We propose a method for high-speed terahertz spectroscopic imaging that is based on electro-optic sampling with a noncollinear geometry of the THz beam and probe laser beam and has a multistep mirror in the path of the probe beam. We made an imaging system that operates in the over 2.0-THz range and enables the sample region corresponding to a (28 × 28)-pixel area on the sensor to be imaged with a spatial resolution of 1.07 mm and a frequency resolution of 0.079 THz. We also show how the proposed method might be extended for faster THz spectroscopic imaging.
© 2011 OSA
Terahertz waves with frequencies from 0.1 to 10 THz have recently been attracting attention because they penetrate nonconducting materials (e.g., paper, cloth, and plastic), enabling us to identify many materials that have spectral fingerprints in the THz range . Terahertz time-domain spectroscopy (THz-TDS) instrumentation can be used for frequency-resolved imaging , which is useful in security , medical , and pharmaceutical  fields as well as in the nondestructive analysis of historical cultural assets . In THz-TDS the frequency spectrum at any point in the sample is obtained by taking the Fourier transform of the time-domain data gathered when the electric field strength is measured while an optical delay line varies the delay between the THz pulse and the optical probe pulse. Because this time-domain data is the result of hundreds of measurements and to get a two-dimensional (2D) spectroscopic image we need to move the sample or measurement system and repeat the measurements at hundreds if not thousands of points in a plane, the data acquisition time is long. It of course depends on the size of the imaged object, the total number of the pixels in the image, and the frequency resolution required but is typically measured in hours. Various methods for reducing the measurement time in THz-TDS imaging have been proposed. A rotary optical delay mechanism with six curved mirror plates, for example, enables data to be generated faster than it can be generated when using a linear stage optical delay line . Also faster than using an optical delay line is asynchronous optical sampling in which two femtosecond lasers each generate and detect THz pulses at slightly different repeat frequencies . Neither of these methods, however, eliminates the need to make a time-consuming 2D scan of the object.
The advantage of electro-optic (EO) sampling is that all the information needed to make an amplitude image of an object can be obtained instantly without moving the object . In conventional EO sampling, the polarization of an optical probe pulse propagating collinearly with the THz pulse changes by an amount that depends on the strength of the THz electric field in the EO sampling medium. When 2D EO sampling is performed, the 2D field distribution in the medium is converted into a 2D optical intensity distribution after the readout beam passes through a crossed polarizer, and the optical image is captured by a camera. Obtaining a frequency spectrum, however, requires this 2D imaging to be performed a few hundred times using a mechanical stage for the optical delay line , so the use of conventional EO sampling is still very time consuming. The optical delay line can be eliminated and the temporal waveforms captured in a single shot by making the THz beam and the probe laser beam being incident on the EO crystal in a noncollinear geometry . The THz color scanner  uses this noncollinear EO sampling method for THz-TDS imaging but still requires the object to be scanned in one direction.
We have therefore developed an optical system that makes it unnecessary to move the object. The method this system uses is based on noncollinear EO sampling and uses a multistep mirror (MSM) for parallel measurements of temporal waveforms at regions on the surface of an EO crystal. In Section 2 of this paper we describe an MSM that ensures that the probe laser pulse front is the same at each of the regions on an EO crystal on which probe laser beam and THz beam are incident. In Section 3 we show an experimental system for spectroscopic imaging, and in Section 4 we explain the results of experiments with that system.
2. Multistep mirror device
2.1 Basic concept
We first describe the noncollinear EO sampling method that can measure temporal waveforms of THz beams without using optical delay lines [11, 12]. As shown in Fig. 1 , in this method the probe laser beam pulse is incident on the EO crystal at an angle of incidence θ and the THz beam focused on the object and passing through it is collimated and is incident on the EO crystal perpendicularly. At the distance x from a point at which the THz pulse front and the probe laser pulse front coincide on the EO crystal, the optical path difference (xtanθ) is proportional to x. Thus the probe laser beam that passes through the EO crystal forms an image on a camera and the temporal waveform f(t) corresponding to a pixel position in the x direction can be obtained without using an optical delay line. The Fourier transform of f(t) is the mathematical representation of the frequency spectrum. Spatial information in the y' direction can be obtained directly from the pixel data in the y direction on the camera. Therefore, a spectroscopic image can be obtained by scanning the object in only the x' direction.
The method we have devised, in contrast, requires no scanning at all. As shown in Fig. 2 ,
- 1) A collimated THz beam passes through the object and
- 2) The relation between the pulse front of the probe laser beam and the THz beam is kept the same in each of the regions in the x' direction.
