The radial angular filter array (RAFA) consists of a series of radially-distributed micro-machined channels, where the long axes of the channels converge at a focal point. The high aspect ratio of each channel provides a means to reject photons with trajectories outside the acceptance angle of the channel. The output of the RAFA represents the angular distribution of photons emitted from the focal point. A series of RAFAs were designed, fabricated, and tested to evaluate the impact of device geometry, inter-channel cross talk, achromaticity, and channel leakage on device performance. As an application example, an RAFA was used together with an imaging spectrometer to capture angle-resolved spectra of turbid samples.
© 2013 OSA
Optical instruments for angle-resolved scattering spectroscopy have been recognized as highly useful tools for characterization of surface topography, particle counting, and characterization of biological tissues at both macro and micro (cellular) levels [1–16]. At macro-scales, angle-resolved light-scattering distributions are conventionally measured by a goniometer-based instrument, where either the sample or detector is mounted on a rotating arm [1, 5, 7, 13], or by a series of detectors placed at different angles [7, 14]. At micro-scales, instruments have employed low-coherence interferometry or related approaches [4–6, 15, 16] to acquire high resolution angle-resolved light distributions. However, these methods have been constrained by limited angle selection, limited angular range, lack of hyperspectral measurement capability, long delays in data acquisition due to angular or wavelength scanning, and complex alignment procedures [1–16].
The radial angular filter array (RAFA) was first introduced by our group (see Ref .). It consists of micro-machined channels in a silicon substrate and provides a means to measure the angular distribution of scattered light from a sample using a single exposure. Each RAFA channel collects photons emitted from a focal point at a specific angle and only photons traveling within a small acceptance angle relative to the channel direction pass through. Most channels contain pre-bending, bending and post-bending sections. Angular filtration is primarily performed in the pre-bending sections. Bending and post-bending sections provide efficient light coupling to the detection optics. By providing channels at a variety of angles, the RAFA collects photons propagating in different directions without scanning either the detector or the sample, enabling easy alignment and fast read-out. Furthermore, the transmission characteristics of the channels do not depend on the wavelength and coherence of the light source; therefore, the RAFA is amenable to multispectral and hyperspectral analysis methods that utilize broadband incoherent sources [17–20].
Our earlier work employed the RAFA to measure the angular distribution of light from a diffuser and a series of Intralipid® dilutions. The results demonstrated that the RAFA could discriminate the angular distribution of light emitted from a sample at the focal point of the device. However, the RAFA device had several drawbacks that limited performance . The primary issue was the large cross talk among channels, which was largely determined by the angular filtration capability of the device and the spatial separation of the output apertures. Inter-channel cross talk is dependent on angular acceptance of each channel, which in turn defines the angle of the photon trajectory upon exiting the device. When the acceptance angle of each channel is reduced, photons are less likely to cross over into the output detection path of neighboring channels thereby lowering cross talk. Increasing the separation of the output apertures reduces inter-channel cross talk as well but at the expense of a larger device size. The reflection of photons inside the channel is known to increase inter-channel cross talk and background noise, as unwanted photons entering channels outside the acceptance angle tend to pass through. The earlier RAFA device had high inter-channel cross talk as the channel shape, channel wall surface, and output apertures were not optimized. The second issue related to the earlier RAFA device was the significant non-uniformity in light output between channels especially those at higher angles. Attenuation by higher angle channels was observed to be much more significant (by up to several orders of magnitude) than by channels nearby the central axis of the device, introducing a dynamic range challenge to the camera and subsequently, the relative noise in the measured intensity was higher for signals detected through the higher angle channels. The issue of uniform angular sensitivity was largely related to the differences in channel shape and channel length at different angles.
2. Objectives and approach
The primary goal of this work was to develop the RAFA from a design concept into a working prototype capable of quantitative angular discrimination of light. Based on the issues discovered with the earlier RAFA device, our first objective was to perform a series of design improvements, including the design of features to lower inter-channel cross talk at the detector, and to reduce the variation of output signal at different angles to within a factor of 10 for an angularly uniform incident beam. Our second objective was to characterize the new device designs, in particular, to examine the inter-channel cross talk, channel leakage, and channel achromaticity to validate the design improvements. Our last objective was to calibrate the device and demonstrate the usefulness of the RAFA as a device suitable for obtaining angle-resolved hyperspectral measures of light scattered from a turbid sample.
