1. Introduction

Optical coherence tomography (OCT) is a low-coherence interferometric optical imaging method that provides cross-sectional images of biological tissue [1,2]. Spectral or Fourier domain OCT (SD/FD-OCT) implementations have largely replaced time-domain OCT (TD-OCT) systems [3–6]. The main reasons for this transition are the high-speed scanning capability and the higher sensitivity of SD/FD-OCT. In addition to enhanced scan speed, SD/FD-OCT improves axial resolution by 2- to 3-times compared to TD-OCT [7,8]. Although SD/FD-OCT systems improve the performance of traditional TD-OCT systems, most systems are still subject to the fundamental limitation of Gaussian beams that the DOF, characterized by the Rayleigh length, and the lateral spot size, characterized by the beam waist, are related as [9]

To mitigate this trade-off, different solutions have been offered to maintain high lateral resolution along a relatively large DOF. This includes adaptive optics [10], dynamic focus [11–13], multi-focus [14], and DOF extension [15–20] methods. While adaptive optics can overcome this trade-off, it should be noted that such systems involve much higher system complexity, including multiple extra telescopes to relay the beam to a wavefront sensor and a deformable mirror [21]. Dynamic focusing is mostly utilized in TD-OCT setups since in this method, different depths are scanned at different times [22]. In addition, dynamic focusing techniques usually sacrifice imaging speed [11,23]. Multi-focus methods require parallel acquisition at different focal depths [12,13]. In comparison to dynamic- and multi-focus approaches, DOF extension methods have been more successful in terms of implementation simplicity and higher speed [14,15]. Alternative methods such as phase apodization and digital refocusing have also been introduced [16]. The phase apodization methods suffer from inefficiencies in illumination and collection from the extended focal region, which result in a loss of ∼ 7 dB in SNR [17,18]. Interferometric synthetic aperture, however, solves the inverse scattering problem using digital refocusing [19]. This method has multiple drawbacks. It requires expensive and rather extensive computation. It needs phase-stable acquisition during all depth profile measurements at different lateral positions, which is experimentally difficult to implement [14]. To address these limitations, the depth-encoded synthetic aperture detection scheme using annular plates has been proposed to extend the depth range [14,15]. This hardware-based adaptive optics approach requires the fabrication of custom-designed complex phase plates [20,24].

Alternatively, Bessel beams have also been used in OCT systems [25] to achieve a large DOF, while maintaining a tight focal spot area along the focal depth. Bessel beams don’t have the limitations of the Gaussian beams. Different methods of generating Bessel beams and integrating them with OCT systems have been explored. A conical-shaped axicon lens can generate a Bessel beam through the interference of two angled deflected beams of light formed by the lens. Despite these promising results, using axicons brings about limitations for OCT systems. The Bessel beams generated by axicons are not as localized as Gaussian beams. Each ring of an axicon-generated Bessel beam contains approximately the same optical power as the central spot, and thus an axicon-generated Bessel beam with N rings, for example, contains only 1/(N+1) of the total energy within the central spot, which is of interest for OCT imaging. In comparison with Gaussian beams, which contain about 86% of their total power within their full width at half maximum (FWHM), a Bessel beam generated by a typical axicon lens only maintains about 5% of the input power within the central lobe when the back aperture of the axicon is fully illuminated [26]. To achieve the largest possible DOF using an axicon-generated Bessel beam, the back aperture of the lens needs to be filled, which means that the number of concentric rings will also increase. Since these rings do not contribute to the imaging process, the fact that the vast majority of the input energy is distributed amongst them makes axicon an inefficient choice for OCT applications. Furthermore, the back-coupling of the reflected light from the sample to the detection fiber through the axicon is inherently inefficient and can cause a signal penalty of about 20 dB [7]. Overall, the axicon lens approaches suffer from ∼26 dB round-trip loss according to Lee et al. [27]. To address the inefficiencies of axicon-generated Bessel beams, Grulkowski et al. [28,29] have combined an external acousto-optic tunable lens with an objective lens and demonstrated a fast dynamic focusing. Although this method has demonstrated promising results in SD-OCT by extending DOF, it has some limitations that hinder its performance in SD-OCT systems. Significant fringe signal wash-out is reported when a continuous illumination was used which results in SNR loss [28]. Furthermore, similar to the previously mentioned methods, this method introduces an active external optical technique for DOF extension. The common aspect of all the aforementioned methods is the ex-situ operation.

