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We developed a method to adjust measurement range within axial–lateral parallel time-domain optical coherence tomography (ALP TD-OCT) using an optical zoom lens and high-order diffracted lights. A two-dimensional (2-D) camera can produce a depth-resolved interference image using diffracted light as the reference beam and a linear illumination beam without axial and lateral scans. The lateral range can be varied continuously from 4 to 8 mm using an optical zoom lens. Axial range could be adjusted discretely by 1st, 2nd, 3rd, and 4th orders because we used a reflective diffraction grating with 300 lines/mm in a 1.3 μm wavelength region. OCT images (320 × 256 pixels) can be displayed at 30 frames per second (fps) by calculating two interference images, captured by an InGaAs camera operated at 60 fps. With a 1.05-ms exposure, the ALP TD-OCT system has sufficient sensitivity (94.6 dB) to image the human finger in vivo.
©2007 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. Imaging sensitivity decreases when faster axial scanning is applied to increase frame rate [2]. Fourier domain OCT (FD–OCT) can allow higher sensitivity and imaging speed than TD-OCT [3–6]. FD-OCT uses either a spectrograph [4] or a frequency swept laser source [5] to measure the echo time delays of light by spectrally resolving the interference signal without axial scanning.
A parallel detection spectral domain (SD)–OCT technique has been developed to obtain cross-sectional images from a single captured image without axial and lateral scanning [7–10]. More recently, this technique has applied linear illumination and a two-dimensional (2-D) charge-coupled device (CCD) camera to measure three-dimensional (3-D) shapes [8], in vivo real-time imaging of human eye structures [9], and in vivo 3-D dermatological investigations [10]. OCT images require mapping and interpolating the axial data from wavelength- to k-space and subsequent application of the Fourier transformation. FD-OCT is known to contain DC and conjugate artifacts and to suffer from a strong fall-off of SNR, which is proportional to the distance from zero delay and a sinc-type reduction of depth-dependent sensitivity because of limited detection line width. To avoid artifacts, SD-OCT requires several phase-shifted spectral interference signals [11,12]. For in vivo imaging of biological samples, the accuracy of phase differences between captured frames did not prove to be promising due to sample motion.
Parallel detection TD-OCT techniques have been developed to obtain transverse (en face) [13–17] and longitudinal [18–20] cross-sectional images. TD-OCT images, which are calculated using interference images, avoid the standard FD-OCT problems of mirror images and decreased SNR with increasing depth range. As full-field (FF) OCT can measure en face images [13–17], this scheme requires an axial mechanical scan to obtain longitudinal cross-sectional images. To obtain a depth-resolved interference image of a sample during exposure by a 2-D camera, the axial-lateral parallel (ALP) detection scheme uses 1st order diffracted light as a reference beam to generate a continuous spatial optical delay, and a linear illumination light as a probe beam [18]. Using a three-step phase-shifting method, we demonstrated in vivo OCT imaging at 10 fps using an indium gallium arsenide (InGaAs) digital camera operating at 30 fps [19]. We were able to obtain OCT images of human fingers with a 90-dB sensitivity for a 4.80 × 2.45-mm2 (lateral × axial) imaging range. Using an ultrahigh-speed complementary metal oxide semiconductor (CMOS) camera, 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 [20]. Lateral and axial ranges were fixed by the imaging lens and the Littrow angle at 1st order diffracted light.
In this paper, we demonstrate a method of adjusting the imaging range in ALP TD-OCT using an optical zoom lens and high-order diffracted lights. Our method allows the lateral range to zoom continuously from 4 to 8 mm using an optical zoom lens. Although zooming decreases the axial range, this can be recovered using higher-order diffracted lights. Because diffraction grating is only used for the reference beam, the low-diffraction efficiency of high-order diffracted light is sufficient to generate the reference beam. The system yields 94.6-dB sensitivity with a 1.05-ms InGaAs camera exposure and can display OCT images (320 × 256 pixels) of the human finger in vivo at 30 fps.
