We develop high-resolution optical coherence tomography (OCT) system with high-speed acousto-optic tunable lens. Stroboscopic pulsed illumination is used for the first time to perform time-resolved OCT imaging with acousto-optic tunable focusing. The operation of ultrahigh-speed tunable acousto-optic lens is demonstrated theoretically and experimentally. Focal position tuning at MHz frequency range is experimentally shown in the imaging system leading to OCT images with extended depth of focus. Imaging with active optical elements is helpful for improvement of photon collection efficiency, depth of focus and enhancement of the image quality.
© 2014 Optical Society of America
Optical coherence tomography (OCT) and its microscopic version (optical coherence microscopy, OCM) form the modalities that enable acquisition of cross-sectional and volumetric data sets and reveal microstructural information on the objects [1, 2]. Different generations of OCT instruments were developed to study objects with depth ranges spanning from millimeters to few centimeters [3–6]. Unique features of the OCT technique enabled its numerous applications in biology, medicine and industry [7, 8].
Resolution is the essential factor influencing the image quality in any imaging technique. Axial resolution in OCT is governed by the wavenumber range (light source bandwidth) recorded by the detection unit. Transverse resolution is determined by the beam spot size incident on the object, and it depends on the optical design of the sample (object) arm. Another important factor influencing the image quality in OCT / OCM is the depth of focus (DOF). In a standard configuration, the beam waist should not change considerably over the entire sampled axial range. In other words, the scanning beam Rayleigh range 2zR (depth of focus) should be at least of the order of the depth range zmax defined by the detection scheme. As a consequence, high-resolution OCT / OCM systems can effectively image relatively shallow structures since tight light focusing makes collection the light from the depths beyond DOF inefficient.
Novel applications of OCT are also characterized by long depth ranges and consequently have special requirements to perform optimized imaging . Unlike OCM, long range OCT utilizes weakly focused beams where the long Rayleigh range is achieved at the expense of transverse resolution. Therefore, both high-resolution OCM and long-range OCT will benefit from novel approaches of depth of focus extension.
Several methods have been implemented to optimize the performance of axial imaging. The easiest solution involves mechanical movement of the sample with respect to the objective lens (and vice versa) [9, 10]. More sophisticated approaches are based on light beam engineering techniques and include utilization of: multi-beam scanning [11, 12], microelectromechanical system technology , non-diffractive beams [14–17], adaptive focus [18, 19] etc. Improved transverse resolution throughout the imaging depth can be also achieved with dynamic focusing using tunable lenses. The technology providing variable focus is based on the electro-optical, electromechanical, thermo-optical or acousto-mechanical effects [20–28]. Recently, computational imaging techniques have been developed for depth of focus extension [29–32].
Laser beam control can be also obtained by the interaction of light with ultrasound [33–37]. The acoustic wave travelling in the medium causes modulation of its optical properties. Consequently, when the light propagates through such a medium, one can observe spatial, temporal and spectral modulations of light. Therefore, the acousto-optic phenomenon has been applied in many photonic technologies involving modulation, beam steering (deflection), filtering, frequency shifting and spectrometry .
The aim of this study is to apply high-resolution OCT / OCM system with high-speed acousto-optic tunable lens in biomedical imaging. For the first time we integrated stroboscopic (pulsed) illumination and active optical element in the OCT system to perform microscopic OCT imaging with dynamic focusing. This approach enabled obtaining microscopic OCT images with extended focus. We also characterized the operation of the designed acousto-optic cell theoretically and experimentally, and we assessed the impact of acousto-optic dynamic focusing on the OCT performance.
2. Theoretical description of tunable acousto-optic cell operation
The acousto-optic device is always composed of the following elements: (i) acoustic (ultrasonic) wave propagating in (ii) the acoustic medium, and (iii) light (electromagnetic) wave. The ultrasound is launched into the medium by a piezoelectric transducer; in our case the transducer has the shape of a hollow cylinder of the length L; Fig. 1(a). The cylinder is closed at both faces with glass windows and filled with water (acoustic medium), thus forming the acousto-optic cell (AOC). Both inner and outer surfaces of the cell are covered with electrode material (e.g. silver). Therefore, wall thickness vibrations occur when the voltage is applied to both surfaces, which results in the spatio-temporal modulation of the density of acoustic medium; Fig. 1(b).
