Open Access
Add to BibSonomyAbstract
Optical coherence tomography (OCT) is an attractive modality in biomedical imaging systems due to its non-invasive imaging character. Since the image quality of OCT may be limited by the decrease of transverse resolution away from the focus spot, working distance tunable probe can be a strategy to overcome such limitation and maintain high transverse resolution at different imaging depths. In this paper, a miniature, working distance-tunable in-fiber OCT probe is demonstrated. The influences of the graded index fiber (GIF) length as well as the air cavity length on the working distance and the transverse resolution are simulated and discussed. Experimental results prove that the working distance can be tuned freely from 337.31 μm to 22.28 μm, producing the transverse resolution from 13.86 μm to 3.6 μm, which are in good agreement with the simulated results. The application of the probe in an OCT system for imagining a standard USAF resolution target is investigated in detail. The best resolutions for the standard USAF resolution target imaging are 4.9 μm and 6.9 μm in horizontal and vertical direction, respectively.
© 2016 Optical Society of America
1. Introduction
Since the tomographic imaging techniques such as ultrasound, X-ray, and magnetic resonance imaging (MRI) have been developed, it has been possible to observe microscopic objects and their internal structures beyond a macroscopic view. Each of these techniques measures a different physical property and has a resolution and penetration range for specific applications. As a novel tomographic imaging system, optical coherence tomography (OCT) has attracted much attention in recent years due to its non-invasive character [1–6]. Resolution is one of the essential parameter that influences OCT performance. Axial resolution is determined by the bandwidth of light source, and transverse resolution is governed by the beam spot size incident on the object, which depends on the design of the sample arm. Depth of focus (DOF) is another important factor that influences the image quality. In order to enhance the performance of OCT, great efforts have been made by improving light source designs [7, 8], scanning method [9–11], and especially, sample arm [12–14]. Various fiber-based endoscopic or handheld OCT probes have been proposed to miniaturize the sample arm configuration and improve the imaging range of OCT [5, 6]. Such fiber-based probe acts as an objective lens as well as a scanner for focusing beam into a sample and obtaining a cross-sectional 2D or 3D image. For most of these conventional fiber-based probes, the resolution reaches ~10 μm for axial direction and ~30 μm for transverses direction [15]. It is difficult to improve the transverse resolution without sacrificing imaging depth since the DOF is proportional to the square of the numerical aperture [16].
In order to obtain the image with high resolution through the entire region of interest, some sophisticated approaches have been proposed to extend the DOF of OCT while maintain a relatively high transverse resolution, such as Bessel beam probes [17–19], multi-beam scanning [20], adaptive focus [21, 22] etc. However, there are some limitations in these technologies. The Bessel beam probes suffer from poor signal collection efficiency while it is difficult to be used as endoscopic probe for both multi-beam scanning and adaptive focus since these systems are complex or large. Improved transverse resolution throughout the imaging depth can also be achieved by using tunable lenses. Such tunable lens can be realized by electro-optical, electromechanical, thermo-optical or acousto-mechanical effects [23–25]. Recently, M. E. Pawlowski et al. [26] have proposed a tunable endoscope by using a tunable electrowetted lens for investigation of middle ear. Y. Zou et al. [27] have demonstrated a solid tunable lens based endoscope according to the Alvarez principle. Gong et al. [28, 29] have simulated the tuning of manipulation distance in an optical fiber tweezer with a graded index fiber taper structure. In this paper, we investigate a miniature working distance tunable forward-view OCT probe by simply combining a single mode fiber (SMF), a graded index fiber (GIF), and a silica capillary tube. Both the work distance and the transverse resolution of the probe can be tuned artificially and their dependences on component sizes are studied. The application of the probe in an OCT system for imagining a standard USAF resolution target is investigated in detail. The proposed probe exhibits great potential in the computational imaging techniques [30–32] for a wide space and high resolution imaging.