2. Experimental setup
Figure 1 presents a schematic of the ALP TD-OCT system. The collimated light of a superluminescent diode (Qphotonics, SLD QSDM-1300-9; center wavelength: λ 0 = 1.31 μm, full-width at half-maximum spectral width: ∆λ = 30 nm, coherence length: lc = 50.3 μm) is split into sample and reference arms by a non-polarizing cube beam splitter (20 mm in size). A cylindrical lens (f= 50 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 a Littrow configuration. The grating equation is given by
where p is the spacing between grooves, 1/300 mm; λ is diffracted wavelength; α and β are incident and diffraction angles, respectively; and n is the order of diffraction. Since the incident angle is equal to the diffraction angle in the Littrow configuration, the Littrow angle θ is determined by
Although the center wavelength beam propagates backward along the incoming path, the diffractive angles of other wavelengths λ can be described as
Backscattered light from samples and diffracted light from the grating were imaged onto an InGaAs camera (Goodrich-Sensors Unlimited Inc., SU320MS-1.7RT; 256 (H) × 320 (V) pixels, 25-μm pixel pitch, active area of 6.4 × 8.0 mm, 12-bit resolution, frame rate of 60 fps) using an optical zoom lens (Edmund Optics, VZM 200i, Parfocal Zoom: 0.5-2×, working distance: 90 mm). We used the camera’s horizontal pixels (N = 256) and vertical pixels (M = 320) to measure axial and lateral ranges in samples, respectively. Imaging depth, ∆Z, generated by the diffraction grating, is given by
where d is the beam diameter. Since the lateral range, ∆X, is measured by the camera’s vertical pixel, horizontal range ∆Y corresponds to N∆X/M. Therefore, the relationship between ∆Z and ∆X can be described as
According to the sampling theorem, when an axial profile, ∆l, is sampled by two pixels, the maximum imaging depth range in air, ∆Z max, can be described as
Because lc = 50.3 μ;m and N = 256, ∆Z max = 3.2 mm in our system. If the actual imaging depth of the camera is greater than ∆Z max, the axial resolution depends on the imaging depth and the number of pixels. The axial-lateral interference image, l, is described as
where Isig, Iref, and Iin are the intensities of the sample beam, reference beam, and incident beam, respectively; R sig is the distribution of the sample reflectance; γ(z) is the amplitude of the modulation, which is determined by the light source’s degree of coherence; ϕ is the phase difference between sample and reference beams; and * denotes the convolution operator.
Fig. 1. Schematic of axial-lateral parallel time-domain optical coherence tomography. SLD: superluminescent diode, BS: beam splitter, CL: cylindrical lens. 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.
Since the camera output contains a noninterference signal, the amplitude of the interference signal, and a phase term, producing an OCT image requires more than three phase-shifted interference images. High-speed imaging requires obtaining OCT images of biological tissues in vivo due to sample motion. Noninterference light is much stronger than the interference signal for imaging biological samples. Therefore, it is very important to eliminate noninterference components using a minimal number of frames. When the phase difference between the two interference images is generated by moving a sample, the squared value, S, of the difference between two captured images (I 1 and I 2) can be calculated as
Although the calculated results include the phase term, residual fringes are not visible because OCT images of biological samples contain speckle noise. Therefore, the calculated image S represents the distribution of the sample reflectance R sig(x,z) that corresponds to an OCT image, although it contains noise. The image averaging procedure is a powerful way of reducing the phase and speckle noise [15,16,18]. Since the calculation is simple, the OCT images can be displayed at 30 fps using homemade software. We used the averaging procedure to reduce this noise using OCT images stored in a personal computer.
3. Results and discussions
3.1 Calculation of measurement range at each order of diffraction
First, we calculated the Littrow angle at each order using Eq. (2), as shown in Table 1. As the light source has spectral width, diffracted light is widespread. Figure 2 shows the diffraction angle β calculated using Eq. (3) and the spectrum of SLD used. At the 5th order, diffracted light is not generated at longer wavelengths, so the diffracted light from the 1st to 4th order can be applied to the reference beam. Furthermore, the measured diffraction efficiencies from the 1st to 4th orders are also shown in Table 1 when the reflectance of the plane mirror is 100%. The measured diffraction efficiencies are less than 20% and sufficient for use as reference beams.
Table 1. Littrow angle at each order diffracted light.
Next, we estimated axial and lateral ranges in our system. When the optical zoom lens is set at a 1.0× magnification, lateral range ∆X corresponds to the horizontal size of the active area (8 mm) in the camera. Lateral ranges vary from 16 to 4 mm for magnifications of 0.5 to 2×. Figure 3(a) presents the calculated lateral range and axial range ∆Z at each order of diffracted light; at the 4th order, the axial range is similar to the lateral range. While the axial range at 4th order diffracted light is greater than maximum value ∆Z max = 3.2 mm, it can be effective for measuring OCT images if the lateral range is set below 3.2 mm by increasing magnification.