Our approach was to optimize the earlier RAFA design, fabricate new RAFA devices, and develop a setup to characterize the new RAFA devices. A RAFA calibration procedure was established with a focused uniform broadband beam. The characterization results were used to assess whether the fabricated devices satisfied the design targets. Finally, the most improved RAFA device design was integrated into a hyperspectral imaging system to perform angularly-resolved spectroscopy of a turbid medium.
3.1. RAFA design optimization
The first design optimization target was to reduce the cross talk between channels via new channel structures. Two angular filtration structures were proposed to minimize the background noise and achieve improved angular resolution. Second, two new output coupling structures were studied to reduce the non-uniformity in channel sensitivity across different angles, but preserve simple readout optics. The third design optimization target was to reduce the probability of detector saturation at channels close to the specular direction. With the new designs, we proposed to avoid the near specular direction measurements by blocking some of the center channels and concentrating on higher angle measurements. It was hypothesized that blockage of the center channels could provide additional benefits related to reduced signal loss as the length of the channels could be reduced.
Channel structure optimization
Two different channel design paradigms, constant aspect ratio and constant acceptance angle, were explored to improve the angular resolution of the RAFA and minimize cross talk. When using the term acceptance angle, by convention, we refer to the nominal acceptance angle of a channel measured in the plane of the device. With the constant aspect ratio paradigm (Fig. 1(a) and 1(c)), the channel width was kept constant within the pre-bending, bending and post-bending sections (where applicable). The acceptance angle of the channel was defined as the width of the channel at the output aperture in regards to the total length of the channel. When in use, photons propagating with trajectories outside the acceptance angle were attenuated by the RAFA. With the constant acceptance angle paradigm (Fig. 1(b) and 1(d)), the cross-sectional area of each channel gradually increased from the input side to the output side. The design maintained the same acceptance angle with respect to the focal point, which was in the plane of the device. Constant acceptance angle designs allowed a smaller entrance aperture for each channel and the potential for higher angular resolution than constant aspect ratio designs. However, the cross talk between channels was expected to be greater as the output apertures in the constant acceptance angle designs were larger and the separation between channels was smaller.
The constant aspect ratio designs had a pre-bending section of 10 mm and the acceptance angle was 0.69° or 0.48° depending on the specific device. The corresponding width of the channel ranged from 80 μm to 120 μm, and the depth was 60 μm. Both width and height were significantly larger than the photon wavelength to minimize diffraction effects. In both designs, the aspect ratio was 83:1, resolution was 2.5° and the device width was 25 mm. The detection angle range of the device presented in Fig. 1(a) was [-35°, −7.5°] and [7.5°, 35°] while the range for the device shown in Fig. 1(c) was [-30°, 30°]. Figure 1(b) and 1(d) show two designs with the constant acceptance angle of 1°. For these two designs, the device width was 25 mm, the channel walls were 100 nm in thickness and 60 μm in height, and the angular detection range was [-30°, −1°] and [1°, 30°].
From previous work, it was confirmed that light entering the channels beyond the acceptance angle could act as a source of background bias at the channel output due to intra-channel reflections . Therefore, in all RAFA devices, the channel walls in the pre-bending section were patterned with photon trapping vertical ridges (width of 5 µm, i.e. at least five times the wavelength of photons in the near infrared (NIR)) at a spatial period of 5~20 µm to effectively trap photons with trajectories beyond the acceptance angle (Fig. 2(c-d) ).