2. Configuration and simulation
Figure 1 shows the schematic of the proposed probe. A section of GIF is fusion spliced to a silica capillary tube, in which an SMF is inserted and aligned with the GIF without fusion splicing. The relative distance between the SMF and the GIF can be accurately tuned by moving the SMF mechanically along the axial direction in the capillary tube. Light is led into the SMF and subsequently expands in the air cavity, then follows a continuous curved trajectory in the GIF due to the radial refractive index profile that maintains the essential lens function in limited cylindrical spaces. The output beam from the GIF could be convergent, collimated or divergent, which depends on the structural parameters. A beam parameter Gaussian matrix transformation method [33, 34] can be used to solve this problem, from which the focal length or the working distance (the length from the output plane to the focus point of the optical beam) Zw and spot size or transverse resolution D can be expressed as:
where a0 = λ / πw02 is a constant related to the profile of the output light from the SMF, λ is wavelength of light, w0 is initial beam radius from the SMF, n0 is the refractive index of space between SMF and GIF, l0 is the spacing between SMF and GIF, ng is the refractive index in the center of GIF, lg is the length of GIF, g is gradient constant of GIF, ns is refractive index of the working space.In this experiment, a GIF with g = 6.5 mm−1, pitch = 2π / g = 966.15 μm, and ng = 1.54 (GIF625, Thorlabs Inc.) is used as objective lens to focus the beam. A tough silica capillary tube (TSP100170, Polymicro Tech.) with an inner diameter of ~100 μm and an outer diameter of ~164 μm, is axially connected to the GIF by using a fusion splicer (FSM-45PM, Fujikura). A thin cladding SMF with an outer diameter of 79.8 μm, NA of 0.29 and mode-filed diameter w0 of 4.4 μm is inserted into the capillary tube to align with the GIF. The output wavelength of the light source is 1550 nm. The maximum air cavity length for beam expanding is confined by the core diameter of the GIF and is calculated as ~100 μm since beyond this expanding length, light will irradiate on the GIF cladding or air and attenuate strongly. Therefore the working distance, transverse resolution and their dependence on the air cavity length as well as the GIF length is shown in Fig. 2. Obviously, the output light distribution is determined by both air cavity length and GIF length, it might be converged at different positions while the minimum spot size occurs at the working distance such as 0.3 pitch length GIF at different l0 in Fig. 2 or divergence while the minimum spot size occurs at the GIF end such as 0.1 pitch length GIF in Fig. 2, of which the working distance keeps 0 μm at different l0; Also, it should be noted that, the performance for 0.2 pitch is multiple. The output light distribution is diverging and the minimum spot size occurs at the GIF end when the air cavity length l0 is less than ~45 μm; As the l0 keeps increasing from ~45 μm to 100 μm, the output light is converged at the focus since the input light meets the conditions for convergence after proper beam expanding. Similarly, the output light distribution for 0.4 pitch is converged as the l0 ranges from 0 μm to ~76 μm and diverging when the l0 is larger than ~76 μm. By selecting proper lengths of the GIF and air cavity, the tunable range of working distance as well as transverse resolution can be controlled.
Fig. 2 Calculations on (a) working distance and (b) transverse resolution with respect to the air cavity length as well as GIF length.
3. Experimental setup and results
Figure 3 displays the experimental setup of the OCT system. The self-made swept source is based on the Fourier domain mode locking (FDML) with central wavelength of 1550 nm, bandwidth of 51 nm, and repetition frequency of 43 kHz. Light from the swept source is split by a 1 × 2 coupler (60/40), with 60% of the power directed to the sample arm and the other 40% to the reference arm. Two circulators are used to redirect the reflected light from both reference arm and sample arm to a 2 × 2 coupler (50/50). The interference signal of the OCT system is detected by a balanced photo detector (PDB570C, Thorlabs Inc.), which is digitized at 41.7 MHz and combined with an oscilloscope (Picoscope 5204, Pico. technology) connected to a computer. The reference arm consists of an optical collimator (F220FC-1550, Thorlabs Inc.) and a mirror which is placed orthogonal to the optical axis and can be moved to adjust the optical path of the reference beam. The sample arm consists of the proposed probe and a standard USAF resolution target (R1DS1N, Thorlabs Inc.) placed orthogonal to the optical axis on a 3D translation stage (M-L01.8A1, Physik Instrumente Co., Ltd.). A software program is written in LabVIEW to simultaneously control the translation stages in the scan engine while digitizing the OCT signal.
