1. Introduction

Optimized imaging and analysis techniques are needed to visualize structures within the human retina, which is nearly transparent and low in contrast [1]. It has particularly been difficult to visualize the deeper structures of the retina, since the superficial layers of the retina are strong reflectors and therefore hinder penetration into the deeper layers [2,3]. We introduced a polarimetry algorithm that shows how contrast, for instance for retinal features such as hard drusen, can be increased by separating directly backscattering light from strong reflectors from light that is multiply scattered in the retinal and subretinal layers [4,5].

The purpose of this investigation is to probe further the light-tissue interactions in the multiply scattered light image, i.e., the depolarized image. A particular application is the analysis of blood vessels in the pathological retina. Vessels in the retina, as elsewhere in the human body, are of differing structures, sizes, and configurations due to the differing structures and demands on blood flow of the tissues subserved. Arteries are exposed to higher pressures and have thicker walls and smaller lumen diameter than accompanying veins [6]. Moreover, arteries and veins differ in the properties of the blood they carry: arteries have a higher percentage of oxygenated hemoglobin than veins do. These differences have been found previously to affect the relative absorption of light passing through them, even in near infrared light [2,7].

Blood vessel measurements in the living human eye depend upon light-tissue interactions. Measurements are typically acquired using a double pass instrument. The returning light is a function of the amount of reflected, backscattered, and absorbed light from the fundus. Absorption by blood in the vessels is the main contributor to the difference between the amount of light returned from the vessel and nerve fiber layer. These blood vessel measurements can include artifacts, with the most obvious being the reflection artifact down the center of blood vessels. This central reflection artifact is particularly prominent in retinal images from confocal instruments in which the vessels appear striped [8]; the small aperture, through which the light reaches the detector, passes primarily light returning from a high angle such as off the top of a vessel. The aperture rejects the light returning from the sides of the vessel walls, which returns from too low an angle and can reach the detector only after a rather indirect optical path. That is, the specular reflection is not on axis with the aperture when it originates from the sidewalls. Although this reflection artifact is less apparent in smaller vessels, it is quite prominent even when small vessels are imaged, if the wavefront aberrations of the eye are reduced and high magnification is used [9]. Several image analysis methods have been used to fit blood vessel profiles, with a Gaussian fitting routine being a typical method [10]. However, none of them accounts for other light-tissue interactions of the vessel or adjacent fundus [11] nor absorption effects of self-screening that would be predicted by Beer’s Law.

We investigated whether our polarimetric algorithm, with the depolarized light image in particular, has advantages over the standard confocal image regarding measurements of contrast and other parameters needed to characterize retinal vessels. To do this we analyzed data from nine patients whose eye disease was not expected to have a major impact on their retinal vessels, but who were old enough to have some aging changes to their ocular media and retinas. We investigated the amount of specular reflection artifact using two methods: a full width at half height method and a Gaussian fit method. For both methods, we included terms related to absorption by blood in the vessel. The depolarized light images provided more systematic diameter measures and higher contrasts for the blood vessels.

2. Materials and methods

2.1 Instrument and subjects

We tested nine patients, six glaucoma suspects with no typical visual field changes and 3 with manifest primary open-angle glaucoma (mean age =56 yr; 5 females, 4 males; 4 right eyes, 5 left eyes). Scanning laser polarimetry was performed using a scanning laser polarimeter (GDx, Laser Diagnostic Technologies, San Diego, CA, USA), with the image series as shown in Fig. 1. The GDx was originally built to measure the thickness of the nerve fiber layer [12], but we further analyze the polarization information to obtain a map of the multiply scattered light returning from the retina to enhance detection of pathological features, as illustrated in Fig. 2.

 

Fig. 1. (479 kB) Movie of raw GDx data from the right eye of a 45 year old, female glaucoma suspect. The retina was illuminated with linearly polarized light, at 20 different polarization angles over range of 90 deg in equal steps. For each polarization angle, two images were acquired: one from a detector configured to collect light with a polarization angle perpendicular (crossed) to the illumination light (left image), the other from a detector configured to collect returning light with a polarization angle parallel to the illumination light (right image). Images have been scaled for easier viewing, since the unscaled image for the crossed detector is considerably darker than its corresponding image from the parallel detector. Scaling parameters were determined from the first frame of the movie, separately for each detector. Parameters were chosen so that the full 256 level grayscale range mapped to the mean plus or minus three standard deviations of the data from the first image. Subsequent frames used the same mapping, so that all frames in the movie were scaled with the same parameters. Note the changes over successive frames in the appearance of the large vessels in the crossed image (left).