Output coupling optimization
In addition to filtering photons according to the direction of propagation, the RAFA must guide and couple the photons to the detector side with minimum loss and good uniformity across channels. To achieve these targets in practical designs, two methods for RAFA output coupling were explored. The first method was related to a simple straight-through coupling scheme, where photons passed through an RAFA that lacked bending or post-bending structures. Device designs utilizing this straight-through scheme are illustrated in Fig. 1(c) and 1(d), where the lack of additional channel structures after angular filtration preserved the propagation direction of photons. In this way, the transmission loss after the channels was expected to be minimal since photons within the acceptance angle of each channel would pass through the device without experiencing reflections. However, this method was expected to result in a wide range of RAFA photon exit trajectories (angles), which necessitated a lens to efficiently couple the RAFA to the detector. The inclusion of a lens increased system complexity and alignment difficulty due to the increased number of degrees of freedom. The second RAFA output coupling method incorporated bending and post-bending structures to redirect the angularly filtered photons in a direction perpendicular to the output edge of the RAFA. In this method, photons from all channels exited the RAFA in the same direction, which was expected to improve and simplify RAFA-detector coupling efficiency and enable the use of an imaging spectrometer. As discovered with an early RAFA device (see Ref .), the bending structure degraded the collimation and uniformity of the output beam significantly. To improve the device, we investigated several output coupling schemes. With constant aspect ratio designs, an aluminum-coated micro-mirror bending structure was incorporated into the RAFA as shown in Fig. 2(a-b). The direction of the front surface of the micro-mirror was selected to ensure that all photons within the acceptance angle of the channel were directed by a single reflection to the output of the RAFA. The length of each micro-mirror was selected to ensure that ballistic photons (i.e. with trajectories parallel to the channel) across the entire channel aperture experienced only one reflection. An advantage of this design was the uniform transmission efficiency across all channels. The second advantage of this design related to the improved collimation properties of the light exiting the RAFA in comparison to preliminary designs , which simplified optical coupling to the imaging spectrometer. Channels in constant acceptance angle designs were separated only by a thin wall, and the micro-mirrors were designed differently due to the lack of space between neighboring channels. For example, for the design shown in Fig. 1(b), no bending structure was incorporated at low angles, but as the angle increased, an aluminum-coated bending structure was used and the length of the bending structure increased with the angle. However, due to the total length limitation of the device, the bending surface was not long enough to reflect all photons, except those travelling within the high angle channels. The design preserved the high angular resolution of the device and minimized the length of the post-bending sections to reduce the signal loss. However, the design introduced non-uniformity in signal transmission efficiency across the output of the RAFA.
Center channel blockage
For samples where the scattering is weak or is forwarded-directed as in biological tissues, a large proportion of photons are expected to travel along or close to the specular direction (optical axis) of the RAFA. According to the measurement results with the earlier RAFA device, signals detected from center channels could be a few orders of magnitude higher than signals detected from the output of channels representing higher angles . Both high angle and center channels carried the post-scattering angular distribution information; however, signals from center channels were corrupted by a high proportion of ballistic and quasi-ballistic photons. The center channels tended to saturate the camera easily necessitating short exposures, which resulted in under exposure of pixels representative of high angle channels. In addition, the center channels of the RAFA provided minimal attenuation due to the lack of bending sections and shorter channel lengths (Fig. 1(a) and 1(b)). For these reasons, the earlier RAFA structure tended to exaggerate the non-uniformity in signal strength. To overcome these deficiencies in new devices, channels within ± 5° of the optical axis were blocked in constant aspect ratio designs, while channels within ± 1° of the optical axis were blocked in constant acceptance angle designs.
A ray-tracing model was simulated (Zemax ver. EE, Radiant Zemax LLC., WA) to validate design optimizations related to reduction of inter-channel cross talk. The simulated rectangular channel was bent by 30° in the model, and it had the same cross-section, pre-bending and post-bending sections as the 30° channel in Fig. 1(a). A collimated broadband beam (650-950 nm, uniform spectrum, total power of 1 mW) was projected into the channel. The detector was placed perpendicular to the channel direction 1 mm away from the output aperture. The channel wall was coated with aluminum, and the reflectivity of the coating layer was 90%. For photons reflected, the probability of scattering due to surface roughness was 10%. The expansion of the output beam indicated the severity of the cross talk between neighboring channels.
