1. Introduction and motivation

Tissue scattering properties have diagnostic value, are important considerations in new optical instrument modalities, and are essential ingredients in increasingly sophisticated models of light transport in tissue. The strength, angular dependence and spectral dependence of scattering provide information about the structure and organization of tissue. Scattering goniometry is the measurement of scattered intensity as a function of angle and is the most direct method of obtaining the phase function, p(θ, ϕ). However, there is currently a lack of direct measurement of the spectral and angular scattering over 4π sr. Such measurement would provide the most complete quantification of tissue scattering and would not require a priori assumption of any particular scattering model. With 4π spectral goniometry, the instrument described here offers a direct way to measure the shape of the entire phase function in isotropic tissue as well as related properties like anisotropy g and scattering coefficient μ_s as a function of wavelength. The capabilities of this instrument are needed to inform next generation tissue modeling and the development of instruments and imaging modalities that exploit scattering for contrast.

Light scattering in tissue results from the spatially varying refractive index of structures including extracellular matrix (ECM), cellular, and sub-cellular elements. Changes in these structures are associated with a wide range of diseases and thus quantification of scattering has diagnostic value. Measuring how light scatters in tissue can provide information about these structures, even if their features are too small to resolve [1,2].

A variety of scattering-related methods have been developed for diverse applications including: optical coherence tomography (OCT) applied to study how muscle cells remodel collagen gels [3], angle-resolved low-coherence interferometry used to detect dysplasia in human esophagus in vivo [4], structured light used to map spatial variations in scattering parameters [5], and low-coherence enhanced backscattering spectroscopy used to detect field carcinogenesis [6–9]. Changes in scattering have also been explicitly linked to subcellular morphological changes, for example, changes in the distribution of chromatin in cell nuclei have been linked to progression toward cancer [10, 11]. Advances in basic understanding of optical scattering in tissue would benefit these related techniques as well.

Scattering in tissue is usually quantified by scattering coefficient (μ_s) and scattering anisotropy (g) that describe the strength and shape of scattering. Optical scattering in tissue is very forward-directed and a convenient phase function parameterization is the Henyey-Greenstein model (HG), originally developed for astronomy [12–15]. The HG model is appealing because of its simple formulation, depending on a single parameter, the anisotropy, g.

The method described in this work addresses this challenge. In isotropic tissue, the entire scattering phase function (4π sr) is reconstructed by combining measurements acquired at different incident illumination angles. In anisotropic tissue one can observe large portions of scattering angle space and a partial phase function can be acquired (Note: anisotropic tissue refers to tissue that does not have the same scattering properties for all incident light beam directions while anisotropic scattering refers to scattering that is preferentially directed forward). Anisotropic tissue presents a rich and complicated area of investigation, but is beyond the scope of this work, which focuses on the description and validation of the instrument and examples of its measurement capabilities in tissue.

Typical optical scattering goniometers illuminate a sample with a collimated laser beam and collect the scattered light using a detector mounted on a pivoting arm, each detector position corresponding to a different observation angle. In the method described here, we instead make use of the Fourier plane or Back Focal Plane (BFP) of a lens. For a telecentric objective, the BFP also corresponds to the exit pupil. In this configuration, collimated light illuminates the sample and scattered light from a range of angles is collected on an imaging detector. Each scattering angle maps to a position in the objective BFP. A fundamental limitation with such an approach is that observed scattering is limited to angles within the lens numerical aperture (NA). Even the most expensive microscope objectives cannot capture light perpendicular to an on-axis incident beam. This constitutes a blind ring about the edge of the sample plane, where scattering cannot be measured. By illuminating at an angle in the sample plane, however, the technique in this work allows for detecting scattering at angles larger than 90° to the incident beam. Using forward and backward objectives permits collecting 4π sr of scattering.

In addition to i) 4π collection, the technique also enables a number of useful capabilities including: ii) measurement in θ and ϕ (solid-angle) of scattering to explore axially asymmetric scattering, iii) the ability to locate and interrogate small local regions of inhomogeneous tissue iv) the concurrent measurement of the scattering coefficient μ_s, and v) the measurement of these scattering properties spectrally from 550 to 800 nm. This instrument configuration is a promising new platform for analyzing tissue and allows for more accurate determination of tissue phase functions and other scattering properties.