Although different methods have been used to achieve an extended DOF for OCT systems, while maintaining a high lateral resolution, the aforementioned inefficiencies and drawbacks of these methods call for an alternative approach. We have recently shown that ultrasound can generate an in-situ virtual optical waveguide by modulating the local density of the medium non-invasively [30]. In this method, ultrasound pressure waves change the local density of the target medium, resulting in a dynamic local refractive index profile. It has been shown that this refractive index profile that extends through the depth of the medium follows the central lobe of a Bessel function in the radial direction surrounded by a low refractive index region. The generated refractive index pattern acts as a Gradient-index (GRIN) waveguide or lens. We have also demonstrated that we can relay an externally-focused Gaussian beam through the medium beyond the focal distance of a single external physical lens, to extend the penetration depth without compromising the spot size [31] using a cascade system of a UVTOW and a short focal-length (SF) external lens. In this work, we experimentally and theoretically demonstrate that the optical beam formed by this cascade system alleviates the trade-off between the DOF and lateral resolution compared to an external lens. Additionally, in contrast to axicon-generated Bessel beams, the optical power is well focused within the central spot, and we do not suffer from the issue of power distribution between the concentric rings. Furthermore, we show that the cascade of UVTOW and an SF lens improves the SNR roll-off of the SD-OCT system compared to the case of using a single external lens with equivalent focal distance in the sample arm. We also demonstrate that the focal length of the beam generated by this cascade system can be dynamically tuned by modifying the ultrasound parameters, i.e., ultrasound signal amplitude without having to use mechanically moving parts. One of the novel aspects of the introduced method is that the UVTOW is implemented within the target medium itself with minimal invasiveness (i.e., in-situ operation). The results of this paper inspire the design of complex optical systems consisting of a virtual optical waveguide sculpted within the target medium in tandem with external optical components to enable an extended DOF non-invasively. The UVTOW can be reconfigured in almost real-time without affecting the overall speed or signal intensity of OCT systems, thus enabling a dynamic method of focusing light. Table 1 qualitatively compares the performance of different methods that can extend DOF while maintaining high lateral resolution.

Table 1. Qualitative comparison of different methods to extend DOF in OCT systems while maintaining high lateral resolution

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2. Cascade system of UVTOW and an SF lens for rxtending DOF

Equation (1) describes the DOF of an external lens that is illuminated by a Gaussian beam. As shown, the DOF is quadratically proportional to the beam waist at the focal point ($\textrm w_0$), which means that by using a single external lens, the lateral resolution should be sacrificed to achieve a longer DOF. We have previously shown that UVTOW can relay an externally-focused Gaussian beam of light through the medium beyond the focal distance of a single external lens, to extend the penetration depth without compromising the spot size [31]. In this paper, we experimentally demonstrate that in addition to extending the focal length with minimal compromise of the spot size, the cascade system can also increase the DOF beyond the DOF of an external lens with the same effective focal length of the cascade system. Figure 1(a) shows the schematic diagram of the proposed cascade system. We have previously demonstrated that by using a cylindrical ultrasonic transducer, we can create a pressure contrast profile inside the target medium by modulating its density [30]. The density modulation creates a refractive index contrast that essentially forms a GRIN waveguide. The spatiotemporal refractive index profile of this waveguide can be expressed as [32]

 

Fig. 1. (a) The schematic diagram of beam propagation using (a) the cascade system of UVTOW and an SL external lens versus (b) an LF external lens. We should note that the two systems have the same effective focal length (${\textrm{f}_{\textrm{eff}}}$).

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A schematic diagram of how the refractive index is changing across the transverse direction to the beam propagation axis is shown in Fig. 1(a) in a blue curve. Our previous work has shown that the GRIN waveguide virtually sculpted in the target medium acts as a thick relay lens that can transfer the focus of an SF external lens deeper into the medium. Commercially available GRIN lenses usually have a reactive index profile that changes parabolically in the transverse directions [34]. The parabolic refractive index profile does not change the focused Gaussian beam DOF considerably. However, if a Gaussian beam is passed through a medium with a Bessel refractive index profile, the output beam will propagate in the form of a Bessel-like beam. This optical beam has a larger DOF compared to a Gaussian beam with the same beam waist radius (${\textrm{w}_0}$). Schematic diagrams comparing these two beams are shown in Figs. 1. In the following section, we discuss our experimental results demonstrating the difference in beam propagation between the cascade system of UVTOW and an SF lens versus an external lens with a long focal length (LF).

To investigate the light path trajectory when light travels through the cascade system of UVTOW and the SF lens versus LF lens, we employed a numerical method based on solving the Eikonal equation under a paraxial approximation [35]. For the case of the cascade system, we assumed a maximum refractive index contrast of n_max ≅ 7 × 10⁻⁴ as shown in Fig. 2(a) created by the UVTOW. Figure 2(b) shows the trajectory of light while traveling through the cascade system of UVTOW and an SF lens with an effective focal length of f₁ = 31 mm. The inset in Fig. 2(b) is a qualitative indication of the DOF of the cascade system (DOF₁) based on x-axis ray density. Figure 2(c) shows the trajectory of light while traveling through the LF lens with an effective focal length of f₂ = 55 mm. Similarly, the inset in Fig. 2(c) is a qualitative indication of the DOF of the LF lens (DOF₂). The qualitative comparison of DOF₁ and DOF₂ demonstrates the DOF extension that the cascade system provides. The DOF extension is due to the refractive index profile which is in the form of the zeroth-order Bessel function of the first kind. The focused Gaussian beam that passes through a modulated medium with such a refractive index profile converts to an elongated optical beam. We should note that, in contrast to axicons, the input beam diameter needs to be as wide as the first lobe of the Bessel profile to couple light into the waveguide as shown in Fig. 2(a). This helps with increasing the light confinement and intensity enhancement, which is a noticeable advantage over Bessel beams generated by passive optical elements such as axicons.

 

Fig. 2. (a) Cross-section of the induced refractive index profile in the medium as a result of the ultrasonic standing wave. The trajectory of light while traveling through (b) the cascade system of UVTOW and the SF lens and (c) the LF lens.

