1. Introduction

Optical coherence tomography (OCT) is an emerging technology which can image tissue microanatomy in real time [1]. Unlike spectral-domain OCT [2], time-domain OCT can easily take the advantage of optical heterodyne detection by introducing a Doppler frequency (or phase) shift in the reference arm using a (scanning) delay line. However, such a Doppler frequency or phase shift is often insufficient in en face and lateral-priority OCT imaging as well as in low-coherence light scattering spectroscopy [3–6]. It has been shown that a sufficient Doppler shift (in addition to the one induced by the delay line) can be achieved by using an electro-optic phase modulator (EOM) when the light source is near 1.3 μm [7]. For source wavelengths in other regions (such as near 800 nm), acousto-optic frequency modulators (AOM) have been demonstrated to be a good choice for introducing the frequency shift [6, 8–10]. Compared to EOM, AOM is advantageous in that it can incorporate a broadband light source for achieving an ultrahigh OCT axial resolution. Recently, it has been demonstrated that a spectral throughput of ~118 nm is achievable using a pair of AOMs with a single-pass, free-space Mach-Zehnder configuration [11]. However, spectral throughput of more than 120 nm has not been reported nor a systematic analysis has been described to optimize the spectral throughput of AOMs. In this paper, we report a generic approach for optimizing the optical spectral throughput of two AOMs in a double-pass configuration as shown in Fig. 1. We found that two key parameters to the spectral optimization are the incident angle of the beam with respect to the first AOM and the relative angle between the two AOMs. We experimentally confirmed that spectral throughput could be easily tuned to accommodate a light source (i.e., a home-built Ti:Sapphire laser) with a bandwidth of ~150-nm. Using an optimized AOM configuration in conjunction with our recently developed dispersion management method for compensating the dispersion introduced by the AOM crystals [12], lateral-priority OCT imaging at an 800-nm center wavelength with an axial resolution of ~3 μm (in air) has been performed in real time. High-resolution imaging of rabbit cornea and bladder ex vivo has also been demonstrated.

 

Fig. 1. Schematic of two AOMs for introducing a sufficient and stable Doppler frequency shift. L is the thickness of the AOM crystal; ϕ ₀ and ϕ′₀ are the incident angles, ϕ ₁ and ϕ′_-1 the diffraction angles of +1^st order and -1^st order, and K ₁ and K ₂ are the propagation constants of the acoustic wave in the two AOMs, respectively. γ is the angle between K ₁ and K ₂.

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2. Theory

The stable modulation frequency of an AOM is generally in the range of several tens to hundreds of MHz. To achieve a Doppler shift of a few MHz for heterodyne OCT detection, two AOMs with opposite diffraction orders can be used [6, 8, 10, 11]. As shown in Fig. 1, AOM1 up-shifts the optical frequency with the +1st order diffraction by f ₁ and AOM2 down-shifts the optical frequency with the -1st order diffraction by f ₂, producing an overall Doppler shift of Δf = f ₁ - f ₂. To investigate the spectrum-dependent diffraction characteristics of a pair of AOMs, we start by analyzing the diffraction efficiency of one AOM. For simplicity, all the angles in Fig. 1 represent those within the AOM crystal(s) (e.g., refraction at the air-crystal interfaces has been taken into account). The diffraction angles by AOM1 and AOM2 are given by [13]

respectively, where K ₁ and K ₂ are the respective propagation constants of the acoustic wave in the two AOMs; ϕ ₀ and ϕ′₀(λ) are the incident angles on AOM1 and AOM2, respectively; k(λ) = 2πn(λ)/λ is the wave-number of light in the AOM crystal of refractive index n(λ), and λ is the optical wavelength in vacuum. It is well known that the diffraction efficiency at wavelength λ reaches its maximum when the incident angle is equal to the Bragg diffraction angle ϕ_B(λ)=K/2k(λ) = Kλ/4πn(λ) (i.e. the phase matching condition). For a broadband incident beam and a given incident angle ϕ ₀, only one wavelength λ_B = 4πϕ ₀ n(λ_B)/K can satisfy the phase-matching condition; for other wavelengths, each of which has its own Bragg angle, the phase-matching condition will thus not be satisfied which consequently affect the diffraction efficiency. The wavelength-dependent diffraction efficiency of one AOM can be expressed as [13]

