Design Considerations for Murine Retinal Imaging Using Scattering Angle Resolved Optical Coherence Tomography

Featured Application: Scattering angle resolved optical coherence tomography offers a new contrast mechanism for murine retinal imaging. Abstract: Optical coherence tomography (OCT), an optical imaging approach enabling cross-sectional analysis of turbid samples, is routinely used for retinal imaging in human and animal models of diseases affecting the retina. Scattering angle resolved (SAR-)OCT has previously been demonstrated as offering additional contrast in human studies, but no SAR-OCT system has been reported in detail for imaging the retinas of mice. An optical model of a mouse eye was designed and extended for validity at wavelengths of light around 1310 nm; this model was then utilized to develop a SAR-OCT design for murine retinal imaging. A Monte Carlo technique simulates light scattering from the retina, and the simulation results are conﬁrmed with SAR-OCT images. Various images from the SAR-OCT system are presented and utility of the system is described. SAR-OCT is demonstrated as a viable and robust imaging platform to extend utility of retinal OCT imaging by incorporating scattering data into investigative ophthalmologic analysis.


Introduction
Optical coherence tomography (OCT) is an optical imaging technique that utilizes the coherence properties of light to obtain cross-sectional images of turbid samples by interfering sample and reference arms [1]. OCT has been used in disciplines ranging from additive manufacturing to cardiology.
OCT has become the standard of care in ophthalmology and is routinely used to monitor changes in the retina and optic nerve [2]. However, standard clinical OCT systems are generally unable to detect changes in backscattered light's scattering angle.
Angle-resolved approaches measure angular distribution of backscattered light, which changes based on tissue anisotropy. A rich literature exists concerning angle-resolved imaging of apoptotic and necrotic tissues specifically, and these studies demonstrate the potential clinical relevance of a scattering-angle resolved imaging platform. One study examined forward scattering changes (5-90 degrees) due to mitochondrial swelling due to oxidative stress in suspensions of intact murine mammary carcinoma cells and found that treated cells scattered less light at low angles [3]. Similarly, wavelengths. These data were extrapolated to the NIR by fitting the four data points from Remtullah to Conrady's dispersion equation [18]: In Conrady's Equation (1), n is the refractive index, n 0 is the refractive index as λ approaches ∞, B (µm) is a parameter affecting the curvature and amplitude of the refractive index at visible wavelengths, and C (µm 3.5 ) influences refractive index in the UV. The Conrady dispersion formula is well suitedfor transparent materials such as the murine eye. The fit yielded the parameters and refractive indices listed in the corresponding section in Table 2 in Section 3.1.

System Design
The materials and methods for designing and constructing a SAR-OCT mouse retinal imager ( Figure 1) are described. In Conrady's Equation (1), n is the refractive index, n0 is the refractive index as λ approaches ∞, B (μm) is a parameter affecting the curvature and amplitude of the refractive index at visible wavelengths, and C (μm 3.5 ) influences refractive index in the UV. The Conrady dispersion formula is well suitedfor transparent materials such as the murine eye. The fit yielded the parameters and refractive indices listed in the corresponding section in Table 2 in Section 3.1.

System Design
The materials and methods for designing and constructing a SAR-OCT mouse retinal imager ( Figure 1) are described. Figure 1. Diagram of the SAR-OCT system for murine retinal imaging. The design includes a 1310 nm ± 70 nm swept source laser and a fiber-based interferometer setup. (CP, fiber coupler; CR, fiber circulator). The sample arm includes a reflective collimator (RC), pathlength multiplexing element (PME), several gradient index lenses (L1-L5), a dual-axis MEMS mirror (MM) conjugate to the ocular pupil plane, and a fundus lens (FL) that interfaces with the mouse cornea. The reference arm includes three lenses for dispersion matching and a mirror pathlength-matched to the mouse's retina. Permission was granted by the publisher to reprint this figure from Gardner et al. with minor modifications [19].
Similar to the Wang design, the SAR-OCT design described here is a fiber-based system for ease of transport to the operating room. Because bulk optics systems are difficult and time-consuming to align single mode fiber optics were utilized when possible. SMF-28e fibers are used here which transmit the 1310 nm (±70 nm) broadband swept source (100 kHz repetition rate, 25 mW output, Axsun) in a single mode. The Axsun laser bandwidth is greater and the sweep repetition rate is faster than that of the Wang design. FC-APC fiber connections are employed to minimize any reflected light from fiber-fiber interfaces and reduce ghost interference signals.
A 90:10 fiber coupler directs 90% of the laser's output to the sample arm optics and 10% to the reference arm ( Figure 1) to give 15 mW average power incident on the mouse cornea. Each arm of the interferometer has a fiber circulator with three arms. Light entering arm 1 exits arm 2, and light returning to arm 2 exits arm 3. After sample and reference optics, the light is interfered in a 50:50 fiber coupler, and each output is measured by a balanced detection scheme. Balanced detection eliminates Figure 1. Diagram of the SAR-OCT system for murine retinal imaging. The design includes a 1310 nm ± 70 nm swept source laser and a fiber-based interferometer setup. (CP, fiber coupler; CR, fiber circulator). The sample arm includes a reflective collimator (RC), pathlength multiplexing element (PME), several gradient index lenses (L1-L5), a dual-axis MEMS mirror (MM) conjugate to the ocular pupil plane, and a fundus lens (FL) that interfaces with the mouse cornea. The reference arm includes three lenses for dispersion matching and a mirror pathlength-matched to the mouse's retina. Permission was granted by the publisher to reprint this figure from Gardner et al. with minor modifications [19].
Similar to the Wang design, the SAR-OCT design described here is a fiber-based system for ease of transport to the operating room. Because bulk optics systems are difficult and time-consuming to align single mode fiber optics were utilized when possible. SMF-28e fibers are used here which transmit the 1310 nm (±70 nm) broadband swept source (100 kHz repetition rate, 25 mW output, Axsun) in a single mode. The Axsun laser bandwidth is greater and the sweep repetition rate is faster than that of the Wang design. FC-APC fiber connections are employed to minimize any reflected light from fiber-fiber interfaces and reduce ghost interference signals. A 90:10 fiber coupler directs 90% of the laser's output to the sample arm optics and 10% to the reference arm ( Figure 1) to give 15 mW average power incident on the mouse cornea. Each arm of the interferometer has a fiber circulator with three arms. Light entering arm 1 exits arm 2, and light returning to arm 2 exits arm 3. After sample and reference optics, the light is interfered in a 50:50 fiber coupler, and each output is measured by a balanced detection scheme. Balanced detection eliminates the background signal to isolate the interference fringe.
Concerning the laser source, a swept source OCT system typically has some advantages over spectral domain for SAR-OCT. The relevant optical design parameter for the pathlength multiplexing element (PME; described in Section 2.2.5) and SAR-OCT is the scan range. In swept source OCT, scan range is given by instantaneous coherence length of the swept laser source. In comparison, for spectral domain OCT, scan range is given by spectral resolving power of the readout spectrometer. In many OCT spectrometers, the scan range is on the order of 4-5 mm. Since the scan range of many swept laser sources is on the order of 10-100 mm, PME design and corresponding pathlength difference between distinct angular paths is greater than that in spectral domain OCT. Thus, most swept-source OCT systems provide greater PME design flexibility and separation of angular paths compared to spectral domain approaches.