3.1 Working distance
As an essential parameter of OCT, the working distance of the proposed fiber probe is measured by monitoring the light power of the beam reflected from the standard USAF resolution target and recoupled to the probe, while the focal length or the working distance is defined as the longitudinal distance between the probe tip and the standard USAF resolution target at which the maximum power occurs [10]. Before the experiment, the standard USAF resolution target is adjusted to make sure the test groups would not affect the detection so that it can be used as a mirror. Axially moving the standard USAF resolution target backward from the probe tip at the speed of 1 μm/s while the probe is fixed on a fiber holder will lead to change in reflective light power. As shown in Fig. 4, the recoupled optical power increases until it reaches a maximum and then decreases during the movement of the standard USAF resolution target for both probe A (the GIF length is ~280 μm as 0.289 pitch length) and probe B (the GIF length is ~371 μm as 0.384 pitch length). Moreover, the loss of probe A is larger than that of probe B when l0 is the same because probe A produces a relatively large working distance and the insert loss is higher than that of probe B. The working distances at different air cavity lengths for both probes are shown in Fig. 5. It decreases monotonously from 337.31 μm to 22.28 μm with an increase of the air cavity length from 0 μm to 100 μm for probe A and decreases from 86.8 μm to 10.06 μm with an increase of the air cavity length from 0 μm to 50 μm for probe B. The working distance tunable range for probe A is larger than that of probe B. The solid curves in the figure are calculated using Eq. (1) and are in a good agreement with the experimental results. The deviation between the measured data and the simulated curve might be caused by the small deformation and refractive index profile change of the GIF when splicing the GIF with the silica capillary tube, since it assumes a perfect square-law refractive index profile of the GIF in computation for the beam parameter Gaussian matrix transformation method [35, 36]. Moreover, it can be concluded that the working distance of the proposed probe is mainly limited by the geometric sizes and refractive index profiles of the commercially available GIFs according to the previous work [35]. In order to improve the maximum working distance as well as the working distance tunable range, one simple way is by selecting proper length of the GIF. As shown in Fig. 2(a), both the maximum working distance and tunable range for 0.2 pitch are larger than that for 0.1 pitch as well as 0.3 pitch. Besides, the working distance could also be improved by optimizing the refractive index profile (parameter g) of the GIF according to Eq. (1).
Fig. 4 Measured reflective light power with respect to the longitudinal distance between the standard USAF resolution target and the probe tip for the GIF lengths: (a) 280 μm and (b) 371 μm, respectively. The inset photograph gives a typical microscope picture of light intensity distribution near the probe tip using 532 nm semiconductor lasers. The converging of light intensity can be observed when the structural parameters are set appropriately.
Fig. 5 Simulated (solid curves) and experimental (points) working distances as functions of the air cavity length.
