1.

Introduction

Optical coherence tomography (OCT) is a noninvasive imaging technique for recording high-resolution cross-sectional images of transparent and translucent tissues.^{1, 2, 3} Conventional OCT measures spatially resolved backscattered intensity with a resolution on the order of a few $\mu \mathrm{m}$ . Polarization-sensitive OCT (PS-OCT) is a functional extension that takes advantage of the additional polarization information carried by the reflected light.^{4, 5} Thereby, PS-OCT can reveal important information about biological tissue that is unavailable in conventional OCT. Several ocular structures can change the light’s polarization state and are therefore of interest in terms of PS-OCT imaging: in the retina, the nerve fiber layer⁶ and Henle’s fiber layer⁷ are birefringent, which is of great importance for glaucoma diagnostics.⁸ The optic nerve head is surrounded by the birefringent scleral rim,⁹ which might be used as a landmark in studies of optic disk anatomy. Furthermore, a polarization scrambling layer is located near the retinal pigment epithelium (RPE) which might be useful for diagnostics of age-related macular degeneration (AMD).^{9, 10} In the anterior segment, the cornea is birefringent,¹¹ which might be of interest for analysis and diagnosis of diseases like keratoconus and corneal scars.¹² The iris has polarization preserving anterior layers and a polarization scrambling pigment epithelium.¹³

Different methods of PS-OCT have been reported in the literature. While early work on PS-OCT^{4, 5} measured only reflectivity and retardation of a sample, in recent years, many proposals have been made to extract more information, e.g., on Stokes vectors,^{14, 15} Müller¹⁶ and Jones matrix¹⁷ distribution, birefringent axis orientation,^{14, 18} and diattenuation.^{19, 20, 21} We developed a method that combines the PS low coherence interferometry setup first devised by Hee ⁴ with a phase-sensitive recording of the interferometric signals in the two orthogonal polarization channels,¹⁸ thus allowing us to measure the three most important parameters, reflectivity, retardation, and birefringent axis orientation, simultaneously. We implemented our PS-OCT technique in several types of OCT systems: classical A-scan-based time domain OCT (TD-OCT),¹⁸ transversal scanning TD-OCT,¹³ and spectral domain OCT (SD-OCT).²² The functionality of the systems was demonstrated in several different ocular tissues: cornea,^{12, 23} iris,¹³ and retina.^{9, 10, 22}

Compared to other methods that probe the sample with light beams of different polarization states, our method has the advantage of requiring only a single input polarization state, which makes the instrument simpler and faster. However, our method also has a drawback: it requires that the beam incident on the sample is in a well-defined (circular) polarization state. While this is no problem for probing superficial tissues like cornea or skin, it can be a problem if the tissue of interest is located behind a birefringent layer. This is exactly the case in retinal imaging: the retina is imaged through the birefringent cornea. In this case, the beam probing the retina is no longer circularly polarized but in an elliptical polarization state defined by the corneal birefringence. The result is that the measured polarization patterns will be distorted.

A similar problem arises in scanning laser polarimetry (SLP),⁶ a technique that measures the thickness of the birefringent retinal nerve fiber layer (RNFL) in the region around the optic nerve head for purposes of glaucoma diagnostics.⁸ It has been shown that a careful compensation of the individual corneal birefringence by a variable retarder is required to provide reliable RNFL thickness measurements by SLP.²⁴

It is the purpose of this paper to report on a method for corneal birefringence compensation that can be used with our single-input-state PS-OCT technique. Our method measures the polarization state of light backscattered from the retinal surface to calculate the corneal retardation and axis orientation. This information is used to compensate for the corneal birefringence by a software algorithm. The method is equally suited for TD- and SD-OCT. We demonstrate the method in combination with a state of the art SD-PS-OCT instrument in a test target measured through a well-defined retarder and in the macula and nerve head region of the living human eye.

2.

Methods

2.1.