2D MEMS Mirror
Most murine retinal images reported in the scientific literature include post-objective scanning systems. In these systems, galvanometers are placed between the final lens (objective) and the retina. Collimated light is directed by mirrors at different angles to reach different parts of the retina. This design limits the field of view of the OCT systems because the ocular pupil clips OCT source light at the system's most extreme angle.
This problem can be mitigated by placing the mirrors at conjugates to the ocular pupil plane and thus steering the beam beyond the aperture of the pupil. However, engineers using this approach have typically used two-mirror galvanometer systems. In this case, the designer must choose either the slow axis, the fast axis, or somewhere in-between as a conjugate plane to the ocular pupil. The slow-axis has historically been chosen to maximize collection efficiency and minimize vignetting [20]. New approaches to limit vignetting and maximize collection efficiency have included pupil tracking to control where the beam enters the pupil [21].
Dual-axis MEMS mirrors have been used in OCT catheter designs and free-space optical setups [22,23], but adoption of dual axis-mirrors for retinal imaging has been more slow. Recent examples include hand-held OCT retina and anterior segment imaging systems [24,25]. The system reported here is the first OCT system to use dual-axis MEMS mirror scanning for mouse retinal imaging, and first reported in less detail in 2017 [19].

Corneal Contact
Many OCT systems, including almost all human retinal imaging systems, are non-contact systems meaning the objective lens does not make contact with the subject's cornea. This is particularly helpful for human subjects who may be told to hold still for several seconds while an OCT image is captured. Patient discomfort is thus minimized by removing the need for an index matching medium between the objective and the patient's cornea. Mice are typically anesthetized when their retinas are imaged using OCT, thus allowing for a corneal contact system.
One issue with non-contact OCT retinal imagers is that the beam wavefront is subject to the natural aberrations of the eye-the air-cornea and aqueous-lens interfaces providing most of the optical power. The mouse eye introduces significant amounts of spherical aberration and coma, with astigmatism [26]. In conflicting reports, the murine eye has been reported as both myopic and hyperopic [15,26]. Significant longitudinal chromatic aberrations exist and the mouse eye has a numerical aperture of 0.5, as opposed to a human eye's 0.2 [15].
A murine retinal imager must account for these aberrations to obtain quality images. Generally, there are two approaches to limiting the effect of aberrations in murine retinal imaging.
First, wavefront sensing and adaptive optics can improve the spot size of the beam on the retina and account for aberrations in the eye. Such systems have been reported for human retinal OCT and scanning laser ophthalmoscope systems [27,28] and for murine retinal OCT systems [29,30]. Classically, these OCT systems employ a wavefront sensor (either with a Shack-Hartmann wavefront sensor or computationally). Based on the sensed wavefront characteristics, an adaptive optic element (e.g., deformable mirror, spatial light modulator) will adaptively alter the incident beam wavefront until the reflected beam has a high-quality wavefront. This intervention ensures that the beam spot size on the retina is small and thus improves spatial resolution. Although these systems are powerful tools, they are more costly and may be slow to make their way to a clinical setting.
The second approach is to design a corneal contact system to limit the effect of aberrations from the air-cornea interface [31]. This interface has the most optical power and contributes significantly to optical aberrations in the mouse eye [16]. For a more cost-effective approach to limiting aberrations, a corneal contact lens can be index matched to the cornea [32].
For non-contact systems, the incident beam is collimated (or its wavefront adjusted with adaptive optics) and relies on the natural optics of the eye to focus on the retina. By removing the optical power of the cornea with a contact lens, light should have some positive (convergent) power upon entering the eye to focus on the retina. Figure 2 presents non-contact and contact designs. size on the retina is small and thus improves spatial resolution. Although these systems are powerful tools, they are more costly and may be slow to make their way to a clinical setting. The second approach is to design a corneal contact system to limit the effect of aberrations from the air-cornea interface [31]. This interface has the most optical power and contributes significantly to optical aberrations in the mouse eye [16]. For a more cost-effective approach to limiting aberrations, a corneal contact lens can be index matched to the cornea [32].
For non-contact systems, the incident beam is collimated (or its wavefront adjusted with adaptive optics) and relies on the natural optics of the eye to focus on the retina. By removing the optical power of the cornea with a contact lens, light should have some positive (convergent) power upon entering the eye to focus on the retina. Figure 2 presents non-contact and contact designs. A custom contact lens was fabricated (Optics Technology, Inc.) by etching down a BK7 window with an anti-reflective (AR) coating. The AR coating was maintained on the non-contact side, and a concave surface was formed at the opposite side (radius = 2 mm). The AR coating limits any unwanted reflections from being coupled back into the fiber interferometer. The concave surface is index-matched to the cornea using methyl cellulose.

