1)
(4)
Where Vπ1 and Vπ2 are the half-wave voltages of the two LiNOb3 crystals, calibrated to be 623 V and 685V respectively, and V1 and V2 are the voltages applied on the crystals.

Equation (4) shows that S0 will modulate with the voltages applied on the two crystals and S0 can be measured. Therefore, Stokes vector of the incoming light, [S0, S1, S2, S3], can be solved as a function of V1, V2and S0. However, when we applied light with known Stokes vectors to validate the technique, the output S0 does not behave as predicated by Eq. (4). For example, we generated horizontal polarized light and Stokes vector of this light were computed as [1, 0.9937, −0.0079, 0.0185]T through channel B. However the Stokes vector computed using channel A was [1, 0.7597, 0.1417, −0.5251]T. Two possible reasons were:

  • a) The two crystals were not aligned perfectly with the optical axis. Slight misalignments can cause a relatively large phase shift along the crystal, leading to polarization rotation if the alignment is not exactly parallel or perpendicular to the polarization. While we performed the alignment carefully, we cannot rule out that this was a problem.
  • b) Manufacturer issues: it is possible that the electrodes of the two crystals were not perfectly parallel with the z axis of the EO crystals, causing the electrical field axis to be at a slight angle with the optical axis of the crystals. This would result in a small deviation in the modulation from the theoretical prediction.

2.2.2 Inverse Matrix Method

To bypass this limitation, we introduced an algorithm to back compute the behavior of the crystals as a function of known input lights. Suppose the polarization properties of the two EO crystals and polarizer can be collectively represented by a matrix X. Equation (4) can be modified as Eq. (5)
Iout=XS
(5)
where Iout is the intensity of light going through channel A, X is the matrix describing the polarization properties of the crystals, and S is the Stokes vector of the incident light. If we can determine matrix X by experiment, then S can be calculated as a function of Iout as

S=(XTX)1XTIout
(6)

Theoretically, the 4 elements of the Stokes vector can be calculated from 4 measurements of Iout, and the size for matrix X only needs to be 4 x 4. In order to increase accuracy, we chose to over-sample and perform a least squares fit. This was desirable, because there is a tradeoff between the number of measurements and the accuracy of the fit. Using a model eye we performed a number of trial experiments to decide how many measurements we should make. As expected, more measurements increased the accuracy, but increasing the number of samples would either decrease the image size of the retina or if we increase the imaging time to compensate would increase the probability of eye motion induced errors. We converged on 7 measurements as a compromise between accuracy and retinal image size. The use of seven measurements required us to scan a single line 7 times with different voltages on the two crystals. The resultant matrix size was therefore 7 x 4. With the line scan rate of our system at 8 kHz, we could form Stokes vector line images at more than 1kilolines/sec.

The setup for measuring matrix X is shown in Fig. 1. A plane mirror was placed in the retinal conjugate plane of the AOSLO system to reflect light into the AOSLO, and into Channels A and B. A quarter wave plate and a half wave plate were used to generate light of different polarization states. The APD detector in channel A was replaced by a 10 mHz adjustable balanced receiver (New Focus) to record the intensity of light. In channel B, a QW polarization analyzer (a rotatable 1/4 wave plate followed by a polarizer and a detector) was used to measure the Stokes vector of the same light. Before calibrating the system, the polarization properties of light at spot A and B were confirmed to be identical by separate polarization state measurements. Lights with 30 different polarization states were used for the calibration. These thirty different polarized lights were generated by rotating a quarter wave plate or half waveplate in front of the plane mirror. To improve the calibration accuracy, the thirty lights were generated such that their Stokes vectors were spread across the Poincare sphere. For each input, we varied the voltage on the two EO crystals from −360 V to 360 V in 120 V steps (7 values). 210 equations were generated, and the least-square fit was performed to determine matrix X. The result is shown as Eq. (7):

X=[147.433111.486101.53816.97494147.954845.9059132.50441.47455145.516850.1475675.478678.30778146.9625113.490124.1471438.84631151.8327127.202937.6634548.7225152.5378116.457244.06670.461144.8684101.442792.85472.152597]
(7)

To verify the accuracy of X, we inverted the process. We used the matrix X and the 30 measured intensities to back calculate the corresponding 30 Stokes vectors. As expected, the computed Stokes vectors agreed well with the actual ones used in the calibration.

