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Abstract
Terahertz (THz) time-domain spectroscopy has been investigated for assessment of the hydration levels in the cornea, intraocular pressure, and changes in corneal topography. Previous efforts at THz imaging of the cornea have employed off-axis parabolic mirrors to achieve normal incidence along the spherical surface. However, this comes at the cost of an asymmetric field-of-view (FOV) and a long scan time because it requires raster-scanning of the collimated beam across the large mirror diameter. This paper proposes a solution by designing a pair of aspheric lenses that can provide a larger symmetric spherical FOV (9.6 mm) and reduce the scan time by two orders of magnitude using a novel beam-steering approach. A hyperbolic-elliptical lens was designed and optimized to achieve normal incidence and phase-front matching between the focused THz beam and the target curvature. The lenses were machined from a slab of high-density polyethylene and characterized in comparison to ray-tracing simulations by imaging several targets of similar sizes to the cornea. Our experimental results showed excellent agreement in the increased symmetric FOV and confirmed the reduction in scan time to about 3-4 seconds. In the future, this lens design process can be extended for imaging the sclera of the eye and other curved biological surfaces, such as the nose and fingers.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz time-domain spectroscopy (THz-TDS) has shown significant promise in the field of biomedical diagnostic imaging and sensing not only due to its non-ionizing photon-energy levels, but thanks to its unique sensitivity to hydration changes [1–3]. One example is in determination of skin burn injuries [4–6]. Classification of burn severity is possible by detecting changes in the THz reflectivity, and using machine learning algorithms [7] such as neural networks [8] and support vector machines [9], the wound-healing outcome can be predicted with high accuracy levels. Additionally, THz imaging has been used for diagnosis of brain cancer tumors [10–13], breast cancer biopsies [14,15], skin cancer delineation [16–18] and in several ophthalmological applications [19–28]. In most of these applications, the only viable imaging modality for clinical applications is spectroscopic imaging in the reflection mode.
THz reflection imaging of a biological surface using a single-pixel detector requires ensuring normal incidence on the target over all scanned pixels. In prior THz imaging studies of burned skin, an f-theta lens was used for this purpose to focus and raster-scan the THz beam on a flat image plane [29,30]. To ensure normal incidence, a fused-silica imaging window was placed in contact with the skin. Curved biological surfaces such as the cornea, cannot rely on traditional raster-scanning techniques to achieve normal incidence due to the target curvature. In addition to normal incidence, a noncontact approach is required given the cornea’s sensitivity to physical touch. For instance, THz hydration sensing of the sclera has been investigated but has required the use of a Golay cell for detection of scattered THz radiation due to a lack of normal incidence [31]. However, the use of diffuse spectroscopy techniques to in vivo corneal imaging applications is not practical due to low signal to noise ration and long data acquisition times [32]. Moreover, the field-of-view (FOV) of the imaging optic should be large enough to cover the entire corneal surface for mapping hydration gradients.
To satisfy these imaging requirements, previous efforts for THz imaging of spherical targets have employed 90° off-axis parabolic mirrors (OAPM) as the focusing optic. As shown in Fig. 1(a), aligning the center of curvature of the cornea to the focal point of an OAPM and steering the collimated beam perpendicular to the mirror aperture result in normal incidence on all pixels scanned along the target surface [33,34]. Using the same optical beam steering layout, we have demonstrated a broadband THz-TDS topographic scanner with spectroscopic bandwidth between 0.1 and 1 THz for imaging spherical targets [35]. Converting variations in the measured time-of-arrival (TOA) of the reflected THz beam to a spatial height profile allows for topographic mapping of the cornea. In addition, analysis of the detected signal in the frequency domain reveals further information about the cornea’s physiological condition through mapping hydration gradients. Recently it has been shown that elevations in intraocular pressure [36] and endothelial layer damage [37] in the cornea can be detected using this system by evaluating changes in the reflected THz spectral area and slope, respectively.
Fig. 1. (a) Illustration of beam-steering across the cornea using an OAPM. Placing the center of the spherical target at the focus of the OAPM ensures normal incidence. (b) Non-uniform scanning trajectory of the collimated THz beam, shown by black circles, is calculated across the OAPM aperture with constant azimuthal (blue lines) and elevation (red circles) angles on the sphere. Beam steering approach in (b) results in an equiangular sampling across the corneal surface (c). The resultant FOV is approximately 8 mm on the corneal surface. The asymmetry of the FOV in the X-axis can be seen. (d) The spot size variation of the THz beam focused by the OAPM on a spherical target is shown by ABCD ray tracing simulations and is in agreement with previous published results in [33], leading to a dramatic change in spatial resolution on the target surface.