Focusing Lens
Because the system uses a contact lens, light should have some optical power upon entering the eye. However, given the variability of optical properties across different mice, particularly the thickness of ocular components, it would be advantageous to have a movable lens to optimize spot size on the retina. Thus, the lens providing the power is placed on a translation stage. For longer eyes, the lens is translated toward the mouse to move the focal plane deeper into the eye, and vice versa. This lens and translation mount are placed before the 2D MEMS mirror, thus the diameter of the beam on the mirror (and the ocular pupil plane conjugate to the pupil) varies with the translation of the lens. Although the beam size on the mirror varies, it never is clipped by the mirror. A custom contact lens was fabricated (Optics Technology, Inc.) by etching down a BK7 window with an anti-reflective (AR) coating. The AR coating was maintained on the non-contact side, and a concave surface was formed at the opposite side (radius = 2 mm). The AR coating limits any unwanted reflections from being coupled back into the fiber interferometer. The concave surface is index-matched to the cornea using methyl cellulose.

Focusing Lens
Because the system uses a contact lens, light should have some optical power upon entering the eye. However, given the variability of optical properties across different mice, particularly the thickness of ocular components, it would be advantageous to have a movable lens to optimize spot size on the retina. Thus, the lens providing the power is placed on a translation stage. For longer eyes, the lens is translated toward the mouse to move the focal plane deeper into the eye, and vice versa. This lens and translation mount are placed before the 2D MEMS mirror, thus the diameter of the beam on the mirror (and the ocular pupil plane conjugate to the pupil) varies with the translation of the lens. Although the beam size on the mirror varies, it never is clipped by the mirror.

Dispersion Compensation
Group delay dispersion mismatch between the sample and reference arms can negatively affect OCT images by causing the full-width at half maximum (FWHM) of a surface to expand. Spectral phase expansion can be written as: where φ(ω) [radians/second] is the Taylor series for about the center optical frequency, ω (ω = 2πν). The zero-order term describes the phase difference at the center optical frequency. The first-order term, φ (1) (ω 0 ), contains the inverse group velocity, that is "group delay", and units are in seconds. The second-order (quadratic) term, φ (2) (ω 0 ), is the group delay dispersion (GDD), and the units are s 2 .
Without dispersion compensation lenses in the reference arm, the SAR-OCT system ( Figure 1) would have dramatic GDD mismatch and loss of longitudinal resolution. To characterize SAR-OCT dispersion mismatch between sample and reference arms, a series of measurements were recorded in which mirror were placed in sample and reference arms. With only a single collimating lens in the reference arm, each lens of the sample arm was added, one-at-a-time, in proper order and dispersion mismatch measured. Table 1 shows the second-order term to characterize dispersion after successive lenses and the contribution of each lens individually. Total GDD dispersion mismatch (5.01 × 10 −28 s 2 ) was measured. Two achromatic lenses were selected to match this dispersion and placed in an afocal configuration in the reference arm of the interferometer thereby reducing total dispersion mismatch by 5X (9.50 × 10 −29 s 2 ). This reduction in dispersion was sufficient for high-quality retinal imaging. The amount of dispersion introduced by the murine eye is sufficiently small to forego dispersion compensation for the ocular components. Length of the mouse eye is relatively short compared to that of humans, and the refractive index of the ocular media is nearly constant over the wavelength range of the OCT source.