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3. Beam formation using the cascade of UVTOW and an SF lens compared to an external LF lens

To study the behavior of light propagation and compare DOF and how light intensity changes along the optical axes of the two systems, we custom-designed a characterization setup, which is schematically illustrated in Figs. 3(a) and 3(d). For the cascade system (shown in Fig. 3(a)), we used a cylindrical piezoelectric transducer (PTYY-0427, inner diameter = 38 mm, outer diameter = 40 mm, length = 20 mm; Physik Instrumente GmbH & Co. KG, Germany) that was immersed in deionized water. To prevent cavitation caused by ultrasonic pressure waves while working in water, we used a detergent solution (1% Triton X-100 Surfact-Amps Detergent Solution; Thermo Fisher Scientific Inc., USA) as a nonionic surfactant. The light source was a fiber-coupled superluminescent emitting diode (SLED) Module (EXS210033-03; Exalos Co., Switzerland) with a measured linewidth of Δλ = 8 nm centered at λ₀ = 650 nm. The piezoelectric transducer was driven by a sinusoidal electric signal of a frequency of 2.455 MHz, generated by a dual-channel function generator (SDG6022X; Siglent Inc., USA) and amplified using an RF power amplifier (ENI 2100L; Electronics & Innovation, Ltd., USA). The amplified signal amplitude was 16 V _pp. The light intensity is modulated using a diode module current driver (CCS-std; Aerodiode Co., France). The SLED module driving signal was a square wave with the same frequency as the ultrasound signal and the signal duty cycle was 10%. Pulsed illumination has been proven to be beneficial for SNR enhancement in OCT applications as it helps to mitigate the lateral scanning induced interference fringe washout [36]. Here, the main reason behind pulsed illumination is that we need to illuminate the sample when the ultrasound standing wave is at its maximum. We have previously shown that the input light needs to be modulated with a pulsed signal and synchronized with the transducer driving signal so that light interacts with the pressure pattern only when the central pressure peak is positive and forms a focusing GRIN lens [35]. This method has also been used in external tunable acoustic lenses as well [37]. The input light was collimated using an achromatic fiber-port collimator (PAF2A-11B; Thorlabs Inc., USA). The input Gaussian beam diameter (∼2.25 mm) was the same in all the comparisons between the two systems throughout this work. For the cascade system, an achromatic lens (AC254-030-A-ML; Thorlabs Inc., USA) with a focal length (FL) of 30 mm (in air) was used to create a focused Gaussian beam that couples into the ultrasonically formed GRIN waveguide. The actual FL of the SF lens was measured to be 31 mm. For the second setup illustrated in Fig. 3(d), a Gaussian beam was generated by an achromatic lens (AC254-050-A-ML; Thorlabs Inc., USA) with an FL of 50 mm (in air). We should note that the actual FL of the system was measured to be 55 mm; this was the physical path length, some of which was in air and some in water (not to be confused with the optical path length). This elongation of the FL is due to the fact that light partially travels in water, which has a larger refractive index than air, leading to a longer effective FL. We designed both optical systems (Figs. 3(a) and 3(d)) to have the same effective FL. To experimentally show the beam propagation in the two arrangements, we used an image acquisition system composed of a monochromatic CCD camera (BFLY-U3-50H5M-C; Teledyne FLIR LLC, USA) and a zoom lens (VZM 600i Zoom Imaging Lens; Edmund Optics Co., USA). The image acquisition system was attached to a vertical translation stage (LTS300; Thorlabs Inc., USA).

 

Fig. 3. (a) The schematic diagram of the focused beam propagation for the cascade system of UVTOW and an SF lens (FL = 30 mm in air). Set of axial cross-sectional images over an axial range of 4 mm (from -2 mm to +2 mm with respect to the focal point (z = 0 µm) for (b) the cascade system of UVTOW and an SF lens (FL = 30 mm in air) and (c) an LF external lens (FL = 50 mm in air). The scale bar is 25 µm in (b) and (c). (d) The schematic diagram of the focused beam propagation for an LF external lens (FL = 50 mm in air).

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Figures 3(b) and 3(c) depict cross-sectional images acquired by the two systems along the optical axis for an axial range of 4 mm. Figure 3(b) shows the cross-sectional images using the cascade system of UVTOW and an SF external lens with an FL of 30 mm (in air). Figure 3(c) shows a set of axial light intensity cross-sections of a focused Gaussian beam generated by an external lens with an FL of 50 mm (in air). The qualitative comparison between these two sets of cross-sectional images clearly shows an extended DOF achieved using the cascade system. The beam formed by the cascade system (Fig. 3(b)) has minor rings around the central focal region. This is due to the aberrations of the refractive index profile that follows a Bessel function. A similar phenomenon has also been previously observed in external tunable acoustic gradient (TAG) lenses [38]. If the refractive index profile of the ultrasonically sculpted optical waveguide was a parabolic function, these focused beams of light would be aberration-free.

