March 15, 2002 / Vol. 27, No. 6 / OPTICS LETTERS
Spectral interferometric optical coherence tomography with nonlinear b-barium borate time gating Y. Yasuno, Y. Sutoh, M. Nakama, S. Makita, M. Itoh, and T. Yatagai Institute of Applied Physics, University of Tsukuba, Tennôdai 1-1-1, Tsukuba, Ibaraki 305-8573, Japan
M. Mori Japan Agency of Industrial Science and Technology, Umezono 1-1-4, Tsukuba, Ibaraki 305-8568, Japan Received September 27, 2001 A high-speed, all optical coherence tomography system was designed and constructed. This tomography system employs spectral interferometry and optical Fourier transformation to reduce the number of mechanical scanning dimensions required for multidimensional profilometry. The system also employs a time gate comprising a b-barium borate crystal driven by a femtosecond laser pulse to improve measurement time. This system has 43-mm depth resolution and 150-fs temporal resolution and is capable of taking 1000 crosssectional image frames per second. © 2002 Optical Society of America OCIS codes: 110.0110, 110.4500, 070.0070, 070.4340, 120.3180.
The latest biomedical techniques and industrial processes are dependent on extremely precise prof ilometry of biomedical materials and industrial products. For prof ilometric techniques to be noncontact and nondestructive, and to measure biomedical materials, they need to be capable of measuring highly light-scattering objects. In the construction of measurement systems that feature these properties, optical coherence tomography (OCT) systems, including broadband light sources, such as white-light sources and superluminescent diodes, have been extensively applied.1 – 6 One of the advantages of the OCT systems is that they are nondestructive, since visible light photons are low-energy particles. Hence, OCT systems are widely applied in the biomedical field.7 – 9 The other advantage is that OCT systems can be used in conjunction with a confocal setup for prof ilometry of highly scattering objects. Although OCT systems have many advantages, they also have a drawback: They require mechanical scanning in a high number of dimensions. To measure the n-dimensional structure of an object, OCT systems demand n-dimensional mechanical scanning. This type of mechanical operation is time consuming, and in some cases it is better to avoid such an operation. With the aim of overcoming the requirement of a high number of scanning dimensions, several research groups have studied OCT systems that employ spectral interferometry.10,11 These systems read out the depth information of an object that is encoded in the temporal prof ile of a probe light in parallel fashion by use of a spectrometer and thus do not depend on mechanical scanning. This technique reduces, by one, the number of scanning dimensions required. In Refs. 12 and 13, an all-optical version of the spectral interferometric OCT system was proposed that requires fewer scanning dimensions. This improved system requires only one-dimensional mechanical scanning for determination of the three-dimensional structure of an object. In this Letter we describe our attempts to further reduce the measurement time required by the spectral interferometric OCT system. Cancellation of the phase term of the spectrum of a probe pulse is a fundamental 0146-9592/02/060403-03$15.00/0
requirement of spectral interferometric OCT systems. In a previous study,13 a CCD camera and a liquidcrystal spatial light modulator were used to convert the spectrum of the probe light into its power spectrum, that is, to cancel the phase term of the spectrum. Although this cancellation is essential, the driving time of the CCD and the liquid-crystal spatial light modulator impedes the further reduction of measurement time. Our next approach, described here, was to replace the CCD camera and the liquid-crystal spatial light modulator with a b-barium borate (BBO) crystal and cancel the phase term of the spectrum by time gating of the BBO crystal, driven by a femtosecond trigger pulse. By using a fast-driven time gate, we remove the limiting factor on the OCT system. Below, we describe the operation of our OCT system. Figure 1 shows the schematic setup of the nonlinear spectral interferometric OCT system. We define the coordinates in terms of a rectangular Cartesian system to align the beam axis with the chosen z axis; the x and y axes are parallel and perpendicular, respectively,
Fig. 1. Schematic setup of the nonlinear spectral OCT system: BS, beam splitter; CC, corner cube; x-CL, y-CL, cylindrical lenses along the x and y axes, respectively; G, grating of 1800 line pairs兾mm; M’s, mirrors. The light source is a regenerated Ti:sapphire pulse laser with 150-fs duration and 1-kHz repetition. The focal lengths of the cylindrical lenses are 60 mm for x-CL1, 120 mm for x-CL2, 150 mm for x-CL3, and 200 mm for y-CL. © 2002 Optical Society of America
OPTICS LETTERS / Vol. 27, No. 6 / March 15, 2002