2. Microscope objective based 4π goniometry

Goniometry for tissue characterization has been studied for decades. Pioneering early work featured a swinging detection arm that could observe a 360° slice through scattering angle space, but sample mounting geometry did not permit observation at and near 90° to the incident beam [22]. Subsequent work utilized a cylindrical sample geometry that allowed for observation of scattering from liquid samples at 90° to the incident beam [1]. Others used a swinging arm detection scheme as well, and flat sample geometry, only collecting observable forward-scattered light. Although observing limited angle space, they employed Monte-Carlo modeling to correct for multiple scattering and ascertain scattering parameters based on fitting to the HG phase function [15]. Recent work combined a cylindrical sample geometry with modeling and was able to observe scattering at 90 degrees to the incident beam [23].

Our work builds on this foundation to improve the measured angular range, spatial resolution, speed, and spectral range. This method also has the ability to investigate the effect of incident polarization. Rather than utilizing a comparatively slow moving detector, this system employs a microscope objective and camera. Since images contain projections of large solid-angles, scattering into large portions of angle-space is captured in a single image and so collection of data is fast. Furthermore, such a camera-based method collects scattering into a solid angle, not just a slice through angle space as a swinging detector does.

Several groups have developed the use of a lens for goniometry or similar techniques [24–26]. It is commonly referred to as back focal plane imaging and is often focused on studying the orientation of dipole-emitters in proximity to a surface. This is done by imaging the back focal plane of an objective, collecting emission from dipoles placed at the focal plane. Burghardt provides some particularly useful discussion of mapping pixels to angles. There are also techniques that have sought to obtain tissue scattering information over a limited angle range by imaging the angle-scattering pattern, showing some similarities to our technique [27–30].

These approaches, however, do not address the limited NA of the lens and so cannot measure scattering at large angles. In our technique, by scanning the incident beam angle, the objective samples a different part of the phase function. This is accomplished by focusing the incident light to different locations in the input objective BFP, producing a collimated beam at different angles as shown in Fig. 1(a) and (b). Light is scattered into all angles, but the objective only collects a range that falls within the NA depicted by the dashed lines. For the on-axis case (a) with illumination focused at the center of the BFP, angles out to the objective NA are observed. However, when the incident light is angled by moving the position of the focus in the input BFP (b), it is possible to collect scattering angles up to 2NA.

 

Fig. 1 Off-axis objective goniometry: (a) Incident light is focused into the back focal plane of an objective, creating a collimated beam through the sample plane. Angle space is only observable up to the objective NA, as indicated by the dashed lines. (b) By moving the location of the input focus, the angle at the sample plane is changed. As a result, angles up to 2NA are observable. Utilizing high-NA objectives, this allows observation of scattering angles beyond 90°. Demonstration of the off-axis approach: (c) forward scattering of circularly polarized 525 nm light by polystyrene spheres in water (azimuthally equidistant projection of the BFP, normalized log intensity scale.) (d) two off-axis scattering acquisitions from opposite sides of the BFP over-layed on (c). While (c) allows observation of scattering out to the objective NA, (d) demonstrates measurement to 2NA. The additional images demonstrate observation of forward scattering past θ = 90°. Color bar shows intensity spanning three orders of magnitude.

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Off-axis illumination is not a new idea in the context of imaging and resolution enhancement. The observation that larger spatial frequencies could be transferred in an optical system (and hence higher resolution achieved) by utilizing off-axis illumination was laid out in optical system filter theory 50 years ago [31] and undergirds many superresolution microscopy techniques. Recent work in Fourier ptychography explicitly utilized multiple illumination angles to enhance resolution and imaging performance [32]. Compared to these efforts to enhance resolution and imaging performance, applying off-axis illumination to goniometry is simply directly increasing measurement capability in angle space.

