Noninvasive 3D functional imaging with high spatial resolution possesses a unique advantage in the field of painless clinical detection and early diagnosis, because the inner detailed and specific information in the body, such as the newborn microvessels and cerebral microbleed, can reflect many early lesions. Optical coherence tomography (OCT), a noninvasive tool for assessing inner cross-sectional images, enables 3D structure imaging with high resolutions (1–30 μm) [1–4]. The structure information offered by traditional OCT is based on scattered light. However, the scattering coefficient’s specificity for molecular, blood vessels, and tumor tissue is relatively poor [5]. OCT angiography (OCTA) has been proposed to image the blood circulation system with high speed and high resolution [6]. However, because OCTA is based on the motion contrast (i.e., the moving of the red blood cell), OCTA is not suitable for the imaging of a static sample, such as static blood, which links with many diseases closely, such as blood stasis, hemorrhage, and so on. As an endogenous physical parameter, the absorption coefficient possesses stronger specificity and sensitivity compared to the scattering coefficient and provides the possibility to perform the functional imaging [7]. To perform the functional imaging by OCT, photothermal optical coherence tomography (PTOCT) has been proposed to obtain the 3D absorption images [5,8–16]. The photothermal signals of the substances with strong absorption properties such as gold nanoparticles [5,8–10], fluorescent dye [11], carbon nanotube [12], blood in vitro [13], and mole [16] can be extracted efficiently by the traditional PTOCT. However, for the weak absorbers, especially when the weak absorbers are under strong background noise, their weak photothermal signals may be presented with low signal-to-noise ratio (SNR) or be lost completely by using the traditional methods. The strong background noise can cause an obvious decline of contrast and effective resolution of the PTOCT image. Moreover, phase accumulation (signal elongating with depth), which produces artifacts in the cross-sectional PTOCT images, can also reduce the axial resolution of the PTOCT image [8]. The optical lock-in technique, which can enhance the SNR of photothermal signals, has been employed in PTOCT imaging [11]. However, as this technique sacrifices the OCT phase signals, the problem of phase accumulation still remains [14]. Time-domain phase differentiation has been employed for the PTOCT imaging to reduce the phase accumulation [15]. However, this approach is highly sensitive to noise and decreases the SNR of the PTOCT image.

To improve both lateral and axial resolution of the PTOCT system, we proposed a cross-correlation photothermal optical coherence tomography (CC-PTOCT) system, which combined the cross-correlation technique with the phase differentiation method to obtain photothermal images. In this system, to resolve phase accumulation, the spatial phase differentiation method was employed to the depth-resolved OCT phase signals. By numerically differentiating the depth-resolved phase signals along the axial direction in each A-line, the phase accumulation can be reduced and the depth-resolved photothermal modulation signals can be obtained. Because the phase difference is highly sensitive to noise, the phase differentiation method can enhance the white noise. The noise brought by the phase differentiation method and the strong background noise can be suppressed efficiently by the cross-correlation technique, which was utilized to extract the weak photothermal signals in our system. With the reduction of phase accumulation and the suppression of the noise, both lateral and axial resolution can be enhanced effectively by using the CC-PTOCT system. In this study, the CC-PTOCT system has been demonstrated for photothermal imaging with high resolution. A theoretical derivation has shown the feasibility of the CC-PTOCT system. A strong-contrast 3D image of the capillaries of a mouse’s ear with enhanced lateral and axial resolution has been obtained.

The detailed theoretical description for CC-PTOCT imaging is presented. Under the excitation of a modulated pumping laser at the angular frequency ($\mathrm{\Omega }$), the targeted absorber generates heat into the microenvironment and leads to the slight change of the refractive index. Since the pumping laser was modulated by a chopper, the photothermal excitation was a square wave, which can be approximately equivalent to the sum of a series of the odd harmonic terms. Because it is too fast for the sample to respond to the high-frequency terms, only the basic component $\sin (\mathrm{\Omega }t)$ was considered and demodulated. Based on the heat conduction equation and the adiabatic approximation, the change of the refractive index can be obtained as

