Common-path optical coherence tomography (CPOCT) is known to reduce group velocity dispersion and polarization mismatch between the reference and the sample arm as both arms share the same physical path. Existing implementations of CPOCT typically require one to incorporate an additional cover glass within the beam path of the sample arm to provide a reference signal. In this paper, we aim to further reduce this step by directly making use of the back-reflected signal, arising from a conical lens-tip fiber, as a reference signal. The conical lens, which is directly manufactured onto the optical fiber tip via a simple selective-chemical etching process, fulfils two functions acting as both the imaging lens and the self-aligning reference plane. We use a Fourier-domain OCT system to demonstrate the feasibility of this technique upon biological tissue. An in-fiber CPOCT technique may prove potentially useful in endoscopic OCT imaging.
©2009 Optical Society of America
Optical coherence tomography (OCT) is now established as a powerful and versatile method for in-vivo optical biopsy . Given that OCT systems rely upon the principle of low coherence interferometry, the interferometric setup is arranged to detect the relative phase difference between the reference path and the sample path. A common problem of having a separate reference arm and a sample arm in an OCT Michelson interferometer setup is that a significant mismatch of group velocity dispersion (GVD) and polarization between these arms may decrease the axial resolution of the system .
Group velocity dispersion (GVD) mismatches cause broadening of the autocorrelation function resulting in poorer axial resolution. Such problems are increased when using broader optical bandwidth (>100nm) light sources e.g. supercontinuum sources and ultra-fast lasers. The GVD mismatch between the reference arm and the sample arm is commonly balanced by using a variable thickness fused silica glass and BK7 glass within the reference arm. These compensation steps can be time consuming and laborious as one has to constantly adjust the fused silica and BK7 due to motion of the sample arm during handling. In addition dispersion mismatch is also system dependent. Any change in optical components may require the user to repeat the entire process. Polarization mismatch can also cause significant phase difference between the two arms giving rise to a distorted autocorrelation function leading to a decreased axial resolution  but this mismatch can be minimized by inserting polarization controllers into each arm.
The problems with GVD and polarization mismatch can be circumvent by having the reference light and sample light travelling in the same optical path or common-path. In a typical common-path OCT (CPOCT) system, the reference signal is obtained by placing a glass slide on the sample and using the glass surface facing the sample as a reference plane . This common-path design has proven to be a straightforward and effective technique in real-time GVD and polarization compensation and eliminates the requirement for a separate reference arm [3–6]. The common-path approach also promotes interferometer stability due to the automatically maintained overlap of the reference and sample beam. It has been experimentally demonstrated that the common-path interferometer is less sensitive to vibrations then the two arm interferometer . It is however noted that although the common-path technique removes all the system dispersion, this technique does not take into account the dispersion introduced by the sample itself. Having the reference arm and the sample arm sharing a single common-path, the length of a fiber probe could be extended for OCT endoscopic applications without any restrictions.
The introduction of a reference plane into the imaging optical path of the CPOCT system by the insertion of an external glass slide is a non-trivial step because it requires accurate alignment of the reference plane and positioning of the glass slide close to the focal point of the imaging lens. The proximity is necessary for high collection efficiency of the back-reflected reference signal  as well as the reduction in the mismatch in curvature between the beam wavefront and the reference surface . These optimization steps increase the system signal-to-noise ratio (SNR) but can be especially difficult during implementations involving small optical fiber probes.
In this paper, we describe a new scheme for the implementation of common-path Fourier domain (FD) OCT. Our system uses a conical microlens that is chemically etched in the core at the fiber tip. Due to the elimination of the alignment process between the microlens and fiber end, there has been recent interest in developing in-built fiber probes for OCT applications [7, 8]. Although the use of bulk conical lenses (often referred to as axicons) have been demonstrated for use in more conventional OCT implementations [9, 10], the use of an optical fiber probe with an in-built conical microlens for CPOCT has not been reported. The advantage of a monolithic conical microlens lies not only in simple fabrication, but also in generating the back reflected reference signal and providing a capability for focusing the light for imaging without the addition of optical elements. As the conical microlens is already an integral part of the fiber core and there is no additional interface medium (air-glass) between the microlens and the fiber end which leads to a high coupling efficiency. The conical-tip fiber probe is fabricated via a straightforward single-step chemical etching technique  that is both time and cost efficient. Moreover, the choice of different chemical concentrations for the etching solution facilitates tunability of the cone angle which in turn modifies both the lateral resolution and imaging depth.