2.3 Verifying EO polarimeter performance

To verify the calibration, an additional 25 lights of different polarization states from those used in calibration were generated and measured by channel B (Fig. 1). For each input, we varied the voltages on the EO crystals from −360 V to 360 V in 120 V steps (7 values). The Stokes vector of the light was then determined by Eq. (6). Intraclass correlation analysis and ANOVA analysis were used to test if the Stokes vector measured by the QW and the EO methods agreed.

2.4 AOSLO System calibration

The polarization properties of the AOSLO were calibrated in 2 steps: First, a QW polarization analyzer was placed at the exit pupil of the system. The Stokes vector of the incident light was confirmed to be linearly polarized. Second, a plane mirror was placed at the retinal conjugate plane of an artificial eye at the exit pupil of the system. The light returning from the plane mirror was measured using channel B. The resultant Stokes vector of the light after passing the double-pass imaging system was calculated as [1,-0.9775, −0.064, 0.0226]T, DOP was computed to be 0.98, within experimental error of the ideal value of 1.0.

2.5 Scanning mode modification

2.6 Image processing

All images were acquired using a 200 µm confocal aperture (4 x the size of the Airy disc). This somewhat large confocal aperture allowed us to collect not only the polarized light returning from the retina but also the scattered light, which is more depolarized. 50 sequential image frames were recorded during each image collecting section in about 3 seconds. Offline image processing requires that we first select a number of good frames (less eye motion, good image quality), and align and average the frames using custom MATLAB programs (MathWorks, Inc.). A group of 7 images corresponding to 7 different voltages on two LiNOb3 crystals were generated. Cross correlation was calculated in the brightest group images at 8 different locations. Centroid of the cross correlations was used to determine the location of best alignment, generating sub-pixel accuracy. Images were then aligned using an approach similar to that of Stevenson and Roorda [45

45. S. B. Stevenson and A. Roorda, “Correcting for Miniature Eye Movements in High Resolution Scanning Laser Ophthalmoscopy,” Proc. SPIE 5688A, 145–151 (2005).

]. The alignment was performed for those detection channel states which produced the highest intensity, and the other 6 conditions were moved accordingly. This allowed us to avoid alignment errors that result from aligning very dim images. Figure 3
Fig. 3 Reconstructed images with different voltages on the two EO crystals. (A) −360 V, (B) −240 V, (C) −120 V, (D) 0 V, (E) 120 V, (F) 240 V, (G) 360 V. Scale bar is 100 µm.
shows the 7 reconstructed images after aligning and averaging (40 frames).

2.7 DOP calculation for individual cone photoreceptors

After the images were aligned and Stokes vector images were computed, individual cone photoreceptors of each subject were located manually in the intensity image. The DOP of each cone photoreceptors was calculated.

2.8 Subjects

3. Results

3.1 Dual EO Polarimeter Performance

Figure 4
Fig. 4 Comparison of Stokes vector and DOP measured with two polarization techniques.
plots the S1, S2, S3 and DOP of the 25 polarized lights measured in the verification phase of the experiment by the QW polarization analyzer and the EO polarization analyzer. A 2-way ANOVA revealed no statistical significant difference between the individual Stokes vectors measured with the two techniques, p = 0.967. We computed the intraclass correlation coefficients between the two polarization techniques and found excellent agreement Correlations for S1, S2, S3 and DOP were 0.996, 0.936, 0.982 and 0.701 respectively, p < 0.001. To test the repeatability, a model eye was imaged using this Dual EO AOSLO polarimeter at different times (5 minutes interval) and Stokes vector images of this model eye were computed at each time point. Normalized cross correlation was performed on the S1, S2, S3 and DOP images at different time, the correlations between these Stokes vector images at different time are over 96% for all 4 parameters.