3.2 Transverse resolution and image
The transverse resolution of the proposed probe is measured by imaging the standard USAF resolution target and illustrated with probe A typically, since probe A has a relatively large tunable working distance. The single-pass loss of the probe is measured to be ~3 dB. In this experiment, the optical path of reference light is adjusted to equal that of the surface reflective light of the SMF by moving the mirror axially. Figure 6 displays the depth resolved signals after FFT at different air cavity lengths and the standard USAF resolution target is placed at the corresponding working distance. The main peak dependent on the interference between the reference beam and the sample light reflected by the standard USAF resolution target, shifts from 772.47 μm to 521.64 μm when the air cavity length l0 is changed from 0 μm to 100 μm. The sensitivity of the peak is ~76 dB and the signal to noise ratio (SNR) is ~30 dB. The shift of the main peak is caused by the optical path change of the sample arm, which can be calculated as ΔOPD = n0Δl0 + nsΔZw + ΔLg, since the reference arm is fixed and the working distance is tuned by adjusting the air cavity length l0. ΔLg is the optical path change when light transmits through the GIF after beam expanding by different air cavity lengths. For different expanded lengths, light irradiates on specific ranges of the GIF end face so that the effective index (set as N) for the propagating light is different accordingly. The propagating length of the light in the GIF can be approximately considered as the GIF length lg since the GIF is short. Therefore ΔLg = ΔNlg = -NAΔl0glg/2, where NA is the numerical aperture of the thin clad SMF and the shift of the main peak can be expressed as ΔOPD = (1 - NAglg/2)Δl0 + ΔZw. Combining the data for probe A in Fig. 5, ΔOPD is calculated as −241.42 μm, which is in good agreement with the shift of main peak in Fig. 6. Besides, it should be noted that the interference signals caused by the surface reflections of the probe, such as optical resonance produced inside the air-gap region as well as the interferences between the surface reflective light and the reference beam, may affect the tomographic imaging. As shown in the box of Fig. 6, peaks caused by the surface reflection of the probe occur when l0 = 100 μm and almost submerge in noise when l0 = 0 μm. However, such influences can be eliminated easily by adjusting the reference arm to make sure all surfaces of the probe as well as the sample are beyond the aplanatic surface. Therefore the depth resolved signals caused by probe surface reflections can be confined less than the minimum optical path between working distance and aplanatic surface. In this experiment, the aplanatic surface is set equal to the end face of the SMF so that all surfaces of the probe as well as the standard USAF resolution target are beyond the aplanatic surface. It means the corresponding OPD for the surface reflective light of the probe is less than 521.64 μm, which is the minimum optical path between working distance and aplanatic surface. Moreover, since the reflective light from the SMF is strong, it could be used as a reference beam so that the proposed probe exhibits potential in common path OCT [16].
By transversely moving the standard USAF resolution target at the corresponding working distance at the speed of 1 μm/s, the B-scan signals are shown in Figs. 7(a) and 7(b) as l0 = 0 μm and 100 μm, respectively. With an increase of l0, the contrast is higher and slope of the curves becomes sharper accordingly. It suggests a decrease in the focal spot size or transverse resolution, which can be defined by the 20% - 80% width of the slope [37]. As illustrated before, the surface reflection caused signals in Fig. 7(b) can be excluded and will not affect the image. The images of standard USAF resolution target after multiple B-scan and data processing are shown in Fig. 8. Despite small deformation caused by non-uniform velocity of the PI during start or end stage, the finest structure (marked by red box) can be clearly observed is element 3 bars in group 6 (12.5 μm spacing) for l0 = 0 μm and part of element 2 bars in group 7 (6.9 μm spacing) for l0 = 100 μm. As the inner diameter of the probe is ~20 μm larger than the outer diameter of the SMF, the focal beam may be stretched in the vertical direction so that the recognizable for cross stripe is not as good as that for the vertical stripe. As shown in Fig. 8(b), the finest cross stripe is observed in element 2 bars in group 7 while the finest vertical stripe is observed in element 5 bars in group 7 (4.9 μm spacing). Moreover, there is no distortion in Fig. 8(a) as l0 = 0 μm, since the end of the capillary tube is collapsed a little during fusion splicing and the optical axes of the GIF and the SMF are aligned well. The relationship between the transverse resolution in air (measured by the width of the slope) and the air cavity length for probe A is shown in Fig. 9. The transverse resolution increases from 13.86 μm to 3.6 μm while the air cavity length increases from 0 μm to 100 μm. Simulated results according to Eq. (2) are also displayed in Fig. 9 and are in a good agreement with the experimental results.
