Common-path all-fiber optical coherence tomography probe based on high-index elliptical epoxy-lensed fiber

Abstract. We propose and demonstrate high-index elliptical epoxy-lensed fiber probes designed specifically for endoscopic common-path (CP) swept-source optical coherence tomography (OCT) imaging inside wet tissues. The high-index epoxy lens uses a beam expansion region of a few hundred microns, which is capped with a spherical surface mounted at the end of an optical fiber. The probe is designed to operate inside wet tissues and shows improved performance over a long imaging depth, compared to bare or simple half-ball-lensed fiber probes. It allows optimal CP-OCT imaging in wet tissues by providing a stable reference power level and optimal beam waist for a long imaging depth. We have fabricated an array of these probes and one with a beam expansion region length of 288  μm and with a lens surface radius of 61  μm exhibiting 25-dB signal-to-noise ratio improvement compared to a bare fiber probe at 1.5-mm distance in water. The proposed probe is tested using a phantom sample comprising several layers of tape in water. The OCT images show that the probe is capable of high-resolution imaging over a distance of 1.5 mm.


Introduction
Compact all-fiber optical coherence tomography (OCT) probes allow insertion into small and tight areas of the body, enabling catheter-based endoscopic imaging. There have been many studies using OCT endoscopic systems for clinical applications, including vascular, digestive, respirator, and reproductive systems. 1 Fiber-based endoscopic OCT probes have been developed for ophthalmic surgery and advanced microsurgical tools. [2][3][4][5][6][7][8] An example includes hand-held automatic OCT-distal sensor-guided ophthalmic surgical devices that can compensate physiological tremors during surgery. [3][4]6 With such systems, OCT-distal sensors should be disposable with a long sensing range. It has been shown that common-path (CP) swept-source OCT (SSOCT) allows the use of a disposable probe of an arbitrary length. It also can be made to be compact, simple, free from dispersion and polarization mismatches, and tolerable to system vibrations.
However, bare fiber probes, commonly used as a sensing probe for CP-OCT, have two main drawbacks: strong divergence of the sample beam and dependence of OCT sensitivity on the refractive index of the working environment. To overcome the strong divergence of bare fiber probes, various lensed probe systems have been proposed and demonstrated. These include fused coreless fiber, 9,10 ball lens, [11][12][13][14] GRIN lens, 15 and conical-frustum tip. 16 While most of them work well for standard OCT configurations, they do not work well for CP setups, especially in vitreous media (i.e., water). This is mainly caused by the inability to readily fabricate the reference surface with an optimized reflectivity. Those designed for CP-OCTs 10,12,15,16 used lens/air interfaces as the reference, and their performance could degrade significantly in water because the lens effectiveness and/or the reference power level are significantly reduced.
For this paper, we designed and fabricated elliptical highrefractive-index epoxy-lensed fiber probes that exhibit long working distances and large depths of focus (DOF) in vitreous media (i.e., water) compared to standard bare or halfball-lensed fiber probes. The refractive index difference between the high-refractive-index epoxy and fiber core keeps the reference beam power independent of the working environment. Additionally, the availability of a wide range of epoxies with different indices allows fine-tuning of the reference reflectivity by mixing them in proportion. To validate our approach, we fabricated multiple probes with a range of beam expansion lengths and lens curvatures. We then measured the signal-to-noise ratio (SNR) of the lensed OCT probes as a function of the target depth and compared them with theoretically calculated SNR. The endoscopic OCT-distal sensors were then tested for OCT B-mode imaging using a phantom target comprising several layers of tape to confirm the improved performance of the proposed lensed fiber probes.