One advantage of using OAPMs is that they do not suffer from broadband attenuation losses or introduce chromatic aberrations. However, as shown in Fig. 1(b, c), beam steering using a 3-inch diameter OAPM yields a limited asymmetric field-of-view (FOV) of approximately 8 mm. Figure 1(b) demonstrates the scanning trajectory of the center of the collimated THz beam on the aperture of the OAPM to achieve a uniform mapping of the corneal surface, shown in Fig. 1(c). In addition, prior quasi-optical simulations have indicated that the focused beam spot size on the corneal surface changes significantly as a function of beam deflection along the asymmetric axis of the OAPM [33], which is also shown in Fig. 1(d). Finally, the current method of 2D mapping across the cornea requires raster-scanning the collimated THz beam across the large mirror diameter (see Fig. 1(a)). This process takes several minutes and is not ideal for clinical imaging, where complete coverage of the cornea should be completed in under a few seconds. OAPM are also difficult to align in the THz regime and custom parabolic mirror designs with desired aperture and focal length are expensive to manufacture. To address this problem, we investigate the use of scanning lenses for coupling light to the corneal surface with matching spherical phase fronts. Replacing the OAPM with a custom scanning lens for focusing the THz beam onto the cornea would allow for a symmetric FOV while still achieving normal incidence for a curved target centered at the focus. In addition, using a pair of lenses of the same design to collimate and focus the THz beam allows for a faster beam-steering approach using a gimballed mirror, which reduces the total scan time from minutes to seconds [38].
Most commercial THz lenses (i.e., plano-convex lenses, such as TPX50, Menlo Systems, Newton, NJ) suffer from spherical aberrations at the focal plane and yield a small FOV because they are not designed for imaging applications via beam-steering. Axicon lenses have been proposed for extracting corneal parameters in the THz regime by extending the depth of focus using a Bessel beam, however the beam’s first-order sidelobes are sensitive to variations in the target’s radius of curvature, making hydration mapping challenging [39–41]. A 220-330 GHz quasioptical system for corneal sensing using a pair of optimized biconvex aspheric lenses has been proposed previously [42,43]. These lenses were designed to achieve a high coupling coefficient between the focused beam and curved target when the corneal surface is displaced to superconfocal and subconfocal positions. However, the application of this quasioptical system was limited to hydration sensing at the center of the cornea, and it cannot be used for 2D imaging over a large surface area, where one may wish to investigate local changes in corneal hydration and topography.
In this paper, we design a hyperbolic-elliptical aspheric lens to image the cornea with normal incidence angle over the entire span of the FOV. The lens’ faces are designed independently from each other to provide a FOV, which is at least as large as that of OAPM, but now rotationally symmetric. The lens design is also optimized to achieve phase-front matching between the THz beam and the target curvature. Upon machining the lenses, they were aligned in a collocated THz-TDS reflection imaging setup. Performance of the lenses were compared to ray-tracing simulations and the previous OAPM measurements by imaging several spherical targets of similar size to the cornea, where the reduction in scan speed and ability to perform topographic imaging was also demonstrated. We show that using a spherical beam steering approach using a pair of such lenses the scan time of corneas can be significantly reduced from minutes to about 1-4 seconds, depending on the THz-TDS trace acquisition rate, which is now compatible with clinical applications. While a pair of OAPM could also be used to collimate and focus the THz beam [28], in addition to the challenges of fabricating custom OAPMs, this would increase the amount of space required to build a portable corneal scanner for clinical imaging, where the total optical footprint should be minimized. In the future, this beam-steering approach with aspheric lenses can potentially be used for imaging other curved biological tissue, such as the sclera of the eye, or skin imaging application on surfaces such as the nose or fingers.