3.2. RAFA characterization
Three chrome photomasks for 4 inch wafers were designed with L-Edit (version: 14.1, Tanner EDA, CA). The lithography steps have been presented in detail in earlier papers (see Refs [17, 21].). Briefly, each device was fabricated using the following steps: 1) grow silicon oxide on a silicon wafer; 2) pattern the oxide layer and use it as the masking layer of silicon in deep reactive ion etching (DRIE); 3) DRIE silicon substrate to form the high aspect ratio channels; 4) strip away the masking oxide layer; 5) coat bending and post-bending sections with an aluminum layer (mirror surface); and 6) enclose the device with a polished silicon top piece. The roughness of the coated aluminum layer was estimated with SEM images and found to be less than 200 nm (i.e. about 1/3 - 1/4 of the test wavelength); therefore, the bending section in each channel had reflection performance close to an ideal mirror.
Optical measurement setup
The RAFA characterization setup consisted of a broadband light source, a diffuser, near infrared filters, collimation optics, a focusing lens, one RAFA and a spectrometer (Fig. 3 ). Specifically, the output of quartz tungsten halogen (QTH) lamp (Oriel, Series Q Lamp Housing, 100 W) was spectrally filtered by a high pass filter (645 nm, part no. 65.1365, Rolyn Optics Co., Covina, CA) then a near infrared short pass filter (950 nm, 950FL07-50S, LOT-Oriel GmbH, Germany). The beam was homogenized by a 15° holographic diffuser and focused at a pinhole (1 mm in diameter). The light from the pinhole was collimated by a NIR doublet spherical lens (ACH-NIR 25 × 50, Edmond Optics, Barrington, NJ), then refocused by an achromatic objective lens (20 × , NA = 0.45; Nikon, 93150). A slice of the beam was collected by the RAFA held by a 6 degree-of-freedom jig (built from multiple components, Thorlabs, NJ) that enabled the alignment and mapping of the RAFA focal point to the focus of the beam and RAFA output to the slit of the spectrometer, the placement of the RAFA at the center of the circular beam, and the adjustment of the distance between the RAFA and the spectrometer. The output of the RAFA was directly coupled into the slit of an imaging spectrometer (CCD sensor: C10151-S10141-1109, Hamamatsu Photonics K.K. Japan, 2048 × 506 active pixels, 12 μm × 12 μm pixel size, 650 nm – 950 nm; spectrometer assembled by P&P Optica Inc., Kitchener, Canada). The acceptance angle of the spectrometer at the slit was approximately 9° (F/3). The slit was 25 mm horizontally and 1 mm high. The spectral resolution of the CCD sensor was 0.05 nm (wavelength) / μm (spatial distance). The angular direction was horizontal, and the spectral direction was vertical. The spectral resolution of the measurement system was defined by the height of RAFA channel (60 μm) and was approximately 3 nm. With this setup, both the angular and spectral distributions of light at the focal point of the RAFA could be captured without mechanical scanning or rotation. The readout time for each image was less than 3 seconds.
3.3. RAFA calibration
The angular distribution of transmitted light is typically presented as the Bidirectional Transmission Distribution Function (BTDF) [22, 23]. The BTDF is defined as the ratio between the power of the incident and the outgoing light. The angle of the output ray, θs is defined as the difference between the output direction and the normal direction to the reflectance surface. The BTDF can be represented by Eq. (1):
Neither the NIR output spectrum from the QTH lamp, nor the quantum efficiency of the spectrometer across the NIR was uniform. This setup specific variation was defined as the setup signature. Furthermore, like other optical devices, each RAFA introduced device specific variation to the measurement results, which was defined as the device signature. With the calibration setup as shown in Fig. 3, each channel of the RAFA received the same incident light intensity and a reference BTDF0(θs0,λ) was estimated with:Equation (2) can be re-written as:Equation (4) states that the BTDF(θs, λ) of a specimen can be obtained by normalizing the measured intensity at each channel output by A0(θs0, λ).