Pathlength Multiplexing Element
An important component to the SAR-OCT system is the pathlength multiplexing element (PME). The PME is a BK7 window, 5 mm thick, with a central clear aperture. The center aperture has a 7 mm diameter. Light in the sample arm of the SAR-OCT system has three potential optical pathlengths: Pathlength 1 is light that travels through the center aperture to and from the retina. Pathlength 2 is light that travels through the PME central aperture once-to or from the retina. Pathlength 3 is light that does not travel through the PME central aperture-to and from the retina. Figure 3 illustrates the three pathlengths. Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 20 Figure 3. The PME introduces three potential optical pathlengths. Light mapped to Pathlength 1 (P1, blue) travels through the center of the PME to and from the retina. Light mapped to Pathlength 2 (P2, green) travels through the PME central aperture only once-travelling either to or from the retina. Light mapped to Pathlength 3 (P3, red) does not travels through the PME central aperture-both to and from the retina. Permission was granted by the publisher to reprint this figure from Gardner et al. with minor modifications [19].
Mathematically, the additional pathlengths added for each path through any PME are described generally below: Additional pathlength added for Pathlength 1 ( ) is Additional pathlength added for Pathlength 2 ( ) is Additional pathlength added for Pathlength 3 ( ) is In Equations (3)-(5), d is the physical PME thickness, and n is refractive index of the glass at the center wavelength of the OCT system. For the 5 mm thick BK7 PME (n = 1.50 at 1310 nm), = 0, = 2.5 mm, and = 5 mm. Thus, each sub image in the OCT interferogram is separated vertically by 2.5 mm. A more rigorous Fourier optical analysis of the PME operation for imaging was previously published [33]. A Monte Carlo model was developed to determine the effect of PME center aperture size on the intensity of light in each pathlength. Photons were randomly generated within the beam area, and each photon was weighted by its position in the Gaussian beam profile of the OCT source. Then, each photon was assigned a scattering angle off of the sample based on an assigned g-factor (anisotropy) of 0.97, a measured g anisotropy value for the neural retina [34]. The Monte Carlo simulation recorded whether the photon travelled through the PME glass once, twice, or never, and each photon contributed to the intensity of its assigned pathlength ( Figure 4). The scattering angle of the photon was also recorded. The results of the Monte Carlo simulation suggested no single PME aperture size exists at which the pathlength intensities are equal. The PME introduces three potential optical pathlengths. Light mapped to Pathlength 1 (P1, blue) travels through the center of the PME to and from the retina. Light mapped to Pathlength 2 (P2, green) travels through the PME central aperture only once-travelling either to or from the retina. Light mapped to Pathlength 3 (P3, red) does not travels through the PME central aperture-both to and from the retina. Permission was granted by the publisher to reprint this figure from Gardner et al. with minor modifications [19].
Mathematically, the additional pathlengths added for each path through any PME are described generally below: Additional pathlength added for Pathlength 1 (L L ) is Additional pathlength added for Pathlength 2 (L H2 ) is Additional pathlength added for Pathlength 3 (L H3 ) is In Equations (3)-(5), d is the physical PME thickness, and n is refractive index of the glass at the center wavelength of the OCT system. For the 5 mm thick BK7 PME (n = 1.50 at 1310 nm), L L = 0, L H2 = 2.5 mm, and L H3 = 5 mm. Thus, each sub image in the OCT interferogram is separated vertically by 2.5 mm. A more rigorous Fourier optical analysis of the PME operation for imaging was previously published [33]. A Monte Carlo model was developed to determine the effect of PME center aperture size on the intensity of light in each pathlength. Photons were randomly generated within the beam area, and each photon was weighted by its position in the Gaussian beam profile of the OCT source. Then, each photon was assigned a scattering angle off of the sample based on an assigned g-factor (anisotropy) of 0.97, a measured g anisotropy value for the neural retina [34]. The Monte Carlo simulation recorded whether the photon travelled through the PME glass once, twice, or never, and each photon contributed to the intensity of its assigned pathlength ( Figure 5). The scattering angle of the photon was also recorded. The results of the Monte Carlo simulation suggested no single PME aperture size exists at which the pathlength intensities are equal.
is scattered at each extreme-both direct backscattering and high-angle backscattering. This simulation relative PME intensities in Figure 4. To maximize utility of the angular discrimination in Pathlengths 1 and 2, a PME aperture size was selected around 72% of the beam diameter. At this aperture size, the intensities of light in Pathlengths 1 and 2 were about equal, while the intensity of light in Pathlength 3 was about half that of Pathlengths 1 and 2. This selection is indicated by the yellow line in Figure 4, and the angular distribution of light at this aperture size is plotted in Figure 5.  Plotting the angular distribution of backscattered photons for each pathlength revealed that Pathlengths 1 and 2 have greatest angular discrimination ( Figure 4). Pathlength 3 contains light that is scattered at each extreme-both direct backscattering and high-angle backscattering. This simulation relative PME intensities in Figure 5. To maximize utility of the angular discrimination in Pathlengths 1 and 2, a PME aperture size was selected around 72% of the beam diameter. At this aperture size, the intensities of light in Pathlengths 1 and 2 were about equal, while the intensity of light in Pathlength 3 was about half that of Pathlengths 1 and 2. This selection is indicated by the yellow line in Figure 5, and the angular distribution of light at this aperture size is plotted in Figure 4.  . Monte Carlo simulation shows the relative intensity of each pathlength as a function of PME central aperture size (diameter; percent of beam diameter). The intensity of light in pathlength one increases monotonically with PME aperture size, and the intensity of light in Pathlength 3 decreases monotonically with PME aperture size. The intensity of light due to photons in Pathlength 2 increases and then decreases, with an infection point at a PME aperture size (diameter) of about 60% of the OCT beam diameter. The yellow vertical line corresponds to the angular distributions in Figure 5. Permission was granted by the publisher to reprint this figure from Gardner et al. with minor modifications [19].
Plotting the angular distribution of backscattered photons for each pathlength revealed that Pathlengths 1 and 2 have greatest angular discrimination ( Figure 5). Pathlength 3 contains light that is scattered at each extreme-both direct backscattering and high-angle backscattering. This simulation relative PME intensities in Figure 4. To maximize utility of the angular discrimination in Pathlengths 1 and 2, a PME aperture size was selected around 72% of the beam diameter. At this aperture size, the intensities of light in Pathlengths 1 and 2 were about equal, while the intensity of light in Pathlength 3 was about half that of Pathlengths 1 and 2. This selection is indicated by the Figure 5. Monte Carlo simulation shows the relative intensity of each pathlength as a function of PME central aperture size (diameter; percent of beam diameter). The intensity of light in pathlength one increases monotonically with PME aperture size, and the intensity of light in Pathlength 3 decreases monotonically with PME aperture size. The intensity of light due to photons in Pathlength 2 increases and then decreases, with an infection point at a PME aperture size (diameter) of about 60% of the OCT beam diameter. The yellow vertical line corresponds to the angular distributions in Figure 4. Permission was granted by the publisher to reprint this figure from Gardner et al. with minor modifications [19].
Given the 12 mm beam diameter after the reflective collimator ( Figure 1) and available discrete drill bit sizes, a 7 mm diameter central aperture was selected for the PME.