Accordingly, specific distribution of the acoustic pressure due to compressions and rarefactions of the medium particles is generated inside the cell. In the vibrating cylinder, the axisymmetric ultrasonic field p(r, t) is described by the Bessel function of the first kind of zero order:Equation (1) indicates that the highest amplitude can be found at the axis of the transducer (focusing of ultrasound), as also shown in Fig. 1(c). Linear case of the acousto-optic effect assumes that the pressure wave inside the medium causes proportional modulation of the optical properties of the medium. This phenomenon can be expressed in terms of refractive index of the medium n(r, t):
The light beam propagates through the optically transparent medium of the AOC. Assuming that the collimated Gaussian beam is incident on the ultrasound, the optical field can be therefore described by:
Determination of both amplitude and phase of the light field at the exit plane of the AOC (z = L) is a key issue in the theoretical description of the acousto-optic effect. From the theoretical point of view, the problem is actually related to the light propagation in the inhomogeneous medium. Various analytical and numerical solutions have been developed to describe light diffraction on ultrasound . However, we use successive diffraction model (SDM), which is a beam propagation method (BPM) modified to the case of inhomogeneous medium [40, 41].
In SDM, specific approach must be taken to account for optical inhomogeneity of the medium, i.e. the entire interaction length L is divided into several layers, each having the thickness Δz = L/M, where M is the number of layers; Fig. 1(b). The number of layers should be high enough to treat each layer as a pure phase grating. It has been proved that this requirement is fulfilled when for each layer :Eq. (5). When the light propagation is calculated, the signal is Fourier-transformed back to Cartesian (x, y) space. Then we take into account that the layer acts as the phase object:Eq. (6) refers to phase factor due to the presence of the acoustic field. Later on, the optical field in the exit plane of the layer becomes the input field of the next layer. The above-mentioned steps are repeated until the exit plane (z = L) of the ultrasound field is achieved.
The same technique can be used to simulate beam propagation through the optical elements behind the AOC.
3. Experimental set-up
The experimental configurations used in this study are shown in Fig. 2. The tunable acousto-optic lens (AOL) is composed of two elements: active AOC (vibrating shell) and passive offset lens OL of the focal length fOL. The set-up to characterize the AOL is demonstrated in Fig. 2(a). The light was emitted by a femtosecond Ti:sapphire laser (Fusion, Femtolasers GmbH, Austria). The light intensity was later modulated using electro-optic modulator (LM0202; LINOS, Qioptiq Photonics GmbH, Germany). The light was then directed to the AOC through fiber coupler. Collimated Gaussian light beam of the width 2w = 800 μm was incident on the AOC. The piezoelectric transducer (Physik Instrumente GmbH) of the length L = 50 mm and wall thickness 2 mm (outer diameter 30 mm, inner diameter 26 mm) that was closed at both faces with optical windows and filled with water to provide effective ultrasound coupling. The cell was excited by a cosine signal of frequency of 1.042 MHz from dual-channel function generator (TGA 12102; Thurlby Thandar Instruments Ltd, UK).
It is important to note that the mutual relation between light beam width and ultrasonic wave frequency should be properly chosen in order to obtain the desired effect of acousto-optic interaction. The width of the light beam (2w = 800 μm) incident on acoustic field should not exceed the first nodal diameter of standing cylindrical ultrasonic wave (1.12 mm). Otherwise, light diffraction would appear that would manifest in separated diffraction orders (rings). This relation is presented in Fig. 1(c).