Our sample geometry consists of tissue slices mounted between cover slips, making it compatible with existing tissue preparation methods such as cryo-sectioning. We are not limited to cylindrical sample geometry and liquid samples in order to observe at 90° to the incident beam. An additional benefit of using flat sample geometry combined with a camera for detection of scattering is that a simple optical configuration change allows for transforming the instrument into a microscope. This is accomplished by removing the ‘Bertrand lens’. The system is designed such that with the Bertrand lens out, the forward objective and tube lens form an image at the same plane as the scattering image. With the Bertrand lens in, the BFP (angle-space) is imaged on the camera. See Fig. 2(a) for a schematic of the set-up. Although not optimized for imaging, the performance is sufficient to navigate the sample and select regions for scattering property measurement.

 

Fig. 2 Experimental set-up and instrument modes: (a) Focused light is directed by galvos into the back focal plane (BFP) of the input objective. Scattered light is collected by an objective in the forward direction as well as by the input objective. Combining patterns from forward and backward channels for different angles allows observation of 4π sr of scattering. Removing the Bertrand lens allows for forward imaging for navigating the sample. Instrument modes: (b) imaging: 1.54 μm polystyrene spheres in water used for scattering calibration. The area illuminated in imaging mode is adjustable from ∼ 25 − 300 μm; scale-bar = 50 μm. Although not optimized for image quality, 1.54μm spheres are easily seen and this functionality allows for navigation of the sample. (c) goniometry: forward Mie scattering pattern observed from area illuminated in (b).

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Additionally, unlike existing methods which utilize a relatively large (mm scale) beam, our beam diameter is small and can be adjusted via an iris from 25–300 μm. This gives a tremendous amount of control and specificity when selecting areas from which to measure scattering properties, see Fig. 2(b) and (c) for for examples of ‘imaging’ and ‘scattering’ mode with a microsphere calibration sample. Certainty of only measuring scattering from a selected region is assured by observing that the incident light spot does not move when the angle is scanned in imaging mode.

2.1. Experimental configuration:

The input objective in our instrument is a 1.4 NA 60× Olympus oil-immersion objective. A useful recent paper investigates some of the advantages and disadvantages of different objective options for angle-space applications [33]. The output objective is a 1.4 NA 63× Leica oil-immersion objective. Combining off-axis images forward and backward gives observation of scattering into 4π sr, except for ∼ 3° directly forward that is obscured by the incident beam. See Fig. 1(c) for a diagram of the apparatus. Note: in the backward direction, problem reflections from elements inside the input objective are mitigated by moving off-axis as well.

The input beam is derived from an NKT SuperK Extreme broadband laser. An accompanying AOTF selects a narrow (2–3 nm) color band and is tunable between 470–1100 nm. The beam is steered with galvos and focused in the back focal plane (BFP) of the input objective. Relay lenses magnify the pupil to match the camera sensor size. The Bertrand lens is mounted on magnetic mount to allow easy and repeatable removal and replacement. In the forward direction, a Hammamatsu Orca-flash 4 is usually employed as it accommodates the high dynamic range required when looking at forward scattering. In the backward direction, a lower cost camera (Thorlabs DCC3240C) is used. This camera has been used in the forward direction as well, but requires combining acquisitions with different exposure times to achieve sufficient dynamic range.

Samples are mounted between two #1.5 (170 μm thick) cover slips. A spacer prevents sample compression. Validation samples consisted of 1.54 μm diameter polystyrene spheres (Bangs Labs) in water.

2.2. Pixel-to-angle mapping:

The analysis of back focal-plane images entails mapping the pixels in the image to their corresponding scattering angles. Refraction between the medium and the glass cover slip as well as distortion from the objective must be corrected. Functionally, distortion is of the form θ ∝ arcsin(x) where x denotes pupil coordinate, resulting in angles that are increasingly compressed toward the edge of the BFP [24,25]. The analysis program, written in Matlab, maps pixel positions to angles and corrects for this distortion. The related issue of brightness compression is corrected by a factor of 1/ cos θ. One notable feature of the analysis program is logic allowing the user to easily exclude from analysis compromised regions in the images, such as bright reflections in the backward direction that originate from surfaces inside the objective.