The in-fiber common path technique works by using the light field that is being reflected back from the glass/air interface at the end of the fiber. This reflection can be used as a reference provided there is sufficient light being coupled back into the fiber core [12, 13]. To verify this effect, we employed a finite-element program (COMSOL) to create a 2-D and a 3-D model of the conical-tip fiber. The 3-D model is used to calculate the global reflectivity coefficient of the fiber including polarization and geometry effects where as the 2-D model, which is more robust and less computational intensive is used simulate the total tip sample interaction. Both model consist of an optical fiber (single mode) and a conical microlens at one end, which has a base width of 8.2μm (fiber core size), and a 128° cone apex angle and 340nm radius of curvature curved tip (as measured from the SEM image in Fig 1(a)). The fiber eigenmode was used as input to the fiber and the reflection coefficient was determined by calculating the coupling efficiency of the back-reflected field to this fiber mode. Figure 1(a) exemplifies the field intensity profile in the case of the 2-D conical-tip fiber including a reference sample. A 2-D model is displayed in Fig. 1(a) for illustration purpose only. Using this model we have calculated the reflectivity of a single air-water interface at 90μm from the fiber tip. Figure 1(b) shows the interference spectrum and its Fourier transform for a broadband illumination of 70nm centered on a wavelength of 1320nm. Figure 1(c) shows the angular divergence plot of the beam from the fiber tip.
The operating principle is based on spectral interferometry. The total optical signal reflected back from a sample consists of multiple elementary waves reflecting from interfaces at different depth z. This signal interferes with the reference wave resulting in spectral fringes (see inset Fig. 1(b)) of constructive and destructive interference. The advantage of this spectral approach is that the full structure signal is obtained in a single measurement and no depth scanning is required. The interference signal I(k) can be described by :
where we have neglected the phase of the reflectivity coefficients. Here, 2z is the path length difference between the sample arm and the reference plane, aR(k) is the spectrally dependent (due to a non-flat fiber tip) amplitude of the reference, a(z) is the backscattered amplitude of the sample signal at different axial positions, S(k) is the spectral intensity distribution of the light source and n is the refractive index of the sample.
From Eq. (1), the total interference signal is a superposition of three terms. The first term describes the DC term from the reference signal. The second term describes the depth information of the sample, which is the sum of cosine functions at scattering amplitude a(z) from different depths, z , within the sample. The third term describes the mutual interference of all elementary waves and may be neglected in most cases of strongly scattering medium. The inverse Fourier transform of I(k) makes it possible to distinguish between these first and second terms. The first term corresponds to the correlogram of the light source which can be filtered out while the second term gives the ranging information of scattering amplitude a(z) at different reflecting interface locations from which a cross-section tomogram of the sample can be constructed (Fig. 1(b)). In the case of the conical-tip fiber, the model shows that the spectral dependence of the reference signal has a small effect on the envelope of the interference signal (see inset Fig. 1(b)). However, the slow varying nature of the spectral dependence of the reference does not destroy the depth information but creates a sideband after Fourier transformation of the spectral fringes as shown by the red curve in Fig. 1(b). The beam generated from the conical-tip fiber follows the form of pseudo-Bessel beam shape in free space, as illustrated by the structure apparent in Fig. 1(c) which shows the zero-order beam and the first-order ring. Such an output from the conical-tipped fiber yields a narrowly focused beam with relatively low divergence [15–17]. Using a 2μm diameter single point scatterer in our model, we see that the sideband is not attributed to the first-order ring but rather to the dispersion of the beam as it propagates through the conical fiber tip. To further strengthen this statement, Fig. 1(c) illustrates the far field angular divergence plot of output beam from the conical-tip fiber. Here we observe that the strength of the Bessel first ring depends on the polarization of the light in the fiber. As the SLD used in this experiment is non-polarized light, the intensity of the first-order ring is expected to be similar to that of the circular polarized input light with a divergence angle of approximately 13°, as seen in Fig. 1(c). Finally, comparing the depth resolution of the cleaved fiber against that of the conical fiber tip in Fig. 1(b), we observe a 20% resolution improvement in favor of the conical-tip fiber when using the full width half maximum measure whereas we see a 25% drop in resolution when using the standard deviation (due to the presence of the sideband).
From the modeling results, we can conclude that most of the back-reflected light field from the conical tip does not couple back into the core of the fiber. This behavior is due to the fact that the angle between the base and the conical side is less than the critical angle for total internal reflection (TIR) between the glass and air, which is ~43° based on fiber core refractive index of ncore=1.467 . As with any convex lens that has no anti-reflection coating, light propagating towards the centre of the lens would be partially reflected back. The model estimates that approximately 0.35% of the light incident on the tip will be reflected and guided for the fiber used in our experiments at the operating wavelength of 1320nm.