The pulsed signal of the same frequency and variable duty cycle from the second channel of the generator was used to drive the electro-optic modulator (EOM). We excited the EOM by the signal with either 100% or 5.5% (pulses of the width of 30 ns) duty cycle. Additionally, we utilized digital delay generator (DG 645, Stanford Research Systems Inc., USA) to control the time delay τ between signal driving the electro-optic modulator and the transducer; Fig. 2(a). This experimental solution enabled stroboscopic illumination synchronized with ultrasound at variable phase of the ultrasonic wave, and made the studies of highly dynamical systems such as the AOL easier (time-resolved measurements). The illumination schemes used in this study are presented in Fig. 2(c).
Other port of the fiber coupler was used to monitor the light intensity illuminating the AOL. Signal from the photodetector (PDB-110C; Thorlabs Inc., USA) and both signals from the function generator were visualized by the oscilloscope. We placed an objective (offset) lens OL (either + 40 mm lens or 20x microscope objective) behind the AOC to transform the light to the far field. Both AOC and OL form the acousto-optic tunable lens (AOL). Light intensity distribution behind the AOL was measured using a beam profiler (WinCamD; DataRay Inc., USA) on a motorized translation stage.
The fiber-optic OCT system equipped with high-speed tunable lens is demonstrated in Fig. 2(b). The light delivery subsystem similar to that in the previous case was used. The light was split into object and reference arm. The object arm employing the AOL with 20x objective was designed. The optical elements (i.e. objective) in the reference arm were used to avoid large dispersion mismatch. The cuvette of the length L = 50 mm filled with water was included in the reference arm to compensate for the water present in the AOC. The custom-built spectrometer was attached to the detection arm of the interferometer. The line-scan CCD camera (AViiVA SM2, 2048 pixels; e2v, UK) was operating at 10 kHz (exposure time 100 μs). The spectral resolution of the spectrometer provided depth range of OCT images of 1.3 mm. The axial and transverse resolutions of the system were 2.7 μm and 20 μm, respectively. The sensitivity of the system was 91 dB when the sample was illuminated with the beam of 0.8 mW power and the system operated at the speed of 10 kHz.
The experiments performed in this study were divided into two main parts: (i) demonstration of high-speed acousto-optic tunable lens operation and its performance, (ii) application of tunable AOL in OCT imaging.
4.1 Acousto-optic system calibration
First of all, we calibrated the acousto-optic system, i.e. we found the relation between voltage applied to the electrodes of the transducer and the Raman-Nath parameter v:
The light beam was not modulated prior to entering the AOC (continuous illumination; AOM off). We placed the beam profiler exactly in the focal plane of the objective (offset) lens OL; Fig. 2(a). The light intensity was captured for increasing voltage values. Although voltage was an easy variable in the experiment, theoretical approach required more objective input value such as the Raman-Nath parameter. Additionally, numerical simulations of the experiment were performed using light, ultrasound and AOC parameters. The calibration itself was based on scaling the abscissas of the experimental points to the theoretical curve. As a result, the scaling factor between the voltage and the Raman-Nath parameter was obtained.
The plot in Fig. 3 shows that light intensity at the axis of symmetry of the system in the far field decreases with increasing ultrasound amplitude. The intensity of light is normalized to the intensity when the AOC is turned off (v = 0 or U = 0 V). We also observe that the experimental results agree very well with the theoretical calculation based on the model presented in Section 2. The obtained results do not depend on the power of the offset lens inserted to the system. It means that comparison of light intensity for particular voltage to that for U = 0 V (AOC off) enables proper system calibration that results in finding corresponding the Raman-Nath parameter value.
4.2 Light beam profiling
In the next experiment, we aimed at three-dimensional reconstruction of the light beam. Continuous illumination scheme was used here. The beam profiler was attached to the translation stage, and the movement of the stage was synchronized with the beam profile acquisition. Three beam profiles were acquired for each axial position to minimize intensity fluctuations.
Figure 4 demonstrates cross-sectional images of the beam behind the tunable AOL when the tunable lens is off and on. However, better visualization of depth of focus (DOF) extension can be achieved if axial light intensity profile is extracted (right panel in Fig. 4). Two offset lenses were used here for comparison: fOL = 40 mm; Fig. 4(a); and 20x microscope objective; Fig. 4(b). Although the maximum axial intensity decreases when the voltage is applied to the AOL, the total energy is conserved.