The axial resolution is not affected by the dispersion of the diffraction grating if the grating plane is optically conjugated with the plane of the camera. Therefore, the axial resolution does not depend on the diffraction order of the grating. However, the axial resolution decreases and depends on the axial range and the number of pixels in the axial direction if the axial range exceeds the maximum imaging depth. We estimated the axial resolution in air using Fig. 3(a) and Eq. (6), as shown in Fig. 3(b). Here, the axial resolution is half the coherence length of the light source when the axial range is smaller than the maximum depth. When the magnification is below 1.0×, the illumination intensity of the samples is too weak for efficient imaging of biological tissue due to the large illumination size. For this reason, we selected a magnification range from 1.0 to 2.0× for taking practical measurements.
Fig. 3. (a) Calculated imaging ranges at each order of diffraction. Solid lines represent axial range. Broken lines represent lateral range. (b) Estimated axial resolutions in air at each order of diffraction.
3.2 Lateral resolutions
We investigated the smallest resolvable element in a test target (USAF1951) while increasing the optical zoom lens magnification. Increased lateral resolution can be obtained by compromising the lateral range. Figure 4(a) presents a line profile of group 3 at 1.0× magnification. Test target contrast was 31% at group 3 element 5 (12.7 line pairs/mm), corresponding to a resolution of about 78.7 μm. Figure 4(b) presents a line profile of group 5 at 2.0× magnification. Although the smallest resolvable element was 40.3-line pairs/mm (group 5 element 3), corresponding to a resolution of about 24.8 μm, this was lower than the 88-line pairs/mm resolution specified by the manufacturer. As the zoom lens was designed to use visible light and its wavelength was intended for a silicon CCD camera (e.g., 640 × 480 pixels), the longer near-infrared wavelengths and a smaller number of pixels result in decreased resolution. Since the camera resolution was twice the pixel pitch (25 μm) and the optical zoom lens used a 2.0× magnification, the resolution of the optical system was estimated to be 25 μm, corresponding to the measured resolution. For actual measurements of biological tissues, the lateral resolution could be decreased as a consequence of coherent cross talk because of the high spatial coherence light used and the degradation resulting from multiple scattering deep in biological tissues.
Fig. 4. (a) Measured line profile of group 3 at 1.0× magnification. (b) Measured line profile of group 5 at 2.0× magnification
3.3 Beam width of linear probe beam
To investigate the influence of aberrations in the cylindrical lens used, we measured beam width (1/e2) in the focusing direction of the probe beam by moving a beam profiler (Coherent, Beam Master) axially in 100-μm steps, as shown in Fig. 5(a). The normalized profile of a Gaussian beam is described as
Here, the beam radius, ω(z), is described as
where the waist diameter is 2ω 0 = (4λ 0 /π)(f/d). Our experimental results were similar to the theoretical curves for an expected incident beam diameter of d = 6.5 mm. The measured beam width at the waist was 27.3 μm, greater than the calculated value of 12.8 μm, due to aberrations in the cylindrical lens. The measured depth of focus was about 600 μm, three times greater than the calculated 197 μm.
The peak intensity ratio of focused beam to incident beam on the beam axis (r = 0) is expressed as
Figure 5(b) shows the peak intensity ratios of the focused beam to the incident beam using a logarithmic scale. The intensity ratio peaked at 23.8 dB at the beam waist and dropped gradually with increasing z, indicating that this focusing allowed our system to gain more than 15 dB.
Fig. 5. (a) Measured linear beam widths. Solid lines represent theoretical curves. (b) Peak intensity ratios of focused beams to the incident beam.
3.4 Sensitivity
We measured the sensitivity of our OCT system by increasing the magnification. A plane mirror was used as a sample with an attenuation of 50 dB. This plane mirror was oscillated using a piezoelectric transducer to provide a 180° phase difference between two sequential interference images. The total illumination power used was about 6.6 mW, corresponding to 20.6 μW optical power per A-line (6.6 mW divided by the camera’s 320 pixels) with a camera exposure time of 1.05 ms. We used a neutral density (ND) filter to adjust the optical power of the reference beam until pixel values were similar to the camera’s saturation level at a 1.0× magnification. Figure 6 presents the pixel values of the captured interference images and sensitivities when we increased the magnification. Because pixel values decreased with increased magnification, the resultant sensitivities decreased from 94.6 to 86.0 dB. The incident power must be adjusted to achieve constant sensitivity in the zoom range.