3.4. Setup for Intralipid® experiments
Once the RAFA was calibrated, it was used to measure the light scattering due to a series of Intralipid® dilutions. Intralipid® has been used as a tissue simulating phantom medium, whose scattering coefficient is about two orders of magnitude higher than the absorption coefficient in NIR. The optical scattering within Intralipid® is expected to be forward-oriented with g around 0.75 [24, 25]. Intralipid® dilutions (0.05 wt%, 0.1 wt%, 0.5 wt% and 2.0 wt%) were diluted from 20 wt% stock Intralipid® (Fresenius, Kabi AB, Uppsala, Sweden) with distilled-deionized water. For a given experiment, the setup was similar to the apparatus shown in Fig. 3. However, the 20 × objective lens was removed. An iris and a 5 mm optical path length cuvette was placed in front of the RAFA, and the focal point of the RAFA was aligned to and within the cuvette. The diameter of the collimated incident beam was adjusted by the iris (from 3 mm to 10 mm). The adjusted beam then illuminated the cuvette loaded with the Intralipid® dilution, where the bulk scattering occurred.
4. Results and discussion
4.1. Output coupling
The RAFA output coupling measurement focused on evaluating the design that offered the minimum RAFA/detector coupling loss. It was performed with uniform incident light at all RAFA input angles. The output of the RAFAs that included bending structures was fully captured by the spectrometer as the output beam angle of the RAFA was compatible with the input acceptance angle ( ± 9°) of the spectrometer. However, the characterizations of the RAFAs that lacked bending structures were limited to lower angle measurements since the high angle channel outputs were outside the acceptance angle of the spectrometer. Figure 4(a-d) show the RAFA output light intensity profiles captured with the spectrometer for RAFAs described in Fig. 1(a-d), respectively. Signals from all channels were captured for designs shown in Fig. 1(a) and (b) (see Fig. 4(a) and 4(b)), but only signals from central channels were observed for designs shown in Fig. 1(c) and 1(d) (see Fig. 4(c) and 4(d)), which indicated that the setup could only fully characterize RAFAs that contained bending structures. Figure 4(a) and 4(b) also revealed that the channel signals with these two designs were of the similar magnitude across the entire profile, which was significantly better than the earlier device (see Ref .), where the variation in signal intensity across the channels due to the device signature was several orders of magnitude.
4.2. Inter-channel cross talk simulation and measurement
Inter-channel cross talk was evaluated with both ray-tracing simulation and experimental measurements. For the original device (see Ref .), cross talk was evident at the output of adjacent channels even after 1 mm of propagation in the air. The curved bending structure in the device introduced output beam divergence that introduced inter-channel cross talk and degraded the angular resolution of the device significantly. With curved bending structures, the simulation results revealed that photons would be reflected multiple times in the channel leading to a significant loss in collimation quality at the output of the RAFA (Fig. 5(a) ). For channels bent by 30°, only 14% of the incident power was delivered to the detector and the size of the output beam expanded over 3 times at the detector location (Fig. 5(c)). For the new reflective bending structure (Fig. 5(b)), the ray-tracing simulation showed that 47% of the incident power was preserved at the channel output, and the collimation of the output beam was dramatically improved. Furthermore, the size of the beam was still roughly the same as the exit aperture at the detector (Fig. 5(d)). The experiment performed with RAFA channels of similar angle and design showed that <1% and 20% of the incident power was preserved by the curved and the micro-mirror bending structures, respectively. Therefore, both simulation and experiment confirmed that the design change increased channel transmission efficiency significantly with a sizable reduction in cross talk. It was noted that the measured signals were weaker than the simulated results. The cause might have been due to a lower than expected channel surface reflectivity.
The improvement in the output beam collimation was further validated by an RAFA with a constant aspect ratio of 120:1 (similar to Fig. 1(a)). Uniform incident beams were projected to the RAFA at all angles. Figure 6(a-c) shows the measured intensity profiles at different distances away from the channel output. The measurements clearly demonstrated that the cross talk between output channels was negligible when the spectrometer input was 1 mm away from the channel output (Fig. 6(a)). When the spectrometer was placed 6 mm away from the output of the RAFA, background noise due to cross talk between output channels became noticeable as shown in Fig. 6(b). The output signal was degraded substantially by inter-channel cross talk when the spectrometer was 11 mm from the output of the RAFA (Fig. 6(c)).
Overall our results demonstrated that cross talk at the RAFA output was much more severe for constant acceptance angle designs compared to constant aspect ratio designs, which corroborates discussion presented in previous work (see Ref .). Based on these findings and the earlier work, we chose to focus optimization and characterization efforts on constant aspect ratio designs.