System Construction
Since the system must be transportable to and from the operating room for imaging mice under anesthesia, the SAR-OCT system was designed to be mounted on an articulating arm, which was mounted on a rolling cart. To fit the arm, the system needed to be compact and stable, yet flexible enough to allow for adjusting high-precision optical components. The SAR-OCT mechanical system was custom-designed in a computer aided design (CAD) software package with a combination of off-the-shelf optical components (ThorLabs) and custom aluminum components for mounting optics. Aluminum parts were machined by the University of Texas at Austin's Mechanical Engineering machine shop. A complete CAD rendering of the SAR-OCT design is pictured in Figure 6, and a photo of the constructed system is in Figure 7. Given the 12 mm beam diameter after the reflective collimator ( Figure 1) and available discrete drill bit sizes, a 7 mm diameter central aperture was selected for the PME.

System Construction
Since the system must be transportable to and from the operating room for imaging mice under anesthesia, the SAR-OCT system was designed to be mounted on an articulating arm, which was mounted on a rolling cart. To fit the arm, the system needed to be compact and stable, yet flexible enough to allow for adjusting high-precision optical components. The SAR-OCT mechanical system was custom-designed in a computer aided design (CAD) software package with a combination of offthe-shelf optical components (ThorLabs) and custom aluminum components for mounting optics. Aluminum parts were machined by the University of Texas at Austin's Mechanical Engineering machine shop. A complete CAD rendering of the SAR-OCT design is pictured in Figure 6, and a photo of the constructed system is in Figure 7.   Given the 12 mm beam diameter after the reflective collimator ( Figure 1) and available discrete drill bit sizes, a 7 mm diameter central aperture was selected for the PME.

System Construction
Since the system must be transportable to and from the operating room for imaging mice under anesthesia, the SAR-OCT system was designed to be mounted on an articulating arm, which was mounted on a rolling cart. To fit the arm, the system needed to be compact and stable, yet flexible enough to allow for adjusting high-precision optical components. The SAR-OCT mechanical system was custom-designed in a computer aided design (CAD) software package with a combination of offthe-shelf optical components (ThorLabs) and custom aluminum components for mounting optics. Aluminum parts were machined by the University of Texas at Austin's Mechanical Engineering machine shop. A complete CAD rendering of the SAR-OCT design is pictured in Figure 6, and a photo of the constructed system is in Figure 7.

System Characterization
After designing the system, experiments were conducted to verify imaging performance of the SAR-OCT system. These involved scattering angle characterization and finally, murine retinal imaging.

Scattering Angle Characterization
To characterize system's sensitivity to changes in scattering angle, an experiment was designed in which light was reflected back at known angles. The dual-axis MEMS mirror was placed just beyond the focal plane of the objective lens and raster-scanned to collect a range of pathlength intensities corresponding to bulk scattering angles (Figure 8). The incident beam was not scanned in this configuration, only the angle at which the light was reflected from the dual-axis MEMS mirror in the focal plane. Orientation of the dual-axis MEMS mirror varied by ±4 degrees in the x-and y-directions; thus, several raster scans were collected with various tilt offsets and stitched together in post-processing.

System Characterization
After designing the system, experiments were conducted to verify imaging performance of the SAR-OCT system. These involved scattering angle characterization and finally, murine retinal imaging.

Scattering Angle Characterization
To characterize system's sensitivity to changes in scattering angle, an experiment was designed in which light was reflected back at known angles. The dual-axis MEMS mirror was placed just beyond the focal plane of the objective lens and raster-scanned to collect a range of pathlength intensities corresponding to bulk scattering angles (Figure 8). The incident beam was not scanned in this configuration, only the angle at which the light was reflected from the dual-axis MEMS mirror in the focal plane. Orientation of the dual-axis MEMS mirror varied by ±4 degrees in the x-and ydirections; thus, several raster scans were collected with various tilt offsets and stitched together in post-processing. Figure 8. A dual axis MEMS mirror located at the focal plane raster scans through a range of bulk backscattering angles. The grayscale beam is the incident beam, and the green beam is an example reflected beam. The green beam, reflected with some angular deviation due to the dual-axis MEMS mirror, depicts more light travelling through the glass of the PME than the incident beam had. One would expect that the resultant images would have higher intensity in Pathlengths 2 and 3 (H2 and H3) and lower intensity in Pathlength 1 (L) compared to a beam that is reflected with no angular deviation.
Depths corresponding to the MEMS mirror at Pathlengths 1-3 were isolated, and then intensity values corresponding to a given reflection angle were averaged azimuthally in reference to the neutral position (degree 0,0). Results are given in Section 3.2.

Imaging Protocol
Murine retinal images were recorded using the SAR-OCT system (IACUC protocol: #AUP-2015-00156) and the total intensities in each pathlength for 32 mice (B6SJL F1/J-JAX #100012) were recorded. The intensities were normalized to the pathlength with the maximum intensity. The relative intensities in Pathlengths 1-3 were compared to the results of the Monte Carlo model to assess the agreement between the model and the imaging system. Figure 8. A dual axis MEMS mirror located at the focal plane raster scans through a range of bulk backscattering angles. The grayscale beam is the incident beam, and the green beam is an example reflected beam. The green beam, reflected with some angular deviation due to the dual-axis MEMS mirror, depicts more light travelling through the glass of the PME than the incident beam had. One would expect that the resultant images would have higher intensity in Pathlengths 2 and 3 (H 2 and H 3 ) and lower intensity in Pathlength 1 (L) compared to a beam that is reflected with no angular deviation.
Depths corresponding to the MEMS mirror at Pathlengths 1-3 were isolated, and then intensity values corresponding to a given reflection angle were averaged azimuthally in reference to the neutral position (degree 0,0). Results are given in Section 3.2.