To quantify the enhancement of DOF, we plotted the cross-sectional intensity profile along the lateral direction (i.e., the x-axis shown in Figs. 3) at different depths. The waterfall cross-sectional intensity plot illustrated in Fig. 4(a) shows a rapid drop in intensity as the distance from the focal point is increased. This is the manifestation of the Rayleigh length limitation of focused Gaussian beams. However, the corresponding intensity waterfall plot versus depth shown in Fig. 4(b) demonstrates that the optical beam created by the cascade system of UVTOW and an SF lens has a larger DOF. Additionally, the intensity drop versus depth in Fig. 4(b) is slower compared to Fig. 4(a). Figure 4(c) shows how the FWHM of the focused beams changes at different depths. We use the definition of DOF as twice the Rayleigh length for Gaussian beams. The DOF of the Gaussian beam generated by the LF external length was ∼1.7 mm (blue curve in Fig. 4(c)). In contrast, the optical beam generated by the cascade system of UVTOW and SF lens has a DOF of more than 4 mm (black curve in Fig. 4(c)). Although the smallest FWHM of the focused beam in the case of the LF lens is slightly better than that of the beam formed by the cascade system, in our recent work, we have experimentally demonstrated that the FWHM of this beam can be changed by changing either the frequency of ultrasound or the distance between the SF lens and the ultrasonic transducer [31]. It is also worthwhile to compare the intensity drop of the two beams as the distance from the maximum intensity point on the optical axis increases. Figure 4(d) demonstrates that the beam intensity generated by the LF lens drops considerably more rapidly compared to the beam that was generated using the cascade system. The intensity versus depth plots of the two systems are shown in blue and black curves, respectively. Figure 4(d) shows the average rate of intensity drop versus depth in the case of the LF external lens is 7-fold faster than the cascade system.

 

Fig. 4. The radial cross-section of the confined beam of light generated by (a) the cascade system of UVTOW and an SF lens (FL = 30 mm in air) and (b) an LF external lens (FL = 50 mm in air). (c) Comparison of the spot size (FWHM) of the beams generated by the two systems versus depth. (d) Comparison of the normalized intensity of the beams generated by the two systems versus depth.

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The extended DOF while preserving the beam intensity along DOF as experimentally demonstrated in Figs. 4(c) and 4(d), can find immediate applications in imaging modalities where extended DOF is desired.

In the following sections, we present how combining the cascade system of UVTOW and an SF lens enhances the SD-OCT system's performance compared to external lenses with LFs.

4. SD-OCT system performance comparison of the cascade system of UVTOW and an SF lens versus an LF lens

We designed and implemented the fiber-optic SD-OCT system in Michelson configuration combined with the cascade system of UVTOW and an SF lens. For comparison, we replaced the cascade system with a single LF lens (FL = 50 mm in air) that can focus light at the same depth as the cascade system. To make the comparison with minimum changes to the setup, we turned off the ultrasonic excitation and replaced the SF lens (FL = 30 mm in air) with the LF lens. The experimental setup illustrated schematically in Fig. (5) has four major components, i.e.: (1) Light source and coupling, (2) Spectrometer, (3) Reference arm, and (4) Sample arm.

First, for the light source and beam splitting segment, the light source that was used is the same as described in section 3 (${\lambda _0}$ = 650 nm, measured bandwidth $\Delta \lambda $ = 8 nm). The input light is modulated using a commercial current driver (CCS-std; Aerodiode Co., France). The SLED driving signal was a square wave with the same frequency as the ultrasound signal ($\textrm{f}$ = 2.455 MHz) and the signal duty cycle was 10%. The light pulse was synchronized with ultrasound signal so that the sample is illuminated when the ultrasonic pressure is at its maximum. The modulated light was split into sample and reference arms using a 10:90 fiber coupler (TW670R2A2; Thorlabs Inc., USA). The polarization mismatch between the sample and reference arms affects the fiber-based OCT performance [39]. To adjust the polarization, we used a fiber polarization controller (FPC030; Thorlabs Inc., USA) on the branch of the fiber coupler that leads to the reference arm. For the reference arm, a collimated beam of light (using an achromatic fiber-port collimator (PAF2A-11B shown with L₁ in Fig. (5); Thorlabs Inc., USA)) was launched toward a mounted continuously variable neutral-density (ND) filter (NDC-25C-4M; Thorlabs Inc., USA) to control the reference arm's light intensity. A container of the length L = 40 mm filled with water was included in the reference arm to balance the phase delay and dispersion of water in the sample arm. An optical focusing element (achromatic lens with an FL = 30 mm shown with L₃ in Fig. (5) - AC254-030-A-ML; Thorlabs Inc., USA) was placed in the reference arm to avoid a large dispersion mismatch. Two identical mirrors (PF10-03-P01-10; Thorlabs Inc., USA) were used in both the reference arm and the sample arm for characterization purposes. To characterize the OCT SNR roll-off as a function of depth, we connected both the reference and sample arm mirrors to traveling stages (LTS150; Thorlabs Inc., USA). For the sample arm, to compare the systems performances of an LF lens (L₂ in Fig. (5)) versus the cascade of UVTOW and an SF lens (L₂ in Fig. (5)), we used the same configurations explained in section 3. For the detection arm, the custom-built spectrometer was attached to the detection arm of the interferometer. We used an achromatic fiber collimator (C80APC-A shown with L₄ in Fig. (5); Thorlabs Inc., USA) that collimated and expanded the interference beam; the free-space outgoing beam diameter was measured at ∼20 mm. The interference was spectrally separated with a diffraction grating (1000 l/mm @ 600 nm; Wasatch Photonics Inc., USA) and then illuminated on an achromatic lens (L₅ in Fig. 5) with an FL of ${\textrm{L}_\textrm{f}}$ = 180 mm (AC508-180-A-ML; Thorlabs Inc., USA) and was focused on a line-scan CMOS camera. The line-scan CMOS camera (spL4096-140 km, 4096 pixels; Basler AG Co., Germany) was operating at the single-line scan rate of 70 kHz (exposure time 100 µs). We should note that since the camera exposure time is much larger than the light pulse duration, each line scan contains ∼244 light pulses (shown in Fig. 5). The nominal axial resolution of the system was 23 µm. The sensitivity of the system was 102 dB when the sample was illuminated with a beam of 0.2 mW optical power.