3.2 Polarization images of cone photoreceptors from healthy subjects

3.3 Degree of polarization of individual cone photoreceptors

The degree of polarization of individual cone photoreceptors was calculated (Fig. 7
Fig. 7 Correlation between cone photoreceptor intensity and degree of polarization. Data are from 3 subjects. All regression slopes are statistically significant, p < 0.0001.
) as a function of intensity of cone photoreceptors for all 3 subjects. Statistical analysis revealed a significant correlation between the degree of polarization and the intensity of the cone photoreceptor (p < 0.001) with brighter cones having a higher degree of polarization.

3.4 Polarization images of nerve fiber layer from healthy subjects

Our new polarimeter can also be used to measure variations in polarization properties for other retinal structures. Figure 8
Fig. 8 Images of nerve fiber layer of subject 2 at 6 degree nasal retina. Different structures showed different polarization properties. Scale bar is 100 µm. Region in dash line in panel A is where the polarization images in B are computed. In panel B, (a) intensity image, (b) S1*intensity, (c) S2*intensity, (d) S3*intensity, (e) DOP*intensity, f) DODP*intensity. Images in panel B is the region in the dashed line in panel A.
shows an image of the nerve fiber layer from subject 2. Panel A shows the nerve fiber layer 6 degree in the nasal retina. Panel B shows the Stokes vector of nerve fiber layer normalized according to the intensity at each location (Stokes vector images). All images are formed using absolute values.

4. Discussion and Conclusion

Alignment of the electro-optical modulators proved to be critical and we could not count on arriving at perfectly aligned crystals. Small misalignment of the crystals can cause a large phase shift across the long axis of the crystal. We consider it most likely that slight misalignments caused errors when we followed the conventional method for operating the systems. These slight phase errors the caused the Stokes vector measurements to be inaccurate when compared to a waveplate polarimeter. To circumvent the problem, we used an inverse method to empirically determine the polarization matrix of the crystals as a function of voltage using a set of known Stokes vectors as inputs. With this algorithm, even in the presence of slight misalignment or imperfections with these crystals, the condition number of the inverse matrix is adequate to quickly and accurately calculate matrix X and use it to calculate the Stokes vector of the incident light. Our data showed that the QW polarization analyzer and the EO polarization analyzer calibrated in this manner produced statistically identical Stokes vector measurement of the same incident light.

The major factor affecting the measured individual differences in the overall Stokes vector of light returned from the retina probably arise from corneal birefringence. Studies have shown that in most corneas, the slow axis pointed nasally downward [2

2. G. J. Van Blokland and S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4(1), 82–90 (1987). [PubMed]

,50

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

]. Spatial variation of birefringence of cornea has also been indicated in some studies [1

1. L. J. Bour, “Polarized Light and the Eye,” Visual Optics and Instrumentation1, (1991).

,51

51. G. J. Van Blokland and S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4(1), 82–90 (1987). [PubMed]

,52

52. 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]

]. In our study, Stokes vector images of retinal structures not only represent the polarization properties of the retinal structures, they also include the polarization information from the cornea. However, our entire scan angle is only about 1.6 degrees, and so the variation of corneal polarization across this field should be small. The cornea will affect the overall image, but not comparisons across cells. Nevertheless we did measure variations in the polarization state between cones. This can be seen when we plot the Stokes vectors of individual cone photoreceptors at 5 degree in the nasal retina for each of the 3 subjects (Fig. 9
Fig. 9 Stokes vectors of individual cone photoreceptors were plotted on the Poincare sphere.
). Stokes vector of cone photoreceptors of each subject clumped together at different locations, presumably depending on the corneal birefringence. Within a single subject’s data the cones varied somewhat in terms of both their depolarization and their polarization angle.

