Directional property of the retinal reflection measured with optical coherence tomography and wavefront sensing

Table of Contents

LIST OF TABLES

..................................................................................... XII

LIST OF FIGURES

.................................................................................

XIII

CHAPTER 1: INTRODUCT ION

................................................................

1

1.1 Optical properties of the

retina

................................................................................. 2

1.2 The Stiles - Crawford effect

......................................................................................... 4

1.3 Measurement of the Optical Stiles - Crawford effect

................................................ 8

1.4 Optical coherence tomography

................................................................................ 12

1.4.1 Principle of optical coherence tomography

......................................................... 14

1.4.2 Resolution

............................................................................................................ 17

1.4.3 Image depth

.......................................................................................................... 18

1.5 Shack - Hartmann wavefront sensin g

....................................................................... 19

1.6 Statement of work/ scope of thesis

........................................................................... 24

CHAPTER 2: RETINAL C ONTRIBUTIONS TO THE OPTICAL STILES- CRAWFORD EFFECT WITH

AT A SINGLE RETINAL ECCENTRICITY

........................................................................................ 27

2.1 Abstract

...................................................................................................................... 27

2.2 Introduction

............................................................................................................... 28

2.3 Methods

...................................................................................................................... 30

2.3.1 Des cription of spectral - domain OCT apparatus

.................................................. 30

2.3.2 Human subjects

.................................................................................................... 33

2.3.3 Data acquisition and proces sing ........................................................................... 34

2.4 Results

........................................................................................................................ 38

2.4.1 Directionality of the retinal layers measured with SD - OCT

............................... 38

2.4.2 Noise reduction by A - scan averaging

.................................................................. 39

2.5 Discussion ................................................................................................................... 43

2.5.1 Directionality of the retinal layers measured with SD - OCT

............................... 43

x

2.5.2 Comparison of directionality with con ventional reflectrometric and psychophysical values in the literature.

........................................................................ 49

2.5.3 Noise reduction by A - scan averaging

.................................................................. 52

2.6 Conclusion

................................................................................................................. 53

2.7 Acknowledgement

..................................................................................................... 54

CHAPTER 3: RETINAL C ONTRIBUTIONS TO DIRE CTIONALITY AS A FUNCTION OF RET INAL ECCENTRICITY US ING CUSTOM OPTICAL COHERENCE TO MOGRAPHY

........................................... 55

3.1 Abstract

...................................................................................................................... 55

3.2 Introduction

............................................................................................................... 56

3.3 Methods

...................................................................................................................... 58

3.3.1 Description of the apparatus

................................................................................ 58

3.3.2 Human subjects

.................................................................................................... 60

3.3.3 Measurement procedure and data analysis

.......................................................... 61

3.4 Res ults

........................................................................................................................ 65

3.4.1 Directionality of retinal nerve fiber layer (RNFL)

.............................................. 67

3.4.2 Directionality of henle’s fiber layer (HFL)

.......................................................... 70

3.4.3 Directionality of photoreceptor (RNFL)

.............................................................. 73

3.5 Discu ssion ................................................................................................................... 75

3.5.1 Retina nerve fiber layer

........................................................................................ 75

3.5.2 Henle’s fiber layer ................................................................................................ 79

3.5.3 Photoreceptor

....................................................................................................... 82

3.6 Conclusion

................................................................................................................. 87

3.7 Acknowledgement

..................................................................................................... 88

CHAPTER 4: DIRECTION ALITY OF THE RETINAL

REFLECTION MEASURED WITH A SHAC K- HARTMANN WAVEFRONT SENSOR

....................................................................................................... 89

4.1 Abstract:

.................................................................................................................... 89

4.2 Introduction

............................................................................................................... 90

4.3 Methods

...................................................................................................................... 92

4.3.1 SHWS Apparatus

................................................................................................. 92

4.3.2 Experimental protocol and data processing ......................................................... 94

xi

4.3.3 Calibration of SHWS system

............................................................................... 99

4.4 Results

...................................................................................................................... 101

4.5 Discussion ................................................................................................................. 105