The edge of the observed BFP circle in an image corresponds to the edge of observable scattering. For high-NA oil-immersion objectives and samples where the scattering emanates from a water layer, the edge of what is observed does not correspond to the quoted (oil immersion) objective NA. The limiting criteria is instead the angle at which light going from oil to water would be totally internally reflected as this corresponds to the maximum angle at which escaped scattering can be observed. In oil, arcsin(n_H2O/n_oil) ≃ 61°, corresponding to 90° in the sample. As a result, the angle at the edge of the BFP circle corresponds to 90° in the sample and is used to calibrate the pixel-to-angle mapping. Brightly illuminating the set-up will generate enough scatter from the oil, glass, etc. outside the sample to illuminate farther out to the quoted objective NA, providing a useful check. During analysis, the location of a pixel is converted to a normalized pupil coordinate, r, and mapped to angle in the sample via θ = arcsin(rNA/n_H2O).

Analyzing the pattern when centered is simple, but with angled illumination the pattern is off-center. As a result, the center of the scattering pattern needs to be located and shifted to coincide with scattering patterns that result from different incident angles. This process is analogous to stitching 2D images into a mosaic but must be done in angle space. The BFP images are projections of angle space so rather than translate images to get overlap, the image needs to be transformed to angle space and coordinates need to be rotated. Scattering and phase functions are naturally expressed in spherical coordinates, but rotations are most easily implemented in Cartesian coordinates. As a result, initial spherical coordinates θ, ϕ, r (where r is the brightness at a location in the image) are converted to Cartesian coordinates, Euler rotation matrices are applied, and then coordinates converted back to spherical (scattering) coordinates. In a coordinate system centered at the center of the lens BFP, an off-center scattering pattern can be rotated to center by x and y rotations where the x and y axes are simply set by the orientation (rows and columns) of the pixels in the image. This spherical coordinate stitching procedure enables incorporation of scattering beyond 90° to the incident illumination.

The center of the scattering pattern is identified by a θ′ and ϕ′ coordinate. The θ′ coordinate is extracted by correcting for the distortion of the lens, θ′ = arcsin(r′NA/n_H2O). The x and y axes are set by the camera pixel orientation, and the ϕ′ angle is given by the projection onto the detector: ϕ′ = arctan(y′/x′), where x′ and y′ are the pixel locations from the the center of the BFP image. We can recast the location of the center of the pattern into perpendicular rotations about the x and y-axes given by the Euler Rotation matrices.

Applying these rotations, where R_tot = R_x R_y to the Cartesian-coordinate scattering pattern converts the images taken at different incident angles to the same coordinate system and allows for averaging measurements from different orientations together. For axially-symmetric scattering such as the Mie scattering pattern from circularly polarized light presented in Fig. 1, the pattern can then be averaged around the azimuth to generate p(θ) as shown in Fig. 3.

 

Fig. 3 Mie calibration: Expected Mie phase function and experimentally observed phase function for scattering of 525 nm light from 1.54 um PS spheres in water. This trace is derived from azimuthal average of Fig. 1(d) and the corresponding backward channel. The Mie pattern angular structure functions as a ‘ruler’ to verify that accounting for refraction, distortion, rotations, and stitching is correctly implemented.

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2.3. Validation with microspheres:

Scattering from spheres is described by the Mie solution [34]. The Mie scattering pattern from a suspension of 1.54 μm diameter polystyrene spheres in water provides a good ruler to test the experimental system. Figure 1 shows experimental images of scattering of circularly polarized green (525 nm) light in the forward direction. On-axis scattering is shown in (c). A composite image of scattering with light input at the edge of the NA is shown in (d), effectively expanding the objective NA as described in the diagram in (a). For circular polarization, this pattern is axially symmetric, and the azimuthal average is used to reduce noise. Figure 3 shows a measured phase function trace derived from this azimuthal average as well as the corresponding Mie solution. This calibration trace features additional motion averaging to reduce speckle and boost contrast.

There are a few important methodological details to note when constructing the experimental plot in Fig. 3 as this procedure becomes the protocol when evaluating tissue. The Mie pattern for 1.54 μm spheres in water, is very forward-directed (like tissue), spanning more than 3 orders of magnitude. This requires either using a camera with large dynamic range such as the Orca-Flash or employing an HDR-like scheme combining scans with different exposure times when using a camera with small dynamic range. Each scan consists of multiple images taken at different angles spanning the NA of the objective. The head-on case is omitted in the backward direction as it is corrupted by strong reflections from inside the objective. The exposure time settings are longer in the backward direction because the backward scattering is weak and light is also lost to the beam splitter in the backward optical path. The input polarization is adjustable between linear and circular by a quarter-wave plate following a polarizing beam-cube and set to circular for the measurements in this study.