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The GDx is a confocal scanning laser device that scans the retina with linearly polarized light at 780 nm in a 15×15 deg visual angle raster pattern, for 20 sequential input polarization angles. Linearly polarized light is rotated by a half wave plate to vary the input polarization angle. Light returning from the retina is captured by two different detectors. (See movie in Fig. 1). One detector collects light polarized at 90 deg to the illumination light, and is called the crossed detector (Left panel of Fig. 1). The other collects the parallel polarized light, i.e., light that has the same polarization as the input illumination, and is called the uncrossed detector (Right panel of Fig. 1). In less than 1 second, 20 pairs of images were digitized, with one image per detector and each pair representing illumination with a different angle of polarization. Each image of a series is saved as 256 × 256 pixels with 8 bits of grayscale. Raw data that are usually not available to the user were saved to the hard disk. These raw data were then processed offline, using the entire GDx image series to generate images based on the polarization content of the returning light.

 

Fig. 2. Diagram describing the polarimetry algorithm that is used to compute images with different polarization content. Top left- images from the parallel detector, outlined in blue. Bottom left- images from the crossed detector, outlined in red. Right- Intensity variation of a single pixel. The data points associated with the red and blue curves show the intensity variation of a single pixel as it changes over the 90 deg range of input polarization. The grayscale for one pixel is calculated for each of the 20 polarization angles, which is sampled in less than one second. The data are low pass filtered in the frequency domain using a Fast Fourier Transform (FFT) to reduce noise, as shown by comparison of the red and blue curves with the individual data points. The blue curve at the upper right shows the modulation of the light returning to the parallel detector, smoothed by FFT. The red curve at the lower right shows the smoothed curve for the crossed detector. The minimum value of light that returns to the crossed detector is taken from the lowest value of the FFT and used to compute the depolarized image. We assume that light that does not modulate with polarization angle has become randomly polarized due to multiple scattering. The thick gray bar in the middle right indicates that the average light returning from both detectors can be used to compute an average image.

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We developed a set of Matlab routines (The Mathworks, Natick, MA, USA) to use for these computations. As for other analyses with this type of imaging, the best computations are obtained from properly focused images series, minimal eye movement artifact, and equal illumination in all quadrants. For each data set, a fast Fourier transform was computed for the grayscale of each pixel as a function of the 20 input polarization angles for both the crossed and uncrossed detectors, to reduce the effects of noise for a given image. We then computed the following two image types shown in Figs. 3(a) and (b): a depolarized light image, computed as the minimum value of light returning to the crossed detector at each pixel for all input polarization angles and an average image of all the light returning to both detectors for all the input polarization angles. The average image is similar to a standard confocal image because the light returns either to one detector or the other, so that no light is systematically lost and the two detectors taken together are like a polarization-insensitive detector. Thus, this average image, which combines all light returning from the 20 input polarization angles, may be thought of as a confocal polarization insensitive image. Both of these images differ from the color image produced by a standard fundus camera, which illuminates the retina over a wide angle of the retina as well as being polarization insensitive, but still may have retinal vessel reflection artifacts (3C).

 

Fig. 3. Retinal images centered on the optic nerve head and corresponding retinal vessel profile data for one subject. A- Depolarized light image. Color bars indicate sampled region. Red bars are for artery profiles and blue for vein profiles. The image is scaled for better visibility, as in Fig. 1, since there is less light return in this image type than in the average images. B- Average image. Red and blue bars indicate sampled region. C- Color fundus image, slightly higher magnification and from a clinical fundus camera. Note central reflections on the largest vein and artery, indicated by black arrows. D- Vessel profiles across one vessel with 11 bisector lines. Left panel- Bisector lines in color on a magnified section of the image in 3A. These lines are selected by a computer algorithm that finds adjacent parallel lines that are perpendicular to the vessel and in the region of interest defined by selecting a pixel on either side of the vessel. Right panel- grayscale of each bisector line plotted as a function of location in the profile. E- Computed data for blood vessel profiles across the retinal vein, plotted as grayscale values as a function of location in the profile. Filled symbols indicate data from veins, open symbols from arteries. Squares- profile from the depolarized image, scaled to match the mean of the average image. Circles- profile from the average image, F- Right column, open symbols- profile across an artery from the same eye as in the left column.