to the plane of the page. The pulse power of the input laser pulse is decreased by a wedge, then split by a beam splitter into a probe pulse and a trigger pulse on a delay line. The probe pulse is one-dimensionally focused on the object by an x-oriented cylindrical lens, x-CL1, and modulated, that is, scattered and ref lected, by the object. The modulated probe pulse is def ined S S T T as Ep1 共x, t兲 苷 Ep1 Ep1 共t兲, where Ep1 and Ep1 共t兲 are, respectively, the spatial and temporal prof iles of the T modulated probe pulse. The temporal prof ile, Ep1 共t兲, contains the depth 共z兲 information on the object as the convolution between a derivative of the refractiveindex distribution of the object, ≠n兾≠z, and the original temporal probe-pulse prof ile. This differential effect is because the ref lectivity of the object is determined by differentiation of the refractive index. The modulated probe pulse is spatially decomposed into its temporal spectral components by a grating and a cylindrical lens, x-CL2, which together constitute a spectrometer, and is superimposed on the BBO crystal as ∑ ∂ µ ∂ µ µ ∂∏ 2p 2px x , T S ˆ p1 exp 2i Ep2 苷 E˜ p1 xt ⴱ E blc f1 blc f1 l c f1 (1) ˜ and E, ˆ respectively, denote the temporal and where E spatial Fourier transforms of E, ⴱ denotes a convolution operator, f1 is the focal length of x-CL2, and b is a constant determined by the pitch and angle of the grating. The spatial width of the probe pulse on the grating is sufficiently wider than its temporal S ˆ p1 , is suff iciently width, so the Fourier transform, E S T ˜ p1. Hence we can regard E ˆ p1 narrower than E as a delta function and ignore it. By means of this approximation, we can ignore the last term of Eq. (1) as a delta function. The Fourier transform of the depth information of the object is spread spatially here, so we can spatially project the depth structure by use of the spatial Fourier-transform lens, x-CL3. However, the second term of Eq. (1) contains a phase term that is rapidly skewed in the temporal domain; moreover, the temporal probe-pulse duration on the BBO crystal is several picoseconds, which induces spatial signal shifting in the CCD camera. To cancel the skewed phase term and signal shifting, we use the BBO crystal as a time gate driven by a femtosecond trigger pulse. The f light time of the trigger pulse is adjusted by means of a delay line. The trigger pulse and the probe pulse are mixed in the BBO crystal and generate a harmonic wave with a short interaction time that corresponds to the temporal duration of the trigger pulse, in this case 150 fs. The harmonic wave has the same spatial prof ile as the spectrum of the probe pulse and has a very short temporal duration that matches the trigger-pulse duration. Because of its short duration, we can regard the skewed phase term as a temporally fixed phase term. Finally, the harmonic wave is spatially Fourier transformed by lens x-CL3. The depth structure of the object is spatially projected on the x axis of the CCD camera as
T Eout ~ Ep1
∂ ∂ µ blc f1 x S , ⴱ Eˆ trig 2pf2 lh f2 l h
where lh is the central wavelength of the harmonic S ˆ trig wave, f2 is the focal length of x-CL2, E is the Fourier transform of the spatial prof ile of the trigger pulse T represents the z structure on the BBO crystal, and Ep1 S T ˆ of the object. Etrig is sufficiently narrower than Ep1 that we can ignore this term as a delta function; hence, expression (2) represents the z differentiation of the refractive-index distribution, that is, the ref lectivity distribution, of the object. As can be seen in Fig. 1, all lenses in the system are cylindrical and do not have a y-oriented structure, and the object is imaged on the BBO surface along the y axis by use of cylindrical lens y-CL. We can thus obtain not only the one-dimensional z structure of the object but also a y z cross-section image on the CCD camera. By employing these techniques, this OCT system is able to determine the cross-section image of the ref lectivity distribution of an object by one-shot measurement. We can also measure the structure of the object three dimensionally, using one-dimensional mechanical scanning. A cross-sectional image taken with a one-shot measurement of the OCT system is shown in Fig. 2. The measured object is constructed from a glass slide substratum and multilayered thin cover glasses attached with nail varnish; the whole object is coated with vapor-deposited aluminum. The horizontal axis in Fig. 2 corresponds to the x axis on the CCD plane, i.e., the depth, the z axis on the measured object; the vertical axis corresponds to the y axis. This cross-section image, called a frame, shows the height–depth step on the surface of the object. Because this frame is taken with one shot of the probe pulse, the temporal resolution of the measurement is 150 fs, the same as the probe-pulse duration. Similarly, the measurement
Fig. 2. Cross-section image taken with a CCD camera. The horizontal axis corresponds to the x axis on the CCD plane, which in turn corresponds to the z axis on the object. The vertical axis corresponds to the y axis of the CCD plane and also the y axis of the object. This image was taken with one shot of the probe pulse.