Matching the forward and backward Mie scattering patterns yields a scaling factor that accounts for the light lost through the beam splitter as well as differences in camera gain, NA and magnification in the two optical paths. That calibration factor is then used to appropriately scale scattering from unknown (tissue) samples. Additionally, in order to suppress the influence of unwanted reflections, especially problematic in the backward direction, we can subtract a background image acquired through a sample of water without scatterers.

The correspondence between the observed and expected scattering in Fig. 3 confirms the pixel to angle mapping. Correspondence is poorer in the backward direction principally because of lower signal to noise. The Mie pattern also has slightly reduced contrast around 90° in part due to increased optical depth of the sample at oblique angles. Improvements could be made in the future by correcting for apodization and by incorporating the effect of multiple scattering via Monte-Carlo modeling [15].

2.4. Scattering coefficient and differential scattering cross sections

As part of a full tissue-scattering characterization, in addition to the shape of the scattering the scattering coefficient μ_s must also be measured. This is accomplished by simple transmission measurement. By attenuating incident laser power to avoid saturating the camera and comparing with and without a sample present, the unscattered transmission is measured and the scattering coefficient is calculated via Beer’s law, T = exp(−μ_sL), assuming absorption is negligible compared to scattering for these thin unstained sections.

Measurement of the scattering coefficient μ_s allows for connecting the shape of the scattering, the phase function p(θ, ϕ), to absolute scattering at a particular angle by noting that their product gives the differential scattering cross section for some volume.

As a result, if the differential scattering cross section can be measured over some angular range, then the scattering phase function can be ascertained over that range as well. In other words, the phase function can be properly normalized without measuring it over 4π sr. The differential scattering cross section for some volume corresponds to the amount of power scattered at some angle (θ, ϕ) per unit solid angle, divided by the incident intensity. It can be calculated based on our measured intensities and the geometry of the system [34]:

Where I_i is the incident intensity, I_s is the scattered intensity, and r is the distance to the detector, which determines the solid angle. For our instrument, r is the effective focal length of our system, and V_exp is the experimental scattering volume determined by the interrogation spot area and sample thickness.

3. Evaluating tissues

While comparison of predicted and measured scattering patterns from microspheres provides excellent validation of the instrument, measurement of several example tissues serves to showcase some of the instrument’s unique capabilities. Brain tissue was used to demonstrate spectral measurement of optical scattering properties μ_s and g. In addition, the fibrous composition of white matter provided an opportunity to distinguish anisotropic tissue, where scattering properties are orientation dependent. Eye tissue was used to demonstrate the ability to discern differences in scattering from highly localized 100 μm regions. Initial measurements show pronounced differences in scattering properties of retinal layers not seen with previous goniometry methods. This appears to be the first measurement differentiating the forward-scattering properties of retinal layers.

3.1. Brain

Rat brain was extracted and preserved in formalin. Preserved specimens were sectioned via vibratome yielding 50 μm thick samples. Fixation allowed time to try many different experimental configurations and optimize the apparatus. First, the scattering coefficient was measured as described in section 2.4. Measurements of scattering were taken at 4 wavelengths: 525, 650, 775, and 900 nm. These colors were chosen to test the limits of our measurable range: our source laser power declines at shorter wavelengths and our camera sensitivity declines at longer wavelengths. Results are shown in the left panel of Fig. 4.

 

Fig. 4 Optical scattering properties of fixed rat brain tissue: Left panel: Scattering coefficient (μ_s). Scattering is larger for white matter than grey matter, as expected. Error bars indicate standard deviation of measurements from 10 tissue locations. Right panel: Anisotropy (g) for scattering from isotropic tissue, grey matter. This technique gives access to the entire scattering phase function, 4π sr of scattering angle space. Values of g are derived from analysis of an experimental scattering curve (an example is shown in the inset). The dashed/dotted trace comes from fitting the Henyey-Greenstein phase function, while the dotted trace is the anisotropy computed directly via integration. Error bars indicate standard deviation from 3 different tissue locations.

