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We developed axial-lateral parallel time-domain optical coherence tomography (ALP TD-OCT) from a single interference image. A two-dimensional camera can produce a depth-resolved interference image using diffracted light as the reference beam and a linear illumination beam without any mechanical scan. An OCT image of biological tissues with sufficient sensitivity requires extraction of interference signals by subtracting the DC image, which contains the intensity of noninterference light and the electrical noise of the camera, from a single interference image and subsequent application of the Hilbert transformation for each axial direction. We measured 300 interference images of a moving human finger in vivo using an indium gallium arsenide (InGaAs) camera (320×250 pixels) operating at 60 frames per second and then obtained OCT images with an imaging range of 5.0×1.7-mm2 (lateral×axial) using a DC image based on averaged interference images. The system sensitivity was 90.5 dB with a 1.05-ms exposure. As the OCT image depends on the interference signals in a single interference image, the OCT signals were stable compared with OCT images based on the phase-shift method.
©2008 Optical Society of America
1. Introduction
Optical coherence tomography (OCT) is a noninvasive, noncontact imaging modality used to obtain high-resolution cross-sectional images of tissue microstructure [1]. Conventional time domain (TD)-OCT can detect the echo time delays of light by measuring the interference signal as a function of time during axial scanning in a reference arm at each position of a probe beam scanning the sample arm laterally. The imaging sensitivity decreases when faster axial scanning is applied to increase the frame rate [2]. Fourier domain OCT (FD-OCT) allows greater sensitivity and faster imaging speeds than TD-OCT [3–7]. FD-OCT uses either a wavelength-swept laser source [3,5] or a one-dimensional (1D) spectrograph [4,6] to measure the echo time delays of light by spectrally resolving the interference signal without axial scanning.
Two-dimensional (2D) detection FD-OCT techniques have been demonstared by multiple groups [8–13]. 2D spectral domain (SD)-OCT techniques have been developed to obtain cross-sectional images from a single captured image without mechanical scans [8–12]. Using a high-speed complementary metal oxide semiconductor (CMOS) camera (1024×256 pixels) operated at 201 frames per second (fps), in vivo three-dimensional (3D) retina imaging with 256 cross-sectional images was performed with an acquisition rate of 0.8 volume/s and a sensitivity of 89.4 dB [12]. Full-field (FF)-FD-OCT was demonstrated by scanning a single wavelength from 760 to 860 nm using a CMOS camera (640×480 pixels) [13]. A sample volume of 1.3×1×0.2 mm3 (640×480×512 pixels) was imaged with an acquisition time of 51.2 s and sensitivity of 83 dB. OCT images require mapping and interpolating the axial data from wavelength to wavenumber and subsequent application of the Fourier transformation. FD-OCT contains DC and conjugate artifacts and suffers from a strong signal-to-noise ratio (SNR) fall-off, which is proportional to the distance from zero delay and a sinc-type reduction of the depth-dependent sensitivity because of the limited detection line width.
2D detection TD-OCT techniques have been developed to obtain transverse (en face) [14–20] and longitudinal cross-sectional images [21–24]. TD-OCT images, which are calculated using interference images, avoid the standard FD-OCT problems of mirror images and a decreased SNR with increasing depth range. FF-OCT methods can measure en face images without bi-directional transverse mechanical scanning. Sinusoidal phase modulation has been applied to FF-OCT imaging using a photoelastic modulator [15,16] and piezoelectric transducer [17,18]. As these methods measure four interference images using a charge-coupled device (CCD) camera operating at 200 fps, an OCT image can be obtained at 50 fps. The experimental sensitivity was achieved at 82 dB by averaging 50 accumulated images [15]. As averaging is permitted only ex vivo, immobile samples were imaged. To improve the temporal resolution, the squared value of the difference of two phase-opposed images was calculated to eliminate the noninterference components (i.e., the DC components) for OCT images. In vivo imaging of the anterior eye of the rat has been demonstrated using the FF-OCT technique based on a 500-fps CMOS camera (1280×1024 pixels) [18]. The measured sensitivity was 80 dB, after 4×4-pixel binning and the averaging of ten consecutive images. We demonstrated 3D OCT imaging of a human finger at 4 volumes/s with a sensitivity of 73 dB by calculating two interference images that were measured using an ultrahigh-speed CMOS camera (512×512 pixels, 3000 fps) and a single reference scan [19]. As the temporal resolution is twice the frame interval, a high-speed camera is needed to image biological tissues in vivo. The temporal resolution of the single-shot FF-OCT imaging technique, which detects four spatially separated interferograms simultaneously using only a CCD camera (1344×1024 pixels), depends on the frame rate of the 2D camera [20]. However, the complex optical setup requires the introduction of four phase-stepped images. The 2D camera requires a large number of pixels because the size of the resulting tomogram image is one-quarter of the captured image size. Although FF-OCT has the advantage of an ultrahigh lateral resolution (~1 µm) resulting from a relatively high numerical aperture microscope objective, it requires averaging of the OCT image or pixel binning to improve the low sensitivity.