3. Experimental procedure
In this section, we detail the chemical fabrication process of the conical microlens and the implementation of the in fiber common-path technique within a Fourier-domain OCT system. A buffered hydrofluoric (BHF) etching solution is used in the selective-chemical etching technique. The solution consists of a volume ratio of ammonium fluoride solution (NH4F) (40 wt%):hydrofluoric (HF) acid (50 wt%), respectively as X:1. In the BHF solution, the concentration of NH4F (given as X) controls the etch rate of the pure SiO2 fiber cladding and the GeO2-doped SiO2 fiber core . A difference in the etch rate, due to different concentrations (X), between the fiber cladding and fiber core will result in different cone angles. The physical process involved in this selective-chemical etching process is a simple single-step process which only requires immersion of a well-cleaved fiber into the BHF solution. In our experiments, we used Corning SMF-28 single mode fiber, which has a core diameter of 8.2μm and a cut-off wavelength at 1270nm. The etching duration, or the minimum time within which the conical microlens is fully formed, is determined by the concentration of the NH4F in the BHF solution. Our etching process was carried out at room temperature (22°C α 1°C) and a scanning electron micrograph of a representative conical-tip fiber is shown in the inset of Fig. 1(a)
The experimental setup of the common-path FD-OCT setup is shown in Fig. 2(a). The low coherence light source is a superluminescent diode (SLD) (DL-BX9-CS3089A, Denselight Semiconductors) with a centre wavelength of 1320nm and spectra width of 70nm. The theoretically predicted axial resolution provided by this source is approximately 11μm. A circulator (OE-3-1310SFC-09-1, O/E Land Inc.) is used instead of a 2×2 coupler because no additional arm is required. A commercial spectrometer (BTC261E, B&W Tek, Inc) which incorporates a 16-bit 512 pixel TE-cooled InGaAs linear array detector, 600 lines/mm grating, 25 μm slit width was used (The measured dynamic range of the system is approximately 40dB). The optical power, from the conical-tip fiber probe, incident on the sample was measured using a photo-detector (PDA10CS, Thorlabs Inc.) to be approximately 5mW. The motorized translation stage (KT-LS13-M, Zaber Technologies Inc.) provides the lateral scanning for the B-scan operation. A custom program was written with Labview version 8.2 (National Instruments) to operate and collect data from this experimental CPOCT system.
We fabricated a conical-tip fiber using a 2:1 BHF solutions yielding a cone angle of 128°. Using a mirror as a sample, the measured axial resolution was approximately 12.1μm, which is 10% larger than the theoretical value. The axial resolution was measured without any requirement for GVD and polarization compensation. We performed these tests while monitoring the autocorrelation function that remained unchanged throughout the experiment proving that the common-path design eliminates the requirement for compensation due to any imbalance in the optical path between signal and reference paths.
The reflected power from the conical-tip fiber end, which was measured by replacing the spectrometer in Fig. 2 with a photodetector (PDA10CS, Thorlabs Inc.) and removing the sample stage, was approximately 0.46%, which is of the same order of magnitude as the modeled results (0.35%).
Figure 3 shows the measured signal to noise ratio (SNR) and the axial resolution as a function of axial distance between the 128° conical-tip fiber end and mirror. The SNR was obtained by using the peak signal of the mirror surface, after inverse Fourier transform, over the noise floor. From these measurements it can be seen that an SNR > 15dB is achievable at an axial distance of 0.5mm from the fiber tip demonstrating the extended imaging depth achievable with this system. The lower curve in Fig. 3 also shows that the measured axial resolution of the system varies between 12μm and 16μm over the axial distance range.
The lateral resolution of the 128° conical-tip fiber was measured using an USAF resolution target card (NT58-198, Edmund Optics). Figure 4(a) shows the bright-field image of the USAF target card, taken with a 50X 0.5NA long working distance objective (Mitutoyo). The dotted line indicates the scan path. The target card is made up of different rectangular gratings with different widths. The line pairs for elements E2 and E6 of group 6 are 13.9μm and 8.8μm respectively. This implies that the corresponding thickness of each line in E2 is 6.95μm and the corresponding thickness of each line in E6 is 4.40μm. The scanning was carried out at a lateral step size of 0.5μm and with the fiber end positioned 30μm away from the target card. A cleaved fiber, using the same experimental setup as in Fig. 1, was used for comparison.