2. Methodology
2.1 THz Reflection geometry
A schematic of the optical layout and a picture of the system is shown in Fig. 2. A broadband THz beam is generated using 1560-nm femtosecond pulses incident upon a GaAs Photoconductive Antenna (PCA) with a 100-MHz repetition rate (Menlo Systems, Newton, NJ). Using a TPX50 lens (Menlo Systems, Newton, NJ), the diverging beam is collimated and incident upon on a silicon beam-splitter (Si BS). The transmitted beam is focused by another TPX50 lens onto a 45° mirror housed within a motorized gimbal. The gimbal, consisting of a stacked combination of a rotation and a goniometer stage (Zaber technologies, Vancouver, BC), allows for a heliostat design that enables beam-steering along the azimuthal and elevation axes, respectively [38]. The gimbal directs the THz beam across the aperture of the aspheric lens pair, which collimates and focuses the beam onto an aligned spherical target at the focus of the second lens. For all scanned pixels, if the incident beam is normal to the surface of the sphere, the reflected beam follows the same optical path back to the Si beam-splitter, where it is focused onto the PCA detector by a third TPX50 lens. Using an Asynchronous Optical sampling technique [44], a time-domain trace of the THz pulse is collected with 0.01-picoseconds temporal resolution.
Fig. 2. (a) Layout of the single-pixel scanner for imaging curved targets, separated into a THz-TDS collocated reflection setup (red box) and beam-steering arrangement for directing the beam across the aspheric lenses, which focuses the beam onto the aligned spherical target (blue box). (b) A photograph of the setup aligned on an optical table is shown with labelled components.
2.2 Lens design
An aspheric lens design is implemented for focusing the beam without introducing spherical aberrations, because the front and back lens’ faces can be designed independently from one another for different imaging applications. Both lenses for the scanner have the same profile, where each lens surface is modeled separately as an aspheric curve with lens height, $z(r )$, defined for each radial position, r, using the following equation [45],
In this work, we chose a hyperbolic-elliptical design with a lens diameter of 3 inches (76.2 mm) which is the same diameter as the OAPM used in our previous THz corneal scanner. The parameters in Eq. (1) need to be chosen to image the target with a large enough FOV and achieve normal incidence across the target surface, which requires phase-front matching between the focused THz beam and target curvature. For optimizing an aspheric lens surface, these parameters include $R$, k and ${a_i}$, which ranges from the 4th to 12th power in increments of 2, giving rise to a total of 14 parameters (i.e., degrees of freedom) for a single aspheric lens design. For determining these aspheric parameters, Nelder-Mead optimization was employed [48]. A block diagram detailing the optimization process is shown in Fig. 3, where a simplex of 15 lenses was created using the rand function in MATLAB for determining initial aspheric parameters. For the hyperbolic face of each lens, the search space for the conic constant was limited to $ - 3\; < \; k\; < \; - 1$ and for the elliptical face, $ - 1\; < \; k\; < \; 0$. For each design, the center thickness was limited to a maximum of 1 inch (25.4 mm) to constrain the attenuation losses. The same aspheric parameters were used for both lenses in the hyperbolic-elliptical pair to limit the number of degrees of freedom for the optimization, allowing for faster convergence. In addition, having identical lenses allows for a linear relationship between the beam deflection from the gimbal and the displacement of the focused THz beam on the target surface. This permits easier mapping of pixels when forming images without requiring additional geometric transformations.
Fig. 3. Block diagram detailing the process for the lens design. The initial inputs to the optimization, including the extracted index of refraction, are used to create a 15-lens simplex. The simplex is updated iterativly using Nelder-Mead optimization, where the cost function is derived from several performance metrics obtained via ray-tracing simulations.
Each design in the simplex is evaluated using ray-tracing simulations, which requires knowledge of the complex index of refraction, $n$, of the lens material. High density Polyethylene (HDPE) was chosen for the material due to its low absorption coefficient and dispersion in our system’s usable bandwidth of 0.1-1 THz [49]. The index of refraction of HDPE in the THz regime has been previously reported to be between 1.53 [50] and 1.54 [51]. However, a sensitivity analysis (which will be explained in section 3) concluded that small variations in the value of n can impact the optical performance for a specific lens design. Before optimizing the aspheric parameters, the value of n for the material sample used for machining the lens needs to be known. An 1-inch thick, 12’’ x 12’’ slab of HDPE (W. W. Grainger, Lake Forest, IL) was placed at the focus of a 4-f THz transmission setup, where the complex value of n was determined using a material parameter extraction method [52]. For twenty spatially-disjointed THz-TDS measurements obtained across the slab, as shown in Fig. 4(a), the measured and theoretical impulse response functions were compared using a total variation error function and the value of n was updated iteratively using gradient descent [52]. With this method, the average value of n for the HDPE was determined to be 1.532, as shown below in Fig. 4(b).
