Ultrathin fiber-optic probes delivered via hypodermic needles enable imaging deep within biological tissue using optical coherence tomography (OCT) [1,2]. Using state-of-the-art broadband light sources, such probes can image with high axial resolutions of a few micrometers. However, it is not straightforward to increase their transverse resolution to similar values without severely compromising the useful imaging depth range due to the strong divergence of the tightly focused beam. This problem has been addressed in bulk-optic OCT scanners by generating focal regions with an extended depth of focus (DOF) using axicons [3,4] or pupil phase masks [5]. Unfortunately, it is not possible to simply scale down the bulk-optic solutions to the dimensions of ultrathin fiber probes with diameters on the order of 125 μm, as in the latter case the formation of the focal region takes place in a regime of Fresnel diffraction where the optical design methods and approximations used in [3–5] are no longer valid. A first demonstration of an ultrathin OCT probe using a fiber-tip micro-axicon [6] has shown that pseudo-Bessel beams can still be generated from such structures at low Fresnel numbers, but with a very short working distance and reduced DOF gain compared to their bulk-optic counterparts. Rather than trying to mimic bulk-optic axicons, we have explored the use of phase-mask structures in the regime of low Fresnel numbers using numerical simulations based on the beam propagation method (BPM). As a result of this, we demonstrate an extended-depth-of-focus (EDOF) fiber probe design that uses a very simple phase mask consisting of a short section of overfilled graded-index (GRIN) fiber, which can yield a DOF gain around 2.

The concept is illustrated in Fig. 1(a). A normal lensed fiber is made by using a section of no-core fiber (NCF) to expand the beam emitted by the single-mode fiber (SMF) and a section of GRIN fiber to focus it with the desired numerical aperture (NA). In order to make an EDOF probe, a phase mask consisting of an additional short section of GRIN fiber with a smaller core diameter is appended to the lensed fiber. The rays traced in Fig. 1(a) show that the effect of this arrangement can be intuitively understood as a “double-focus” lens, with the small core of the phase mask affecting only the central portion of the converging wavefront [see Fig. 1(b)]. The output beam from such a probe was simulated at a wavelength of 820 nm using a split-operator BPM algorithm [7], where the propagation operator is applied in the spatial frequency domain after fast Fourier transform (FFT) of the transverse field amplitude. The EDOF probe has design lengths of $L_{\mathrm{NCF}}=300\mathrm{\mu m}$, $L_{\mathrm{GRIN}}=190\mathrm{\mu m}$, and $L_{\mathrm{PM}}=14\mathrm{\mu m}$, connected to SMF with a mode-field diameter of 5.6 μm. The lens section is a 100 μm core diameter GRIN fiber with a gradient parameter of $g=4.5{\mathrm{mm}}^{-1}$, and the phase mask is a 32 μm core diameter GRIN fiber with $g=10{\mathrm{mm}}^{-1}$. The simulated output beam intensity in water (refractive index $n=1.33$) is shown in Fig. 1(c). The full width half maximum (FWHM) beam diameter and the normalized on-axis intensity are shown in Fig. 1(d). The minimum FWHM beam diameter (which corresponds to the maximum OCT resolution) is 6 μm, and the DOF is 874 μm. Compared with an ideal Gaussian beam of the same minimum FWHM diameter [dotted curves in Fig. 1(d)], a DOF gain of 1.9 is obtained at the cost of a 4.8 dB reduction of the peak signal-to-noise ratio (SNR). The sidelobes visible in Fig. 1(c) have an intensity below 5% of the peak over most of the DOF. In this work, we have chosen to define the DOF as the region over which the FWHM beam diameter is smaller than twice its minimum value. This definition allows more tolerance for beam-width fluctuations in the focal region of non-Gaussian beam profiles than the Rayleigh range criterion. We believe that this is justified because the Rayleigh range underestimates the perceived useful imaging depth range in OCT. A 40% (factor of $\sqrt{2}$) change in transverse resolution is hardly visible due to the effects of logarithmic compression of the images and speckle.

 

Fig. 1. EDOF probe using a GRIN fiber lens and a GRIN fiber phase mask. (a) Schematic of the design: PM, phase mask. (b) Illustration of the index profiles of the GRIN lens (green; upper line) and the phase mask (blue; middle line) relative to the Gaussian beam intensity profile (red; bottom line): $n_{\text{clad}}$, cladding index. (c) Simulated output beam intensity distribution in water. (d) Simulated FWHM diameter and normalized on-axis intensity of the output beam in water. The dotted lines show the values for an ideal Gaussian beam. The vertical green lines indicate the boundaries of the extended DOF.

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An alternative EDOF probe design is shown in Fig. 2(a), in which a GRIN phase mask is used in conjunction with a refractive lens. The simulated output beam in water at 820 nm wavelength is shown in Figs. 2(b) and 2(c) for a structure with lengths of $L_{\mathrm{NCF}}=340\mathrm{\mu m}$, $L_{\mathrm{PM}}=20\mathrm{\mu m}$, and a hemispherical lens with $R_{\mathrm{Lens}}=80\mathrm{\mu m}$ and $n=1.7$ (a typical value for photoresist). The GRIN phase mask has a 32 μm core diameter and $g=10{\mathrm{mm}}^{-1}$. The minimum FWHM beam diameter is 6.5 μm, and the DOF is 1060 μm. Compared with an ideal Gaussian beam of the same minimum FWHM diameter [dotted curves in Fig. 2(c)], a DOF gain of 2 is obtained at the cost of a 5.2 dB reduction of the peak SNR. The sidelobe intensity is below 5% of the peak over most of the DOF.