Design of Lensed Fiber Probe
A key performance metrics of OCT-distal sensors is long sensing depth, and the region of DOF outside the probe is considered the effective sensing range. The working distance, DOF, and beam waist depend on the beam expansion length and the lens curvature, which can be calculated with the ABCD matrix method. 17 For the lensed fiber, ABCD can be calculated as *Address all correspondence to Soohyun Lee, E-mail: slee452@jhu.edu † Present Address: GE Global Research Center, Niskayuna, New York, United States where L is the length of expansion region, R is the surface radius of the lens, n e and n h are the refractive indices of the sample environment (i.e., in air or in water) and high-index epoxy, respectively, and x is the propagation distance from the lens surface. For the case of bare fiber probes, the second and third matrices are identity matrices, and x is the distance from the fiber end. Working distance can be calculated by finding x, satisfying AC þ a 2 BD ¼ 0, where a is λ∕n g πω 2 0 for lensed fiber and λ∕πω 2 0 for bare fiber. Beam waist diameter (2ω f ) at the focal length is expressed as 18 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 6 3 ; 6 0 6 2ω f ¼ 2ω 0 (2) where 2ω 0 is the mode-field diameter of the fiber and λ is the wavelength in vacuum. The DOF can be expressed as (3) Figure 1 shows the calculated working distance, beam waist diameter, DOF, and effective sensing range as a function of beam expansion length and lens curvature. The working distance is a distance from lens surface to the beam waist, where a plus/minus sign indicates which side of the lens surface the beam waist lies. It is positive when the beam waist lies outside the probe, and, conversely, it is negative when the beam waist is virtual and occurs inside the fiber probe. To obtain effective sensing range longer than 500, 1000, 1500, or 2000 μm, beam expansion length must be longer than 157, 228, 282, and 327 μm, respectively. Lens curvature must be around 1/5 of the expansion length. Because the fiber has a 125-μm cladding, it is easier to make a lens of 60-μm curvature. Therefore, we set the lens curvature to 60 μm and targeted expansion region length around 300 μm, because it provides the longest effective sensing range (1.6 mm) for the curvature. The beam waist diameter of the targeted lensed fiber was expected to be 31 μm in water. The red stars indicate the geometry of fabricated lenses.

Fabrication of Lensed Fiber
The lensed fiber OCT sensor was fabricated using UV curable epoxy (Norland Optical Adhesive, n ¼ 1.7). First, a semispherical lensed probe was fabricated by applying the epoxy to the fiber end, which naturally forms a semispherical shaped lens, owing to surface tension. Two fibers having semispherical epoxy ends were placed inline and brought together so that the epoxy lenses were in contact. We controlled axial and transverse positions of the fibers using x-y-z linear stages while monitoring them using digital microscopes and our CP-SSOCT system to ensure they were perfectly aligned. A beam expansion rod was fabricated by curing the combined epoxy using ultraviolet light and breaking connection with one of the fibers. The length of the expansion rod was controlled by changing the distance between fiber ends. The fabricated expansion rod length was limited to around 120 μm because of the limited amount of epoxy that could be applied to bare fibers. A beam expansion rod of ∼240 μm was fabricated by applying more epoxy on the 120-μm expansion rod via repeating the process. The end of the expansion rod was capped by applying a semispherical epoxy lens. This process can be highly reproducible when the direction and position of the fiber are controlled precisely. Another factor in the reproducibility is the amount of the epoxy picked up by the fiber. This is also related to the precise control of the fiber. An epoxy lens can be quickly distorted when even a small amount of epoxy touches the sidewall of the fiber or the expansion rod. However, once epoxy forms a spherical shape at fiber end and expansion rod end, the shape of the lens is highly repeatable and durable. Figure 2 schematically shows the fabrication steps from bare fiber to the designed ellipticallensed fiber. For comparison, we also constructed lensed fibers having different expansion region lengths and lens curvatures. Lens 1, lens 2, and lens 3 were fabricated by applying and curing spherical epoxy on bare fiber, 120-μm beam expansion rod, and 240-μm beam expansion rod, respectively.  expansion rod. The curvature of the spherical surface was measured using OCT images with customized Matlab code, which uses least squares to fit a sphere on a manually selected edge. The length of beam expansion region was measured by our OCT system. Beam expansion lengths and curvatures of fabricated lenses are listed in Table 1. Lens 3 is the one closest to our design. Only lens 3 has positive working distance because it has a sufficient beam expansion area that allows the focusing of the beam. Lens 1 and lens 2 simply reduce beam divergence. We measured and verified the output-beam characteristics of the fabricated probes by comparing the beam spot diameter measured from knife-edge method 19 to simulated beam diameter via the ABCD method. Figures 4(a) and 4(b) show the erf function result using the knife-edge measurement and resultant beam shapes of bare fiber and each lensed fiber at 1mm distance. We performed knife-edge measurements of each lensed fiber at various distances. Figure 4(c) shows the measured and calculated beam diameter in air. The mode-field diameter was 3.2 μm, and the lens geometry listed in Table 1 was used for calculation. Calculated and measured beam diameters match reasonably well throughout the distance ranges, confirming the measured geometry of our lens and calculation. Although it is difficult to measure beam diameter in water, we can use the calculated values shown in Fig. 4(d).