Imaging Protocol
Murine retinal images were recorded using the SAR-OCT system (IACUC protocol: #AUP-2015-00156) and the total intensities in each pathlength for 32 mice (B6SJL F1/J-JAX #100012) were recorded. The intensities were normalized to the pathlength with the maximum intensity. The relative intensities in Pathlengths 1-3 were compared to the results of the Monte Carlo model to assess the agreement between the model and the imaging system.

Initial Processing
With inclusion of the PME, three sub-images are observed in every B-scan, each corresponding to three different bulk scattering angles. To align the images for analysis, the first sub-image (Pathlength 1) is used as a reference. Sub-images are selected manually, each with the same height (typicallỹ 150 pixels). Then, Pathlengths 2 and 3 are shifted in the z-direction (axially) to align with Pathlength 1. The MATLAB function "imregister" is set to perform only axial shifting for precise alignment. Simple axial shifting, in contrast to other more complex methods, is appropriate for this system because it is known a priori that each A-scan location contains the exact same retinal cross section in the three sub-images. Any image registration that goes beyond simple axial shifting risks mixing A-scans across different locations and corrupting the scattering angle analysis. After the sub-images are aligned, each pathlength sub-image is saved as a tiff stack. This results in three image stacks with size 150 (height) × 512 (width) × 4096 (depth). These image stacks are stored without any image compression to maintain signal fidelity.
This first initial processing step outputs three aligned image stacks. With these three stacks, intensity processing, speckle processing, and segmentation may be performed before the four subsequent analysis steps for feature extraction.

Intensity Processing
Before analysis can be performed, eight repeating B-scans in each B-scan location are first averaged together and collapsed into one B-scan. Thus, the three sub-images previously aligned and saved are taken from size 150 × 512 × 4095 to 150 × 512 × 512. Averaging over the eight repeated B-scans yields higher signal-to-noise ratios (SNR). These three volumes, corresponding to each of the three pathlengths, are later used in scattering angle analysis.
The second process under intensity processing is to average the three sub-images (150 × 512 × 512) voxel-by-voxel. Averaging further increases SNR and permits more repeatable analysis of layer thickness and reflectance index.

Speckle Processing
Several established methods exist to determine areas of blood flow using OCT for biomedical imaging. One approach is complex differential variance (CDV), which intrinsically limits phase noise due to bulk motion [35]. Because of its outperformance of other methods based on angiographic analysis of collected SAR-OCT retinal images, CDV was selected as the angiographic method for this SAR-OCT device.
The CDV signal for any given A-scan can be described as where M is the total number of repeating B-scans, L (more precisely, 2L + 1) is the length of the kernel, w is the depth window function, and R is the complex analytic OCT signal at time point t (R = A(z,t)e iϕ(z,t) ). The coherent average is normalized by division with the incoherent average of the original A-scan data. Three sequential processes take CDV volumes as input to obtain high-fidelity angiograms: (1) filtering to remove bulk motion; (2) Frangi vesselness filter to improve SNR; and (3) adaptive thresholding for binarizing angiograms.
Despite the CDV algorithm's robustness compared to other methods, the problem of bulk motion can still be observed such that vertical lines obscure vascular structures. These vertical lines are due to bulk movements of the mouse including heart beat and breathing. For filtering to remove bulk motion artifacts, these lines are first detected manually, with the user clicking to the left and right of a line in the superficial plexus image. The width of the line is then determined by a custom MATLAB script, and the entire artifact is replaced with values taken from the left and right of the obscuring line. The same replacement process is repeated automatically in the intermediate and deep plexuses.
The second filtering process applies the Frangi vesselness filter [36] to the filtered image to isolate those areas of the image that are vessel-like. The Frangi filter, which uses Gaussian-like distributions with user-defined widths to search for vessel-like features, is a helpful tool for the retina because the sizes of the vessels are generally known, a priori. The Frangi filter takes as inputs the size distribution of vessels and searches for structures that are around that size. A range of three sigma values suited the vessel size distribution are selected. Additional Frangi parameters included β 1 (0.5) and β 2 (5). If not handled judiciously, Frangi filtering could introduce false vessel structures from noise.
The final step was to binarize image such that more intensive vascular analysis could be performed. The image was binarized using a built-in MATLAB filter with adaptive thresholding. One note here is that adaptive filtering assumes the presence of a vessel.

Segmentation
The murine retinal segmentation algorithm for the SAR-OCT images used here can be characterized as three kinds of processes interspersed throughout the algorithm: (1) stack conditioning; (2) Sobel edge detection; and (3) error removal, each custom-designed in MATLAB.
As a part of the stack conditioning process, the angiography and intensity scans are simply summed. Because the vasculature of the murine retina is highly localized to particular regions, the addition of SAR-OCT intensity volume with the angiography image intensifies the boundaries between retinal layers.
Another part of the stack conditioning process occurs after detection of the ONL/RPE boundary. The retina is flattened with reference to the ONL/RPE boundary. Then, a median filter is applied (50 × 50 × 1 voxels). Because the retina has been flattened, this process works to provide some uniformity within each layer and present retinal layers more distinct.
The second category of segmentation is edge detection. Each boundary is determined by examining volumes that have been filtered with a Sobel edge detection filter [37]. The Sobel filter has a convolution kernel given by: The ONL/RPE boundary is, for the most part, the most prominent edge detected by the Sobel filter. However, spurious noise could also be detected by the filter, thus a secondary means of eliminating wrong boundaries was employed. Before the edge is selected by the MATLAB script, the user of the script must manually click throughout the image over several boundaries as prompted by the script. The user input is used as an initial guess for boundary detection; that is, boundaries are only considered as the possible correct boundary if they are within a physiologically reasonable range of the inputted boundary. This clicking technique is applied to three of the five boundaries detected: the ONL/RPE, INL/OPL and the vitreous/ILM boundaries.
Finally, inputs of these user inputs are also used to form a 3D second-order polynomial that is utilized in the third processing step, error removal. Occasionally as edge selected by the MATLAB script is incorrect, and, perhaps, the edge is not even reasonably determinable by the human eye. In such cases, edge location is estimated based on the surrounding tissues (e.g., under vessel shadows). In these cases, the 3D polynomial is manually selected (in those regions alone) to replace the semi-automatically detected edges.