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2.2 Data analysis

Retinal blood vessels were selected in a relatively featureless region of retina in the average image to provide a stable grayscale for the baseline measurement, including sufficient separation of vessels to obtain a baseline. We sampled on an adjacent pair of vessels, one artery and one vein. The distance between the edge of the optic nerve head and the vessel sample ranged from 370 to 1439 microns, 734 microns on average. We used our previously developed method to semi-automatically measure blood vessel diameters [4], as shown in Fig. 3(d). This algorithm is based on the idea that blood vessels tend to have features that are longitudinally homogenous. Thus, when candidate bisector lines are perpendicular to a blood vessel, the minimum brightness will tend to be at the same position on each bisector line, and therefore the variation of this point is minimized across bisector lines. To begin the computation, we manually selected two pixels, one on either side of a vessel, defining a line roughly perpendicular to the vessel. The algorithm creates 11 parallel bisector lines, 5 on either side of the manually defined line. Then the set of lines is rotated by ± 20 deg in 2 deg increments to optimize the vessel intersection angle. This large range permits the operator to quickly select vessel locations for sampling, even with curved vessels. For each of the 11 parallel bisector line at a given rotation angle, the minimum image intensity value is found, and its location along the bisector line is noted. We then calculate the standard deviation of this location over the 11 lines. The optimal angle is selected to minimize the standard deviation of the locations of the minimum values in the 11 bisector lines. An average blood vessel profile was then calculated from the 11 bisector lines, to reduce the effects of noise in an individual bisector line. The profile in the depolarized light image is computed automatically from the same dataset and locations as the average image, and thus all points in the vessel profile are paired and collocated for the two image types.

Figure 1 shows why our method is superior to the fixed crossed polarizer method. The background intensity goes up and down with polarization angle, seen by comparing the frames in the video. Further, there is also a possible effect of light that has passed through or reflected off the nerve fiber layer and other structures may alter the amount of light available to pass out through the blood vessels. For macular images, we previously showed that the depolarized light image method removed more of the central reflection artifact than did the method using the mean of the crossed detector images [4].

The mean grayscale value of the entire depolarized image is expected to be much less than for the average image, so that scaling is necessary to compare the profile shapes directly. We computed the relative light return for the depolarized light image and the average image. This is a measure of the amount of depolarized light in the sample, since one half the depolarized light is assumed to pass through the crossed detector and one half the total light is represented by the average. To compare vessel profiles of the dark images to the brighter ones, we used a scaling method that did not include assumptions regarding the profile shape or weighting of different parts of the profile. We stretched the depolarized image profile so that its mean grayscale value matched that of the average image profile. Figure 3(e) shows the vessel profile for the average image and the stretched profile for the depolarized image in a vein, and Fig. 3(f) shows the corresponding artery.

To compare the shapes of the curves, we used two common metrics. First, to examine the effect of decreasing glint off the center of the blood vessels walls and other artifacts due to light that is polarization preserving, we computed the Michelson contrast, C = (Lmax -Lmin)/(Lmax + Lmin), where Lmax is the average grayscale from the two most peripheral points on either side of the vessel profile, which is selected to be featureless retina, and Lmin is the midpoint of the vessel, where the reflection artifact is expected to be greatest. Michelson Contrast has the advantage that differences in illumination, overall light return, and scaling are minimized. Second, to examine the possible shape change due to artifacts of polarization preserving light anywhere off the surface of or through the blood vessels, we measured the width at half height. For each of these methods, we performed an Analysis of Variance (ANOVA, Statview, SAS, Cary, NC), with the factors being vessel type (artery vs. vein) and image type (depolarized vs. average image). Pairwise comparison of the means was performed, adjusting the significance level according to number of tests, so as to maintain the same overall level of type I error. To correspond to the maximum possible contrast of the vessel profile, a second Michelson Contrast was computed by selecting the darkest point anywhere on the curve as Lmin, with Lmax remaining the same.

To characterize the blood vessel diameters in our sample, we computed the full width at half height. For the baseline we used the baseline from the first Michelson contrast, based on the two most peripheral points on either side of the vessel profile. The height is computed as the distance from this baseline to the midpoint of the vessel profile. This has the advantage of having no assumptions concerning the profile shape, but the disadvantage of not using all the data in the metric.

To compare further the potential improvement in the shape of the blood vessel profile after the central reflection was reduced, we fit the profiles with a Gaussian curve using nonlinear least squares, by means of the Levenberg-Marquardt method, and computed the RMS error between the profile and the fit [13]. This has the advantage of using all the data for the depolarized light image profile, but the disadvantage of assuming a profile shape that is only an approximation of the absorption of blood within the vessel. For the average image we have to omit the data at the reflection. However, with the Michelson method we use less of the data, which may decrease accuracy. In addition to the RMS error metric for goodness of fit, there are four parameters: μ is the horizontal position of the mean, σ is the standard deviation of the Gaussian on the horizontal axis, A is the amplitude on the vertical axis at the mean, and C is the vertical offset. The width of the Gaussian at half the area under the curve, 2^*0.675 σ, provides a measure of the blood vessel diameter. Again, this uses all the data but is not assumption-free.