We estimated the theoretical sensitivity of ALP TD-OCT using values for FF-OCT, which calculates two interference images [16]. Assuming measurements are limited by shot-noise, the minimum detectable reflectivity, R min, without image accumulation is approximately
where Rref, is reference reflectivity, ξmax is the camera’s full-well capacity, and Rinc is the reflectivity of incoherent light. Our InGaAs camera has a large full-well capacity, ξmax ≈ 8 × 105. The reference reflectivity was determined by the optical density used in the ND filter and the diffraction efficiency in the reference arm. We measured reference reflectivity to be Rref = 2.5% when the reflectivity of a plane mirror was measured at Rref = 100%. The incoherent component of signal lights was negligible when a plane mirror was used as the sample. Therefore, these values gave a predicted sensitivity of 10log(Rmin) ~ -78.1 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, optical density at the sample is greater than at the reference because the cylindrical lens focuses the probe beam linearly. Considering the 23.8 dB gain in the sample arm of our system, the theoretical sensitivity is reached at 101.9 dB. The measured sensitivity in our system was approximately 7 dB lower than the theoretical estimate due to electrical noise from the InGaAs camera.
Fig. 6. (a) Pixel values and (b) sensitivities with an attenuation of -50 dB in the sample arm for each magnification.
3.2 In vivo OCT imaging of human fingers
We conducted in vivo OCT imaging of human fingers at 1.0 and 2.0× magnifications using the 2nd order of the diffracted light as a reference beam. The incident power used was about 0.8 mW with a 1.05-ms camera exposure time. We averaged 30 OCT images, which were calculated using two sequential interference images to reduce speckle noise, and the averaged OCT images were presented on an inverse logarithmic scale. Figure 7(a) shows an OCT image of a human nail fold region at 1.0× magnification. The imaged area (lateral × axial) was 8.0 × 2.6 mm2. The nail root is visible beneath the skin. The lunula, which is the whitish, half-moon shape, can be seen at the nail base underneath the plate. Figure 7(b) shows an OCT image at the same position when magnification was increased to 2.0×. The imaged area (lateral × axial) here was 4.0 × 1.3 mm2. The size of this OCT image was reduced to 50% and then overlapped with Fig. 7(a), as shown in Fig. 7(c). The OCT image at 2.0× magnification, displayed as the gray region, agrees with the OCT image at 1.0× magnification.
Fig. 7. In vivo OCT images of a human nail fold region (a) at 1.0× magnification, with an imaging range of 8.0 × 2.6 mm2 (x × z); (b) at 2.0× magnification, with an imaging range of 4.0 × 1.3 mm2 (x × z); and (c) with images overlapped, where the gray region corresponds to Fig. 7(b).
Since the axial range decreased when we increased magnification of the optical zoom lens, we used high-order diffracted lights to recover the axial range. Figure 8 presents in vivo OCT images of a human nail fold region at a 2.0× magnification using 2nd , 3rd, and 4th orders of diffracted lights; axial ranges were 1.3, 2.3, and 4.1 mm, respectively. These images were resized to imaging range. Figure 9 presents axial profiles of the nail plate at each image (red line). Here, the position at the nail surface was set to zero. At the 4th order, the axial profile of the nail plate surface was broad because the maximum axial range (3.2 mm) had been exceeded. According to Fig. 3(b), the axial resolution in air is about 32 μm at the 4th order of diffraction and 2× magnification. Therefore, a 3rd order of diffracted light is suitable for use of the reference beam.
Fig. 8. In vivo OCT images of a human nail fold region at (a) 2nd, (b) 3rd, and (c) 4th orders of diffracted light. Axial ranges were 1.3 mm, 2.3 mm, and 4.1 mm, respectively. The red lines correspond to the region of axial profiles in Fig. 9.
4. Conclusion
We demonstrated the adjustment method for ALP TD-OCT using an optical zoom lens and high-order diffracted lights for a variable imaging range. When the lateral range was adjusted from 8 to 4 mm using an optical zoom lens, the resultant lateral resolution improved from 78 to 25 μm. The reduced axial range was recovered by using higher-order diffracted lights. Since the InGaAs camera used only had 256 × 320 pixels at 60 fps, this low number of pixels limited lateral resolution and axial range, and the frame rate limited the time resolution of OCT images. These limitations could be diminished by using a commercially available high-performance InGaAs camera (SU640SDWH-1.7RT: 512 × 640 pixels, 109 fps). Our ALP TD-OCT system is artifact-free, sufficiently sensitive (94.6 dB) to image biological tissue, and can display OCT images in real time because it uses only simple calculations. In addition, its adjustable range can be useful for OCT imaging in a diverse range of fields.
Acknowledgments
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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