The ability to tune the focal position offered by the AOL depends on the amplitude of ultrasound (Raman-Nath parameter) and the focal distance of the offset lens. This effect was studied theoretically by numerical calculations of time-averaged axial intensity profiles using BPM described in Section 2. In order to calculate the depth of focus (DOF), we used the definition similar to that in Gaussian optics, i.e. DOF was defined as the distance between two axial points at which the light intensity has decreased to 50% of its peak intensity (i.e. full width at half maximum of the axial intensity profile). Figure 5 shows the DOF as a function of the Raman-Nath parameter and the focal distance of the offset lens.
The relations from numerical simulations presented in Figs. 5(c) and 5(d) can be also confirmed qualitatively when the AOL is considered as a compound lens consisting of two phase elements (lenses): a lens of variable focus (AOC) and an offset lens. Assuming that the AOC operates in the Raman-Nath regime (pure phase object), total phase retardation of light wave passing through the AOC can be calculated using Eq. (2). Next, taking into account approximation of the Bessel function for small arguments: , the corresponding power (reciprocal of the focal length) of the AOC can be derived in the following form :
Considering extreme positions of the focal point in time, we can estimate:Equation (10) confirms the calculations presented in Fig. 5(c) (for v ≥ 2) and Fig. 5(d). The fact that DOF is proportional to the square of the focal length of the offset lens corresponds also to the DOF formula derived in Gaussian optics for a single lens.
4.3 Time-resolved tunable lens operation
In order to determine the temporal performance of the designed AOL, special illumination scheme was introduced. Application of EOM enabled obtaining pulsed operation at the frequency of the ultrasound that was synchronized with the ultrasound phase. In a pulsed operation, we took advantage of the stroboscopic effect by illumination in a particular, well controlled ultrasound phase; Fig. 2(c) . As a result, it enabled application of the detectors that do not have high temporal resolution. In particular, illumination synchronous with the ultrasound phase allowed for precise determination of the dynamics of the light field due to acousto-optic effect.
We acquired beam profiles when the time delay (phase) between both signals was changed for different axial positions of the detector. Central light intensity from each image was extracted and time-resolved light intensity profiles are shown in Fig. 6.
The focus crosses a given plane twice within a period of ultrasound because the ultrasonic wave generated inside the transducer is actually a standing wave. Moreover, the results demonstrate the dynamic focusing effect due to the acousto-optic interaction of light beam with the ultrasound of cylindrical symmetry.
We also investigated theoretically how the transverse resolution changes when the AOL performs temporal wavefront modulation. Comparison of beam profiles at the extreme positions of the focus (i.e. for t = 0 and t = ½T) indicated that the beam spot size increased by ~30% (for fOL = 40 mm) or ~10% (for 20x objective) with respect to the beam width when no ultrasound is present (v = 0). This change depended on the ultrasound amplitude. Moreover, the set-up with higher numerical aperture was less prone to those spot size variations.
4.4 OCT system performance
The performance of the OCT system equipped with the high-speed AOL in one of the arms is altered by rapidly varying phase of light wave travelling through the AOL. Therefore, the impact of the light interaction with ultrasonic field on the interference fringes acquired by the OCT system is an essential part of the study. This enables demonstrating the strengths and limitations of the proposed approach with respect to OCT method. Different factors influencing OCT signal were investigated in this part of study.