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The general trend of decreasing scattering coefficient with longer wavelength is expected and the measurements are comparable to quoted values in the literature for coagulated brain matter, see for example [35]. Grey matter is a relatively isotropic tissue and as a result scattering from it was axially symmetric. This allows us to observe and measure the entire phase function. Scattering phase function curves are derived using the same procedure as in section 2.3. Summarized results from grey matter are presented in the right panel of Fig. 4. Each point on this figure is an anisotropy, g, computed from an average of 4π goniometry reconstructions from three different tissue locations. This is done in two different ways: (1) numerical integration, see equation 6 (where p(θ) is the scattering phase function normalized over angle space according to 2π ∫ p(θ)sin(θ)dθ = 1), and (2) by fitting the HG phase function via a weighted least-squares procedure.

Measured anisotropy values are reasonable and the trend of larger values at longer wavelengths is as expected. Scattering anisotropy g is often used to specify tissue scattering properties. Usually this is done by fitting the HG phase function. Note: such fitting for g depends on the chosen angle range, so excluding the first 5° vs. the first 3° will yield slightly different results. With our method, we have access to 4π sr of angle space, so we are able to directly compute the anisotropy without assuming a functional form. Interestingly, these methods give slightly different and distinguishable results. This could give insight into the appropriateness of the HG model for a particular tissue. There are examples of tissues such as lung where the HG function does not work well to model bulk scattering. This work provides a direct way to evaluate if a phase function such as HG or other candidates such as Whittle-Matérn is a good model for scattering in isotropic tissues [21].

Another instrument capability that is highlighted when investigating brain tissue is seen when comparing isotropic (grey matter) and anisotropic tissue (white matter). While scattering from isotropic tissue is axially symmetric and can be averaged around the azimuth, scattering from anisotropic tissue is not axially symmetric. This behavior is immediately apparent in the BFP image in Fig. 5 corresponding to a location in white matter. Although 4π sr scattering cannot be reconstructed in this case because the shape changes with incident angle, a large portion of angle space can be observed in a single image. This would not be apparent in techniques with a swinging detector that slice through angle space. Solid-angle measurement capability is an ongoing direction of inquiry with this instrument beyond the scope of this current report. Future work will explore issues such as how best to characterize and parameterize scattering from anisotropic tissue and how such complex phase functions can best be computationally modeled.

 

Fig. 5 Anisotropic tissue such as rat brain white-matter shows a scattering pattern that is not axially symmetric. As a result, intensity curves at different ϕ angles have broader or narrower scattering profiles. Inset: raw BFP image showing the asymmetrical pattern with approximate location of corresponding intensity curves.

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3.2. Eye tissues

Eye tissues present another excellent opportunity to highlight capabilities of this instrument. The development of better measurements of retinal scattering are of great interest to those developing new imaging modalities [36]. To better understand light propagation in the retina, models of scattering with fine spatial resolution, including all the retinal layers, are needed and must be informed by detailed characterization of scattering parameters. However, existing tissue scattering goniometry methods do not have the ability to measure scattering from small volumes as is required to differentiate the properties of the (very thin) retinal layers. There are some reports of scattering properties for bulk ‘retina’ [37–39]. However, these measurements represent the combined scattering response from all the individual layers taken together. Figure 6 demonstrates the capability of this instrument to measure scattering from small regions, making it clear that different retinal layers can have very different scattering properties.

 

Fig. 6 Measurement of μ_s and g in mouse eye tissue. The small size of the ∼100 μm diameter interrogation spot enables measurements of distinct layers in ocular tissue. (a) Scattering coefficient, μ_s, decrease with wavelength as expected. The sclera is the most scattering, followed by photoreceptor (PR) layer and outer nuclear layer (ONL). Although both part of the retina, the ONL is much less scattering than the PR layer. (b) Anisotropy, g, is computed via integration, see equation 6. g increases with wavelength as expected. Error bars indicate the standard deviation from 3 spots for each tissue type. Although sclera and the photoreceptor layers exhibit similar g, the ONL has significantly higher g. (c) A dark-field image from a commercial microscope shows consistent results with higher scattering from sclera and PR, but lower scattering from the ONL: Dashed circles indicate representative relative locations and interrogation beam spot size. (d) Goniometer in ‘imaging’ mode showing the view of the sample used for navigation by removing the Bertrand lens. A wide-field image is obtained by illuminating a diffuser in the optical and the green overlay is an image of the spot used during a measurement of the PR layer.