Here Δϕ(λ) = ϕ ₀-ϕ_B(λ)is the difference between the incident (ϕ ₀) and Bragg angles (ϕ_B(λ)) at wavelength λ for AOM1 (and for AOM2, we have Δϕ′(λ) = ϕ′₀(λ)-ϕ′_B(λ)). ν(λ) = π|S|pLn ³ (λ)/λ. is the Raman-Nath parameter, where S is the amplitude of the acoustic wave, p is the elasto-optic coefficient and L is the crystal thickness. Neglecting the weak dependence of p on wavelength, the Raman-Nath parameter can be rewritten as ν(λ) = ν _rn ³ (λ)λ_r/[n ³ (λ_r)λ] where ν_r = ν(λ_r) is the reference Raman-Nath parameter at a reference wavelength λ_r. In practice, the Bragg diffraction efficiency (e.g., when Δϕ(λ) = ϕ ₀ - ϕ_B(λ) = 0) at λ_r is given and denoted by η_r. From Eq. (2), we have ${\nu }_r=\arcsin \left(\sqrt{2{\eta }_r}\right).$ Thus the Raman-Nath parameter at any given wavelength can be calculated by $\nu \left(\lambda \right)=\arcsin \left(\sqrt{2{\eta }_r}\right)n^3\left(\lambda \right){\lambda }_r/\left[n^3\left({\lambda }_r\right)\lambda \right].$ The diffraction efficiency at any wavelengths can then be calculated using Eq. (2). In our case, the manufacturer-specified Bragg diffraction efficiency is η_r = 75% at the center wavelength of our femtosecond Ti:Sapphire laser λ_r = 825-nm (o-beam). Choosing the incident angle equal to the Bragg angle at 825 nm, i.e. ϕ ₀ = ϕ_B(825nm), the spectrum-dependent single-pass throughput of one AOM was calculated using Eq. (2) and shown by the blue dashed line in Fig. 2(a). Notice that the AOM throughput is not symmetric with respect to the center wavelength λ_r = 825 nm because ν(λ) decreases explicitly versus the wavelength according to Eq. (2).

A symmetric AOM throughput with respect to the source center wavelength would accommodate a broad incident source spectrum with minimal spectral distortion. For this purpose, the diffraction efficiency should be increased at longer wavelengths. Eq. (2) indicates that this can be achieved by increasing the incident angle. Accordingly, the Bragg diffraction wavelength λ_B = 4π|ϕ ₀|n(λ_B)/K will also become longer (e.g.,λ_B >λ_r(=825 nm)), thus reducing the angular difference |Δϕ(λ)| at longer wavelengths and elevating the corresponding diffraction efficiency. According to this general trend, the diffraction efficiency was calculated systematically by setting the incident angle to Bragg angles at different wavelengths until the diffraction efficiency peak was achieved at a target wavelength (e.g., the center wavelength of the light source). The red solid curve in Fig. 2(a) shows that, by slightly increasing the incident angle from ϕ ₀ = ϕ_B (825 nm) = 0.22° to ϕ ₀ = ϕ_B(882 nm) =0.24°, the maximal AOM throughput can be shifted to 825 nm with the overall throughput nearly symmetric. This result reveals that the spectrum-dependence of the AOM diffraction efficiency is very sensitive to the incident angle.

 

Fig. 2. (a) Single-pass diffraction efficiency through one AOM with an incident angle of ϕ ₀ = ϕ_B (825 nm) (blue dashed line) and ϕ ₀ = ϕ_B (882 nm) (red solid line), respectively. (b) Double-pass diffraction efficiency through two AOMs with an incident angle of ϕ ₀ = ϕ_B (825 nm) (blue dashed line) and ϕ ₀ = ϕ_B (882 nm) (red solid line), respectively. (c) Measured input spectrum (black dotted line) to the first AOM and the output spectra after double-passing the two AOMs with the incident angle equal to the Bragg angles at 825 nm (blue dashed line) and 882 nm (red solid line) , respectively. The curve indicated by cross signs (x) on panel (c) represents the predicted double-pass spectral throughput, which is given by the measured input spectrum (as shown by the black dotted line in (c)) modulated by the calculated double-pass throughput efficiency (as shown by the solid red curve in (b)).