We measured the fringe amplitude and total intensity of light from the object arm captured by the spectrometer for increasing values of the Raman-Nath parameter (ultrasound amplitude) when continuous (EOM off) or stroboscopic (EOM on) illumination was used. The fringe amplitude was calculated from the peak amplitude after Fourier transformation, whereas the light intensity from the object arm was obtained by integrating the intensity from all spectral channels of the spectrometer in the case of blocked reference arm. The results are presented in Fig. 7(a). The interference signal drop is higher when the ultrasound is illuminated continuously (black dots in Fig. 7(a)), and it cannot be fully explained by the lower signal coming from the object arm. This is the additional impact of the fringe averaging since all time points are illuminated and contribute to the observed spectral fringes. On the other hand, decrease in fringe amplitude coincides with the signal drop when a particular phase of ultrasound is illuminated by light pulses (red dots in Fig. 7(a)). Comparison of illumination schemes demonstrates also the advantage of stroboscopic (pulsed) illumination scheme in terms of interference signal drop with the amplitude of ultrasound (open black vs. open red dots in Fig. 7(a)).
Later on, we wanted to check if the AOL influences the signal drop with depth. Spectral fringes were acquired whereas the reference mirror was moved. The plots in Fig. 7(b) show that the signal-to-noise ratio (SNR) roll-off remains the same but the SNR itself decreases with higher Raman-Nath parameters (as shown in Fig. 7(a)).
In the next experiment, the object mirror was translated from the offset lens. The results in Figs. 7(c) and 7(d) have been obtained for continuous and pulsed illumination, respectively. Both the amplitude of interference fringes and light intensity collected from the sample arm reconstruct temporal behavior of the focal point in the case of operating AOL; Fig. 7(d). Similar to the observations in Fig. 7(a), time-averaged profile of the amplitude of interference fringes does not correspond to the profile of collected light intensity, which indicates that additional fringe averaging (wash-out) is observed; Fig. 7(c).
Finally, we checked how the fringe amplitude decreases when we increase the pulse width of light illuminating the AOC. It is demonstrated in Fig. 7(e) that short illumination pulses synchronous with the ultrasound frequency make it possible to avoid OCT signal drop due to the phase averaging. When the pulse becomes longer, the effect is closer to the case of continuous illumination scheme.
4.5 Optical coherence microscopy with extended focus
The above-mentioned steps enabled optimization of our OCT set-up for imaging. In the final stage of our experiments, we performed imaging of different samples with the OCT system equipped with the tunable AOL; Fig. 2(b). The phantoms were selected and designed to visualize tunable focusing with the AOL. The samples / phantoms were scanned laterally using a motorized stage. The scanning was repeated for different phase values between the ultrasound and illumination pulse (delay τ in Fig. 2) so that one obtained a set of cross-sectional images of the same object with different axial position of the focus. In the post-processing, we selected the centers (depth positions) of the focus for each image and performed Gaussian windowing of the image. The width of Gaussian window depended on the number of partial image acquisitions (number of phase steps). The final (combined) image with extended illumination depth was obtained by combining the images filtered with Gaussian windows.
Figure 8(a) shows cross-sectional images of the stack of microscopic cover glasses. The focal position tuning allowed for enhancing light reflection from a particular glass interface.
Furthermore, a scattering phantom (an elastomer with titanium dioxide) was used to demonstrate the impact of moving focus on the amplitude of collected light from specific depths. High-definition B-scans at different phase delays between the pulse and ultrasound wave were acquired. The images presented in Fig. 8(b) show that the focus of the beam can be controlled and adjusted for the sake of image improvement. Stroboscopic illumination allows for enhancement of photon collection efficiency from particular depth. This effect is even better visualized when one generates an averaged depth profile (A-scan), as indicated in the plot in Fig. 8(b). The amplitude of light in deeper depths is lower due to the multiple scattering that limits light penetration into the sample.
Finally, to demonstrate the applicability of our new set-up we imaged a lemon as an example of the biological object. The scanning protocol was similar to that used in previous experiments. The images in Fig. 9 clearly demonstrate that the image quality in selected depths can be enhanced using dynamic focusing. The signal from the out-of-focus depths is blurred and reduced due to the low collection efficiency. When we control the position of the focus, it is possible to improve the image quality at particular depth. In the panel demonstrating the combined image we were able to reconstruct sharp cross-sectional image of the lime internal structure with fairly good and homogenous backscattered intensity. High contrast reconstruction was obtained for the total imaging depth two times larger than that in the original image without extended DOF.