Signal-to-Noise Ratio
The SNR versus depth was measured to show improved performance of the lensed fiber probes. Theoretical SNR was also calculated using the following equation to confirm the measured SNR: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 3 2 6 ; 4 3 3

S N
For the calculation, the detector quantum efficiency (η) was 0.9, noise equivalent power (NEP) was 5 pW∕ p Hz at 1-mm depth, relative intensity noise was −130 dB∕Hz, the bandwidth of the optical receiver (B) was 68.8 MHz, and the number of samples (N) was 1376. The digital processing loss was set to 1.8 dB for a Hann window. 20 Sample power at each depth was estimated by returned sample beam diameter at the fiber end because the peak intensity of a Gaussian beam is inversely proportional to the square of the beam diameter. Coupling loss was considered when P r and P s were calculated. For reflected sample beam diameters, ABCD can be calculated as A mirror was used as a sample, and the power at the fiber end was set to 0.15 mW to avoid saturation. Noise was limited by detector noise because of the low power. Detector noise has frequency dependence. 20 Thus, we estimated NEP from the measurement of detector noise (i.e., A-scan   image without an input signal) assuming NEP at 1 mm is 5 pW∕ p Hz. Figures 5(a) and 5(b) show the SNR of each lensed fiber versus its depth in both air and water, respectively. Bare fiber showed relatively high SNR in air, despite its large divergence caused by higher reference power. However, it degraded significantly in water. Lens 3 showed the highest SNR in water. The 10-dB range of the bare fiber was 200 μm, and it increased to 1600 μm with lens 3. The measured and calculated SNR fits reasonably well throughout the distance range, except for lens 3 in water. The difference is probably caused by the large mode mismatching caused by the tight beam focus.

Optical Coherence Tomography Imaging Performance
To confirm the improved SNR and resolution, B-scan images of a phantom target comprising several layers of tape were obtained at various distances using the lensed fibers. The fiber probe was attached to a motorized translation stage (Thorlabs MT1-Z8), and the probe was scanned horizontally across the phantom. Figures 6 and 7 show the OCT images working in water and air, respectively. The OCT images showed similar trends as with the previous beam diameters and SNR measurements. In water, the designed lensed fiber showed the best image quality at all distances. All probes showed similar image quality at 300-μm distance except bare fiber, which has a lower SNR because of low reflection at the fiber end. However, the designed lensed fiber showed better quality than other lensed fibers when the probe was further away from the sample because of its long working distance and DOF. The quality improvement from the designed lensed fiber can be clearly seen at the 1500-μm distance. In air, fiber probes without a lens and with lens 2 showed better quality, as expected. A fiber probe with lens 3, optimized for working in wet environments, showed the worst image quality because of strong divergence and smaller reference than bare fiber.

Conclusion
We have demonstrated that CP-SSOCT imaging and sensing in water can be enhanced using a high refractive index elliptical epoxy-lensed fiber probe. We designed lensed fibers having long working distances and DOFs in water to obtain sufficiently long effective distal sensing ranges. Enhanced performance was confirmed by SNR and B-scan OCT images. The SNR of the proposed fiber probe, compared to a bare fiber at a distance of 1.5 mm, was increased by 25 dB and the resolution improved from 476 to 47 μm. We can conclude that the improved performance in water indicates that such high refractive index epoxy-lensed fibers can work effectively in ophthalmic and vascular applications.