To keep the same relation between the pulse front of the probe laser beam and the THz beam in number k of regions in the x' direction, we added a multistep mirror to the noncollinear EO sampling system to create a pulse front that has k steps of equal width. Thus, points at which the THz beam and the probe laser pulse fronts coincide are spaced equidistantly on the EO crystal surface, and from each of the k regions the temporal waveform in the x direction is obtained. Spatial information in the y' direction is also obtained from this image. Since the time window of the temporal waveform is reduced to 1/k, we considered three methods for broadening the time window (see Fig. 3 ). In the first method, shown in Fig. 3(a), an optical delay line is used to obtain an image at every time window T and the total temporal waveform is synthesized from these images. With this method, it is possible to freely expand the total time window of the temporal waveforms by changing the number of times that the optical delay line is moved. In the second method, shown Fig. 3(b), the femtosecond laser beam sequentially passes through glass plates with different thicknesses on a rotary plate, and optical delays are produced by the difference between the refractive indexes of glass and air. Images are acquired faster this way because the rotary movement in method 2 is faster than the linear movement in method 1. The third method, shown in Fig. 3(c), involves repeated measurements of temporal waveforms within each region (“cell”) by using MSMs arrayed in the step-height direction so that the probe pulse front also has steps in the y' direction. This method enables THz spectroscopic imaging without an optical delay line. Several variations of these methods are possible, but in this paper, we focus on confirmation of the feasibility of using an MSM to produce pulse front steps in the x' direction and use the first method to extend the time window of the temporal waveform. Although time delays could also be produced by using a transparent optical element such as a multistep glass block, a reflective optical element has the advantage of not dispersing the femtosecond laser pulse.
2.2 Design of multistep mirror
To design a mirror that has multiple steps in the x' direction, the first thing we did was to calculate the angle θ needed for obtaining the desired resolution Δt of the temporal waveform. If the probe laser beam passing through an EO crystal of width D forms an image on N pixels of a CMOS camera with sensor pitch p as shown in Fig. 4 , the following relation holds:
The temporal waveform resolution Δt from the angle θ and the magnification M can be determined by Eqs. (1) and (2). The frequency range of the THz spectrum determined from the Fourier transform of the temporal waveforms is 1/(2Δt) and the waveform time resolution Δt is set to 0.10 ps to enable measurement of the 5-THz frequency range. If D is 30 mm, p is 20 µm, and N is 448, noncollinear angle θ is 27 degrees and image-formation magnification M is 0.33. Note that the number of pixels in the y' direction differs from those in the x' direction, because the EO crystal surface is not perpendicular to the probe laser beam. The number of pixels in the y' direction is DM/p and corresponds to 504 pixels. We will explain the reason why N is 448 in the end of this section.
We next discuss the design of an MSM for THz spectroscopic imaging of a (k × k)-cell area. The simple structure in which the reflective surfaces of the MSM are perpendicular to the probe’s optical axis is shown in Fig. 2. The time difference generated by a step height d of the MSM is 2d/c. Since the time difference at the origins of cells that are separated by N/k pixels on the CMOS camera is NΔt/k, we set the step height d to NcΔt/(2k) in order to make sure that the time difference is the same at all the cells on the camera. And since the total width Dcosθ of the probe laser beam is divided into k steps, the step width w is Dcosθ/k. This makes it possible for a temporal waveform to be obtained with time resolution Δt and duration NΔt/k at each cell. The measurement configuration shown in Fig. 2, however, has a beam splitter reflecting the probe laser beam to the MSM before it reaches the EO crystal, complicating the optical system and resulting in a loss of probe laser power. We eliminate the need for this beam splitter by using an MSM structure in which the reflective surfaces are inclined at 45 degrees and the beam is reflected through 90 degrees. Not all of the reflected-beam area contains probe light because, as shown in Fig. 5 , no light is reflected from step areas in the shadows of adjacent neighboring steps. If the width of the beam reflected by a single step is w' and the optical path difference is d', the width of the unused area is the optical path difference d'. Since this must be set to NcΔt/k,
Since the step height d and the step width w are given by and , we can determine d and w of the MSM from Eqs. (3) and (4). The time window T is w'/(w' + d') times narrower than it would be if the probe laser beam was incident perpendicularly to the MSM steps, and we can use Eqs. (2) - (4) to obtain the following equation:
If we assume the number of cells k is 14, step height d is calculated to be 0.68 mm and step width w is calculated to be 2.03 mm. Therefore, both width w' and the unused width (d') are calculated to be 0.96 mm, and the utilized duty of the probe laser beam, w'/(w' + d'), is 50%. Because resolution Δt is 0.10 ps, we can also determine time window T is 1.6 ps from Eq. (5). In other words, temporal waveforms are measured on each cell by using 16 camera pixels ( = 448 pixels/14 × 50%). Here, we assume that the number of pixels of the CMOS camera is 512 × 512 pixels. The maximum value of N is 448 because N should be divisible by 14 (the number of cells) and the number of pixels in the y' direction should be less than 512 pixels.