 

Fig. 5. Schematic of the implemented SD-OCT setup.

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Using the experimental setup illustrated in Fig. ( 5), in the following subsections, we compare the performance of the SD-OCT system in two scenarios in the sample arm: (1) an LF external lens and (2) a cascade system of UVTOW and an SF external lens. We should note that the effective FLs of both systems are the same.

4.1 SNR roll-off with depth

SD/FD-OCT systems suffer from a depth-dependent sensitivity (or SNR) loss [40]. This limitation is inherent to these imaging techniques and is rooted in optical resolution limits of the spectrometer, finite pixel width, aliasing at high spatial frequencies, and inter-pixel cross-talk in the spectrometer [41–43]. The overall sensitivity profile is determined by a combination of the fundamental depth-dependent sensitivity loss and the effect of focus [44]; meaning, the SNR roll-off is exacerbated as the focused beam FWHM increases with depth [45]. The optical beam with extended DOF generated by the cascade system of UVTOW reduces the SNR roll-off rate versus depth. We attribute this behavior to the much slower decline of the focused beam FWHM versus depth that the cascade system provides compared to the Gaussian beam generated by an LF external lens as experimentally demonstrated in Fig. 4(c). In particular, the axial point spread function (PSF) directly impacts the SNR of the OCT signal [46]. The importance of the axial PSF is more pronounced as the depth increases (i.e., the distance from the nominal focal point increases). The rapid enlargement of the focused beam FWHM with depth hence the loss of intensity using conventional focusing optical elements is a limiting factor in determining the ultimate maximum depth of imaging. Therefore, enhancing the DOF is essential to lift this fundamental limitation for both SD/FD-OCT systems.

To experimentally demonstrate the enhancement of SD-OCT performance by reducing the SNR roll-off rate with depth using the cascade system and the comparison with an LF external lens, we used a perfect reflector (i.e., a silver-coated mirror) in the sample arm and measured the interference signal. The OCT interference intensity A-scans involved spectral resampling, linear spline interpolation, and a fast Fourier transform (FFT) [47]. We acquired OCT interference intensity images at different depths with respect to the focal point of each system (We define the focal point where the sample arm signal intensity is maximum). A schematic diagram of the sample arm mirror positions is shown in Fig. 6(a). The OCT signal acquisition was done by collecting the CMOS line-scan camera (camera exposure time = 100 µs) data through a frame grabber device (PCIe-1437; National Instruments Co., USA). The sample arm mirror was moved with a step size of 100 µm in water. The maximum signal intensity is where the delay between the sample arm and the reference arm is zero. Figure 6(b) shows the OCT interference signal intensity roll-off as a function of depth when the LF lens (FL = 50 mm in air) was employed in the sample arm. We plotted the OCT interference signal intensity versus the optical path (optical path length = refractive index of water × geometrical length) distance from the zero-delay point. Figure 6(b) shows a total signal intensity drop of 16 dB within an actual range of 1 mm in water. Figure 6(c) shows the OCT interference signal intensity roll-off as a function of depth when the cascade system of UVTOW and the SF lens (FL = 30 mm in air) was employed in the sample arm. We observe an OCT signal intensity drop of 8 dB over the same depth range as shown in Fig. 6(c). This shows that the DOF extension provided by the cascade system enhances the OCT signal intensity by about 8 dB over an actual depth of 1 mm in water. This enhancement is illustrated in Fig. 6(d). By dividing the maximum signal intensity by the noise floor level, we calculated the SNR at different depths. The blue curve in Fig. 6(d) shows the inherent SNR roll-off versus depth. This curve was obtained by moving the reference arm mirror while the sample arm mirror was stationary. The red and black curves show the SNR roll-offs versus depths using the cascade system of UVTOW and SF lens and LF lens, respectively. Comparing the black and red curves in Fig. 6(d) demonstrates that the exacerbation of the SNR roll-off due to the limited Rayleigh length of focused Gaussian beams generated by external lenses (the black curve) is reduced.

 

Fig. 6. (a) Schematic diagram of the sample arm mirror movement to obtain signal intensity roll-off versus depth. The dashed line shows the relative positions of the sample arm mirror as we collected A-line scans. The step size of the sample arm mirror movement in the axial direction was 100 µm. The OCT interference signal intensity roll-off versus depth when (b) An LF lens (FL = 50 mm in air) was employed in the sample arm, (c) the cascade system of UVTOW and the SF lens (FL = 30 mm in air) was employed in the sample arm. (d) SNR roll-off versus depth. The blue curve is the inherent SNR roll-of of this SD-OCT system and was obtained by moving the reference arm mirror. The red and black curves are the SNR roll-offs that were obtained using the cascade system of UVTOW and SF lens and LF lens, respectively.