The axial-lateral parallel (ALP) detection technique uses diffracted light as a reference beam to generate a continuous spatial optical delay, and line illumination light as a probe beam to obtain a depth-resolved interference image of a sample during exposure with a 2D camera [21–24]. In line scanning optical coherence microscopy, the sensitivity of line illumination has been demonstrated to be 10 dB higher than that of full-field illumination [25]. Using an ultrahigh-speed CMOS camera at 3000 fps, we obtained OCT images (512×512 pixels) with a 5.8×2.0-mm2 (lateral×axial) imaging range at 1500 fps by calculating two sequential images [24]. By scanning the linear probe beam, we imaged a sample volume of 5.8×2.8×2.0 (x×y×z) mm3 (corresponding to 512×250×512 pixels) at 6 volumes/s. The lateral and axial ranges were fixed by the imaging lens and the Littrow angle at 1st order diffracted light. To overcome this limitation, we have proposed a method of adjusting the imaging range in ALP TD-OCT using an optical zoom lens and high-order diffracted light [24]. We measured in vivo OCT images of human fingers at 30 fps using an indium gallium arsenide (InGaAs) camera operating at 60 fps. The experimental sensitivity reached 94.6 dB. The phase differences of each frame interval were variable due to sample motion and the resulting OCT signals fluctuated. It is necessary to obtain an OCT image from a single frame. As an InGaAs camera has a small number of pixels (320×256 pixels), the above-mentioned single-shot technique is not suitable for application to ALP-TD OCT with an InGaAs camera.
In this papaper, we report ALP TD-OCT from a single interference image. The subtraction of DC images required OCT imaging of biological tissues with sufficient sensitivity. We extracted interference signals by subtracting the DC image, which was an averaged interference image, from a single interference image, and then applied the Hilbert transformation to obtain complex analytic signals for each axial direction. Although an OCT image depends on the interference signals in a single interference image, this method is not a perfect single-shot technique due to the requirement of a DC image. Hence, we call it a quasi-single-shot technique. The OCT system yields sensitivity of 90.5 dB with a 1.05-ms exposure of the InGaAs camera (320×256 pixels, 60fps) and can obtain OCT images of a human finger in vivo with 5.0×1.7 mm (lateral×axial) at 60 fps.
2. Experimental setup
Figure 1 shows a schematic of the ALP TD-OCT system. A non-polarizing cube beam splitter splits the collimated light of a superluminescent diode (QPhotonics, SLD QSDM- 1300-9; center wavelength: λ0=1.31 µm, full-width at half-maximum spectral width: Δλ=30 nm, coherence length: lc=50.3 µm) into sample and reference arms. A cylindrical lens (f=100 mm) was inserted in the sample arm to illuminate the sample with a linear beam. A reflective diffraction grating was installed in the reference arm with the Littrow configuration. The Littrow angle θ is determined by
where p is the spacing between grooves and is 1/600 mm, and n is the diffraction order. We used first-order diffracted light, and the Littrow angle was θ=23.14°.