Fig. 7 B-scan of the standard USAF resolution target at the corresponding working distance when l0 is: (a) 0 μm and (b) 100 μm, respectively.
Fig. 8 Images of standard USAF resolution target by using probe A when l0 is: (a) 0 μm and (b) 100 μm.
4. Conclusion
We present a miniature, working distance-tunable forward-view in-fiber OCT probe by simply integrating of a single mode fiber, a graded index fiber, and a silica capillary tube. The measured working distance is tuned freely from 337.31 μm to 22.28 μm, meanwhile the corresponding transverse resolution in air changes from 13.86 μm to 3.6 μm. The influences of the GIF length on working distance and resolution are discussed. Calculated results are in good agreement with the experimental results. The application of the probe in an OCT system for imagining a standard USAF resolution target is investigated in detail. The best resolutions for the standard USAF resolution target imaging are 4.9 μm and 6.9 μm in horizontal and vertical direction, respectively. The proposed probe exhibits great potential in the computational imaging with a wide space and high resolution.
Funding
The National Science Fund for Distinguished Young Scholars of China (No. 61225023); The Guangdong Natural Science Foundation (No. S2013030013302).
References and links
1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]
2. G. J. Tearney, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern, and J. G. Fujimoto, “In vivo endoscopic optical biopsy with optical coherence tomography,” Science 276(5321), 2037–2039 (1997). [CrossRef] [PubMed]
3. N. Nassif, B. Cense, B. Park, M. Pierce, S. Yun, B. Bouma, G. Tearney, T. Chen, and J. de Boer, “In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve,” Opt. Express 12(3), 367–376 (2004). [CrossRef] [PubMed]
4. L. Liu, J. A. Gardecki, S. K. Nadkarni, J. D. Toussaint, Y. Yagi, B. E. Bouma, and G. J. Tearney, “Imaging the subcellular structure of human coronary atherosclerosis using micro-optical coherence tomography,” Nat. Med. 17(8), 1010–1014 (2011). [CrossRef] [PubMed]
5. B. C. Quirk, R. A. McLaughlin, A. M. Pagnozzi, B. F. Kennedy, P. B. Noble, and D. D. Sampson, “Optofluidic needle probe integrating targeted delivery of fluid with optical coherence tomography imaging,” Opt. Lett. 39(10), 2888–2891 (2014). [CrossRef] [PubMed]
6. K. Wijesundara, C. Zdanski, J. Kimbell, H. Price, N. Iftimia, and A. L. Oldenburg, “Quantitative upper airway endoscopy with swept-source anatomical optical coherence tomography,” Biomed. Opt. Express 5(3), 788–799 (2014). [CrossRef] [PubMed]
7. T. Klein, W. Wieser, C. M. Eigenwillig, B. R. Biedermann, and R. Huber, “Megahertz OCT for ultrawide-field retinal imaging with a 1050 nm Fourier domain mode-locked laser,” Opt. Express 19(4), 3044–3062 (2011). [CrossRef] [PubMed]
8. A. Unterhuber, B. Považay, A. Müller, O. B. Jensen, M. Duelk, T. Le, P. M. Petersen, C. Velez, M. Esmaeelpour, P. E. Andersen, and W. Drexler, “Simultaneous dual wavelength eye-tracked ultrahigh resolution retinal and choroidal optical coherence tomography,” Opt. Lett. 38(21), 4312–4315 (2013). [CrossRef] [PubMed]