2.3 Lens system correcting the effects of diffraction by the multistep mirror
The previous parts of this paper have used the geometrical optics approximation, but diffraction must also be taken into account because each reflective surface of the MSM works as a narrow slit aperture. If W is the width of a step on the MSM (0.96 mm), R is the distance from the MSM to the EO crystal, and the wavelength λ of the probe light is 800 nm, at R < W 2/λ the diffraction will be Fresnel diffraction and the intensity up at the coordinate x 0 on the crystal (corresponding to the coordinate x on the MSM) can be calculated using the following equation :
Calculated and measured intensity distributions of an 800-nm laser beam diffracted by a slit 0.96 mm wide are shown in Fig. 6(a) . The full width at half maximum of the beam diameter decreases with distance from the slit, is smallest at 300 mm, and then again increases with distance. The distance R between the MSM surface and the EO crystal is limited to 400 mm by our optical table. These results therefore indicated that the MSM should be placed as close as possible to the EO crystal in order to ensure that the width of the beam on the EO crystal is close to the width of the MSM step. Because in our noncollinear EO sampling system the MSM cannot be closer than 100 mm from the crystal, we use a telecentric lens system to correct the effect of diffraction. The experimental result shows that if a distance from the slit to the diffraction-correction lens system is the focal length (100 mm), the width of the plateau in the intensity distribution at R' (100 mm) from the exit of the diffraction-correction lens system is close to the width of the slit shape [see Fig. 6(b)]. This result indicates that a beam profile on the EO crystal almost the same as that on the MSM surface can be obtained by using the diffraction-correction lens system. Nevertheless, taking account of problems such as chipping at the edges of the fabricated MSM, we neglect the single pixels at each end and use only the center 14 pixels in a cell for measurement of the temporal waveforms.
3. Experimental setup
The experimental system is shown schematically in Fig. 7 . A THz beam is generated by a photoconductive antenna (BATOP Gmbh, PCA-40-05-10-800-h) driven by pulses emitted by a Ti-sapphire femtosecond laser (Mai Tai by Spectra Physics, pulse energy = 13 nJ, pulse duration = 100 fs, central wavelength = 800 nm, repetition rate = 80 MHz). A bias voltage of ± 40 V is applied to the photoconductive antenna with a modulation frequency of 125 Hz. The THz beam is collimated to a beam diameter of 60 mm by an aspherical plano-convex lens (Tsurupica, by Pax Co., focal length = 112 mm) and forms an image (at 1:1) on the EO crystal after passing through two THz aspherical plano-convex lenses (focal length = 120 mm). The imaging lens system is designed in such a way that the image spot at maximum image height on the EO crystal is not larger than the diffraction-limit spot size at 1 THz (diameter = 1.97 mm). The EO crystal is a (110) ZnTe single crystal (30 mm × 30 mm, 1.5 mm thick). The probe laser beam passes through a polarizer and a Berek compensator, is expanded to a diameter of 60 mm, is reflected by the MSM, passes through the diffraction-correction lens system, and is incident on the EO crystal. The diffraction-correction lens system is two aspherical plano-convex lenses having a focal length of 100 mm. The probe laser beam that passes through the EO crystal is incident on a CMOS camera (Intelligent Vision System, by Hamamatsu Photonics K.K., number of pixels = 512 × 512 pixels, pixel size = 20 µm × 20 µm, frame rate = 250 fps, digital output = 12 bits) with macro lens (the image-formation magnification = 0.33). The CMOS camera is synchronized with the bias voltage of the photoconductive antenna, and an image is acquired at 125 fps by a dynamic subtraction technique . The Berek compensator retards the phase of the probe laser by about 7 degrees from zero bias in order to ensure that the sampling sensitivity increases within a range in which the CMOS sensor is not saturated. The diameters of the THz beam and the probe laser beam are expanded larger than the EO crystal size to reduce the intensity distribution as possible.