Experimental Setup

Details of our SD-PS-OCT system have been published elsewhere.²² This section contains a brief summary and a description of the polarizing elements in the interferometer to explain the principle of corneal birefringence compensation.

Figure 1 shows a sketch of the optical setup. It is based on the original polarization-sensitive low-coherence interferometer first described by Hee ⁴ Light emitted from a superluminescent diode (SLD) (fiber pigtailed, collimator focal length $3.5\mathrm{mm}$ , center wavelength $840\mathrm{mm}$ , bandwidth $50\mathrm{mm}$ ) illuminates, after being vertically polarized, a Michelson interferometer, where it is split by a nonpolarizing beamsplitter (NPBS) into an object and a reference beam. The reference light passes through a variable density filter, a dispersion compensation unit, and a quarter wave plate (QWPr), oriented at $22.5\mathrm{deg}$ , and is reflected by a mirror. After double passage of QWPr, the orientation of the polarization plane is at $45\mathrm{deg}$ to the horizontal, providing equal reference power in both channels of the polarization sensitive detection unit. The sample beam passes quarter wave plate QWPs (oriented at $45\mathrm{deg}$ ), which provides circularly polarized light to the sample via an $x\text{-}y$ galvanometer scanner.

Fig. 1

Schematic drawing of a spectral domain PS-OCT instrument. DC, dispersion compensation; FC, fiber coupler; L, lens; M, mirror; NPBS, nonpolarizing beamsplitter; PBS, polarizing beamsplitter; PMF, polarization-maintaining fiber; POL, polarizer; QWP, quarter wave plate (r, reference arm; s, sample arm); S, sample; SC, scanner; SLD, super luminescent diode; SP, spectrometer. VDF, variable density filter.

After recombination of the two beams at the NPBS, light is directed toward a polarization-sensitive detection unit, where it is split into orthogonal polarization states by a polarizing beamsplitter. The two orthogonally polarized beam components are guided by polarization maintaining fibers toward two identical spectrometers that record the spectral interferograms corresponding to the horizontal and vertical polarization channels.

Each spectrometer consists of a reflection grating (1200 lines/mm), a camera lens with a focal length of $200\mathrm{mm}$ , and a 2048-element line scan CCD camera (Atmel Aviiva M2 CL 2014) with a resolution of 12 bits per pixel. The cameras were operated with an integration time of $50\mu \mathrm{s}$ per A-scan, which provided a sensitivity of $98\mathrm{dB}$ at a power of $700\mu \mathrm{W}$ onto the sample. The sensitivity decay was $14\mathrm{dB}$ along the measurement range of $3\mathrm{mm}$ . To reduce the amount of data, only 1024 pixels of each camera where read out. Data post-processing was performed as previously described.²²

3.

Results

In a first step, the compensation method was demonstrated in a test target consisting of a lens $(f=20\mathrm{mm})$ and a stack of birefringent tape resembling the retina. In front of the lens, a liquid crystal variable retarder (LCVR) was mounted to simulate measurements through a birefringent cornea.

We recorded B-scan images of the artificial retina with the LCVR set to zero retardation and to a value mimicking the corneal birefringence (measured value: $\delta =16\mathrm{deg}$ or $\sim 37\mathrm{nm}$ for our wavelength of $840\mathrm{nm}$ ). Figure 2 shows the result. Figure 2a is a reflectivity image. The individual layers of the stack of tape are clearly seen. Figures 2b, 2c, 2d show retardation images, recorded with ${\delta }_{LCVR}=0\mathrm{deg}$ (2b), ${\delta }_{LCVR}=16\mathrm{deg}$ (2c), and ${\delta }_{LCVR}=16\mathrm{deg}$ , but with cornea compensation [Fig. 2d], as described in Sec. 2.2. In Fig. 2b, near-zero retardation is observed at the surface of the sample, increasing gradually with depth. In the uncompensated measurement through the retarder [Fig. 2c], the surface already shows higher retardation that further increases with depth. To obtain ${\delta }_C$ and ${\theta }_C$ of the artificial cornea, we extracted the surface of the sample by a peak detection algorithm working on the reflectivity image and calculated $\delta$ and $\theta$ from the interferometric signals corresponding to the peaks found in the A-scans. For the compensation algorithm, we used mean values of ${\delta }_C$ and ${\theta }_C$ derived from all A-scans. After compensation, the surface shows again blue color [Fig. 2d], indicating near-zero retardation.