Backscattered light from samples and diffracted light from the grating were imaged onto an InGaAs camera (Goodrich-Sensors Unlimited, SU320MS-1.7RT; 256×320 (H×V) pixels, 25-µm pixel pitch, active area 6.4×8.0 mm, 12-bit resolution, frame rate 60 fps, exposure time 1.05 ms) using an achromatic lens (f=100 mm). We used the horizontal (N=256) and vertical (M=320) pixels of the camera to measure the respective axial and lateral ranges in the samples. The continuous spatial optical delay, Z, generated by the diffraction grating is given by
where d is the beam diameter. As the lateral range, ΔX, is measured by the vertical pixels of the camera, the horizontal range, ΔY, corresponds to NΔX/M. Therefore, the axial range ΔZ can be described as
As the measured lateral range was ΔX=5 mm, the axial range was ΔZ=1.7 mm. The measured lateral resolution was about 35 µm, which was close to twice the pixel size (31.25 µm). For actual measurements of biological tissues, the lateral resolution was decreased as a consequence of coherent cross-talk because light with high spatial coherence was used and degradation results from multiple scattering deep in biological tissues.
When the speed of the sample motion is described as V, the camera output during exposure time τ at the i-th frame is described as
where ti is the starting time of the exposure, Iref, Isig, and Iinc are the intensities of the reference, sample, and incoherent light, respectively, γ(z) is the amplitude of the modulation, which is determined by the coherence degree of the light source, ϕ is the phase difference between the sample and reference beams, and * denotes the convolution operator. The sinc function is sinc (2πVτ/λ 0)=sin(2πVτ/λ 0)/(2πVτ/λ 0). IDC and IAC are the DC component, τ(Iref+Isig+Iinc), and the amplitude of the interference signal, 2[IrefIsig(x,z)*|γ(z)|]1/2 sinc(2πVτ/λ 0), respectively. The amplitude of the interference signal is weighed by the sinc function with increasing sample speed. The interference signal is washed out when the sample moves a distance of 655 nm axially during the 1.05 ms exposure time used with the camera.
Fig. 1 Schematic of axial-lateral parallel time-domain optical coherence tomography. SLD: superluminescent diode, BS: beam splitter, Inset is the camera area. The horizontal pixels (N=256) and vertical pixels (M=320) were used to measure axial and lateral ranges in samples, respectively. Dash line: imaging ray
3. Calculation of OCT images using quasi-single-shot method and two-phase-shift method
The camera output contains noninterference components (i.e., DC components), the amplitude of the interference signal, and a phase term. Previously [23, 24], we obtained an OCT image approximately by calculating the squared difference of two sequential phase-shifted interference images. Although this calculation reduces the DC components, the calculated results still contain the phase term. In practical measurements of living biological samples, the phase difference between two frames is not constant and the residual DC components of the differential image are not negligible due to sample motion. To clear these problems, first, we describe the calculation of an OCT image using two phase-shifted images.
The difference between two sequential captured images, which are obtained at frame interval, T, can be calculated as
The differential image contains the phase term and its amplitude is influenced by the phase difference (2πVT/λ0) between two sequential captured images. The differences of incoherent light are not negligible when the sample moves markedly in the interval between two frames. To overcome these problems, we applied a high-pass filter and the Hilbert transformation to the differential image. High-pass filtering of the axial data was performed to reduce the residual DC components of the differential signals. In addition, we performed the Hilbert transformation for complex analytic signals in each axial direction. The quadrature signals can be obtained as
where P is Cauchy’s principal value of the integral. We used the FFT-based Hilbert transformation to act as a high-pass filter and the Hilbert transformation simultaneously in the frequency domain. The FFT-based Hilbert transformation is described as
where F and G are the 1-D Fourier transforms of f and g in the axial direction, respectively. Finally, the OCT image can be obtained as
As this procedure requires two phase-shifted interference images for one OCT image, we call it a two-phase-shift method. Note that the calculated OCT image still contains the influence of the phase difference (2πVT/λ0) between two frames.