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4.2 Lateral resolution

The lateral resolution of the SD-OCT system with both the external LF lens and the cascade of UVTOW and the SF lens was quantified by performing A-scans of the sharp-edge rectangular features on a 1-inch Negative 1951 USAF Test Target (R1DS1N; Thorlabs Inc., USA). For characterizing the lateral resolution of this system, we replaced the sample arm mirror (shown in Fig. (5)) with the USAF target. The A-line scans were acquired while the largest square shape (with dimensions of 557 µm × 557 µm) on the USAF target shown in Fig. 7(a), was moved laterally (along the x-axis illustrated in Fig. (5)) using a traveling stage (LTS150; Thorlabs Inc., USA) over the focal point of the beam on the sample arm. On this target, the dark background region is reflective and the areas shown in white are transmissive. The lateral speed of the stage was 100 µm/s. The OCT interference signal intensities acquired by the A-line scans are plotted in Fig. 7(b). The black and blue curves were obtained using the cascade system of UVTOW and SF lens and LF lens in the sample arm, respectively. In order to quantify the lateral resolution, we calculated the derivative of the OCT interference signal intensity with respect to the lateral axis (red dashed rectangle in Fig. 7(b)). The derivative function is plotted in Fig. 7(c). The FWHM of the derivative of the OCT signal shows the lateral resolution of the system. In other words, the curvature of the edge profile changes, and therefore, the second derivative should have an extremum and thus the first derivative will be a “narrow” lineshape curve, the width of which is the resolution. The calculated lateral resolution when the LF lens was employed in the sample arm was 12 µm (blue curve in Fig. 7(c)). Similarly, the calculated lateral resolution when the cascade system of UVTOW and SF lens was employed in the sample arm was 15 µm (black curve in Fig. 7(c)). We should emphasize that the slight discrepancy between the FWHM of the focused beams using an LF lens versus the cascade system of UVTOW and an SF lens would not significantly change the comparison between DOF values and the extension obtained using the cascade system involving UVTOW. For example, if we assume an LF with a spot size of 15 um that matches the spot size of the cascade system, the DoF of the LF lens would be 2.65 mm, which is still much smaller than that of the cascade system (i.e., >4 mm).

 

Fig. 7. (a) The 1951 USAF target used for lateral resolution characterization. (b) The OCT interference signal intensities acquired by the A-line scans. (c) The derivative of the OCT interference signal intensity with respect to the lateral axis (The derivative is performed over the x-axis range shown with the red dashed rectangle). In both figures (b) and (c), the black and blue curves were obtained using the cascade system of UVTOW and SF lens, and LF lens in the sample arm, respectively.

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Since OCT imaging systems are mainly used to provide depth information, it is crucial to characterize the performance of these systems along the depth of imaging. In subsection 4.1, we characterized the SNR roll-off with depth. Here, we present a thorough comparison between the two systems based on lateral resolution. A-line scans were acquired while the three parallel vertical lines (group 2 of element 2 on the USAF target shown in Fig. 7(a)) were moved laterally (along the x-axis illustrated in Fig. (5)) over the focal point of the beam on the sample arm at different axial positions (along z-axis illustrated in Fig. (5)). The lateral speed of the stage was 100 µm/s. The OCT interference signal intensities were acquired at different positions along the z-axis with a step size of 200 µm. Figures 8(a) and (b) show the normalized OCT interference signal amplitude while three parallel lines were swept laterally over the focal region of the optical beams formed by each system. Similar to the procedure in Figs. 7(b) and 7(c) to calculate the lateral resolution, we calculate the derivative of the OCT interference signal intensities (Figs. 8(a) and 8(b)) with respect to the lateral axis (x-axis). Figures 8(c) and 8(d) show the OCT interference signal derivatives. The FWHMs of the sharp transition derivative regions determine the lateral resolution at different depths. Since we have six sharp transitions (See Group 2 of element 2 on the USAF target shown in Fig. 7(a)), we calculated the means and standard deviations of the FWHMs and plotted them in Fig. 8(e).

 

Fig. 8. Normalized OCT interference signal amplitude versus lateral direction for different depths using (a) the LF lens and (b) the cascade system of UVTOW and SF lens in the sample arm. (c) and (d) The normalized derivative of the OCT interference signals shown in (a) and (b) for lateral resolution versus depth characterization. (e) Lateral resolution versus depth characterization. The black and blue curves were obtained using the cascade system of UVTOW and SF lens and LF lens in the sample arm, respectively.