Fig. 2

PS-OCT images of test sample. Image size: $1.5\left(x\right)\times 1.1\left(z\right){\mathrm{mm}}^2$ . (a) Reflectivity image. (b) to (d) Retardation images [for color code, see Fig. 4a]. (b) ${\delta }_C=0\mathrm{deg}$ ; (c) ${\delta }_C=16\mathrm{deg}$ , uncompensated; (d) ${\delta }_C=16\mathrm{deg}$ , compensated.

Fig. 4

En face PS-OCT images from human macula in vivo (left eye). Scanned area: $\sim 10\mathrm{deg}\times 10\mathrm{deg}$ . Orientation: left, nasal; top, superior; right, temporal; bottom, inferior. (a) Retardation at retinal surface (color bar: deg); (b) slow axis orientation at retinal surface (color bar: deg); (c) retardation at IS/OS boundary [color coding as in (a)]; (d) slow axis orientation at IS/OS boundary [color coding as in (b)]; (e) depth-integrated reflectivity image (dark horizontal stripes are motion artifacts); (f) reflectivity B-scan image (optical depth: $1\mathrm{mm}$ ; RNFL, retinal nerve fiber layer; ILM, inner limiting membrane; HF, Henle’s fiber layer; ELM, external limiting membrane; IS/OS, inner/outer photoreceptor segment boundary; ETOS, end tips of outer photoreceptor segments; RPE, retinal pigment epithelium).

For a better quantitative evaluation of the results, we calculated histograms of the $\delta$ values obtained at the sample surface and histograms of $\theta$ corresponding to the second band of the tape. (Because in the case of $\delta \sim 0\mathrm{deg}$ , the interferometric signal in the vertically polarized detection channel is very low, the phases are rather random and no meaningful axis can be derived; therefore, we used the signal from the second band where a better signal strength is obtained.) Fig. 3 shows the results.

Fig. 3

Histograms of surface retardation [(a) to (c)] and axis orientation measured in the second band [(d) to (f)]. (a), (d): ${\delta }_C=0\mathrm{deg}$ ; (b), (e): ${\delta }_C=16\mathrm{deg}$ , uncompensated; (c), (f): ${\delta }_C=16\mathrm{deg}$ , compensated.

Figures 3a, 3b, 3c show the surface retardation values derived from Fig. 2b, 2c, 2d, respectively. In Fig. 3a, the peak of the histogram is at $\delta =4\mathrm{deg}$ , very low as expected from the fact that zero retardation was adjusted. (The noise and imperfect polarization components cause the residual $\delta$ value). When switching the retarder to the value mimicking the cornea, a larger surface $\delta$ value of $16\mathrm{deg}$ is observed [Fig. 3b]. After compensation [Fig. 3c], the value is again close to zero $(\sim 4\mathrm{deg})$ ; however, due to noise, the distribution is somewhat broadened. The axis histogram obtained without retarder [Fig. 3d] has a peak at $\theta \sim 5\mathrm{deg}$ . On measuring through the retarder, the value is changed to $\theta \sim -10\mathrm{deg}$ [Fig. 3e]. After compensation, the value is $\theta \sim 8\mathrm{deg}$ [Fig. 3f], close to its original value. These results in the test target demonstrate that our software compensation method works well to restore the original birefringence patterns.