Next, we describe the calculation of an OCT image from a single frame. In Hilbert phase microscopy, the interference signal is isolated using high-pass filtering, and the Hilbert transformation was then applied to obtain the complex analytic signal [26]. For practical measurements, however, this does not result in sufficient elimination because the intensity distribution of the DC components is not uniform. We performed high-pass filtering for each axial direction after subtracting the DC image from the captured interference image. The interference signal was given by
The quadrature signals g(x,z) can be obtained using the Hilbert transformation for each axial direction, and then the OCT image can be obtained as
An OCT image depends on the interference signals in a single interference image, although this method requires a DC image. Hence, we call it a quasi-single-shot method. Figure 2 shows the flowchart of the quasi-single-shot method and two-phase-shift method.
3. Results and discussions
3.1 Quasi-single-shot method vs. Perfect single-shot method
We compared our quasi-single-shot method to the perfect single-shot method, which has been used to isolate the interference signals from a single interference image by high-pass filtering and calculate the complex analytic signal using the Hilbert transformation [26]. First, we obtained interference signals using high-pass filtering and then applied the Hilbert transformation. Figure 3(a) shows the calculated amplitudes of the interference image. Here, we used a plane mirror as the sample and reduced the intensity of the reflected light by inserting a neutral density (ND) filter in the sample arm. The calculated image contains a great deal of noise caused by the nonuniformity of the DC components and the electrical noise of the camera, which the high-pass filtering cannot eliminate.
Next, we measured the reference arm signal as a DC image by blocking the sample arm because the reference beam is much more intense than the sample beam and dominates the DC components. The measured DC image contains not only the intensity distribution of the reference beam, but also electrical noise. Figure 3(b) shows the calculated amplitude image after subtracting the DC image and performing high-pass filtering. We can see the rejection of the electrical noise of the camera and the influence of the nonuniformity of the DC components. Figure 3(c) shows the axial profiles with a log scale for each image (yellow squares). The SNR was improved by about 18 dB after subtracting the DC image.
Fig. 3 Amplitude of interference images (a) without (b) with subtraction of the reference arm signal. The scale bar: 1mm. (c) SNR(signal to noise ratio) at each image
The electrical noise of the camera consists of the shot noise due to the dark current, the shot noise of the photocurrent, and the read-out noise in equivalent electrons. The read-out noise only occurs once per read, while the shot noise increases with the total number of integrated dark and signal electrons. To investigate the read-out noise of the InGaAs camera, we captured the images without incoming light. The mean and standard deviation of the pixel value in the captured image were 141.61 and 32.931, respectively. This mean value corresponds to 3.46% of the maximum pixel value of the camera output (4095 digital number). By calculating the difference between two captured images, the mean and standard deviation of the pixel value in the differential image decreased markedly to 0.068 and 1.16, respectively. The calculation of the difference between two captured images effectively eliminated the read-out noise. Consequently, we must subtract a DC image that contains the DC components and the electrical noise of the camera in OCT imaging of biological tissues. The inset in Fig. 3(c) shows the axial profile with a linear scale and the fitted Gaussian curve. The estimated axial resolution was about 25 µm in air, which agreed with the theoretical value of 25.2 µm, and corresponds to about 18 µm in tissue (n=1.38).
3.2 Comparison of sensitivity at single frame and two frames
We compared the sensitivities of OCT images using the quasi-single-shot method and the two-phase-shift method. A plane mirror with a calibrated attenuation of 60 dB was used as the sample. This mirror was oscillated using a piezoelectric transducer (PZT) to provide a 180° phase difference between two sequential interference images. The total illumination power used was about 5.5 mW, which corresponded to 17.2 µW optical power per A-line (5.5 mW divided by the 320 camera pixels) with a camera exposure time of 1.05 ms. We used an ND filter to adjust the optical power of the reference beam until the pixel values were similar to the saturation level of the camera. We obtained the DC image by averaging 300 interference images. Figure 4(a) shows the normalized amplitudes of interference signals and the noise levels. Although the amplitudes of the two frames were twice that of a single frame, these values were dependent on the phase difference between two sequential images and would be lower if the oscillation were stopped. The noise levels in the two frames were 1.4 times higher than that in the single frame. Figure 4(b) shows the sensitivity of a single frame and two frames. The measured sensitivity of a single frame was 90.5 dB, and that of two frames reached 93.4 dB when the phase difference between two sequential captured images was 180°.