4.5.1 Comparison of directionality with conventional reflectrometric measurements

105

4.5.2 Directionality of core and tail of SHWS spots ................................................... 110

4.5.3 Influence of optical SCE on SHWS measurements of ocular aberrations

......... 112

4.6 Conclusion

............................................................................................................... 113

4.7 Acknowledgment

..................................................................................................... 114

CHAPTER 5: SUMMARY

...................................................................... 115

5.1 Summary of thesis research

................................................................................... 115

5.2 Future research direction

....................................................................................... 117

BIBLIOGRAPHY

...................................................................................... 120

xii

List of Tables

Table 1.1

Directionality values measured using different reflectometric designs: ρ Gorrand – Delori

, ρ de Lint et al.

, and ρ van Blokland (0 and 2 deg) (Marcos & Burns, 1999).

..................................................... 11

Table 1.2

The first 14 Zernike polynomials, with numbering followi ng the OSA notation.

........ 21

Table 2.1

Directionality values obtained from SD - OCT, two conventional reflectometers, and a psychophysical technique at 2 degree eccentricity. For SD - OCT, ρ oct

values are shown for three retinal layers (IS/OS, PTOS, and RPE) and four subjects (S1, S2, S3, and S4) as determined by fitting the five parameter model defined by Eq.(1) to the measured reflectance. ρ oct

is an average of the fits along the horizontal and vertical meridians. To fac ilitate comparison with directionality values in the literature, ρ Marcos equiv

and ρ Gorrand equiv

are equivalent values that take into account wavelength and definition differences for the conventional reflectometer measurements in Marcos and Burns ( 1999 ) and Gorrand and Delori ( 1995 ). ρ psycho

is a measurement of the psychophysical SCE at 2 degree eccentricity ( He et al ., 1999, Marcos & Burns, 1999 ) …………………………50

Table 3.1

Mean variation and standard deviation of locations of SCE peaks o n ISOS, PTOS and RPE reflection…………………………………………………………………………………….82

Table 4.1 : Relevant parameters of the different reflectometric techniques …………………….118

xiii

List of Figures

Figure 1.1

(Top) The psychophysical SCE results from the waveguiding property of photoreceptors. Rays (or waves) are readily captured by the photoreceptor when incident at small angles (relative to the photoreceptor axis) compared to at large angles. (Bottom) The op tical SCE is an equivalent effect, except with the light path reversed. Rays (or waves) contain more energy when exiting the photoreceptor at small angles (relative to the photoreceptor axis) than at large angles.

.............................................................................................................................................. 7

Figure 1.2

Half of the incident light passes through the photoreceptor and the other half passes between photoreceptors. Light not absorbed by photopigment and melanin is scattered by the RPE. Dir. U/B

pathway represents the small portion of light that is captured b y the photoreceptor, scatters from the RPE, gets recaptured by the photoreceptor, and finally exits the retina. Light following this path forms the directional component. Dif. U/B

pathway represents light that is captured by the photoreceptor, scatters from the RPE, passes between photoreceptors, and finally exits the retina. Light following this path contributes to the diffused component. Dif. C

pathway represents light which is not captured by the photoreceptor on either pass and contributes to the diffus ed component (Van Blokland, 1986).

..................................................................................... 9

Figure 1.3

Entry and exit pupil configurations for four different reflectometric techniques: (a) Gorrand and Delori (b) de Lint et al.,

(c) van Blokland, (d) Burns et al., and Marcos & Burns. (Marcos & Burns, 1999)

................................................................................................................ 11

Figure

1.4

Schematic layout of the spectral domain optical coherence tomography system. (a) It is realized by a Michelson interferometer with four channels: illumination, reference, sample and detection channel. (b) The sample reflectivity profile, for this case

it is single mirror, is achieved by a Fourier transform of the interference spectrum in k - space.

................................................... 15

Figure 1.5

The Shack - Hartmann principle. (A) Wavefront slope across a single lens can be measured by measuring the shift of the focal point. (B) Wavefront slope

across multiple lenses can be measured by measuring the many focal point shifts (Liang et al. , 1994).