In the next step, we performed PS-OCT imaging in a healthy eye of a human volunteer, after full informed consent was obtained. We recorded 3-D data sets of the macula area and cross-sectional circumpapillary scans (nerve head area). A 3-D data set consists of 60 B-scans, each B-scan containing 1000 A-scans. The scanned area covers $\sim 10\mathrm{deg}\times 10\mathrm{deg}$ , or $\sim 3\times 3{\mathrm{mm}}^2$ . A circumpapillary scan consists of 4000 A-scans. In each B-scan and circumpapillary scan, the retinal surface and the inner/outer photoreceptor segment boundary (IS/OS boundary) were extracted by searching for the corresponding intensity maximum, and from the interferometric signals corresponding to these maximum values, retardation and axis orientation values were determined.

Figure 4 shows the uncompensated data obtained in the macula. Figures 4a and 4b show the retardation and slow axis orientation (referenced to the vertical instrument axis), respectively, measured across the retinal surface at the inner limiting membrane (ILM). These maps resemble the cornea’s birefringence, i.e., Figs. 4a and 4b show the distribution of ${\delta }_C$ and ${\theta }_C$ . Figures 4c and 4d show the distribution of $\delta$ and $\theta$ at the IS/OS boundary, respectively. These patterns resemble the combined birefringence of the cornea and retina. For comparison, Fig. 4e shows a depth-integrated reflectivity image of the same area, and Fig. 4f a conventional (reflectivity) B-scan across the fovea centralis, where individual retinal layers can be identified. Since the RNFL is rather thin in the imaged area, the only retinal structure that has a noticeable birefringence is the Henle’s fiber layer. In this layer, the fibers are arranged in a pattern running radially away from the fovea centralis. Therefore, the Henle’s layer acts as a retarder with an axis orientation that changes linearly with azimuth angle around the fovea (the slow axis is parallel to the fiber orientation). If such a retarder is combined with a retarder of approximately constant axis orientation and retardance (as the cornea), the combined retardation pattern will show areas of increased retardation (where the axes of cornea and Henle’s layer are parallel) and areas of reduced retardation (where the axes are orthogonal). The result is a bow-tie pattern well known from SLP.²⁷ This bow-tie pattern is clearly visible in Fig. 4c. The dark arms of the bow-tie pattern are parallel to the fast axis of the cornea, the bright arms are parallel to its slow axis. The pattern orientation indicates a corneal slow axis oriented at $\sim 40\mathrm{deg}$ nasally downward near the foveal center. The interpretation of the uncompensated axis orientation pattern in Fig. 4d is not straightforward.

The polarization states measured at the retinal surface were used to compensate for the corneal birefringence, as described in Sec. 2.2. As can be seen in Figs. 4a and 4b, ${\delta }_C$ and ${\theta }_C$ are not constant across the entire image. There is a slow variation across the images, overlaid by noise. To allow for the slow variation of the surface states and to reduce the noise, we used a floating average based filter algorithm to obtain the surface states that entered into our software compensation algorithm [Eq. 8]. The window size of the filter was $100\left(x\right)\times 6\left(y\right)$ data points, corresponding to $\sim 1\mathrm{deg}\times 1\mathrm{deg}$ .

Figure 5 shows the compensated images corresponding to Fig. 4. Figures 5a and 5b show retardation and slow axis at the surface, Figs. 5c and 5d the values at the IS/OS boundary, respectively. The $\delta$ values obtained at the surface of the retina [Fig. 5a] are now rather constant across the image and lower than in the uncompensated case. The slightly higher $\delta$ values observed near the center of the fovea are probably caused by the rather poor signal intensity obtained in that area at the retinal surface (due to the curvature of the retinal surface near the foveal pit, the backscattered light in this area is usually rather weak). A low signal power is known to distort PS-OCT signals, usually biasing very low $\delta$ toward higher values in this type of PS-OCT configuration.²⁶ The axis orientation at the surface is rather random, as expected if the corneal influence is removed (no axis is defined in that case).