The variation between cones in a single subject probably has at least two sources. First, there should be differences locally due to variations in retinal birefringence (such as the nerve fiber layer) and also due to differences between cones. Again because the field size is small, the variation across the field, which arises from nerve fiber layer birefringence, should be small particularly for this region of the retina where the fibers tend to be aligned in a common direction and show little local curvature. The second possibility for individual differences in DOP is associated with the fact that the light from the cones appears to be the light scattered within the cones and guided back towards the pupil. It is well known that the cones are directionally tuned, a property known as the Stiles-Crawford effect [53

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

56

56. W. Gao, B. Cense, Y. Zhang, R. S. Jonnal, and D. T. Miller, “Measuring retinal contributions to the optical Stiles-Crawford effect with optical coherence tomography,” Opt. Express 16(9), 6486–6501 (2008). [PubMed]

]. It has been shown [57

57. G. J. van Blokland and D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26(3), 485–494 (1986). [PubMed]

,58

58. S. A. Burns, S. Wu, F. C. Delori, and A. E. Elsner, “Direct measurement of human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12(10), 2329–2338 (1995).

] that the portion of light guided by the photoreceptors retains its polarization, while light that has been scattered more widely did not. Simple mixing of the scattered and guided components of light predicts that cone photoreceptors with higher intensity should have higher degree of polarization, as we measured. Using just the portion of the light that maintains polarization greatly increases the contrast of the cone images. In comparison, the shadows of blood vessels are illuminated by a higher proportion of multiply scattered light and therefore have a higher DODP. The final possibility is that there are slight differences between cones in their birefringence, although confirming this will require future experiments.

Acknowledgments

This work was supported by the National Institutes of Health (NIH) EY04395, EY14375 and P30EY019008. We thank Toco Yuenping Chui for help with data collection and Yanming Zhao for discussions on data analysis. We thank Ann Elsner, Brian Marks and Don Miller for constructive feedback on the manuscript.

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2.

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3.

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S. Michels, M. Pircher, W. Geitzenauer, C. Simader, E. Götzinger, O. Findl, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Value of polarisation-sensitive optical coherence tomography in diseases affecting the retinal pigment epithelium,” Br. J. Ophthalmol. 92(2), 204–209 (2008). [PubMed]

30.

M. Miura, M. Yamanari, T. Iwasaki, A. E. Elsner, S. Makita, T. Yatagai, and Y. Yasuno, “Imaging polarimetry in age-related macular degeneration,” Invest. Ophthalmol. Vis. Sci. 49(6), 2661–2667 (2008). [PubMed]

31.

A. Weber, M. C. Cheney, Q. Y. J. Smithwick, and A. E. Elsner, “Polarimetric imaging and blood vessel quantification,” Opt. Express 12(21), 5178–5190 (2004). [PubMed]

32.

M. Miura, A. E. Elsner, M. C. Cheney, M. Usui, and T. Iwasaki, “Imaging polarimetry and retinal blood vessel quantification at the epiretinal membrane,” J. Opt. Soc. Am. A 24(5), 1431–1437 (2007).

33.

T. Y. Chui, H. Song, and S. A. Burns, “Adaptive-optics imaging of human cone photoreceptor distribution,” J. Opt. Soc. Am. A 25(12), 3021–3029 (2008).

34.

T. Y. P. Chui, H. Song, and S. A. Burns, “Individual variations in human cone photoreceptor packing density: variations with refractive error,” Invest. Ophthalmol. Vis. Sci. 49(10), 4679–4687 (2008). [PubMed]

35.

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]

36.

A. Roorda, Y. H. Zhang, and J. L. Duncan, “High-resolution in vivo imaging of the RPE mosaic in eyes with retinal disease,” Invest. Ophthalmol. Vis. Sci. 48(5), 2297–2303 (2007). [PubMed]

37.

D. C. Gray, W. Merigan, J. I. Wolfing, B. P. Gee, J. Porter, A. Dubra, T. H. Twietmeyer, K. Ahamd, R. Tumbar, F. Reinholz, and D. R. Williams, “In vivo fluorescence imaging of primate retinal ganglion cells and retinal pigment epithelial cells,” Opt. Express 14(16), 7144–7158 (2006). [PubMed]

38.

Z. Zhong, B. L. Petrig, X. Qi, and S. A. Burns, “In vivo measurement of erythrocyte velocity and retinal blood flow using adaptive optics scanning laser ophthalmoscopy,” Opt. Express 16(17), 12746–12756 (2008). [PubMed]

39.