.......................... 21

Figure 2.1

(top) Conceptua l layout of the adaptive optics SD - OCT instrument that was used to measure the retinal contributions to the optical SCE. (bottom) en face

view of the eye’s pupil and the 13 sub - aperture positions along the geometrical horizontal and vertical meridians thro ugh which the retina was illuminated and imaged in a sequential fashion. Key: SLD (superluminecent diode), BS (fiber - based beam splitter), AO (adaptive optics sub - system), P (pellicle beamsplitter).

....................................................................................................................................................... 34

Figure 2.2

Representative A - scan of the retinal reflectance at 2 degree eccentricity. The A - scan was generated by averaging 510 A - scans. Location of labels are consistent with that widely reported in the OCT literature. Key: ILM (inner limiting membrane), IPL (inner

plexiform layer), OPL (outer plexiform layer), ELM (external limiting membrane), IS/OS (inner segment/outer segment junction), PTOS (posterior tip of outer segment), and RPE (retinal pigment epithelium).

....................................................................................................................................................... 38

Figure 2.3

Averaged A - scans of the same proximal patch of retina, but with different beam entry positions along the vertical meridian. Entry positions are at 1 mm intervals and spe cified relative to the geometric pupil center. A - scans are normalized to the inner retina reflection (see text for details).

........................................................................................................................................... 39

Figu re 2.4

Dependence of the normalized retinal reflectance on beam entry position in the pupils of four subjects (S1, S2, S3, and S4). Rectangles, triangles and circles denoted measured reflectance of the IS/OS, PTOS and RPE layers, respectively. Red, blue an d black curves

xiv

represent the best fit of the five parameter model to the measured reflectances. The ordinate is in linear intensity.

............................................................................................................................... 41

Figure 2.5

Standard deviation over mean as a function of A - scans averaged. The asterisks indicate the experimental results and the solid curves represent fits of 1/ √ N effective , where N effective

is defined as N divided by the correlation width. Correlation widths were found to be 1.0, 5.0, 6.0, and 5.2 µ m, respectively, for the vitreous, GCL, PTOS, and RPE, yielding maximum N effective

values of 510, 102, 85, and 98. Although not shown, the standard deviation ove r mean was also determined for the IS/OS and found similar to that of the PTOS. ................................................. 44

Figure 2.6

Variability in reflectance of the PTO S layer of subject S2 depending on number of A - scans averaged. Error bars are superimposed on the Figure 2.4 (S2, PTOS) plot and represent the standard deviation in the reflectance for (left) single and (right) averaged (510) A - scans. The two cases have an

average contrast (standard deviation / mean) of 1 and 0.13, respectively. Speckle at the PTOS layer is assumed fully developed and the dominate noise source in the SD - OCT A - scans.

.............................................................................................................................................. 46

Figure 3.1

A schematic layout of the custom SD - OCT system. Light from the broadband source was distributed to the sample and reference channel via an 80/20 fiber coupler. The sample channel consists of XY

galvo - scanners that are mounted on a computer - controlled XY translation stage; a dichroic beam splitter to transmit and reflect visible and near infrared wavelengths, respectively; and a relay telescope consisting of two achromatic doublets. The reference

channel consists of a variable neutral density filter (ND) for attenuation; a water vial (WV) for dispersion compensation in eye tissue; and collimating optics and a planar mirror. The detection channel consisted of a collimating achromatic doublet (f= 100mm), a 1200 line/mm transmissive grating, a multi - element lens (f =135mm), and a 2048 pixel Atmel line scan CCD that operated at 23,000 A - scans per second.

....................................................................................................................... 60

Figure 3.2

(a, b, c, d, e) Averaged B - scans of the same proximal patch of retina, but with different beam entry positions at the pupil (nasal, center, temporal, superior, and inferior). Entry locations are marked in (f), which is a captured image of the subject’s dilated (8 mm) pupil. Henle’s fiber layer is indicated by white arrows.

........................................................................... 66

Figure 3.3

Averaged A - scans acquired at different entry positions (a) before and (b) after normalization. S and I in the color table refer to superior and inferior, respectively. GCL (ganglion cell layer), IPL (inner plexiform layer), and OPL (outer plexiform layer). Number in millimeters refers to beam entry location relative to pupil center.