Scattering Angle Feature
Ratio processing is the simplest approach to leveraging the utility of SAR-OCT, and is the approach previously described by Wang et al. [31]. Wang looked to Pathlength 3 as it contains the highest possible scatterers and found that the ratio of Pathlength 1 to Pathlength 3 (L/H 3 ) correlated with known azimuthal variation of retinal ganglion cell size.
However, as was demonstrated in the Monte Carlo simulation, Pathlength 2 and Pathlength 1 provide the greatest angular discrimination. Although Pathlength 3 contains higher backscattering angles than Pathlength 2, Pathlength 3 also contains the lowest possible angles (direct backscattering). Thus, L/H 2 was decided upon as an image feature. A visual explanation of the PME and L/H 2 is provided in Figure 9.
Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 20 highest possible scatterers and found that the ratio of Pathlength 1 to Pathlength 3 (L/H3) correlated with known azimuthal variation of retinal ganglion cell size. However, as was demonstrated in the Monte Carlo simulation, Pathlength 2 and Pathlength 1 provide the greatest angular discrimination. Although Pathlength 3 contains higher backscattering angles than Pathlength 2, Pathlength 3 also contains the lowest possible angles (direct backscattering). Thus, L/H2 was decided upon as an image feature. A visual explanation of the PME and L/H2 is provided in Figure 9.

Mouse Eye Optics
Combined, the radii of curvature and refractive indices for each murine eye segment (Table 2) yielded a suitable optical model in OpticStudio (Zemax). Figure 10 shows a real mouse eye cross section from Remtalluh superimposed with the optical model described above.  Figure 11 shows sample B-scans from the scattering angle characterization experiment. Figure  12A shows the intensity of each pathlength for each angular displacement, and Figure 12B plots the intensities after azimuthal averaging. The sample A-scans ( Figure 11) are also indicated in the same color by vertical dashed lines in Figure 12B.

Mouse Eye Optics
Combined, the radii of curvature and refractive indices for each murine eye segment (Table 2) yielded a suitable optical model in OpticStudio (Zemax). Figure 10 shows a real mouse eye cross section from Remtalluh superimposed with the optical model described above.  Figure 11 shows sample B-scans from the scattering angle characterization experiment. Figure 12A shows the intensity of each pathlength for each angular displacement, and Figure 12B plots the intensities after azimuthal averaging. The sample A-scans ( Figure 11) are also indicated in the same color by vertical dashed lines in Figure 12B  Experimental results determined that the SAR-OCT murine retinal imaging system can detect changes in bulk scattering angle up to eight degrees from a direct backscatter. That is, from a zerodegree backscattering angle to an eight-degree backscattering angle, the combination of light from Pathlengths 1-3 have unique contributions to the total image intensity. Light scattered from a sample at an angle greater than eight degrees is not recorded by the SAR-OCT system.  Experimental results determined that the SAR-OCT murine retinal imaging system can detect changes in bulk scattering angle up to eight degrees from a direct backscatter. That is, from a zerodegree backscattering angle to an eight-degree backscattering angle, the combination of light from Pathlengths 1-3 have unique contributions to the total image intensity. Light scattered from a sample at an angle greater than eight degrees is not recorded by the SAR-OCT system. Figure 11. Sample B-scans show how the intensity of Pathlengths 1-3 vary for different angles. At A-scan 300 of B-scan 50, Pathlength 3 (H 3 ) has the strongest intensity. This indicates that the mirror was at an extreme angle. In contrast, for A-scan 300 of B-scan 800, Pathlength 1 (L) has the strongest signal; this indicates that the mirror was at an angle closer to zero (direct back-scatter). A-scan numbers represent a linear increase in bulk scattering angle in one dimension, and B-scan numbers represent a linear increase in bulk scattering angle in the other dimension. See Figure 12A for the transformation from A-scan/B-scan number to angle.

Scattering Angle Characterization
Experimental results determined that the SAR-OCT murine retinal imaging system can detect changes in bulk scattering angle up to eight degrees from a direct backscatter. That is, from a zero-degree backscattering angle to an eight-degree backscattering angle, the combination of light from Pathlengths 1-3 have unique contributions to the total image intensity. Light scattered from a sample at an angle greater than eight degrees is not recorded by the SAR-OCT system.  Figure 11. The red dashed line matches the location of the red line in Figure 11.

Imaging
Based on the Monte Carlo model results (Figures 4 and 5), light intensities in Pathlengths 1 and 2 are expected to be about equal, and the intensity of light in Pathlength 3 should be about 50% of that in Pathlengths 1 and 2. Light intensities in Pathlengths 1 and 2 were not statistically different, but the experimental results also show a greater intensity of light in Pathlength 3 than the Monte Carlo simulation predicted (Figures 5 and 13). Nevertheless, this increase in Pathlength 3 intensity (compared to the simulation results) is beneficial because greater balance among the pathlengths yields higher quality composite images and a greater dynamic range for scattering angle analysis. Sample SAR-OCT images are also shown in Figure 14.