 

Fig. 2. EDOF probe using a refractive lens and a GRIN fiber phase mask. (a) Schematic of the design. (b) Simulated output beam intensity distribution in water. (c) Simulated FWHM diameter and normalized on-axis intensity of the output beam in water. The dotted lines show the values for an ideal Gaussian beam. The vertical green lines indicate the boundaries of the extended DOF.

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The EDOF probe designs presented in Figs. 1 and 2 are both tolerant of length errors of up to $\sim 20\%$ in the GRIN phase-mask section, and our fabrication method, which uses a micrometer translation stage mounted to the fiber cleaver, can achieve this level of accuracy (fabricated lengths are validated by inspection under a phase-contrast microscope). However, attempts to fabricate designs of the type shown in Fig. 1 revealed that the beam profile is sensitive to deviations of the refractive index profile of the GRIN lens section from the ideal parabolic shape (which is often the case in commercial GRIN fibers [8]), and we were able to confirm this in simulations (results not shown here). To experimentally validate our EDOF probe concept, we therefore chose to fabricate a probe of the type shown in Fig. 2, which avoids the use of a GRIN lens section, and we modified the design to use a phase mask consisting of 50 μm core diameter GRIN fiber (GIF50, Thorlabs, USA) with $g=6.2{\mathrm{mm}}^{-1}$ ($g$ was obtained from fits of beam profiles of test structures). In order to overfill this GRIN fiber, the beam from the SMF (SM800, Fibercore, UK) had to be expanded to a relatively large $1/e^2$ diameter of 52 μm, which resulted in a noticeable degradation of the beam quality due to the spherical aberration of the refractive lens. The achievable DOF gain in the simulation was, therefore, limited to $\sim 1.7$. The fabricated structure is shown in Figs. 3(a) and 3(b). It has dimensions of $L_{\mathrm{NCF}}=400\mathrm{\mu m}$, $L_{\mathrm{PM}}=32\mathrm{\mu m}$, and $R_{\text{Lens}}=68\mathrm{\mu m}$, and the lens was made by dipping into UV optical adhesive (Norland 81, Thorlabs, USA) with $n=1.56$. The beam profile was measured using a beam profiler (Ophir Spiricon, USA) and is shown in Fig. 3(e) (because the refractive lens was designed for water immersion, the probe tip was immersed in a drop of water on a microscope cover slip and the profile was measured in air behind the coverslip). The horizontal axis for the measured beam profile in Fig. 3(e) is rescaled by the refractive index of water for comparison with the simulated beam profile in water. The simulation is in fairly good agreement with the measured values, but the measured DOF of 980 μm is slightly lower than the simulated one. The maximum resolution is 7 μm.

 

Fig. 3. Results for the fabricated EDOF probe. (a) Fiber probe before formation of the refractive lens. The red arrow indicates the splice between the NCF and GRIN phase mask. (b) After formation of the lens. (c) and (d) OCT images of lemon pulp, log scale with 35 dB dynamic range. (e) Measured and simulated beam profile in water. The horizontal axes of plots (c), (d), and (e) are identical. The vertical green lines indicate the boundaries of the DOF.

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In order to demonstrate the achieved DOF gain, a normal refractive-lens fiber probe with the same resolution as the EDOF fiber probe was fabricated, again using the process of dipping into optical adhesive. Its dimensions are $L_{\mathrm{NCF}}=504\mathrm{\mu m}$ and $R_{\text{Lens}}=65\mathrm{\mu m}$. The measured beam profile is shown in Fig. 4(c), with the simulated curves showing good agreement with the measured values. The asymmetric axial intensity distribution is caused by the spherical aberration of the refractive lens. The DOF is 630 μm, and the maximum resolution is 7 μm.

 

Fig. 4. Results for the fabricated normal refractive-lens probe. (a) and (b) OCT images of lemon pulp, log scale with 35 dB dynamic range. (c) Measured and simulated beam profile in water. The horizontal axes of plots (a), (b), and (c) are identical. The vertical green lines indicate the boundaries of the DOF.

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The measured DOF gain of the EDOF probe compared to the normal probe is therefore 1.55. The question remains whether this DOF gain results in a visible improvement in the OCT imaging performance. This was tested by interfacing both probes with an 840 nm spectral-domain OCT (SDOCT) system, which has been described previously [2], with an axial resolution of 7 μm in water. OCT images of a lemon pulp sample were acquired with an exposure time of 5.8 μs. The sample was imaged through a microscope coverslip while the water-immersed fiber probe was scanned laterally in 1 μm steps using a motorized stage. The results are shown in Figs. 3(c) and 3(d) for the EDOF probe and in Figs. 4(a) and 4(b) for the normal probe. Two images are shown for each probe, where the second image shows the same sample region as the first image but with the distance from the probe tip to the coverslip increased by $\sim 800\mathrm{\mu m}$ in order to allow clear imaging in the far range of the probe’s DOF without the effects of attenuation at depth due to sample scattering. The regions of good image resolution correspond well with the measured and simulated DOF of the two probes, indicated by the vertical green lines. We therefore conclude that the DOF gain of 1.55 is a practically useful and visible improvement.

In summary, we have presented a simple and power-efficient technique for extending the DOF of ultrathin fiber probes for OCT using GRIN fiber phase masks that are spliced in series with the distal focusing optics and thereby require no additional fabrication processes. A DOF gain of 1.55 compared to a conventional lensed fiber probe was demonstrated in a prototype device with a lateral resolution of 7 μm. Using GRIN fibers with suitable parameters, our simulations show that a DOF gain of 2 can be obtained at the cost of a modest reduction in peak SNR of about 5 dB. Because modern preform fabrication processes can produce custom GRIN fibers with high optical quality [8], this approach could facilitate the development of high-transverse-resolution extended-DOF ultrathin needle probes for OCT.