................................................ 67

Figure 3.4

Portion of the A - scan that traverses RNFL (Top:

3 degree ecc.; Bottom: 6 degree ecc.) , one for each of the 17 entry pupil locations (color bar) along (left) vertical and (right) horizontal meridians. T, S, N, and I in the color table refer to temporal, superior, nasal, and inferior, respectively. Numb er in millimeters refers to beam entry location relative to pupil center. The anterior and posterior edges of RNFL are indicated by solid circles and triangles, respectively.

....................................................................................................................................................... 68

Figure 3.5

Average RNFL thickness of four subjects. Thickness is plotted as a function of retinal eccentricity and entry position in the pupil: (left) vertical and (right) horizontal meridians. Error bars corre spond to +/ - 1 standard deviation and are shown only for one curve. The other curves have similar standard deviations.

................................................................................................... 69

Figure 3.6

Mean and standard deviation of RNFL thickness measured at discrete nasal locations (blue). Black triangle represents data reported by Bagci et al . (2008).

......................................... 69

xv

Figure 3.7

Plots of RNFL intensity, at 5(blue) and 6 (red) degree retinal eccentricities, of a representative subject as a function of beam entry positions, along (left) vertical and (right) horizontal meridians. ...................................................................................................................... 70

Figure 3.8

Portion of the A - scan that traverses HFL, one for each of the 17 entry pupil locations (color bar) along (left) vertical and (right) horizontal meridians. The anterior and posterior edges of HFL are indicated by solid circles and triangles, respectively.

................................................. 71

Figure

3.9

Averaged HFL thickness over 4 subjects, plotted as a function of entry positions on pupil, which were sampled along (left) vertical and (right) horizontal directions. The error bar for the single representative curve corresponds to +/ - 1 standard devia tion. The legend stands for retinal locations (in degree) of data acquired.

................................................................................ 72

Figure 3.10

Mean intensity of HFL over the defined region of 4 subjects plotted as a function of pupillary entry positions, along (left) vertical and (right) horizontal meridians. The error bar for the single representative curve corresponds to +/ - 1 standard deviation. Intensity of A - scans is normalized to the inner retina reflections, which are assumed to be uniform across the eye.

....... 73

Figure 3.1 1

Directionality as a function of retinal eccentricity over four subjects. Circles, upper and lower triangles stand for the directionality of IS/OS, PTOS and Retina, respectively. Error bars denoted the standard deviation.

.............................................................................................. 74

Figure 3.12

Geometry of light scattering by a cylinder. (A) When an incident ray strikes the cylinder, (B) the light scattered by a cylinder is confined by a conical sheet coaxial with the cylinder axis (Knighton, 1992).

..................................................................................................... 76

Figure 3.13

The spatial distribution of retinal nerve fiber layer in

human eye. (Source from http://umed.med.utah.edu/neuronet/lectures/2002/Optic%20Disk.htm.)

....................................... 79

Figure 3.14 Henle fibers spatial distribution, marked with black arrow heads (Yamada, 1969)

. 80

Figure 3.15

Schematic diagram of scattered light with different incident angles and HFL fiber orientations. (a) When scanning plane is perpendicular to the fiber axis, the light is scattered back toward the opposite direction. When the scanning plane parallels to the

fiber axis and (b) the incident beam (from nasal side) forms large angles with fibers axis, the scattering light deviate away from the beam with different degrees, thus less or even zero thickness is detected. (c) For the case that incident beam (from tem poral side) has small angles with fiber, there is less change with the scattering angle. The full thickness therefore could be measured. (The red arrows mark one of the edges of the scattering cone (knighton et al. , 1992))

.................................................... 82

Figure 3.16

Comparison of directionality of IS/OS and POS layers measured in the current study (black bar) and that reported in chapter 2 (white bar). Retinal ecc entricity is 2 degree nasal.