Next, we estimated the theoretical sensitivity of the quasi-single-shot method in ALP TD-OCT using an InGaAs camera. The minimum detectable reflectivity of shot noise-limited silicon-based FF-OCT systems using the phase-shifting method has been previously reported [15]. Furthermore, it has been modified for InGaAs-based FF-OCT because the electrical noise, including the read-out noise and the dark noise of commercial InGaAs cameras, may not be negligible compared to the shot noise [17]. According to the results in Section 3.1, however, the electrical noise would be minimized by calculating the difference of two captured images if the read-out noise dominates. Therefore, we introduced the minimum detectable reflectivity to estimate the sensitivity of our system using the shot noise-limited model. Shot noise that obeys a Poisson distribution is assumed to dominate over any other noise. The variance in the number of detected photons is equal to the number of detected photons itself. When ξ is the number of photoelectrons stored by each pixel of the camera, the properties of noise ν are described as follows:
where the angle brackets denote a time average. The calculated OCT image signals with noise are represented by
When the interference fringe is zero (f=0 and g=0), the noise of the calculated image can be obtained as
If the camera is operated near its maximum full-well charge storage capacity ξmax, we obtain the following relationship:
where Rref and Rsig are the reflectivities of the reference mirror and sample, respectively, Rinc is the proportion of incoherent light, and Iin is the intensity of incident light. Here, the fringe contrast C can be expressed as
Since noise can be found in the case of zero fringe of interference, the number of photoelectrons in the captured image is expressed as
Therefore, the signal S and the noise Snoise are rewritten as
Assuming that 1≪ξ max and Rsig≪Rref Rinc, the SNR is approximated by
The minimum detectable reflectivity Rmin (SNR=2) can be expressed as
Our InGaAs camera has ξ max=8×105. We measured the reference reflectivity to be Rref=2.5% when the reflectivity of a plane mirror was measured at Rref=100%. The incoherent component of the signal light was negligible when a plane mirror was used as the sample. Therefore, these values gave a predicted sensitivity of the InGaAs FF-OCT of 75.1 dB. In the FF-OCT scheme, which uses microscope objectives in both arms, the sample has an illumination area equal to that of the reference. In ALP TD-OCT, the optical density at the sample is greater than at the reference because the cylindrical lens focuses the probe beam linearly. The measured beam width at the waist was w 0=36.2 µm, which is greater than the calculated value of (4λ 0/π)(f/d)=28.8 µm for an incident beam diameter of d=5.8 mm due to aberrations in the cylindrical lens. At the waist, the intensity of the probe beam was 10log(d/w 0) ~23 dB, which is greater than the intensity of the reference beam. Therefore, the estimated theoretical sensitivity of the ALP TD-OCT system is about 98.1 dB. The experimental value was 7.6 dB lower than the theoretical sensitivity, which can be attributed to the low fringe visibility due to the tilted reference beam and losses in the sample arm optics.
Moreover, we estimated the theoretical sensitivity of the two-phase-shift method. According to Eqs. (8) and (10), when the phase difference of two frames is fixed at 180°, the OCT signal of the two-phase-shift method is four times higher than that of the quasi-single-shot method. The noise of the OCT image is Snoise=4ξ, which is twice that of the quasi-single-shot method because the two-phase-shift method uses the two interference images for calculating an OCT image. Therefore, the sensitivity of the two-phase-shift method is 3 dB greater, which corresponds to the experimental result, as shown in Fig. 4(b). Since the phase is shifted due to the sample motion with in vivo imaging, it is uncontrollable and is influenced in OCT images. Therefore, the two-phase-shift method can effectively image immobile samples by using reference phase modulation. For example, this modulation can be generated by the diffraction grating placed on a PZT. Although the quasi-single-shot method can also obtain OCT images of fixed samples with reference phase modulation, it requires more acquisition time (300 interference images requires 5 seconds in our system) to estimate the DC image. Therefore, considering the 3 dB higher sensitivity and two-frame acquisition, the two-phase-shift method is suitable for imaging fixed samples.