9. H. Y. Lee, H. Sudkamp, T. Marvdashti, and A. K. Ellerbee, “Interleaved optical coherence tomography,” Opt. Express 21(22), 26542–26556 (2013). [CrossRef] [PubMed]
10. E. J. Min, J. Na, S. Y. Ryu, and B. H. Lee, “Single-body lensed-fiber scanning probe actuated by magnetic force for optical imaging,” Opt. Lett. 34(12), 1897–1899 (2009). [CrossRef] [PubMed]
11. S. Moon, S. W. Lee, M. Rubinstein, B. J. F. Wong, and Z. Chen, “Semi-resonant operation of a fiber-cantilever piezotube scanner for stable optical coherence tomography endoscope imaging,” Opt. Express 18(20), 21183–21197 (2010). [CrossRef] [PubMed]
12. B. C. Quirk, R. A. McLaughlin, A. Curatolo, R. W. Kirk, P. B. Noble, and D. D. Sampson, “In situ imaging of lung alveoli with an optical coherence tomography needle probe,” J. Biomed. Opt. 16(3), 036009 (2011). [CrossRef] [PubMed]
13. V. X. D. Yang, Y. X. Mao, N. Munce, B. Standish, W. Kucharczyk, N. E. Marcon, B. C. Wilson, and I. A. Vitkin, “Interstitial Doppler optical coherence tomography,” Opt. Lett. 30(14), 1791–1793 (2005). [CrossRef] [PubMed]
14. X. Li, C. Chudoba, T. Ko, C. Pitris, and J. G. Fujimoto, “Imaging needle for optical coherence tomography,” Opt. Lett. 25(20), 1520–1522 (2000). [CrossRef] [PubMed]
15. M. E. Brezinski, G. J. Tearney, B. E. Bouma, S. A. Boppart, M. R. Hee, E. A. Swanson, J. F. Southern, and J. G. Fujimoto, “Imaging of coronary artery microstructure (in vitro) with optical coherence tomography,” Am. J. Cardiol. 77(1), 92–93 (1996). [CrossRef] [PubMed]
16. B. Yin, K. K. Chu, C. P. Liang, K. Singh, R. Reddy, and G. J. Tearney, “μOCT imaging using depth of focus extension by self-imaging wavefront division in a common-path fiber optic probe,” Opt. Express 24(5), 5555–5564 (2016). [CrossRef]
17. R. A. Leitgeb, M. Villiger, A. H. Bachmann, L. Steinmann, and T. Lasser, “Extended focus depth for Fourier domain optical coherence microscopy,” Opt. Lett. 31(16), 2450–2452 (2006). [CrossRef] [PubMed]
18. D. Lorenser, C. Christian Singe, A. Curatolo, and D. D. Sampson, “Energy-efficient low-Fresnel-number Bessel beams and their application in optical coherence tomography,” Opt. Lett. 39(3), 548–551 (2014). [CrossRef] [PubMed]
19. K. M. Tan, M. Mazilu, T. H. Chow, W. M. Lee, K. Taguichi, B. K. Ng, W. Sibbett, C. S. Herrington, C. T. A. Brown, and K. Dholakia, “In-fiber common-path optical coherence tomography using a conical-tip fiber,” Opt. Express 17(4), 2375–2384 (2009). [CrossRef] [PubMed]
20. B. A. Standish, K. K. C. Lee, A. Mariampillai, N. R. Munce, M. K. K. Leung, V. X. D. Yang, and I. A. Vitkin, “In vivo endoscopic multi-beam optical coherence tomography,” Phys. Med. Biol. 55(3), 615–622 (2010). [CrossRef] [PubMed]
21. M. Pircher, E. Götzinger, and C. K. Hitzenberger, “Dynamic focus in optical coherence tomography for retinal imaging,” J. Biomed. Opt. 11(5), 054013 (2006). [CrossRef] [PubMed]
22. A. Kumar, W. Drexler, and R. A. Leitgeb, “Subaperture correlation based digital adaptive optics for full field optical coherence tomography,” Opt. Express 21(9), 10850–10866 (2013). [CrossRef] [PubMed]