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A similar analysis can be performed for AOM2. As shown in Fig. 1, the incident angle for AOM2 is given by ϕ′₀(λ) = ϕ ₁(λ) + γ/n(λ), where γ is the angle between the two AOMs. According to Eqs. (1a) and (1b), the diffraction angle at an arbitrary wavelength λ by AOM2 and the difference between the incident angle on AOM2 and the Bragg angle Δϕ′(λ) = ϕ′₀(λ) - ϕ′_B(λ) are found to be

Numerical calculation confirms that the term (K ₁ - K ₂)/k(λ) ~ 0.008° is very small compared to ϕ ₀ for a Doppler frequency shift of ~1 MHz, and thus can be neglected in Eq. (3). By setting the two AOMs in parallel (i.e., γ= 0°) and ignoring the term(K ₁ - K ₂)/2k(λ) ~ 0.004°in Eq. (4), we have ϕ′_-1(λ) = ϕ ₀ and Δϕ′(λ) ≈ Δϕ(λ) according to Eqs. (3) and (4), suggesting the beam after AOM2 will be nearly in parallel with the incident beam on AOM1 and the two AOMs will have a nearly identical throughput spectrum. Under this condition (γ=0°), all the wavelengths will recombine after a double-pass configuration, and the total diffraction efficiency is then given by η ⁴(λ). Figure 2(b) shows the wavelength-dependent double-pass diffraction efficiency through the two AOMs with an incident angle equal to ϕ ₀ = ϕ_B (825 nm) and ϕ ₀ = ϕ_B(882 nm), respectively. Notice that the throughput spectrum is strongly dependent on the incident angle. A throughput spectrum nearly symmetric with respect to the source center wavelength can be achieved over a broad bandwidth of more than 200 nm when the incident angle is tuned to the Bragg angle at 882 nm. In the case when the incident angle is equal to the Bragg angle at the source center wavelength (i.e., 825 nm), the throughput is severely skewed toward shorter wavelengths. As indicated by Fig. 2(b), achieving a symmetric spectral throughput with respect to the source center wavelength when ϕ ₀ = ϕ_B (882 nm) is at the expense of an ~40% power reduction (compared to the throughput efficiency when ϕ ₀ = ϕ_B(825 nm) ). However, the light power in the delay line provides a sufficient optical heterodyne gain and the ~40% power reduction due to the optimization of the throughput spectrum is generally not a concern.

3. Experimental results

The schematic of the 800-nm real-time OCT imaging system with two AOMs is shown in Fig. 3. A Doppler frequency of 1.26 MHz was generated by setting the modulation frequencies of the two AOMs at 80 MHz (constant) and 79.37 MHz (adjustable), respectively. The two AOMs were separated by about D=200 mm so that the 0^th order diffraction beam was sufficiently apart from +1^st order and therefore could be blocked. The orientation of the two AOMs was precisely controlled (by using a precision rotational stage with a locking mechanism to keep the angular position stable). According to the above analysis, the beam incident angle on AOM1 |ϕ ₀| was chosen to be the Bragg angle at 882 nm (i.e., 0.24°) and the two AOMs were set in parallel. The output spectrum was checked with an optical spectrum analyzer during the alignment. Figure 2(c) shows the measured input and double-pass output spectra in the reference arm (which includes a pair of AOMs and a lens-grating phase delay line as shown in Fig. 3). The two spectra are very similar with a slight difference that can be caused by aberrations in other optical components and any sub-optimal alignment. In comparison, the measured spectral throughput with ϕ ₀ =ϕ_B(825 nm) is also shown in Fig. 2(c), illustrating the spectral asymmetry (e.g., with longer wavelengths strongly attenuated) as predicted by the theoretical analysis. Additionally, the predicted spectrum throughput, which is given by the measured input spectrum modulated by the calculated double-pass efficiency for an incident angel at ϕ ₀ =ϕ_B(882 nm) , is also shown in Fig. 2(c) (i.e., the curve indicated by the cross sings (x)). We note that the predicted double-pass spectrum is very similar to the measured one (shown by red solid curve in Fig. 2(c)).