March 15, 2002 / Vol. 27, No. 6 / OPTICS LETTERS
Fig. 3. Three-dimensional surface of the sample whose cross-section image is shown in Fig. 2. We take 41 frames of the y z cross section and reconstruct this structure from them.
speed (frames per second) is determined by the repetition rate of the pulse laser light source. In this case, the ratio is 1 kHz and the measurement speed is 1000 frames兾s. Although the peak width in Fig. 2 shows the depth resolution of the measurement to be 43 mm, the theoretical resolution should be better than this actual f igure. The resolution is determined by the bandwidth of the light source, that is, the temporal coherence length of the probe pulse. The resolution is also restricted by the spatial window size of the BBO crystal, or the spatial width of a trigger pulse on the BBO crystal: see the second term of expression (2). In our prototype, the aperture of the BBO crystal is 5 mm, the beam width of the trigger pulse on the BBO crystal is wider than the aperture, and the focal length of x-CL3 is 150 mm. According to these parameters, the theoretical resolution is estimated to be 17 mm. In an actual setup, the resolution is also restricted by the complex refractive-index distribution of the object that is being measured and the alignment errors in the optical setups; this is why our prototype does not have so good a resolution as the theoretical version. Although the actual z resolution of the prototype of 43 mm is not particularly high, its accuracy should be higher than the resolution. The z accuracy is determined by the pixel pitch of the CCD camera, so it can be improved by use of a higher-resolution CCD camera or by placement of a magnifying lens in front of the CCD camera. Using a magnifying lens, however, reduces the power density of the output image, leading to a trade-off between signal-to-noise ratio and accuracy. The z-dynamic range is restricted by the spatial beam width of the probe pulse on the grating [see the last term of Eq. (1)], the numerical aperture of spectrometer lens x-CL2, and the resolution of the BBO crystal. These parameters determine the resolution of the spectrometer formed by the above-mentioned optical elements. We confirmed that our prototype actually has a 1-mm dynamic range. Next, we reconstructed the three-dimensional surface of this stepped object. The frame shown in Fig. 2 is a y z cross section of the object, so that by
taking multiple frames during mechanical scanning of the object along the x axis we an reconstruct its three-dimensional surface prof ile. The reconstructed three-dimensional profile is shown in Fig. 3. To reconstruct this surface, we mechanically scanned the object and took 41 y z cross-section frames. In this figure, we can clearly identify the steps on the surface. The x and y resolution are theoretically estimated from the numerical apertures of x-CL1 and y-CL and the wavelength of the probe light to be 1.4 and 3.8 mm, respectively. In conclusion, we have improved the temporal resolution and the measurement speed of a previously described spatiotemporal joint-transform OCT system13 by employing femtosecond light pulses as the light source and a BBO crystal as a time gate for canceling the phase term on the spectrum of the probe pulse. A prototype of the improved OCT system was able to determine the surface prof iles of sample objects with a depth resolution of 43 mm and a depth dynamic range of 1 mm and has 150-fs temporal resolution at a measurement time of 1000 frames兾s. Although, in this Letter, we give results for a measured mirror surface, we have obtained some rough surface images in pilot experiments.14 Y. Yasuno thanks the Japan Society for the Promotion of Science Research Fellowship Program for its support of this postdoctoral studies. Y. Yasuno’s e-mail address is [email protected]
References 1. P. A. Flournoy, R. W. McClure, and G. Wyntjes, Appl. Opt. 11, 1907 (1972). 2. B. S. Lee and T. C. Strand, Appl. Opt. 29, 3784 (1990). 3. B. Bowe and V. Toal, Opt. Eng. 37, 1796 (1998). 4. E. A. Swanson, Opt. Lett. 17, 151 (1992). 5. B. W. Colston, Jr., M. J. Everett, L. B. Da Silva, L. L. Otis, P. Stroeve, and H. Nathel, Appl. Opt. 37, 3582 (1998). 6. A. C. Oliveira, F. M. M. Yasuoka, J. B. Santos, L. A. V. Carvalho, and J. C. Castro, Rev. Sci. Instrum. 69, 1877 (1998). 7. J. K. Barton, J. A. Izatt, M. D. Kulkarni, S. Yazdanfar, and A. J. Welch, Dermatology 198, 355 (1999). 8. A. M. Rollins, M. D. Kulkarni, S. Yazdanfar, R. Ung-arunyawee, and J. A. Izatt, Opt. Express 3, 219 (1998), http://www.opticsexpress.org. 9. W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kartner, J. S. Schuman, and J. G. Fujimoto, Nature Med. 7, 502 (2001). 10. D. Meshulach, D. Yelin, and Y. Silberberg, IEEE J. Quantum Electron. 33, 1969 (1997). 11. R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker, and A. F. Fercher, Opt. Lett. 25, 820 (2000). 12. Y. Yasuno, Y. Sutoh, N. Yoshikawa, M. Itoh, M. Mori, K. Komori, M. Watanabe, and T. Yatagai, Opt. Commun. 177, 135 (2000). 13. Y. Yasuno, M. Nakama, Y. Sutoh, M. Itoh, M. Mori, and T. Yatagai, Opt. Commun. 186, 51 (2000). 14. Y. Sutoh, Y. Yasuno, M. Itoh, M. Mori, and T. Yatagai, in Digest of Conference on Lasers and Electro-Optics (CLEO/Pacif ic Rim) (Optical Society of America, Washington, D.C., 2001), paper TuGl-2.