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Fresh mouse eyes were obtained and cryo-sectioned to produce serial 30 μm thick sections. Eyes were oriented optic-nerve up to produce coronal sections through the retina, rather than the familiar transverse sections. Sections were preserved with formalin and sealed between cover slips. Initial sections, starting closest to the optic nerve head, present mostly sclera and choroid, while later deeper sections present larger and larger diameter slices through the back of the eye, with the various retinal layers present as rings. See Fig. 6(c) for an example showing different eye tissues present in a coronal section sample. Deeper slices expose new rings/layers as they move further into the inner retina. Sections with clearly discernible sclera, photoreceptor and outer nuclear layers (ONL) were chosen for these initial measurements. The sclera, photoreceptor layer and ONL were measured on the goniometer with an ∼100 μm diameter spot size. See Fig. 6(d) for a visualization of the interrogation spot. 4π phase function reconstruction was performed as well as measurement of the scattering coefficient. These measurements were performed with 4 colors: 575, 650, 725, and 800 nm. Results are presented in the traces in Fig. 6.

Theses initial measurements in mouse eye tissue demonstrate the ability of this instrument to measure scattering properties of small regions in a sample. This is exciting and opens up the prospect of detailed mapping of the scattering properties of other structures. This is a significant advance over existing techniques that measure the scattering of bulk tissue or suspensions and do not have this location specificity.

4. Conclusions and future directions

This work describes an advancement on traditional optical scattering goniometry techniques for analyzing tissue. Utilizing incident light angled in the sample plane allows for capturing scattering perpendicular to the incident beam and reconstructing 4π sr of scattering in isotropic tissue. The method makes use of microscope objectives and components, is fast and avoids moving detectors used in previous methods. The ability to adjust the beam diameter to a small size enables interrogation of small regions of interest in a sample and the prospect of mapping the scattering properties over a sample with 10’s of μm resolution. Since the system is lens and camera based, large solid angles of scattering are collected. This allows for the measurement of non-axially symmetric scattering phase functions in anisotropic tissue or polarization studies, difficult tasks for scanning-detector based goniometry methods.

4π scattering measurement and scattering coefficient measurement functionality is demonstrated in rat grey matter and mouse eye tissues over visible and near IR wavelengths. Characterization of anisotropy g is performed by fitting the HG phase function, but also by direct integration of the measured scattering shape, which is not possible in methods that do not collect 4π sr of scattering. Solid-angle acquisition is demonstrated with a BFP image of scattering from white matter showing the non-axially symmetric shape. The ability to differentiate scattering properties between small regions is demonstrated in mouse eye tissue, with pronounced differences observed between photoreceptor and outer nuclear layers in the retina. This work paves the way for future detailed layer by layer studies of scattering properties of the retina to inform next-generation high-resolution models.

Applying the instrument to anisotropic tissue and the study of tissues where the scattering depends strongly on the incident illumination angle promises to be a rich area of study. Although reconstruction of the scattering phase function in 4π in such tissue is not possible with the current reconstruction procedure, the instrument allows for observing large portions of angle space in a single image. Also, 4π reconstruction is not required for computation of a properly normalized phase function for such portions of angle-space. Additionally the instrument allows observation of how the scattering phase function in anisotropic tissue changes with illumination angle. As a result, this instrument is well positioned to make contributions to the study of scattering from highly anisotropic tissues, such as fibrous components common in many tissues.

This instrument used oil immersion objectives to maximize NA and minimize reflections from air-glass interfaces, but with a different objective configuration, the technique could be adapted to analyze samples on slides under a cover slip. This would allow investigating scattering properties in histological samples.

Future work includes updating analysis to incorporate Monte-Carlo modeling to better understand effects like change in projected sample thickness with incident angle, as well as extending measurement work to un-fixed tissue and explore changes in scattering due to chemical fixation. Improvements to the instrument including full polarization control and stage scanning will enable more detailed investigations of locally aligned anisotropic tissue and could provide full Mueller matrix measurements.