When the sample (such as the tissue) is inhomogeneous, the refractive index of the sample $n(l)$ varies with depth $l$. The change of the refractive index of the sample also varies with depth $\mathrm{\Delta }n(l)$ because the absorption coefficient $\alpha (l)$ varies with depth. In the case of inhomogeneous tissue, the optical path length (OPL) of light at depth $L$ can be written as $\mathrm{OPL}(T_0)={\int }_0^{L}n(T_0,l)\mathrm{d}l$, where $T_0$ is the initial temperature of the sample. When there is an increase in temperature $\mathrm{\Delta }T(l)$ in the sample, two phenomena should contribute to the change of OPL at the depth of $L$: the change in the refractive index with temperature at each layer that was passed through by the light and the expansion in the tissue at $L$ caused by thermal expansion [15]. Then, the OPL with a temperature increase is given by

The schematic setup of our system is shown in Fig. 1. A 532 nm laser used as the excitation light was modulated by a chopper. This pumping beam was combined to the object arm of the OCT system and illuminates on the sample. Meanwhile, the output of the power supply of the chopper was used as the cross-correlation reference signal, which was a sinusoidal signal. A traditional OCT system is used as a detector in M-scans. Low coherence light with a central wavelength of 1310 nm and full width at half-maximum (FWHM) of 85 nm is emitted from the superluminescent diode (DL-BX9-CS3307A, Denselight) for OCT imaging. The axial resolution in air is 9.0 μm, determined by the FWHM of the low coherence light. The transverse resolution is 7.0 μm, determined by the beam-waist radius of the object arm. The focused beam spot diameter of the 532 nm laser is about 7.0 μm. The acquisition time of one A-scan is around 0.028 ms. The acquisition time for one CC-PTOCT A-scan is 0.014 s. A $2\times 2$ fiber coupler is used to split the low coherence light beam into a reference arm and an object arm. The fiber coupler is 50:50. The light reflected from the sample and the mirror is collected into the fiber coupler for interferometry. The output interference light is dispersed and received by a spectrograph system, which consists of a spectro-grating (1145 lines/mm, $f=50\mathrm{mm}$, 1004-2, Thorlabs) and a linear array CCD (SU1024-LDH2, Goodrich). Five hundred axial lines were detected at a single location.

 

Fig. 1. Schematic of the CC-PTOCT system. SLD, super-luminescent diode; FOC, fiber optic couple; DG, diffraction grating.

Download Full Size | PDF

To demonstrate that CC-PTOCT can improve both lateral and axial resolution of the photothermal images, blood capillaries of a mouse ear were imaged by traditional PT-OCT and CC-PTOCT systems for comparison. The right ear of a mouse who has been dead for 2 h was shaved and disinfected. A pumping laser with power of 9.8 mW and wavelength at 532 nm was used to excite the photothermal effect. The modulation frequency of the pumping laser was 1 kHz. The transversal imaging region was $4.0\mathrm{mm}\times 4.0\mathrm{mm}$. The number of A-scans per B-scans is 500. The number of B-scans per C-scans is 500. Figures 2A and 2B are the traditional PTOCT images of the mouse ear with and without using phase differentiation. Figures 2(a) and 2(b) are the cross-sectional images of the white-dashed line in Figs. 2A and 2B, respectively. These traditional PTOCT images show that no matter whether the spatial phase differentiation was used or not, the major blood vessels can be seen, but the capillaries are blurred in both lateral and axial sections. Both lateral and axial resolutions were relatively low. Figures 2C and 2D are the CC-PTOCT images of the mouse ear with and without using phase differentiation. Figures 2(c) and 2(d) are the cross-sectional images of the white-dashed line in Figs. 2C and 2D, respectively. Compared to the traditional PTOCT images (Figs. 2A and 2B), more small vessels can be seen in the lateral CC-PTOCT images (as indicated in the white boxes and arrows in Figs. 2C and 2D), even when the spatial phase differentiation was not used. The reason is that the cross-correlation technique is an efficient tool of denoising. However, without using phase differentiation, there are many artifacts that were produced by the phase accumulation in the CC-PTOCT images [Figs. 2C and 2(c)]. As shown in Fig. 2(c), vast elongated signals (i.e., phase accumulation artifacts) blurred the small vessels and decreased the axial resolution. With the use of the phase differentiation based on Eq. (4), the artifacts were removed and the small vessels can be recognized clearly as shown in the red boxes in Fig. 2(d). The axial resolution of CC-PTOCT was obviously increased. It can be seen that by using this method, the lateral resolution in Fig. 2D was also increased compared to Fig. 2C.