 

Fig. 4. Computed data for blood vessel profiles across retinal vessels from 9 patients (one vein and one artery from each), plotted as grayscale values as a function of pixels along the cross-sections. Circles- profile from the average image, without scaling, with the grayscale values plotted from 0 – 140 out of a total possible range of 0 – 255. Squares- profile from the depolarized image, scaled to match the mean of the average image. Left column, closed symbols- profile across a vein. Right column, open symbols- profile across an artery from the same eye as in the left column. Note that while the overall curve shapes are similar, there is an elevated portion in the middle of the average image profiles, shown as the circles being elevated above the squares.

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3. Results

The shape of the vessel profiles was typically altered for the depolarized light images, in comparison with the average images, as shown for both arteries and veins in Fig. 4. The reflection and other artifacts in the center of the blood vessels were significantly reduced for the depolarized light images, as expected, leading to a higher contrast for the vessel profiles in the depolarized light images (p < 0.0001). This minimized central vessel reflection is seen in the individual images, illustrated by comparing the depolarized image in Fig. 3(a) to the average image in 3B. The central reflection artifact was reduced for both arteries and veins (p = 0.002, 0.023, respectively)(Fig. 5). This same finding was true for the maximum possible Michelson Contrast, with depolarized light vessel profiles having significantly more contrast (p= 0.005), in agreement with the appearance of the individual images. The maximum possible Michelson contrast was significantly higher for both arteries and veins (p = 0.0001, 0.0241, respectively). However, despite greater difference between the image types in the mean contrast for arteries vs. for veins, the interaction in the ANOVA was not significant for either the midpoint and maximum Michelson Contrast computations (p = 0.0726, p = 0.4747, respectively).

 

Fig. 5. Michelson contrast for vessel profiles for arteries and veins, comparing depolarized and average images. Michelson contrast for the nine individuals, using the midpoint. Symbols: squares- depolarized image, circles- average image, filled symbols- veins, open symbols-arteries. Note that the contrast is typically higher for veins than for arteries and for depolarized light image profiles compared with average image profiles.

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The Michelson Contrast computed from the vessel midpoint is greater for veins than for arteries (p = 0.019). This increased contrast is expected because veins absorb more light, containing generally higher volumes and also having more absorption per unit volume of blood at 780 – 790 nm [2]. The maximum possible contrast was also greater for veins than for arteries (p = 0.0060). Comparing the Michelson contrast computed from the midpoint to the maximum possible contrast, it is clear that Michelson Contrast can be increased in the average images by selecting a dark point on the vessel that avoids the reflection artifact, as shown in Fig. 6. There are still remaining artifacts that allow the maximum possible Michelson contrast of the depolarized light images to be higher for some vessel profiles. This is illustrated in Figs. 4 and 5, such as noise in the data for the eighth patient from the top in Fig. 4, as well as uneven background reflectance as shown in the second patient from the top in Fig. 4.

 

Fig. 6. Michelson contrast for vessel profiles for artery and veins, comparing contrast using the midpoint of the vessel profile to that by manually selecting the darkest point. Small triangles-Michelson contrast computed from the baseline retinal grayscale and the midpoint of vessel. Large triangles- maximum possible Michelson contrast, computed from the baseline retinal grayscale and the darkest point on the vessel.

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The depolarized light images were considerably darker than the average images in this confocal scanning laser polarimeter. The average amount of depolarized light for the blood vessel profiles was 13 + 3.7 % of the total light returned to the instrument. The relative amount of depolarized light was 9 – 18 % for arteries and 5 – 21 % for veins, not statistically different for our sample (p = 0.615). Retinal blood vessels are not highly scattering structures, particularly in comparison to pathological tissues, and thus the relative amount of depolarized light could be much higher elsewhere in a retinal image.