Fig. 4. (a) The real index of refraction n of the HDPE slab at 20 different locations extracted using THz-TDS transmission measurements. Plotted in each box is the average value for a bandwidth of .1 to 1 THz. (b) Average extracted index of refraction of HDPE over the twenty spatially-disjointed measurements as a function of frequency with error bars showing the standard error.
Given the refractive index, the focal length f of each design in the simplex was calculated using the lens maker’s equation for a thick lens,
The ray-tracing simulation for evaluating each design is separated into several stages, starting at the back focus of the first aspheric lens with rays propagating towards its hyperbolic surface. Located at this point would be the pivot center of the gimballed mirror responsible for beam-steering. In the simulation, the THz beam is treated as the superposition of 250 single rays directed to equally spaced positions along the lens aperture. After collimation, each ray is focused by the second lens onto a spherical target of similar size to the cornea (8-mm radius) centered at the focus. All rays that strike the target with normal incidence are reflected back through both lenses via the same optical path. Since the distance of our target surface from the focus (8 mm) is greater than the calculated Rayleigh length, it is adequately sufficient to rely on geometrical optics for a simpler initial design of these lenses. However, future optimization and refinement of this design should utilize physical optics methods. Figure 5 shows the different stages of the ray-tracing simulation, where the blue rays represent the incident beam for different initial beam deflection positions, including for angles that miss the lens. The red rays show the path of the reflected rays from the spherical target. The phase of the incident chief ray (${\textrm{s}_0}$) at the corneal surface is determined using the ray’s propagation path through free space and the aspheric lenses, assuming a center frequency of 0.5 THz. For all other rays, the phase, $\textrm{s}$, is similarly calculated at different locations from the second aspheric lens surface to the focal point. In order to calculate the beam’s phase front, represented by the green curves in Fig. 5, we minimized the parameter $\Delta \textrm{s}$ defined as the sum of $|{\textrm{s} - \textrm{}{\textrm{s}_0}} |$ for all rays. This calculation confirms that for our optimized lenses, the spherical phase-front matches the corneal surface.
Fig. 5. Ray-tracing simulation for two aspheric lenses of the same design. (a) A set of incident rays (blue) are steered across and focused by the pair of lenses onto an aligned spherical target (purple). Also plotted is the spherical beam phase front at 0.5 THz for various locations (green), including at the target surface. (b) Reflected rays (red) from the target are collimated and focused by the lens back to the starting point of the simulation.
For each beam-deflection angle defined from $\theta = \; $0° to ${\theta _{max}}$, four optical metrics were used for evaluating a lens’ performance in the simplex; (1) deviation of $\Delta s$ between the focused THz beam phase-front and target curvature, (2) deviation of the angles of the incident rays ${\mathrm{\varphi }_i}$ from 90°, (3) average arc-length spot size $\bar{z}\; $ of the beam on the target and (4) FOV(${\theta _{max}}$) on the spherical target such that the reflected beam returns to the starting point. The initial diverging THz beam has a Gaussian distribution; therefore, a bundle of rays is evaluated for each deflection angle when calculating these four performance metrics. Each ray in the bundle is given a weight as part of a normalized Gaussian distribution defined by the system’s measured beam divergence of 18.4°. Incident/reflected rays that miss either lenses or the target are given a weight of zero. Once the Gaussian-weighted values are calculated, each performance metric is given a subsequent weighting term and added together in a cost-function, CF, given by,
Table 1. Optimized aspheric parameters for front (1st row) and back (2nd row) lens surfaces
3. Results
3.1 Simulation results
Using the described optimization and ray-tracing simulations, a pair of 3-inch diameter HDPE aspheric lenses were designed. The center thickness and front focal length for each lens is approximately 22 mm and 23 mm, respectively. Figure 6 shows the performance metrics of the optimized lens pair on an 8-mm radius target aligned at the focus of the second lens. Figure 6(a) shows a larger symmetric FOV of 9.6 mm can be achieved with a beam deflection angle ${\theta _{max}}\; $ of ${\pm} $40° to scan the lens aperture. With a 3-inch OAPM, a similar FOV of 8-8.8 mm was possible, but was asymmetric in one axes due to the mirror’s parabolic profile [35].