Imaging
Based on the Monte Carlo model results (Figures 4 and 5), light intensities in Pathlengths 1 and 2 are expected to be about equal, and the intensity of light in Pathlength 3 should be about 50% of that in Pathlengths 1 and 2. Light intensities in Pathlengths 1 and 2 were not statistically different, but the experimental results also show a greater intensity of light in Pathlength 3 than the Monte Carlo simulation predicted (Figures 4 and 13). Nevertheless, this increase in Pathlength 3 intensity (compared to the simulation results) is beneficial because greater balance among the pathlengths yields higher quality composite images and a greater dynamic range for scattering angle analysis. Sample SAR-OCT images are also shown in Figure 14.  Figure 11. The red dashed line matches the location of the red line in Figure 11.

Imaging
Based on the Monte Carlo model results (Figures 4 and 5), light intensities in Pathlengths 1 and 2 are expected to be about equal, and the intensity of light in Pathlength 3 should be about 50% of that in Pathlengths 1 and 2. Light intensities in Pathlengths 1 and 2 were not statistically different, but the experimental results also show a greater intensity of light in Pathlength 3 than the Monte Carlo simulation predicted (Figures 5 and 13). Nevertheless, this increase in Pathlength 3 intensity (compared to the simulation results) is beneficial because greater balance among the pathlengths yields higher quality composite images and a greater dynamic range for scattering angle analysis. Sample SAR-OCT images are also shown in Figure 14.

Image Processing
Example angiography results and edge detection results are shown in Figures 15 and 16. With angiography and edge detection, the scattering angle indices can be categorized by vascular zone or retinal layer. Figure 15. Results of CDV angiography and additional filtering. Original CDV images (Row 1) are manually filtered to remove bulk motion artifacts due to breathing and heart beat (Row 2). A Frangi vesselness filter is then applied to improve SNR (Row 3). Lastly, the Frangi-filtered images are binarized using adaptive filtering (Row 4). Columns 1-3 show different vascular plexuses, and Column 4 shows composite images of the Frangi-filtered and binarized angiograms. Scale bars indicate 300 μm.

Image Processing
Example angiography results and edge detection results are shown in Figures 15 and 16. With angiography and edge detection, the scattering angle indices can be categorized by vascular zone or retinal layer.

Image Processing
Example angiography results and edge detection results are shown in Figures 15 and 16. With angiography and edge detection, the scattering angle indices can be categorized by vascular zone or retinal layer.   To obtain a L/H2 tomogram, Pathlengths 1 and 2 are divided at every voxel position. With this approach, the segmentation output can be superimposed on the volume to sort the retinal L/H2 values into their corresponding layers ( Figure 17).

Conclusions
A simple mouse eye optical model at a wavelength 1.3 μm is introduced for the first time. This model informed SAR-OCT system design. Extensive design analysis and performance characteristics are presented for murine retinal imaging system, including laser and fiber optic components, the 2D MEMS mirror for beam scanning, the value of corneal contact for mouse eye imaging, dispersion compensation, PME computational modeling, and system construction. Image processing techniques are described in relation to unique SAR-OCT demands, including intensity processing, angiography, and retinal segmentation. Finally, the results of the analysis are presented in murine eye. The reported SAR-OCT system is shown to be sensitive to angular scattering up to eight degrees off normal. Example B-scans of mouse retinas, angiography images, and retinal segmentation results are presented to demonstrate the capacity of SAR-OCT to maintain retinal imaging fidelity, similar to that of other reported devices, while also adding the contrast mechanism due to scattering angle. Using a SAR-OCT imaging device such as the one described here enables new methods of scattering To obtain a L/H 2 tomogram, Pathlengths 1 and 2 are divided at every voxel position. With this approach, the segmentation output can be superimposed on the volume to sort the retinal L/H 2 values into their corresponding layers ( Figure 17). To obtain a L/H2 tomogram, Pathlengths 1 and 2 are divided at every voxel position. With this approach, the segmentation output can be superimposed on the volume to sort the retinal L/H2 values into their corresponding layers ( Figure 17).

Conclusions
A simple mouse eye optical model at a wavelength 1.3 μm is introduced for the first time. This model informed SAR-OCT system design. Extensive design analysis and performance characteristics are presented for murine retinal imaging system, including laser and fiber optic components, the 2D MEMS mirror for beam scanning, the value of corneal contact for mouse eye imaging, dispersion compensation, PME computational modeling, and system construction. Image processing techniques are described in relation to unique SAR-OCT demands, including intensity processing, angiography, and retinal segmentation. Finally, the results of the analysis are presented in murine eye. The reported SAR-OCT system is shown to be sensitive to angular scattering up to eight degrees off normal. Example B-scans of mouse retinas, angiography images, and retinal segmentation results are presented to demonstrate the capacity of SAR-OCT to maintain retinal imaging fidelity, similar to that of other reported devices, while also adding the contrast mechanism due to scattering angle. Using a SAR-OCT imaging device such as the one described here enables new methods of scattering

Conclusions
A simple mouse eye optical model at a wavelength 1.3 µm is introduced for the first time. This model informed SAR-OCT system design. Extensive design analysis and performance characteristics are presented for murine retinal imaging system, including laser and fiber optic components, the 2D MEMS mirror for beam scanning, the value of corneal contact for mouse eye imaging, dispersion compensation, PME computational modeling, and system construction. Image processing techniques are described in relation to unique SAR-OCT demands, including intensity processing, angiography, and retinal segmentation. Finally, the results of the analysis are presented in murine eye. The reported SAR-OCT system is shown to be sensitive to angular scattering up to eight degrees off normal. Example B-scans of mouse retinas, angiography images, and retinal segmentation results are presented to demonstrate the capacity of SAR-OCT to maintain retinal imaging fidelity, similar to that of other reported devices, while also adding the contrast mechanism due to scattering angle. Using a SAR-OCT imaging device such as the one described here enables new methods of scattering angle analysis for animal disease models that affect the morphology of biological structures in the retina, such as Alzheimer's disease, glaucoma, and traumatic encephalopathy.