23. A. Divetia, T. H. Hsieh, J. Zhang, Z. Chen, M. Bachman, and G. P. Li, “Dynamically focused optical coherence tomography for endoscopic applications,” Appl. Phys. Lett. 86(10), 103902 (2005). [CrossRef]
24. K. C. Heo, S. H. Yu, J. H. Kwon, and J. S. Gwag, “Thermally tunable-focus lenticular lens using liquid crystal,” Appl. Opt. 52(35), 8460–8464 (2013). [CrossRef] [PubMed]
25. I. Grulkowski, K. Szulzycki, and M. Wojtkowski, “Microscopic OCT imaging with focus extension by ultrahigh-speed acousto-optic tunable lens and stroboscopic illumination,” Opt. Express 22(26), 31746–31760 (2014). [CrossRef] [PubMed]
26. M. E. Pawlowski, S. Shrestha, J. Park, B. E. Applegate, J. S. Oghalai, and T. S. Tkaczyk, “Miniature, minimally invasive, tunable endoscope for investigation of the middle ear,” Biomed. Opt. Express 6(6), 2246–2257 (2015). [CrossRef] [PubMed]
27. Y. Zou, W. Zhang, F. S. Chau, and G. Zhou, “Miniature adjustable-focus endoscope with a solid electrically tunable lens,” Opt. Express 23(16), 20582–20592 (2015). [CrossRef] [PubMed]
28. Y. Gong, A. Y. Ye, Y. Wu, Y. J. Rao, Y. Yao, and S. Xiao, “Graded-index fiber tip optical tweezers: numerical simulation and trapping experiment,” Opt. Express 21(13), 16181–16190 (2013). [CrossRef] [PubMed]
29. Y. Gong, W. Huang, Q. F. Liu, Y. Wu, Y. Rao, G. D. Peng, J. Lang, and K. Zhang, “Graded-index optical fiber tweezers with long manipulation length,” Opt. Express 22(21), 25267–25276 (2014). [CrossRef] [PubMed]
30. W. Drexler, U. Morgner, F. X. Kärtner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, “In vivo ultrahigh-resolution optical coherence tomography,” Opt. Lett. 24(17), 1221–1223 (1999). [CrossRef] [PubMed]
31. J. Mo, M. de Groot, and J. F. de Boer, “Focus-extension by depth-encoded synthetic aperture in Optical Coherence Tomography,” Opt. Express 21(8), 10048–10061 (2013). [CrossRef] [PubMed]
32. Y. Z. Liu, N. D. Shemonski, S. G. Adie, A. Ahmad, A. J. Bower, P. S. Carney, and S. A. Boppart, “Computed optical interferometric tomography for high-speed volumetric cellular imaging,” Biomed. Opt. Express 5(9), 2988–3000 (2014). [CrossRef] [PubMed]
33. W. L. Emkey and C. A. Jack, “Analysis and evalution of graded-index fiber-lenses,” J. Lightwave Technol. 5(9), 1156–1164 (1987). [CrossRef]
34. Y. Mao, S. Chang, S. Sherif, and C. Flueraru, “Graded-index fiber lens proposed for ultrasmall probes used in biomedical imaging,” Appl. Opt. 46(23), 5887–5894 (2007). [CrossRef] [PubMed]
35. D. Lorenser, X. Yang, and D. D. Sampson, “Accurate modeling and design of graded-index fiber probes for optical coherence tomography using the beam propagation method,” IEEE Photonics J. 5(2), 3900015 (2013). [CrossRef]
36. K. R. Kim, S. Chang, and K. Oh, “Refractive microlens on fiber using UV-curable fluorinated acrylate polymer by surface-tension,” IEEE Photonics Technol. Lett. 15(8), 1100–1102 (2003). [CrossRef]
37. A. Dubois, L. Vabre, A. C. Boccara, and E. Beaurepaire, “High-resolution full-field optical coherence tomography with a Linnik microscope,” Appl. Opt. 41(4), 805–812 (2002). [CrossRef] [PubMed]