The MSM (shown in Fig. 8 ) was made by bonding 14 glass plates that had been optically polished to a thickness of 0.68 mm ( ± 12 µm) and then applying a gold reflective coating. As described in the previous section, the utilized duty of the probe beam is 50%, and THz beam cannot be measured within regions in which the probe laser is not incident on the EO crystal. Therefore, to measure the temporal waveforms in 28 regions (twice as many regions as the steps on the MSM), we measure the waveforms in 14 regions, shift the object 1.07 mm ( = 30 mm/28 cells) in the x' direction, and measure the waveforms again. Contrary to the x' direction, each camera pixel has spatial information on the object in the y direction. To conform spatial resolution in the y direction to that in the x direction, we average the data of a row of 18 pixels ( = 504 pixels/28 cells) within each cell. Finally, the spectroscopic image of a (28 × 28)-cell region is calculated. Because the object size is 30 mm × 30 mm corresponding to the EO crystal size, the size of each cell in this case is 1.07 mm × 1.07 mm.
4. Results and discussion
The main peaks of the temporal waveforms measured with no object in the THz beam are shown in Fig. 9 , where green represents positive and red represents negative amplitudes of the electrical field. It is confirmed that the temporal waveforms for each of 14 cells (equivalent to the number of steps of the MSM in the horizontal direction of the image) are displayed. The dark areas in the four corners are due to blocking of the THz beam and probe laser beam by the metal plate holding the EO crystal. The retardation distribution due to both residual birefringence of the EO crystal and oblique incidence of the probe laser beam to lens surfaces  should be corrected in the captured image. Hence we correct the image using the method in Ref. 16, and the corrected image is shown in Fig. 9.
To evaluate the effects of the diffraction-correction lens system, we measured the distribution of sampling sensitivity in a cell. We compared the relative sampling sensitivity of each cell, using the maximum value of the temporal waveform, while moving the optical delay line in 0.10-ps steps. The shift of the maximum values of the temporal waveforms at the 7th line from the left in Fig. 9, which corresponds to the optical axis of the diffraction-correction lens system, and the lines at the edges furthest from the axis (the 1st and 14th lines from the left in Fig. 9) are shown in Fig. 10 . The lowest sampling sensitivity in the 16-pixel region illuminated by the probe laser was 43%, but the lowest sampling sensitivity in the central 14-pixel region was 70%, confirming the effectiveness of the diffraction-correction lens system. Since the probe laser is incident on the EO crystal obliquely, at the two edges away from the optical axis the image-formation position of the diffraction-correction lens system varies by a as much as ± 14 mm. The profiles there are almost the same as the profile at the optical axis, so this system is suitable for practical use. Because of this position variability at the edges, though, in the experiments we set the time window to 1.4 ps (14 pixels).
We then evaluated (28 × 28)-cell spectroscopic imaging with no object in the THz beam. The optical delay line is moved 9 times in steps of 210 µm. With this condition, the time window of the temporal waveform is 12.6 ps, with a resolution of 0.10 ps. As a result, we can obtain a frequency spectrum of over 2.0-THz range with a resolution of 0.079 THz. Figure 11(a) and 11(b) show the temporal waveform and the THz spectrum at the center cell by integrating 500 frames. The signal to noise (SN) ratio of temporal waveform, which is the ratio of the peak-to-peak amplitude to the standard deviation of the data before main peak, is 35. The absorption peaks indicated by arrows in the THz spectrum in Fig. 11(b) are at 1.10, 1.20, 1.40, and 1.66 THz, and these values correspond to the water-vapor absorption peak pattern in the NASA database [17, 18]. Thus we confirmed the accuracy of the measured THz spectrum.