Fig. 6. The performance metrics of the optimized aspheric lens design was calculated using the Gaussian-weighted ray-tracing simulations as a function of the beam deflection angle. (a) The FOV, defined as the arc-length distance on the spherical target from the apex, and the incident power of the Gaussian beam as a function of deflection angle. The power drop after ∼30° is due to clipping of the beam towards the edges of the lenses. (b) Angle of incidence of the incoming beam on the target. (c) Expected beam spot size on the target, defined as an arc length. The dashed lines indicate the starting point where the beam is clipped by the edge of the lenses.
Similar beam analysis in Fig. 6(b) indicates that for all deflection angles, the maximum deviation from normal incidence for the incoming beam is less than 0.03°. Finally, the expected average arc-length spot size of the beam on the cornea was determined to be 1.3 mm as shown in Fig. 6(c), which is comparable to the 1-mm spatial resolution measured previously using an OAPM to image a spherical Bohler star target [35]. This analysis shows that beyond a certain deflection angle (dashed lines in Fig. 6(c)), part of the THz beam is clipped by the edge of the lenses; as part of the process for calculating the performance metrics, any rays that extend past this deflection angle are given a weight of zero. For determining the threshold for acceptable beam cutoff, an SNR of 5 (20% of the incident power remaining after clipping) was used.
Compared to a plano-convex lens, our aspheric lenses do not suffer from spherical aberrations or a significant deviation from normal incidence across the entire FOV. Ray-tracing simulations for the optimized lenses indicate excellent matching between the focused THz beam’s spherical phase-front and the target’s curvature across the FOV as shown in Fig. 7. As mentioned before, a sensitivity analysis was performed to evaluate the impact on the optical performance of the lens due to changes in the refractive index, $n$, from design values. As seen in Fig. 8, adjusting the real part of n by ${\pm} $0.003 from the extracted value causes the incoming rays to diverge from normal incidence on the sphere. In addition, towards the edges of the scanning range, the spherical phase-front begins to deviate from the target curvature. This indicates that for any future lens design, the index of refraction of the exact batch of material used for machining must be measured beforehand within a certain degree of accuracy.
Fig. 7. (a) Simulation of the focused THz beam (blue) on the cornea (purple) after passing through a pair of TPX50 plano-convex lenses. The spherical phase front (green) of the beam is not coupled with the target curvature and the reflected beam (red) does not follow the same optical path back to the detector. (b) The focused THz beam on the cornea after passing through our custom designed lenses, which shows phase-front matching along the FOV and no spherical aberrations.
Fig. 8. (a) Ray-tracing simulation of the optimized lens design using the average extracted value of the index of refraction, $n$ = 1.532. (b-c) Ray-tracing simulations showing the impact of adjusting n by ${\pm} $0.003, i.e., $n$ = 1.529 and $n$ = 1.535 in (b) and (c), respectively, for the same lens design. (d-f) Deviation of the incident/reflected beam from normal incidence towards the edges of the scanning range as well as the mismatching between the spherical THz phase front and target curvature at the edge of the FOV, marked by the black boxes in (a-c) respectively.