...... 83

Figure 3.17

Comparison with retinal directionality values in the literature. The filled squares are the measurements from the OCT. Error bars represent +/ -

1 standard deviation. The open circles, upward- pointing and downward - pointing triangles stand for equivalent measurements from Zagers et al . (2003), Marcos et al . (1998) and Marcos & Burns (1999), respectively.

................. 85

Figure 4.1 Layout of the laboratory SHWS for measuring the optical SCE. The beam of a 788 nm pigtailed SLD (linear ly polarized) passes through an artificial pupil, limiting the beam size to 2 mm at the eye’s pupil. The XY position of the beam at the eye’s pupil is controlled via a tip - tilt mirror that is conjugate to the retina. After entering the eye, the beam focuse s to a small spot on the retina. The fixation target and pupil camera are used to align the eye to the system. The camera also confirms location of the beam entry position. Light reflected from the retina, exits the eye and after a relay telescope is sampl ed by a lenslet array and captured by a CCD camera. ‘p’ refers to planes conjugate to the pupil; ‘r’ refers to planes conjugate to the retina. The system contains no polarization controlling components. See text for additional system details.

............. 94

xvi

Figure 4.2

(left) Raw SHWS image acquired on one subject using the Fig. 4.1 system. Colored boxes are superimposed across (middle) the entir e spot array and (right) an enlarged subsection. Red and blue boxes are positioned to sample the core and tail portions of the spots, respectively, and are the regions used for data analysis in this study. The raw image is displayed using an inverted grays cale. T, N, S and I represent temporal, nasal, superior and inferior sides of the pupil, respectively.

................................................................................................................................... 96

Figure 4.3

Wavefront (a)

aberration and (b) amplitude maps reconstructed from the same raw SHWS data on one subject. The wavefront aberration map is composed of 18 Zernike modes (3 rd

through 6 th

order). The contour interval is 0.2 μ m, and the peak - to - valley across the 6.8 mm pupil is 3.56 μ m. Data points in the amplitude map correspond to intensity measurements, one per lenslet (red boxes in Fig. 4.2). The superimposed surface is a least - squares fit of Eq. (1) to the data points.

..................................................................................................................................... 97

Figure 4.4

Wavefront amplitude reconstructed from SHWS images acquired at 2 degree retinal eccentricity on the same subject. The f our plots represent the four possible combinations of pupil entry position (on and off the optical SCE peak) and summation box location (core and tail of SHWS spots): (a) on SCE peak and core, (b) off SCE peak and core, (c) on SCE peak and tail, and (d) of f SCE peak and tail. Beam entry positions differed by 2 mm. Data points correspond to intensity measurements, one per lenslet.

...................................................................................... 102

Figure 4.5

Pupil intensity (wavefront amplitude) reconstructed from raw SHWS images for (a) fovea, (b) 1 degree, (c) 2 degree, and (d) 3 degree retinal eccentricity of the superior retinal field. Data points correspond to intensity measurements, one per le nslet, with corneal reflex removed.

..................................................................................................................................................... 103

Figure 4.6

Fit of the SHWS measurements on five subjects to the five - parameter model (Eq. 1) . (left) Average directionality is plotted as a function of retinal eccentricity and summation box location (core, tail). Error bars represent +/ -

one standard deviation. (right) A simplified Eq.(1) (defined in text) is plotted as a function of pupil posit ion. The simplified equation captures the relative contribution ( I /( I + B ) ) and the directional strength ρ core of the Gaussian portion.

......... 104

Figure 4.7

The filled squares are the measurements from the SHWS. Error bars represent the +/ - 1 standard deviation. The open circles, upward - pointing triangles and downward - pointing triangles stand for equivalent measurements from Zagers et al.

(2003), Marcos

et al.

(1998) and Marcos and Burns (1999), respectively. ................................................................................................... 111

1

Chapter 1: Introduction

Vision is a complex process. It begins with the formation of an image on the neuro- sensory retina, which lines the inside of the eye, and ends with a visual percept in the visual cortex. The retina plays a critical role, capturing and transuding

photons i nto an electrical signal , and providing the first steps of signal processing. Normal vision requires normal function of the retina , and thus the retina has significant clinical and scientific interest. Since the invention of the ophthalmoscope by Helmholtz in 1851 , there has been an ongoing effort to develop imaging methodologies that use light to probe, noninvasively, structure and function of the living retina. All of these method ologie s rely fundamentally on the retina’s ability to return light back throu gh the natural pupil of the eye. Proper interpretation of the detected return thus requires

an understanding of how light interacts with retinal tissue – that is the optical properties of the retina.