Fig. 4 (a) Normalized amplitudes of interference signals and (b) sensitivities using quasi-single-shot method and two-phase-shift method.
3.3 OCT imaging of a moving sample
We measured 300 interference images of a human fingertip in vivo within 5 seconds and then calculated the OCT images using the quasi-single-shot and two-phase-shift methods. In the quasi-single-shot OCT imaging method, we obtained the DC image by averaging 300 interference images.
Fig. 5 (2.44 Mbyte) in vivo OCT images of a human fingertip. (a) and (c) are the OCT image calculated from 249th and 250th interference image, respectively. (b) and (d) are the OCT image obtained from the difference between 249th and 250th interference images and the difference between 250th and 251st interference images respectively. The white arrow shows the decreased region of OCT signals. The scale bar: 1mm [Media 1]
Typically, the backscattered signal levels of biological tissues are less than ‒50 dB of the incident light. In our system, the OCT signals of biological tissues have approximetely 40 dB-SNR (20 dB-SNR in the amplitude of the interference signal). Since this averaging decreased the amplitude of an interference signal by 10log(1/300)≈-24.8 dB, the interference signals were negligible in the averaged image. If OCT signals have a higher SNR, we need to average more than 300 interference images to obtain an adequate DC image. We performed high-pass filtering of the axial data to reduce the residual DC components comprising the difference between the DC image and the incoherent light of the captured image. In the two-phase-shift method, we also performed high-pass filtering to reduce the residual DC components that were included in the differential signals of the two captured images. Figures 5(a) and (c) are the OCT images calculated from the 249th and 250th interference images, respectively. Figures 5(b) and (d) are the OCT images obtained from the differences between the 249th and 250th and the 250th and 251st interference images, respectively. The white arrow shows the decreased region of the OCT signals because the phase differences between two frames are close to 2nπ (where n is an integer). The movie shows OCT images obtained from a single frame (left) and two frames (right) at 60 fps. We often see that OCT images are missed due to axial motion. Figure 6 shows the root mean square (RMS) of the OCT images. The OCT images with the quasi-single-shot method are stable compared to the OCT images using the two-phase-shift method due to the influence of the phase difference between two frames.
Fig. 6 The root mean square (RMS) of OCT images using (a) quasi-single-shot method (b) two-phase-shift method
4. Conclusion
We demonstrated quasi-single-shot imaging in ALP TD-OCT and compared the results with OCT imaging using the two-phase-shift method. The calculation of the OCT requires eliminating the DC image, which contains the intensity of noninterference light and the electrical noise of the camera, from interference images and applying the Hilbert transformation to obtain a complex analytic signal. We measured OCT images of a human finger in vivo with an imaging range of 5.0×1.7 mm (lateral×axial) and a sensitivity of 90.5 dB using an InGaAs camera (320×256 pixels, 60 fps, 1.05-ms exposure). Here, we obtained the DC image by averaging 300 interference images. As the interference fringes of moving samples such as living biological tissues vary throughout image acquisition, averaging cancels this variation. If we obtain OCT images of fixed samples, reference phase modulation is required because the interference fringes of fixed samples are stable. The two-phase-shift method is more effective for imaging fixed samples with the phase modulation of a reference light because its sensitivity is 3 dB greater due to the 180° phase difference between two sequential interference images. Therefore, we need to choose between the quasi-single-shot method and the two-phase-shift method for ALP TD-OCT imaging in diverse applications.
Acknowledgements
This study was supported by Industrial Technology Research Grant Program in ’05 from New Energy and Industrial Technology Development Organization (NEDO) of Japan.
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