J. A. Martin and A. Roorda, “Direct and noninvasive assessment of parafoveal capillary leukocyte velocity,” Ophthalmology 112(12), 2219–2224 (2005). [PubMed]

40.

H. Song, Y. Zhao, X. Qi, Y. T. Chui, and S. A. Burns, “Stokes vector analysis of adaptive optics images of the retina,” Opt. Lett. 33(2), 137–139 (2008). [PubMed]

41.

B. Wang, A. Leadbetter, and R. R. Rockwell, “Evaluation of a dual PEM Stokes polarimeter using different signal processing methods,” J. A. Shaw, and J. S. Tyo, eds. (SPIE, San Diego, CA, USA, 2005), pp. 58880W–58888.

42.

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).

43.

W. A. Shurcliff, “Polarized Light: Production and Use,” Harvard U. Press (1962).

44.

R. A. Chipman, “Polarimetry,” Handbook of Optics2, 22.21–22.37 (1995).

45.

S. B. Stevenson and A. Roorda, “Correcting for Miniature Eye Movements in High Resolution Scanning Laser Ophthalmoscopy,” Proc. SPIE 5688A, 145–151 (2005).

46.

A. E. Elsner, A. Weber, M. C. Cheney, D. A. VanNasdale, and M. Miura, “Imaging polarimetry in patients with neovascular age-related macular degeneration,” J. Opt. Soc. Am. A 24(5), 1468–1480 (2007).

47.

M. Miura, A. E. Elsner, A. Weber, M. C. Cheney, M. Osako, M. Usui, and T. Iwasaki, “Imaging polarimetry in central serous chorioretinopathy,” Am. J. Ophthalmol. 140(6), 1014–1019 (2005). [PubMed]

48.

J. M. Bueno, “Measurement of parameters of polarization in the living human eye using imaging polarimetry,” Vision Res. 40(28), 3791–3799 (2000). [PubMed]

49.

T. A. Maldonado, “Electro-optics Modulators,” Handbook of Optics2, 13.11–13.35 (1995).

50.

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

51.

G. J. Van Blokland and S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4(1), 82–90 (1987). [PubMed]

52.

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]

53.

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

54.

G. T. D. Francia, “Retinal cones as dielectric antennas,” J. Opt. Soc. Am. 39(4), 324 (1949).

55.

A. W. Snyder and C. Pask, “The Stiles-Crawford effect--explanation and consequences,” Vision Res. 13(6), 1115–1137 (1973). [PubMed]

56.

W. Gao, B. Cense, Y. Zhang, R. S. Jonnal, and D. T. Miller, “Measuring retinal contributions to the optical Stiles-Crawford effect with optical coherence tomography,” Opt. Express 16(9), 6486–6501 (2008). [PubMed]

57.

G. J. van Blokland and D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26(3), 485–494 (1986). [PubMed]

58.

S. A. Burns, S. Wu, F. C. Delori, and A. E. Elsner, “Direct measurement of human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12(10), 2329–2338 (1995).

OCIS Codes
(120.3890) Instrumentation, measurement, and metrology : Medical optics instrumentation
(170.4460) Medical optics and biotechnology : Ophthalmic optics and devices
(180.1790) Microscopy : Confocal microscopy
(330.4300) Vision, color, and visual optics : Vision system - noninvasive assessment

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: July 29, 2010
Revised Manuscript: September 18, 2010
Manuscript Accepted: September 19, 2010
Published: September 30, 2010

Virtual Issues
Vol. 5, Iss. 14 Virtual Journal for Biomedical Optics

Citation
Hongxin Song, Xiaofeng Qi, Weiyao Zou, Zhangyi Zhong, and Stephen A. Burns, "Dual electro-optical modulator polarimeter based on adaptive optics scanning laser ophthalmoscope," Opt. Express 18, 21892-21904 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-21-21892