For vessel diameter, as measured by full width at half height, the veins were on average larger than the arteries for both the depolarized and the average method (p = 0.0010). There was no significant difference between image types, depolarized or average image (p = 0.2050). Analyzing the depolarized and average images separately, the veins were still larger than the corresponding arteries in each eye (p = 0.0046, p = 0.0026, respectively). There was no interaction between vessel type and image type (p = 0.9340), indicating that neither arteries nor veins looked relatively larger in average images than in the depolarized images. The Gaussian curve fitting method provided similar results for the improvement in vessel profile shape by computing using depolarized light images, as shown in Fig. 7. The ratio (RMS error for average images/ RMS error for depolarized light) was greater than one for 8 of 9 retinal arteries and 7 of 9 veins, with the remaining 3 vessel profiles having RMS ratios only slightly less than one. The larger the RMS error ratio, the poorer the fit for the average image compared with the depolarized light image. For ratios larger than 2.5, we found that 5 of 9 were for arteries, but only 2 of 9 for veins, indicating the most improvement for arteries in this sample. The amount of improvement did not systematically vary with the diameter of the vessel for veins. However, the improvement was greater for the largest arteries in the sample, 60–70 microns by the Gaussian half area method, with RMS ratios of about 3.

 

Fig. 7. RMS fitting errors of a single Gaussian curve to each blood vessel profile, showing improved Goodness of Fit for the depolarized light images. The ratio (RMS error for the average images/ RMS error for the depolarized light image) is plotted as a function of the mean vessel diameter measurement from the Gaussian fitting for average and depolarized light images. Filled symbols indicate veins, open symbols arteries. Ratios greater than 1 indicate a poor fit of the Gaussian profiles to average image data compared with depolarized light image data.

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The diameters of the full width at half height were compared with the Gaussian half area method, as shown in Fig. 8. There are no systematic differences in the two methods, other than the blood vessel diameters of the Gaussian method being smaller, a function of the arbitrary scaling parameter chosen. Previous authors selected their scaling parameter, larger than our half-area, from their manual measurements from the same image data [10], and a similar adjustment of the scaling parameter could bring the two measurements in agreement.

 

Fig. 8. A comparison of the diameters from the half height method to the Gaussian fit half area method. A- Average image. B- Depolarized image. Closed symbols- vein. Open symbols-artery. Note that there is general agreement between the two methods, but fewer outliers with the depolarized light images.

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4. Discussion

The polarimetry method successfully removed polarization retaining light from the depolarized or randomly polarized light, which is a small but important component of the overall light captured by the instrument. The appearance of the retina was altered in the depolarized light images, to the extent that the central reflection artifact found for blood vessels imaged with confocal instruments all but disappeared. This was indicated by the higher Michelson Contrasts found for the blood vessel profiles in the depolarized light images as compared with the average images. This method, then, will allow more accurate measurements of the absorption components of the light-tissue interactions of blood vessels, which in turn will improve methods such as oximetry for characterizing the blood within the retinal vessels [14]. There are additional light-tissue interactions that the present analysis does not consider, including the multiple pathways of light through the retinal vessels [11]. Moreover, we analyzed only arteries and veins, not the smaller vessels, nor did we study vessels’ gross pathological changes. For both oximetry and topological studies, optical artifacts in vessel profiles have led to considerable complexity in image processing that might be simplified or made more rapid with improved optical methods. One image processing example is the double Gaussian method, with one Gaussian being used to fit the sides of the vessel profile and a second for the central reflection artifact [10]. Several of the more complex algorithms run into difficulties when used on pathological vessels, and thus simplifying the problem by removing a source of artifact may lead to better evaluation of retinal images. Recent studies concerning the relation of retinal microvascular characteristics to age-related eye disease have found statistically significant relations, but these were inconsistent and sometimes weak [15]. By improving these measurements and using a technique that is well-tolerated by patients, such as the one described here, clearer results may be obtained.

These reflection artifacts due to the tissues of interest are compounded in severity if there are also artifacts from the anterior segment structures. Considerable effort has been made recently to examine the effect of intra-individual differences in corneal polarization properties. The main axis of retardance differs among subjects with normal corneas to the extent that reducing this artifact improves the accuracy of imaging measures of retinal nerve fiber layer thickness [16]. Polarization effects were examined for intra-ocular lenses that are implanted in large numbers of patients after cataract surgery, and all but one type of those studied should not increase the anterior segment artifact appreciably [17].

The use of Mueller matrix polarimetry may provide potential benefits in the computation of both polarization preserving and depolarized light. The present analyses were based on the assumption of linear polarization, with birefringence being a dominant polarization characteristic of the human retina. This is in agreement with measurements by Dreher and colleagues, and has and has led to successful clinical instruments [12,16], it may not provide an estimate for other polarization characteristics that would be confounded with depolarization in a more complex biological model [18]. A Mueller matrix method may allow more accurate characterization of blood vessels by reducing both potential linear and circular polarization artifacts due to the interaction of corneal and retinal polarization properties [18]. Such an instrument is not commercially available, and basic research will determine which applications would realize significant benefit from a full Mueller matrix characterization and which measurements are well-approximated by an incomplete polarimeter [19,20].