3.2 Optical performance characterization
Both lenses were aligned to a co-located THz reflection system as previously shown in Fig. 2. To determine the axial resolution of the scanner and compare the lenses to ray-tracing simulations, an 8-mm radius metallic sphere, shown in Fig. 9(a), was aligned to the focus of the second aspheric lens. THz-TDS imaging of the sphere was performed using the gimballed mirror stage, which consisted of a 360° rotation stage and a goniometer with a maximum deflection angle limit of ${\pm} $20° for steering the beam in the azimuthal and elevation axes, respectively. Given that the maximum deflection angle needed to scan the entire aperture of the lens is ${\pm} $40°, the current iteration of the scanner is limited in the elevation axes only. Future designs will replace the goniometer to utilize the full symmetric FOV of the lenses. To form topographic images, the time-of-arrival (TOA) of the THz-TDS pulse was obtained for all pixels and compared to the TOA of an apex measurement that corresponds to 0° beam deflection. A 200-µm-thick tape cross was placed on the metallic sphere, as shown in Fig. 9(a). The width of the cross strips was 2 mm and the length of the vertical strip was 8 mm. Figure 9(b) shows a topographic image of this target with a 3°-pixel size. As expected, at the pixels located near the edges of the cross, a portion of the focused beam is reflected from the metallic sphere while the rest of the beam is reflected from the air/tape interface. Due to the difference in the surface height, a superposition of the two reflected pulses is detected in these pixels. This superposition results in a decreased amplitude and increased pulse width (FWHM). A 2D Gaussian filter was applied to the THz topographic image to smooth the edges, which is shown in Fig. 9(b), where the tape-cross is clearly distinguishable from the metallic backing within the scanner’s FOV. For extracting surface height variation traces from the image, the FWHM edge-detection filter used in [35] was implemented. Figure 9(c) shows an example trace along the azimuthal axis (red line in Fig. 9(a)) and a reference trace measured on the metallic sphere before mounting the tape (dashed blue line in Fig. 9(a)). This reference measurement, shown as the blue line in Fig. 9(c), can be used to determine the axial resolution of the corneal scanner. Assuming the metallic sphere is smooth, variations in the reference surface profile indicate that this system can measure surface height changes that are larger than 15-20 µm. This minimum surface height detection threshold matches the result previously obtained using an OAPM.
Fig. 9. (a) Photograph of a smooth metallic sphere with a 200-µm-thick tape cross. Also, two azimuthal trajectories are marked with solid red line and dashed blue line for subsequent surface profile measurements, (b) THz topographic image of the cross, which shows surface height variations between the tape and metal backing with respect to a baseline TOA measurement taken at the apex. (c) Surface height variation profiles along the marked traces from the photograph, (a), which show the symmetric FOV and the thickness of the tape in the red trace and the minimum surface height measurement threshold in blue trace.
To demonstrate the improvement in the system’s imaging speed, a resin sphere of similar size to the cornea was aligned to the aspheric lenses. In two quadrants contained within the FOV, aluminum foil was taped to the sphere as indicated in Fig. 10(a). Using the new beam-steering approach [38], the normalized peak-peak amplitude of the reflected THz beam from the target was mapped out in about 3-4 seconds, where contrast was shown between the resin and highly-reflective aluminum foil as seen in Fig. 10(b). The total imaging time is determined by several predetermined settings, including the pixel size (set to 3° in both azimuthal and elevation axes), the number of averages taken of the THz-TDS waveform (5 averages), the time per measurement at each pixel (here, 0.05 seconds, limited by ASOPS trace acquisition rate of 100 waveforms per second) and the speed settings of the rotation (253°/second) and goniometer (87°/second) stages used for the gimbal. Future versions of the scanner will replace the ASOPS system with a 2 kHz electronically controlled optical sampling (ECOPS) technique [38], which will reduce the time per measurement at each pixel and reduce the total imaging time to under 2 seconds by reducing the time per pixel to about 2.5 milliseconds.
Fig. 10. (a) A resin ball target with 2 patches of reflective aluminum taped underneath to the surface. (b) THz image of the peak-peak amplitude for all scanned pixels on the resin ball, obtained in about 3-4 seconds (see Visualization 1).
4. Conclusion
THz imaging of curved targets, such as the cornea, has previously used parabolic mirrors for focusing the THz beam with normal incidence along the target surface. However, using OAPM provides an asymmetric FOV and results in an extended scan time due to the required beam-steering approach. Here, we present a new hyperbolic-elliptical lens design for focusing and scanning the THz beam with normal incidence onto a spherical target. In addition to ensuring phase-front matching to the surface curvature of the target and achieving an improved symmetric FOV, the total scan time is reduced from minutes to a few seconds. To accomplish this, we introduced a novel spherical beam steering strategy composed of a pair of these hyperbolic-elliptical lenses and a daisy-chained stack of a rotational and a goniometer stage. Our approach to custom-design a spherical scanning lens pair system can be generalized to other imaging applications, for example in detection of skin carcinomas on surfaces such as nose or fingers, and diagnosis of ocular diseases on the sclera of the eye.
Funding
Stony Brook University; National Institute of General Medical Sciences (R01GM112693).
Acknowledgments
The authors thank Dr. Brandon Kovarovic for printing the resin sample and the Stony Brook University Physics Machine Shop for fabricating the lenses.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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