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It is worth noting that there is a discrepancy between the behavior of lateral resolution in the OCT system and what we characterized in Section 3 for the cascade system while the LF lens behavior remains consistent. In particular, by comparing Fig. 4(c), which shows the lateral resolution versus depth behavior of the cascade system in the transmission mode, and Fig. 8(e), which shows the lateral resolution versus depth behavior of the cascade system in the reflection mode, we observed degradation in the lateral resolution versus depth behavior of the cascade system of UVTOW and SF lens while we moved from transmission to reflection configuration. We attribute this degradation to the non-reciprocity of the forward and reflected beam paths when working with the optical beams generated by the cascade system. The optical beams generated by the cascade system of UVTOW and SF lens suffer from a lack of reciprocity in the forward and reflected paths. This is arising from the nature of the Bessel beams, where rays of focused light do not converge to a point. The rays converge along the DOF region at different axial positions as illustrated in the ray-tracing simulation result shown in Fig. 2(b). In contrast, Gaussian beams generated by a conventional lens mostly travel back within the same cone of illumination after reflecting off of a perfect reflector surface. Therefore, we have a fairly high level of reciprocity in the forward and reflected beam paths while working with Gaussian beams. The indirect manifestation of this lack of reciprocity in the case of the cascade system of UVTOW and SF lens is demonstrated by comparing Fig. 4(c) and Fig. 8(e). One remedy to address the lack of reciprocity that degrades the performance of the cascade system is to decouple the illumination (forward) and detection (reflected) paths in the sample arm. Previously, it has been shown that decoupling the illumination and detection paths can eliminate this problem when an axicon is used in the sample arm for extending DOF [17].

4.3 Axial resolution

One of the characteristics of OCT imaging systems that differentiates this interferometric imaging technique from other traditional imaging modalities such as microscopy is the decoupling of axial resolution from lateral resolution. In OCT systems, the axial resolution is solely determined by the source central wavelength (${\lambda _0}$) and its spectral bandwidth ($\Delta \lambda $) and can be expressed as [48]

The calculated axial resolution for the implemented SD-OCT system was 23.3 µm. Figure 9 shows the PSF of the axial resolution using the cascade system (shown with the black curve) and the LF lens (shown with the blue curve) in the sample arm. The axial resolution should remain constant throughout the depth of imaging. We calculated the axial resolution of the two systems by acquiring A-line scans (shown in Figs. 6(b) and 6(c)) and calculating the FWHM of the OCT interference SNR. The axial resolutions were 24 µm and 27 µm for the cascade system of UVTOW and SF lens and LF lens, respectively.

 

Fig. 9. PSF of the axial resolution when the SLED has a center wavelength of 650 nm and a measured bandwidth of 8 nm. The black and blue curves were obtained using the cascade system of UVTOW and SF lens and LF lens in the sample arm, respectively.

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4.4 Reconfigurability

One of the advantages of using a cascade system of UVTOW and an SF lens is the ability to tune the focal length of the formed optical beam without any mechanical movement. We have previously shown that by changing the amplitude of the ultrasound signal (i.e., changing the electric potential applied to the piezoelectric transducer), we can scan the effective focal length of the cascade system [35]. We leveraged this capability in our SD-OCT system to actively tune the focal length of the extended DOF beam formed by the cascade system by changing the ultrasound intensity. We should note that this tunability can be performed very fast, almost at the frequency of ultrasound (${\textrm{f}_0}$ = 2.455 MHz) which is orders of magnitude faster than commonly used dynamic focusing methods based on adaptive optics [49–51]. We experimentally demonstrated tunability by applying different voltage levels to the piezoelectric transducer. Figures 10(a-c) show the effective focal lengths of the cascade systems when the piezoelectric transducer was driven at 22 V _pp, 16 V _pp, and 14 V _pp, which resulted in effective focal lengths of 53 mm, 55 mm, and 57 mm, respectively, To characterize the SNR roll-off of these axially-shifted optical beams, we have performed the same sample arm mirror scanning procedure performed to acquire Fig. 6(d) at these three focal lengths. Figure 9(d) shows the SNR roll-off of these axially shifted beams versus optical path length from point o (Point O is the curved surface of the SF lens (L₂) shown in Fig. 5). We should note that the SNR roll-off rate is faster at shallower depths (See the blue curve in Fig. 10(d)). The main reason is that as the ultrasound signal amplitude increases, the DOF of the generated optical beam decreases, and the SNR roll-off due to the decreased DOF is more pronounced.

 

Fig. 10. Schematic diagram of the axial scanning of the effective focal length of the cascade system when the piezoelectric transducer was driven at (a) 22 V_pp, (b) 16 V_pp, and (c) 14 V_pp. The effective focal lengths at the aforementioned voltage levels were measured to be 53 mm, 55 mm, and 57 mm. (d) SNR roll-off versus optical path length (The optical path length is calculated from point O as shown in Fig. 5) for effective focal lengths of 53 mm, 55 mm, and 57 mm.

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5. B-Scan imaging quality comparison

Thus far, we have thoroughly characterized the SD-OCT system combined with the cascade system of UVTOW and an SF lens. We have shown the extended DOF provided by the cascade system. Here, to demonstrate the DOF extension in SD-OCT B-scan imaging, we used a metallic mesh (stainless steel wire mesh, McNichols Co., USA) as the object in the sample arm. The mesh wire diameter was 35 µm and the distance between consecutive wires was 43 µm. The mesh was embedded in a 1% agar (A5306, Sigma-Aldrich Co., USA) gel sample. The agar sample was tilted by 30°C and was translated laterally over the focused beam in the sample arm using a traveling stage as shown in Fig. 11(a). This sample was placed instead of the sample arm mirror in Fig. 5. As the sample was moving over the focal spot, we acquired A-line scans at each point to obtain B-scans. The lateral speed of the linear stage was 100 µm/s. The camera exposure time was 500 µs. Figures 11(b) and 11(c) show the B-scan images of the metallic mesh strings. We can see that in Fig. 11(c), due to the limited DOF of the focused Gaussian beam generated by the LF lens, the mesh strings identified by the red arrows are out of focus. In contrast, the same mesh strings were in focus when we used the optical beam generated by the cascade system of UVTOW and SF lens in the sample arm. The comparison between Figs. 11(b) and 11(c) demonstrate the benefit of the extended DOF provided by the cascade system.