 

Fig. 2. Projection view (x–y) from the 3D photothermal OCT images. A: The projection view (x–y) from the 3D traditional PTOCT image without using phase differentiation. B: The projection view (x–y) from the 3D traditional PTOCT image with the use of phase differentiation. C: The projection view (x–y) from the 3D CC-PTOCT image without using phase differentiation. D: The projection view (x–y) from the 3D CC-PTOCT image with the use of phase differentiation. (a)–(d) were the cross-sectional images of the white-dashed line of A–D, respectively. The scale bars represent 150 μm.

Download Full Size | PDF

It should be mentioned that by using phase differentiation, the SNR of the traditional PTOCT image was lowered as shown in Figs. 2B and 2(b). The reason is that spatial phase differentiation is highly sensitive to noise and can enhance more white noise in the images. On the contrary, by combining the phase differentiation method with cross-correlation, the image quality was obviously increased as shown in Figs. 2D and 2(d). The reason is that the white noise enhanced by the phase differentiation method was suppressed efficiently by the cross-correlation technique. This group of results further proved the denoising ability of the cross-correlation technique. Overall, by combining the cross-correlation technique with spatial phase differentiation, both lateral and axial resolutions of the photothermal images can be improved, and the image quality can be increased effectively.

To explain the method of spatial phase differentiation in more detail, time-dependent phase curves of the pixels in the tissue and blood under the photothermal excitation were obtained. Figures 3A and 3B are the cross-sectional CC-PTOCT images with and without using spatial phase differentiation. Pixel t1 was in the upper layer, and pixel t2 was in the lower layer. These two pixels were adjacent. It can be seen that the phase curves of t1 and t2 in Fig. 2C have the similar pattern over time. The reason is that the phase signal is a function of OPL, which integrates with depth; the fluctuation of the upper layer will be accumulated to the phase signals of the lower pixels even though the refractive index of the lower pixels was not modulated. So far, artifacts were produced at all the pixels below. This is why elongated signals exist in the photothermal image without using phase differentiation, as shown in the red box of Fig. 3A. The curve t3 in Fig. 3C is the spatial phase difference at the red point in Fig. 3B (at the same location as t1 and t2 in Fig. 3A). It can be seen that the curve of t3 is featureless and the accumulated part was removed, indicating that the refractive index of the tissue was not modulated by the pumping laser. Then, by using cross-correlation to process this differential signal, the photothermal signal in Fig. 3B (as shown in the red point) was obtained. It can be seen that the elongated signal whose refractive index was not modulated actually was removed by using phase differentiation. The same procedure was employed to the pixels located around the blood (as indicated in the red point b1, b2, and b3). The curve of b3 is the time-dependent phase difference signal, which represents the change of the refractive index over time at the red point in the blood vessel under the photothermal excitation. It can be seen that by using phase differentiation, the accumulated part (as shown in b1 and b2) was removed, and the modulated signal whose modulation frequency was at 1 kHz stood out as shown in Fig. 3D.

 

Fig. 3. Time-dependent phase curves of the pixels of the sample under the photothermal excitation. A: Cross-sectional CC-PTOCT image of mouse ear without using phase differentiation. B: Cross-sectional CC-PTOCT image of mouse ear with the use of phase differentiation. C: Time-dependent phase curves (t1 and t2) of the pixels in tissue. Curve of t3 is the phase difference as a function of time, obtained by using the phase differentiation. D: Time-dependent phase curves (b1 and b2) of the pixels in blood vessel. Curve of b3 is the phase difference as a function of time, obtained by using phase differentiation. The scale bars represent 150 μm.

Download Full Size | PDF

In summary, we developed a CC-PTOCT system that can improve both lateral and axial resolution of photothermal images. A theoretical derivation has shown the feasibility of the CC-PTOCT system. By using the CC-PTOCT system, the image of mouse ear capillaries with high lateral and axial resolution has been obtained.

With the combination of the high-efficiency capability to extract the absorption signal and the contact-free and high-resolution tomography, we expect that this method will aid the ongoing development of the accurate 3D functional imaging with high spatial resolution.