Figure 4(b) presents the lateral plot from element E2 to E6 of a single scan OCT data performed with the 128° conical-tip fiber and a cleaved fiber. From the data in Fig. 4(b), it can be observed that the conical-tip fiber is able to clearly resolve the lines in element E6 whereas the cleaved fiber is barely able to. Scanning of group 7 was also carried out to further assess the lateral resolution of this system. Group 7 consists of 6 elements with a maximum line width of 3.9μm, however in the case of this group, it was not possible to resolve any of the lines with the conical-tip fiber. As the smallest line thickness that the conical-tip fiber is able to resolve is 4.4μm, which lies in element E6 of group 6, we have taken this to determine the lateral resolution that the 128° conical-tip fiber could achieve. We also investigated the lateral resolution of the system at the extreme end of our measurement range (0.6mm from the fiber tip) where we found that the lateral resolution of our 1280 fiber decreased to ~16μm.
An additional test was carried out to find out the angular orientation sensitivity of measurement using conical-tip fiber and a mirror. The conical-tip fiber was first aligned perpendicular to a mirror and the peak intensity was recorded. The measurement was then repeated with the same mirror tilted at different angles, while the fiber position remained unchanged. A comparison between normalized signal intensity observed for the conical-tip fiber and the cleaved fiber as a function of mirror tilt angle is shown in Fig. 5. The results show that the conical-tip fiber has a larger angular orientation tolerance, which gives a lower sensitivity to misalignment than the cleaved fiber. This larger angular orientation tolerance of the conical-tip fiber compared to the cleaved fiber also implies a larger acceptance angle. The maximum tilt angle that the conical-tip fiber can tolerate before the peak collected signal drops 1/e2 is approximately 15°.
To demonstrate the imaging capability of the conical-tip fiber through the common-path technique, a two dimensional cross sectional scan of a sample of fresh onion was performed. Figure 6 depicts a cross-section OCT tomogram of the onion sample obtained with the 128° conical-tip fiber. The image size is 256 × 1000 pixel giving an area of 1.28mm × 2mm. The step-size set on the translation stage used for the scanning was 2μm step. The image in Fig. 6 is displayed in logarithmic gray scale. From the cross-section OCT tomogram of the onion in Fig. 6, the conical-tip fiber CPOCT system is able to achieve an imaging depth of approximately 600μm. The cell wall layer making up the epidermis layer is clearly evident from the rest of the section. In addition the vascular bundle, which plays the vital role of transporting nutrients to the surrounding tissue, can also be observed in the tomogram. Although the current OCT tomogram is obtained by fixing the conical-tip fiber probe and moving the translation stage, scanning at the fiber end itself could be achieved using small piezoelectric actuators . As the conical-tip fiber is fabricated on a standard single mode fiber with an external diameter of 330μm diameter, including the polymer buffer layer, this inbuilt microlens fiber probe might provide an advantage for future potential microprobe for ultrasmall needle-based diagnosis applications such as tumor diagnosis through refractive index measurement .
In conclusion, we have demonstrated, for the first time to our knowledge, a proof of principle study on the feasibility and the OCT imaging capability of a simply fabricated conical-tip fiber employing a common-path technique. The resolution for a 128° conical-tip fiber used in this work were measured to be 12.1μm axially and 4.4μm laterally. The preliminary test on the imaging of onion sample is encouraging and shows that imaging depth of ~0.6 mm is achievable. The conical-tip fiber can be readily fabricated via a selective-chemical etching technique at low cost and with high reproducibility. This selective-chemical etching technique could be used to create an array of multiple conical microlenses in a dedicated fiber bundle, which may prove useful in implementing a full-field OCT imaging system. Such an in-fiber CPOCT system may pave the way for future practical designs of needle-based OCT because with an in-fiber conical lens that is self-aligned onto the fiber core a relatively high optical coupling efficiency is ensured. The conical-tip fiber is also robust and resistant to environmental conditions such as mechanical vibrations, which arise from the scanning stages, and temperature variations. The reference intensity of the conical-tip fiber can also be adjusted by coating the tip with a thin layer of cold for example. Our 3D modeling shows that a 5nm thin layer of gold changes the reflectivity of the tip from 0.35% to 0.55%. This thin layer of gold has the additional benefit of allowing the common-path technique to be used directly in high refractive index media such as water. Future work on the studies of the imaging properties of the conical-tip fiber for various angles and the development of the needle-based probe will be conducted in the next phase of work.
The authors would like express our thanks Professor Shuji Mononobe for useful discussions on the fabrication of the conical-tip fiber probes. Funding from the UK Engineering and Physical Sciences Research Council and the European Union FP7 ARAKNES programme are gratefully acknowledged. K. Dholakia is a Royal Society - Wolfson Merit Award Holder.
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