 

Fig. 11. (a) The schematic diagram of the imaged sample. The sample consisted of a metallic wire mesh embedded in an agar gel. DOF comparison: The B-scan images of the metallic mesh when we used (b) the LF lens and (c) the cascade system of UVTOW and SF lens in the sample arm.

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6. Conclusion

In conclusion, we have demonstrated that using a cascade system of the ultrasonic virtual tunable optical waveguide (UVTOW) and a short focal-length lens can provide both a larger DOF and a comparable focused beam diameter compared to an external lens that has the same effective focal length. This DOF extension is due to the formation of the optical waveguide through the medium, which has a radial refractive index profile that follows a Bessel function that keeps light confined through the medium. We have demonstrated that the fast SNR roll-off due to the limited DOF of the focused Gaussian beam can be mitigated using this cascade system. In addition, we have shown that, without the need for any mechanical movement, we can tune the focal length of the formed optical beam, simply by changing the ultrasound amplitude. Finally, we have demonstrated the DOF extension in B-scan images when the cascade system is used in the sample arm.

Another benefit of using this cascade system in SD-OCT systems is the ability of such a system in enhancing light throughput in scattering media. We have recently demonstrated light throughput enhancement achieved by using ultrasonically sculpted virtual optical waveguides to focus light inside a turbid medium compared to other light focusing methods using external optical devices such as optical lenses [52]. These findings highlight the ability of virtual optical waveguides to both focus ballistic light and recycle and refocus scattered light. The ability of recycling scattered photons can further enhance the SNR of OCT images taken from scattering samples. The benefit of light throughput enhancement and its effect on improving the OCT performance can be studied in the future. In this paper, we only showed the geometrical advantages of UVTOW when combined with an external lens. It has been shown that the DOF can be extended by dynamically changing the effective focal length using a combination of an external tunable acoustic lens (i.e., TAG lens) and an objective lens [28,29,53]. In this method, the effective focal length of the objective lens is changed as the input beam angle is changed. However, it should be noted that the focal spot size will also change at different focal lengths. We note that the smallest diffraction-limited spot size can only be achieved when a collimated beam of light fills the back aperture of the objective parallel to the optical axis. While this method based on cascading a TAG lens and an objective lens is effective in extending DOF, it is fundamentally different from our cascade system design, in which, the UVTOW is located after the external SF lens and guides and projects light into the medium, thus we can benefit from the extended DOF of the UVTOW. Another notable difference is the in-situ operation of our method, which allows forming the ultrasound waveguide inside the target medium, thus shaping the focused beam of light in situ. Furthermore, a key advantage of our design is that in the reflection path, the SF lens interfaces with the optical fiber, thus providing much higher back-coupling efficiency into the single-mode fiber compared to the TAG lens used in the previous implementation (Table 1) [28]. The extended DOF that we can achieve using our cascade system is because of the sculpted optical waveguide with a refractive index profile that follows a 0^th-order Bessel function of the first kind along the radial direction. This is achieved at the cost of higher level of aberrations. In the case of SD-OCT, the image is obtained by raster scanning the desired field of view. Therefore, each measured datapoint represents one pixel of the reconstructed image and small aberrations will not affect the quality of the reconstructed image.

One of the challenges of using the cascade system of a lens and UVTOW is the optical beam follows a different path in reflected direction compared to the forward (illumination) direction, that degrades the system performance in terms of lateral resolution (Discussed in subsection 4.2). We have shown the high lateral resolution of the generated optical beam is maintained over a larger depth range in the transmission mode compared to the reflection mode. One of the potential solutions to mitigate this issue is to decouple the illumination and detection paths in the sample arm.

The results in this paper were obtained using a cylindrical ultrasonic transducer. The closed-cavity cylindrical transducer will limit the application of this technique to scenarios where the target tissue can be enclosed within the cylindrical cavity. It has been shown that ultrasonic virtual waveguides can also be formed using traveling-wave ultrasonic waves, which can be launched into the tissue from the surface [54], thus making the integration with OCT more practical for biological applications. Furthermore, in this paper, the sample is scanned in the lateral direction by moving the sample using an XY-stage. An interesting capability of UVTOW is reconfigurability, which enables steering the beam of light. We have previously shown that reconfigurable patterns of light can be formed in the target medium using an ultrasonic phased array [32,55]. These patterns of light can be used, in the future, to scan the sample in the lateral direction without any moving mechanical parts and perform OCT scanning. This will be an additional advantage of using UVTOW in OCT systems. Overall, the UVTOW can be used in SD-OCT systems to enhance the performance of this imaging method.