4.3. Channel leakage
Channel leakage was measured for the RAFA shown in Fig. 1(a). The apparatus described in Fig. 3 was used to obtain the measurements; however, the lens was removed. A collimated beam with a spectrum covering 720-770 nm was projected onto the input of the RAFA. The size of the beam was adjusted to ensure coverage of all channel input openings. The light output (P(θc)) of each channel with angle θc was recorded. For the test RAFA, the center channel was blocked; therefore, the experiment was repeated with an RAFA that had a single channel in the center along the specular direction. The single channel RAFA was designed to have the same aspect ratio, depth and photon trapping ridges as the test RAFA. The single channel RAFA was fabricated together with the other RAFAs, following the same process. The measured light output P(0) from the single channel RAFA was treated as the reference intensity along the specular direction. The leakage represented by L(θc) of each channel was defined as:Table 1 . The leakage for channels with |θc| > 27.5° was not presented due to low signal. In general, the test RAFA demonstrated low channel leakage for all θc when adequate signal was present. For channels with |θc| = 7.5°, the leakage signal was < 10−4 of the incident light in the specular direction, and ≤ 10−5 for channels satisfying 17.5° ≤ |θc| ≤ 27.5°.
4.4. Achromaticity of the RAFA
The RAFA was expected to have achromatic transmission characteristics due to the size of each channel aperture being significantly larger than the wavelength of visible and NIR light. The achromatic property of the RAFA described in Fig. 1(a) was investigated by a reference measurement with a focused broadband beam (see apparatus in Fig. 3). The light output of the RAFA was captured by the spectrometer, then interpolated and mapped into a 2D map (Fig. 7 ). Since the numerical aperture of the achromatic lens was 0.45, the analysis was restricted to channels with |θc| ≤ 22.5°. The angular resolution of the measurement prior to interpolation was 2.5°. During data processing, the signal intensities for every 12 nm were added together to reduce periodic noise inherent to the imaging spectrometer (due to etaloning). The resultant spectral resolution and angular resolution of the final 2D map were interpolated to 1.2 nm and 0.25°, respectively. The data at each angle was normalized as a function of wavelength to the median value (Fig. 7(a)). The normalized 2D map revealed that the spectral response due to the setup/device signatures was similar for the angles tested. The data for each wavelength was normalized as a function of angle to the median value (Fig. 7(b)). The resultant 2D map showed that the angular response was consistent across the different spectral bands to within ± 10% of the mean. Therefore, the transmission properties of the RAFA did not depend greatly on wavelength.
4.5. Use of an RAFA for angle-resolved spectroscopy of a turbid medium
The RAFA shown in Fig. 1(a) was selected to measure the scattering property of Intralipid®. Measurement results for 0.05 wt%, 0.1 wt%, 0.5 wt% and 2.0 wt% Intralipid® solutions at each channel were corrected for the setup and device signatures and plotted in Fig. 8(a-d) . To improve interpretation, the light output of each channel was normalized as a function of angle to the peak intensity value at each wavelength. The normalized results were assembled into a 2D intensity map (wavelength versus angle) (Fig. 8(e-h)). The 2D map had the same spatial and spectral resolutions as described in Section 3.2 and 4.4. A slight asymmetry was observed between the left and right halves of the spectral map. The cause of the asymmetry was not fully determined; however, it could be due to a slight rotation of the sample surface with respect to the RAFA or the presence of defects in the RAFA channels.