 

Fig. 3. Schematic of a fiber-optic, lateral-priority OCT imaging system, in which two AOMs and a lens-grating phase delay line are implemented in the reference arm. An extra length of single-mode fiber (indicated by “Extra SMF”) in the sample arm is introduced in conjunction with the phase delay line in the reference arm to fully compensate the dispersion in the OCT system up to the third order. Fast lateral beam scan is performed by a PZT-driven miniature probe and slow depth scan is achieved by scanning the end mirror in the phase delay line.

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Depth scanning in the above OCT system was performed by an optical phase delay line in the reference arm which consisted of an 800-nm grating (300 lines/mm), a lens (f=100 mm) and a scanning end mirror. In addition to depth scanning, the phase delay-line along with an extra length of single-mode fiber in the sample arm was also used to compensate the dispersion introduced by the AOM crystals up to the third order as previously reported [12]. The resultant axial resolution was approximately 2.3 μm in tissue.

 

Fig. 4. Interference fringes at the surface of water (a) and a mirror 0.75-mm below the water surface (b). OCT axial resolution is given by then FWHM of the interference fringe envelopes.

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It has been shown that even a slight dispersion mismatch between the reference and sample arms in an 800-nm OCT system can cause a severe degradation in axial resolution [12]. To minimize the resolution degradation during depth scan, the phase delay line was configured so that the depth-dependent water dispersion can be compensated up to the third order by the scanning phase delay line [12, 14]. As shown in Fig. 4, the interference fringes at the water surface and a mirror 0.75-mm below the water surface were very similar and the axial resolution remained nearly the same (~2.3 μm in water).

The sample arm consisted of a miniature forward-viewing probe that performs fast lateral scanning at an ~1.2 kHz repetition rate [5]. An imaging rate at 2 frames per second can be achieved given 600 lateral scans per image. Different from conventional side-viewing endoscopes, the forward-viewing probe permits imaging of tissues directly in front of the probe. In addition, the lateral-priority scanning scheme enables dynamic focus tracking in real time [15]. The transverse resolution of the imaging probe was ~10.5 μm with a measured confocal parameter of 0.21 mm.

 

Fig. 5. Ultrahigh-resolution OCT images of (a) rabbit cornea and (b) rabbit bladder. Both images were acquired at 2 frames/s with a size of 572×364 pixels (0.9mm×0.55mm, transverse × depth). EP: Epithelium; BM: Bowman’s membrane; SP: Substantia Propria; EN: Endothelium (single cell layer); TE: Transitional Epithelium; SM: Submucosa; ML: Muscular Layers. Both images were taken with an incident power of ~9 mW on the sample.

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Real-time lateral-priority OCT imaging of biological tissues was conducted to demonstrate the performance of the ultrahigh-resolution OCT system which utilized a pair of AOMs for introducing a sufficient Doppler shift (1.26 MHz). The incident power from the fast lateral-scanning probe onto the sample was about 9 mW and the image rate was about 2 frames/s. Figure 5(a) illustrates a false-color OCT image of a fresh rabbit cornea with an image size of 0.9mm×0.55mm (572×526 pixels, transverse×depth). Structures including the epithelium (EP), Bowman’s membrane (BM), substantia propria or stroma (SP), and the single cell layer endothelium (EN) can be clearly identified. Figure 5(b) shows a representative OCT image of fresh rabbit bladder tissue (0.9mm×0.55mm or 572×526 pixels, transverse×depth). Again, layered structures including the transitional epithelium (TE), submucosa (SM) and muscular layers (ML) are clearly delineated.

4. Conclusion

In summary, we have demonstrated that a frequency modulator based on two AOMs can be configured to have a broad spectral throughput with a tunable peak response depending on the incident source spectrum. The basic configuration requires accurate control of the beam incident angle on the first AOM and the parallelism of the two AOMs. This modulation scheme in conjunction with a broadband light source enables real-time heterodyne OCT imaging with an axial resolution of ~2.3 μm. The spectral throughput optimization method presented here can be generally applied to other configurations that involve two AOMs in tandem with one up-shifting the frequency and the other down-shifting the frequency (regardless of single- or double-pass). The proposed method can also be potentially applied to an AOM-based frequency shifter for applications such as Lidar [16], when using multiple optical wavelengths over a broad spectrum.