The tunable acousto-optic lens presented in this study operates in MHz frequency range. Therefore, it allows for ultrahigh-speed tuning of the focus position. The ultrahigh tuning rate of the focus demonstrated here is faster than commercially available tunable lenses. This feature enables development of novel approaches to scanning scenarios. Although the tuning speed is fixed by the resonance mode of shell wall vibrations (thus, it depends on the thickness of the walls and properties of the piezoelectric material), the acousto-optic lens enables full control of the axial tuning range. To our best knowledge, this is the fastest method for dynamic focusing. Another advantage of using axisymmetric acousto-optic element is that it does not require high electrical power levels to obtain the desired effect. This is due to the fact that the ultrasound energy is accumulated at the axis of the vibrating piezoelectric shell. Moreover, due to the nature of the ultrasonic field, the AOL presented in this study does not introduce any non-axisymmetric aberrations like tunable electro-optic liquid lenses. We did not observe any chromatic effects when the AOL was operating although spectrally broadband light was used in this study.
The implemented successive diffraction model of the interaction of ultrasound with light demonstrates general numerical approach to solving the problem of light propagation through non-homogenous medium. We obtained very good agreement between numerical simulations of the AOL performance and experimental results, which indicates that the numerical calculation technique based on Fourier optics is correct.
Tunable focusing generates time-averaged light intensity distribution that is characterized by the extended DOF. The degree of DOF extension depends linearly on square of the focal length of the offset lens and on the amplitude of ultrasound (Raman-Nath parameter). This is the feature enabling improvement of capabilities of imaging devices.
We benefited from the pulsed illumination strategy implemented in our study. Although similar approach was applied in reducing motion artifacts [43, 44] we applied illumination synchronous with the focus tuning frequency in order to demonstrate cross-sectional imaging where focus position is well-defined. Analogical effect can be observed when the detector (camera) is gated e.g. with the shutter. However, this is not optimum since most of light is not detected. Stroboscopic effect may be also applied when ultrafast periodic changes in the sample properties are expected to be observed. Therefore, it is especially suited for studies of rapid phenomena.
We have presented careful assessment of utilization of high-speed tunable lens in the OCT technology. Although slower rates of focus tuning (ultrasound frequency) would be better for OCT to demonstrate its applicability, advances in OCT technology might fully take advantage of the presented approach. Dynamic focusing (or focus position adjustment) in OCT was demonstrated with different technologies [13, 18, 20, 21, 25]. Most of them enable static tuning and the tuning speed is limited but this report explores impact of temporal focus behavior on OCT signal when tuning at much faster time scales is provided. Although acousto-optic tunable lenses have been already employed in other imaging techniques [37, 45–47], this is the first demonstration of interference-based imaging with fast acousto-optic lens.
The control and tuning of focus position along with stroboscopic illumination enable better collection of light from deeper depths of the scattering sample. Furthermore, dynamic focusing applied to imaging allows also for increase in effective depth of focus when the system with high numerical aperture is used. However, the proposed method does not overcome the light penetration limits. Another challenging issue is the fact that the operation of the AOL impacts the interferometric signal in coherence-based imaging, which requires careful choice of the illumination method.
7. Summary and conclusions
To summarize, ultrahigh-speed tunable lens based on acousto-optic element was designed and implemented into OCT system. The results demonstrated the ability of the device to obtain ultrahigh-speed (MHz frequency range) dynamic focusing in OCT with stroboscopic illumination. We believe that imaging with active optical elements can improve photon collection efficiency, depth of focus and enhance image quality in OCM as well as in long depth range OCT.
IG and MW acknowledge support from the National Science Center within the MAESTRO Programme (#2011/02/A/ST2/00302). KSz and MW acknowledge the TEAM project (TEAM/2011-8/8) financed by the European Union within the frame of Operational Programme Innovative Economy coordinated by the Foundation for Polish Science. Additionally, IG is supported by the scholarship of the Polish Ministry of Science and Higher Education for 2013-2016. Finally, the authors thank Szymon Tamborski, MSc for technical help.
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