Fig. 5

En face PS-OCT images from human macula in vivo, with software compensation of corneal birefringence (same area as in Fig. 4). (a) Retardation at retinal surface [color coding as in Fig. 4a]; (b) slow axis orientation at retinal surface [color coding as in Fig. 4b]; (c) retardation at IS/OS boundary [color coding as in Fig. 4a]; (d) slow axis orientation at IS/OS boundary [color coding as in Fig. 4b].

To better quantify the effectiveness of corneal compensation, we calculated histograms of $\delta$ and $\theta$ as measured at the retinal surface for the uncompensated case [Figs. 6a and 6b ] and for the compensated case [Figs. 6c and 6d]. Before compensation, the width of the $\delta$ distribution is broad, stretching from $\sim 10$ to $30\mathrm{deg}$ [Fig. 6a]; after compensation, a rather narrow distribution with a peak at $\delta =6\mathrm{deg}$ is observed [Fig. 6c]. Ideally, the compensated $\delta$ should be zero; however, this value is not reached because of noise. (The algorithm used to calculate $\delta$ [Eq. 4] always provides positive values, so the mean will be larger than zero for a noisy signal.) The $\theta$ distribution shows a very pronounced peak in the uncompensated case [Fig. 6b], i.e., a rather well defined corneal slow axis at $\sim -53\mathrm{deg}$ (referenced to the vertical instrument axis). This corresponds to an orientation of $\sim 37\mathrm{deg}$ nasally downward, in good agreement with the $\sim 40\mathrm{deg}$ obtained from the bow-tie pattern. After compensation [Fig. 6d], $\theta$ is much more evenly distributed, however, the compensation is not perfect.

Fig. 6

Histograms of polarization states at retinal surface, derived from Figs. 4 and 5. (a) Uncompensated retardation; (b) uncompensated slow axis orientation; (c) compensated retardation; (d) compensated slow axis orientation.

At the IS/OS boundary, the bow-tie pattern is removed after compensation [Fig. 5c], as expected. A slightly increased retardation around the central fovea is observed, probably indicating the birefringence of the Henle’s layer. The compensated axis orientation image now shows a pronounced pattern around the fovea: two full-color oscillations from blue over green, yellow to red, corresponding to an axis change of $2\times 180\mathrm{deg}=360\mathrm{deg}$ , are observed along a circle around the fovea, indicating the radially oriented Henle’s fibers.

Figure 7 shows a circumpapillary scan with a diameter of $\sim 10\mathrm{deg}$ $(\sim 3\mathrm{mm})$ . Figure 7a is a reflectivity image, Figs. 7b and 7c show the uncorrected retardation and axis orientation, respectively. In the thick superior bundle of the RNFL (left) an increase of retardation is observed with depth [color change from dark blue to green; Fig. 7b]. A similar effect is expected in the inferior RNFL bundle (right); however, due to corneal birefringence varying with scan position, an increased retardation is already observed at the anterior surface of the retinal tissue, distorting the expected retardation pattern. The axis orientation is expected to vary by a total of $360\mathrm{deg}$ as we go along the circumpapillary scan (because the nerve fibers emerge approximately radially from the nerve head). This would mean two full-color oscillations from blue over green, yellow, orange, to red along the scan. Although a color change can be observed, some colors are missing.

Fig. 7

Circumpapillary PS-OCT scan from human retina in vivo (left eye). Orientation of scan (from left to right): temporal, superior, nasal, inferior, temporal. Scan diameter: $\sim 10\mathrm{deg}$ (corresponds to a circumference of $\sim 9.4\mathrm{mm}$ , equal to horizontal image width; optical image depth: $1.8\mathrm{mm}$ ). (a) Reflectivity image; (b) and (c) Uncompensated retardation and slow axis orientation, respectively; (d) and (e) compensated retardation and slow axis orientation, respectively. Color coding as in Fig. 4.