With 764 cells (excluding the 5 cells in each of the four corners), the in-plane dispersion of the peak-to-peak amplitude of the temporal waveforms, calculated by dividing the standard deviation by the mean, was 29%. This was caused by the power distribution of the THz beam generated from a photoconductive antenna. Due to the interface reflection between the GaAs substrate and Si lens, the power at the center of the Si lens is lower than the area around the center . The standard deviation of the times at the maximum of the temporal waveforms, on the contrary, was 0.11 ps. We assume that this variation is caused by the dimension error of the MSM, the wavefront aberration of the THz and/or probe laser beam, and quantization error due to the measurement of camera pixels. When the least significant bit is q, quantization error is normally-distributed in a range of ± q/2. Quantization error has a mean of zero and the standard deviation of quantization error σ QE, is given by:
The results obtained when measuring a test sample by integrating 500 frames are shown in Fig. 12 . The sample, shown in Fig. 12(a), is an aluminum plate into which 2-mm-wide lines forming letters were cut. Figure 12(b) shows an amplitude image that is the peak-to-peak amplitudes of the temporal waveforms converted to 8-bit grayscale. The letters can be clearly recognized. The temporal waveforms of two cells indicated by rectangular frames in Fig. 12(b) are shown in Fig. 12(c), and the THz spectrum at cell A in Fig. 12(b) is shown in 12(d). The THz spectrum has the absorption peaks as is the case in absence of the object.
The pure image-acquisition time was 72 seconds: 4 seconds × 9 images × 2 (due to one movement of the sample), when the CMOS camera operated at 125 fps. Because moving the sample took one second and moving the delay-line stage for each image took 0.5 seconds, the overall measurement time was 81 seconds. It should be noted that it was necessary to move the object once because we used an MSM that made the utilized duty of the beam 50%. If an MSM of 28 steps with reflective surfaces perpendicular to the optical axis was used, the object would not have to be moved and the measurement time would be only 40 seconds.
A THz beam generated by a low-peak-power Ti-sapphire femtosecond laser and a photoconductive antenna was used in our experiments, but the measurement time could be shortened by instead using a high-peak-power laser and a nonlinear optical crystal. As an example we estimate what the measurement time would be when using the high-intensity THz beam generated by a regenerative amplified femtosecond laser (Spectra-Physics Hurricane, pulse energy = 600 µJ, pulse duration = 150 fs, central wavelength = 800 nm, repetition rate = 1 kHz, beam diameter = 10 mm) and a nonlinear optical crystal, ZnTe, in an experimental setup similar to that described in Ref. 12. We assume in this case that the MSM has reflective surfaces perpendicular to the optical axis (see Fig. 2) and it is thus not necessary to move the object. In Ref. 12 the same CMOS camera that was used in our experimental system was used and the image-acquisition time with the camera driven at a frame rate of 125 fps is 8 ms, so the measurement time for synthesizing the temporal waveforms from 9 images would be 72 ms. If a usual stepping motor stage for the optical delay line was used, however, 500 ms would be necessary for each delay. So the total time would be 4.072 seconds and the measurement time would depend largely on the mechanical stage movement time. If the same range of delay times was obtained by using the method shown in Fig. 3(b), however, the measurement time would be only about 72 ms.
Finally, we show the result of THz spectroscopic imaging of metal hole arrays (MHAs, Mutsumi Corporation). A MHA is a metal plate with circular holes arranged in an equilateral-triangle lattice and acts as a bandpass filter in THz range. We imaged MHAs whose center frequencies were 0.4 THz (pitch = 0.75 mm, hole diameter = 0.50 mm) and 1.0 THz (pitch = 0.30 mm, hole diameter = 0.13 mm), and the other areas in the imaging field were covered by aluminum plates with no holes [see Fig. 13(a) ]. Figure 13(b) shows spectroscopic imaging results obtained by integrating 2000 frames. Each MHA is bright at the center frequency and distinguished from the other area. Figure 13(c) shows the spectra at cells A and B in Fig. 13(b). The number of images integrated affects image quality, such as uniformity and contrast. Figure 14 shows the spectroscopic imaging results obtained by integrating different numbers of frames. For 500, 2000, and 5000 frames the contrast ratios of the 0.4-THz MHA area to the aluminum plate area were respectively 2.0, 3.1, and 6.0. We infer from this that the integration of a larger number of frames results in an image with higher contrast.
We have proposed a high-speed THz spectroscopic imaging method using noncollinear EO sampling and using an MSM forming pulse-front steps in the probe laser beam for two dimensionally parallel measurements of temporal waveforms. Our prototype imaging system using a Ti-sapphire femtosecond laser and operating in the over 2.0-THz range can image a region corresponding to a (28 × 28)-pixel area with a frequency resolution of 0.079 THz and a spatial resolution of 1.07 mm. Its 81-second measurement time can be reduced to 0.072 seconds by using a regenerative amplified laser instead of a Ti-sapphire oscillator. As a next step, we will explore the feasibility of measuring the temporal waveforms within each cell on the EO crystal when making pulse fronts that have steps in both the longitudinal and lateral directions for faster THz spectroscopic imaging.
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