The last thirty years have experienced tremend ous advanc ement

in our understanding of light - tissue interactions in the retina , and in fact the body of literature on this topic is quite large. Nevertheless major gaps remain

in our understanding of the underlying complexities of these interactions,

and our modeli ng of light return from the back of the eye continues to evolve . It is in this context that the work of this thesis was carried out . The objective of the thesis is to investigate the directional properties of the retina l reflection , in particular that of c one photoreceptors, using novel optical methodologies to probe the retina in ways not previously possible. This chapter is divided

2

into six

sections. Section 1.1

provides a brief overview of

light - tissue interaction s

in the retina followed by Sections 1.2 and 1.3 that

detail the most important light - tissue interaction for this thesis: the Stiles - Crawford effect. Sections 1.4 and 1.5 describe optical coherence tomography (OCT) and Shack - Hartmann wavefront sensing (SHWS),

two optical technologies used in the thesis for probing the retina. The chapter ends with Section 1.6 that provides the statement of work.

1.1 Optical properties of the r etina

Light - tissue interaction in the retina is complex, in large part because the retina is

itself

complex and there are many types of interactions

( Porter et al ., 2006 ) . While thin (<½ mm), the retina consists of more than ten distinct neural layers, each contributing to specific stages in the visual process. Most of these layers are transparent so as

to pass light to the underlying photoreceptors , which capture photons and initiate the

vis ual process . The layers are not completely optically homogeneous, however, having slightly different refractive indices that vary spatially across the retina. These differences perturb the incident light, causing a small portion of the light to change directions as manifested in the form of reflections and scatter ( Webb & Delori, 1988 ). Reflections are predicted by the law of reflection and are often referred to as s pecular (mirror - like) or directiona l. Scatter on the other hand is

changes

in direction

that deviate from the law of reflection. Scatter is characterized as single or multiple. Single scatter refers to a single scattering event that deviates the light once

– polarization is preserved and the light carries local tissue information. Multiple scattering refers to multiple scattering events of the same light ray. Polarization is reduced and the light acquires tissue information over a diffuse

3

(as opposed to loc al) retinal area. Sometimes it is more meaningful to characterize scatter based on its ability to conserve photon energy: elastic scatter (Rayleight, Mie, and geometric scatter) and inelastic scatter (Raman scatter).

The total return

from the bulk retina a nd choroid (reflection plus scatter) is about 10% of the illumination, though this value varies markedly with wavelength ( Delori & Pflibsen, 1989 ). In particular, longer wavelengths (near infrared) generate a stronger return than shorter wavelengths (visib le light). This is primarily because longer wavelengths are absorbed less by ocular pigments (melanin, hemoglobin, oxyhemoglogin, photopigment), allowing deeper penetration and

increase d probability to reflect and scatter.

There is no one light - tissue int eraction that characterizes

the entire retina and choroid. Instead, individual layers of the retina often exhibit spec if ic types of reflection (specular and directional) and scatter (single and multiple scattering). Here are

a few examples. The inner limit ing membrane (ILM) is the boundary between the vitreous and retina, formed by astrocytes

and the end feet of Müller cells . A high degree of specular reflectance originates at the membrane boundary, the intensity of which varies as a function of membrane curvature and orientation, and on beam entry/exit position in the pupil ( Charman & Jennings, 1976; O’Leary & Millodot, 1978; Delori & Pfibsen, 1989 ; Gorrand & Doly, 2009 ). Immediately below the ILM is the retinal nerve fiber layer (RNFL) that scatters ligh t into a conical sheet coaxial with the RNFL bundles. The anterior edge of the conical sheet follows the law of reflection and therefore at least this portion of the RNFL return