After software compensation of the corneal birefringence (the surface state was averaged over a window size consisting of 400 adjacent A-scans), the artifacts are largely removed: the retardation measured at the surface of the retina is low (blue color) along the entire scan [Fig. 7d], and the axis orientation now shows the expected two full-color oscillations from left to right [Fig. 7e].

4.

Discussion

The PS-OCT method we use is based on the assumption that the sample is illuminated by a circularly polarized beam. While this condition can usually be met with a free-space PS-OCT setup and samples that are directly accessible, it is usually not fulfilled in retinal imaging where the sample beam first traverses the birefringent cornea. This is no problem if only qualitative polarization information is required, e.g., to identify a depolarizing (or polarization scrambling) layer as the RPE. However, other applications require quantitative information on tissue birefringence, e.g., glaucoma diagnostics via measuring RNFL retardation. In this case, the birefringence of the cornea has to be compensated.

In SLP, a similar problem arises, and it was solved by placing a variable retarder in front of the cornea that cancels the corneal birefringence. The advantage of this method is that it is straightforward and fast: after one measurement of corneal birefringence in the macular region, the variable retarder is set appropriately and the nerve head area is scanned. In principle, this method can also be used for PS-OCT. However, the method has some disadvantages: it requires additional hardware and an additional calibration measurement (in the macula), and it assumes that the birefringence of the cornea is constant, regardless of the scanning position.

In a previous paper,²³ we have shown that this is not necessarily the case. If the sampling beam deviates from perpendicular incidence, the birefringence encountered by the beam in the cornea changes. The assumption of constant corneal birefringence therefore requires a very precise alignment of the instrument with the measured eye. Furthermore, certain diseases such as corneal scars and keratoconus can cause a very irregular birefringence pattern in the cornea.^{12, 28} To allow for these variations of corneal birefringence with scan position, we decided to use a software-based compensation method. This method models the hardware-variable retarder by an additional Jones matrix whose components are derived from the polarization state measured at the surface of the retina. Since the surface state can be measured locally, the corneal birefringence variations with scanning angle can be accommodated. However, because of signal noise, a certain averaging is required to determine reliable surface states. The window size we used was $\sim 1\mathrm{deg}\times 1\mathrm{deg}$ for 3-D data sets and 1/10 of the circumpapillary arclength for the 2-D circumpapillary scans. The latter is coarser than the averaging used in a previous study,²⁹ where the circumpapillary arc was divided into 48 sectors in which tissue birefringnece was obtained from an average of 32 adjacent A-scans. However, in our case, only the surface state is averaged, not entire A-scans. (The retardation is calculated A-scan wise.) Since the surface state varies only slowly [at least with normal corneas; see Figs. 4a and 7b], we think that this coarser averaging is justified because surface speckle is more efficiently removed. However, our averaging window might be too coarse for measuring through a cornea with keratoconus. (In this case, the aberration-induced image degradation might anyway prevent meaningful OCT imaging.)

By using the retinal surface polarization state as input for corneal birefringence compensation, our method has similarities to the Stokes vector–based method that uses the polarization state observed at the retinal surface as a reference state.^{29, 30} Compared to that technique, our method has the advantage of requiring only one input polarization state. However, the disadvantage is that our method assumes that the retarder anterior to the retina has a $\delta$ value between 0 and $90\mathrm{deg}$ . While this is true if there is only the cornea as an anterior retarder, this assumption is in general not true if additional retardation is introduced by other optical elements, e.g., a single mode fiber. Therefore, our method cannot easily be extended to a fiber-based PS-OCT setup.

A disadvantage of software-based methods over hardware solutions is certainly the increased computational effort. The compensation of a 3-D data set such as that in Fig. 5 presently takes several minutes (Pentium 4, $3.0\mathrm{GHz}$ , LabView code). However, since our software code consists essentially of matrix multiplications performed for each data point, optimized parallel code could greatly reduce computation time.