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References

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  22. M. C. Cheney, A. E. Elsner, S. A. Burns, M. B. M. Kairala, C. L. Trempe, K. Lashkari, J. J. Weiter, M. Miura, M. Osako, and M. Usui, “Polarization amplitude and phase changes in retinal exudation,” Invest. Ophthalmol. Vis. Sci. 44, U691–U691 (2003).
  23. A. E. Elsner, M. Miura, J. B. Stewart, M. B. M. Kairala, and S. A. Burns, “Novel algorithms for polarization imaging resulting in improved quantification of retinal blood vessels.,” in Medicine Meets Virtual Reality, J. D. Westwood, ed. (IOS Press, Washington, D.C., 2003), pp. 59–61.
  24. M. B. Mellem-Kairala, A. E. Elsner, A. Weber, R. B. Simmons, and S. A. Burns, “Improved contrast of peripapillary hyperpigmentation using polarization analysis,” Invest. Ophthalmol. Vis. Sci. 46(3), 1099–1106 (2005). [PubMed]
  25. R. N. Weinreb, C. Bowd, and L. M. Zangwill, “Glaucoma detection using scanning laser polarimetry with variable corneal polarization compensation,” Arch. Ophthalmol. 121(2), 218–224 (2003). [PubMed]
  26. M. T. Nicolela, C. Martinez-Bello, C. A. Morrison, R. P. LeBlanc, H. G. Lemij, T. P. Colen, and B. C. Chauhan, “Scanning laser polarimetry in a selected group of patients with glaucoma and normal controls,” Am. J. Ophthalmol. 132(6), 845–854 (2001). [PubMed]
  27. S. A. Burns, A. E. Elsner, M. B. Mellem-Kairala, and R. B. Simmons, “Improved contrast of subretinal structures using polarization analysis,” Invest. Ophthalmol. Vis. Sci. 44(9), 4061–4068 (2003). [PubMed]
  28. C. Ahlers, E. Götzinger, M. Pircher, I. Golbaz, F. Prager, C. Schütze, B. Baumann, C. K. Hitzenberger, and U. Schmidt-Erfurth, “Imaging of the retinal pigment epithelium in age-related macular degeneration using polarization-sensitive optical coherence tomography,” Invest. Ophthalmol. Vis. Sci. 51(4), 2149–2157 (2010).
  29. S. Michels, M. Pircher, W. Geitzenauer, C. Simader, E. Götzinger, O. Findl, U. Schmidt-Erfurth, and C. K. Hitzenberger, “Value of polarisation-sensitive optical coherence tomography in diseases affecting the retinal pigment epithelium,” Br. J. Ophthalmol. 92(2), 204–209 (2008). [PubMed]
  30. M. Miura, M. Yamanari, T. Iwasaki, A. E. Elsner, S. Makita, T. Yatagai, and Y. Yasuno, “Imaging polarimetry in age-related macular degeneration,” Invest. Ophthalmol. Vis. Sci. 49(6), 2661–2667 (2008). [PubMed]
  31. A. Weber, M. C. Cheney, Q. Y. J. Smithwick, and A. E. Elsner, “Polarimetric imaging and blood vessel quantification,” Opt. Express 12(21), 5178–5190 (2004). [PubMed]
  32. M. Miura, A. E. Elsner, M. C. Cheney, M. Usui, and T. Iwasaki, “Imaging polarimetry and retinal blood vessel quantification at the epiretinal membrane,” J. Opt. Soc. Am. A 24(5), 1431–1437 (2007).
  33. T. Y. Chui, H. Song, and S. A. Burns, “Adaptive-optics imaging of human cone photoreceptor distribution,” J. Opt. Soc. Am. A 25(12), 3021–3029 (2008).
  34. T. Y. P. Chui, H. Song, and S. A. Burns, “Individual variations in human cone photoreceptor packing density: variations with refractive error,” Invest. Ophthalmol. Vis. Sci. 49(10), 4679–4687 (2008). [PubMed]
  35. 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]
  36. A. Roorda, Y. H. Zhang, and J. L. Duncan, “High-resolution in vivo imaging of the RPE mosaic in eyes with retinal disease,” Invest. Ophthalmol. Vis. Sci. 48(5), 2297–2303 (2007). [PubMed]