The results were evaluated from four perspectives: location of the intensity peak, intensity versus angle, intensity versus Intralipid® concentration and intensity versus wavelength. First, the peak values in the angle-resolved intensity spectra were located at the longest wavelength and at angles of ± 7.5° (Fig. 8(a-d)) for all Intralipid® solutions. This result was consistent with the fact that scattering was lower at longer wavelengths. Second, the intensity distribution across all angles was more uniform as the concentration of Intralipid® increased. The intensity ratio between the output from the high angle channels and the central channels ( ± 7.5°) increased with the concentration of Intralipid® (see Fig. 8(a) to 8(d)). With 2.0 wt% Intralipid®, the ratio was nearly 1, indicating that the intensity variation between different RAFA channels was negligible when the scattering was high. The finding was also observed in Fig. 8(e-h), where the angle-resolved intensity spectrum was least uniform for the sample with 0.05 wt% Intralipid®, but was nearly flat for the sample with 2.0 wt% Intralipid®. Third, it was noticed that the intensity at the output of high angle channels increased when the Intralipid® dilution was increased from 0.1 wt% to 0.5 wt% and decreased afterwards. Such biphasic behavior was not observed for channels close to the center (e.g. ± 7.5°), where the intensity dropped as the concentration of Intralipid® increased. The primary reason for this phenomenon was due to the multiple effects of the scattering. At a higher scattering level, more photons would be delivered to high angle channels via scattering, causing the intensity reduction for central channels, but an intensity increase for higher angle channels. At the same time, fewer photons overall would survive the transit through the cuvette as the concentration of Intralipid® increased. The net effect of the above two effects could explain the biphasic intensity versus Intralipid® concentration relationship for high angle channels and the consistent drop in intensity with increasing Intralipid® concentration for channels more closely aligned with the optical axis. Last, it was noticed that the spectra were somewhat U-shaped for Intralipid® at lower concentrations. As the concentration increased, the U-shaped spectra evolved into a monotonic shape that increased from short to long wavelengths. The spectra were nearly flat for the 2.0 wt% Intralipid® solution. The shape transition in the intensity spectra could have resulted from the interaction of two processes. First, as described in Ref , scattering decreases at longer wavelengths, particularly when the Intralipid® concentration is low. This results in an intensity increase for all channels from short to long wavelength. Second, as described above, fewer photons overall would be scattered into higher angle channels at longer wavelengths, causing the intensity to drop. The combination of the above two effects could potentially explain the intensity versus wavelength relationship observed in Fig. 8(a-d).
Two design concepts, constant aspect ratio and constant acceptance angle, and two output coupling strategies, bending and no bending, were explored in this work to solve the issues associated with a previous RAFA design (as presented in Ref .). The new RAFA designs included features such as improved bending structures, lower acceptance angles, and center channel blockage. The RAFAs were characterized by hyperspectral optical imaging and compared. One constant aspect ratio design with a bending structure and central channel blockage proved to have the best performance compared to three competing designs. With the best performing design, signal output intensity at different angles was reduced from a few of orders of magnitude (compared to the previous RAFA design) to within one order of magnitude while an angularly uniform input beam was measured. Simulations and experiments revealed that the output light distribution was well-collimated even 6 mm from the output of the device, which indicated that the inter-channel cross talk was minimal for the design. The RAFA was used to measure a series of Intralipid® dilutions, and the results were consistent with the optical scatter properties of the Intralipid®. The measurements support the idea that the optimized RAFA design is well-suited to real-time angle-resolved spectroscopic measurements of turbid media.
The results from this study guide us towards a device that has an angular detection range larger than ± 20° and a resolution better than 5°. It has similar performance to what most goniometer-based systems offer; however, the RAFA device eliminates rotational scanning and the use of more than one detector. Furthermore, the single shot acquisition of the angular response is limited only by the exposure time of the camera. In addition, the RAFA offers a competitive advantage over low-coherence interferometry systems by enabling multispectral and hyperspectral measurements with simple instrumentation.
In the future, calibration and validation of the RAFA design could be performed with other materials, where the size of the scatters is well known and the results could be compared against Mie theory. Also, the range of detection angles could be improved by adopting a design that avoids the use of center blocking channels, but incorporates other techniques to reduce the transmission efficiency for channels about the optical axis. Lastly, the current RAFA design is essentially a point detector; however, device stacking could be used to realize a device capable of angularly-resolved measurements across a line on the sample.
This project was funded by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) to J. J. L. Carson and B. Kaminska. Y. Zhang and M. Najiminaini were supported by NSERC, the British Columbia Innovation Council, and Natural Resources and Applied Science (BCIC NRAS) grants. F. Vasefi was supported by a LRCP Translational Breast Cancer Research Trainee Fellowship.
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