  37. D. C. Gray, W. Merigan, J. I. Wolfing, B. P. Gee, J. Porter, A. Dubra, T. H. Twietmeyer, K. Ahamd, R. Tumbar, F. Reinholz, and D. R. Williams, “In vivo fluorescence imaging of primate retinal ganglion cells and retinal pigment epithelial cells,” Opt. Express 14(16), 7144–7158 (2006). [PubMed]
  38. Z. Zhong, B. L. Petrig, X. Qi, and S. A. Burns, “In vivo measurement of erythrocyte velocity and retinal blood flow using adaptive optics scanning laser ophthalmoscopy,” Opt. Express 16(17), 12746–12756 (2008). [PubMed]
  39. J. A. Martin and A. Roorda, “Direct and noninvasive assessment of parafoveal capillary leukocyte velocity,” Ophthalmology 112(12), 2219–2224 (2005). [PubMed]
  40. H. Song, Y. Zhao, X. Qi, Y. T. Chui, and S. A. Burns, “Stokes vector analysis of adaptive optics images of the retina,” Opt. Lett. 33(2), 137–139 (2008). [PubMed]
  41. B. Wang, A. Leadbetter, and R. R. Rockwell, “Evaluation of a dual PEM Stokes polarimeter using different signal processing methods,” J. A. Shaw, and J. S. Tyo, eds., (SPIE, San Diego, CA, USA, 2005), pp. 58880W–58888.
  42. 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).
  43. W. A. Shurcliff, “Polarized Light: Production and Use,” (Harvard U. Press, 1962).
  44. R. A. Chipman, “Polarimetry,” in Handbook of Optics (McGraw-Hill, 1995) Vol. 2.
  45. S. B. Stevenson and A. Roorda, “Correcting for Miniature Eye Movements in High Resolution Scanning Laser Ophthalmoscopy,” Proc. SPIE 5688A, 145–151 (2005).
  46. A. E. Elsner, A. Weber, M. C. Cheney, D. A. VanNasdale, and M. Miura, “Imaging polarimetry in patients with neovascular age-related macular degeneration,” J. Opt. Soc. Am. A 24(5), 1468–1480 (2007).
  47. M. Miura, A. E. Elsner, A. Weber, M. C. Cheney, M. Osako, M. Usui, and T. Iwasaki, “Imaging polarimetry in central serous chorioretinopathy,” Am. J. Ophthalmol. 140(6), 1014–1019 (2005). [PubMed]
  48. J. M. Bueno, “Measurement of parameters of polarization in the living human eye using imaging polarimetry,” Vision Res. 40(28), 3791–3799 (2000). [PubMed]
  49. T. A. Maldonado, “Electro-optics Modulators,” in Handbook of Optics, M. Mass, ed., (McGraw-Hill, Orlando 1995).
  50. R. W. Knighton and X. R. Huang, “Linear birefringence of the central human cornea,” Invest. Ophthalmol. Vis. Sci. 43(1), 82–86 (2002). [PubMed]
  51. G. J. Van Blokland and S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4(1), 82–90 (1987). [PubMed]
  52. 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]
  53. W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. Lond. 112(778), 428–450 (1933).
  54. G. T. D. Francia, “Retinal cones as dielectric antennas,” J. Opt. Soc. Am. 39(4), 324 (1949).
  55. A. W. Snyder and C. Pask, “The Stiles-Crawford effect--explanation and consequences,” Vision Res. 13(6), 1115–1137 (1973). [PubMed]
  56. W. Gao, B. Cense, Y. Zhang, R. S. Jonnal, and D. T. Miller, “Measuring retinal contributions to the optical Stiles-Crawford effect with optical coherence tomography,” Opt. Express 16(9), 6486–6501 (2008). [PubMed]
  57. G. J. van Blokland and D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26(3), 485–494 (1986). [PubMed]
  58. S. A. Burns, S. Wu, F. C. Delori, and A. E. Elsner, “Direct measurement of human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12(10), 2329–2338 (1995).

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