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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 12507–12518
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Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator

David Shrekenhamer, Claire M. Watts, and Willie J. Padilla  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 12507-12518 (2013)
http://dx.doi.org/10.1364/OE.21.012507


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Abstract

We present a single pixel terahertz (THz) imaging technique using optical photoexcitation of semiconductors to dynamically and spatially control the electromagnetic properties of a semiconductor mask to collectively form a THz spatial light modulator (SLM). By co-propagating a THz and collimated optical laser beam through a high-resistivity silicon wafer, we are able to modify the THz transmission in real-time. By further encoding a spatial pattern on the optical beam with a digital micro-mirror device (DMD), we may write masks for THz radiation. We use masks of varying complexities ranging from 63 to 1023 pixels and are able to acquire images at speeds up to 1/2 Hz. Our results demonstrate the viability of obtaining real-time and high-fidelity THz images using an optically controlled SLM with a single pixel detector.

© 2013 OSA

1. Introduction

Terahertz (THz) radiation has great potential for imaging applications [1

1. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999) [CrossRef] .

,2

2. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. on Prog. in Phys. 70, 1325–1379 (2007) [CrossRef] .

] due to its ability to penetrate most dielectric materials and non-polar liquids. Its harmless interaction with human tissue suggests imaging in this regime has immediate applicability in the fields of biodetection [3

3. T. M. Korter and D. F. Plusquellic, “Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared,” Chem. Phys. Lett. 385, 45–51 (2004) [CrossRef] .

], system inspection [4

4. N. Karpowicz, H. Zhong, C. Zhang, K. -I. Lin, J. -S. Hwang, J. Xu, and X. -C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005) [CrossRef] .

], and detection of illegal drugs [5

5. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11, 2549 (2003) [CrossRef] [PubMed] .

]. However, a significant limitation currently preventing wide-spread THz imaging is the absence of efficient sources and detectors operating between 0.1 and 10 THz - a band of the electromagnetic spectrum often referred to as the “THz gap” [6

6. G. P. Williams, “Filling the THz gap – high power sources and applications,” Rep. Prog. Phys. 69, 301–326 (2005) [CrossRef] .

]. Although there exists great technical difficulty in feasibly performing THz imaging, there has been moderate progress over the past 25 years. Multi-element detector schemes, both microbolometer arrays [7

7. A. W. Lee and Q. Hu, “Real-time, continuous-wave terahertz imaging by use of a microbolometer focal-plane array,” Opt. Lett. 30, 2563–2565 (2005) [CrossRef] [PubMed] .

, 8

8. N. R. Butler, R. J. Blackwell, R. Murphy, R. J. Silva, and C. A. Marshall, “Low-cost uncooled microbolometer imaging system for dual use,” Proc. SPIE 2552583–591 (1995) [CrossRef] .

] and electro-optic sampling with high-performance CCD cameras [9

9. Q. Wu, T. D. Hewitt, and X. -C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996) [CrossRef] .

], provide accurate and real-time THz images. However, these imaging systems often require high powered sources and/or expensive complex detectors that lack the sensitivity of single element detectors. The use of a single detector has been employed to obtain THz images by mechanically raster scanning the object plane to acquire spatial information [10

10. B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20, 1716–1718 (1995) [CrossRef] [PubMed] .

]. While the latter technique has the benefit of high spatial resolution and accurate imaging, major shortcomings are the long acquisition time [11

11. M. C. Nuss, “Chemistry is right for T-ray imaging,” IEEE Circ. Dev. Mag. , 12, 25–30 (1996) [CrossRef] .

] and the mechanical nature of the scanning system.

An alternative single pixel solution - relying on spatial multiplexing - could help overcome many of the disadvantages involved with more conventional imaging techniques. The imaging of complex scenes is enabled with sparse detector arrays or even single pixels using spatial light modulators (SLMs) to multiplex the image. Mechanical masks that are either manually exchanged or placed onto spinning discs have demonstrated proof of principle THz imaging using, for example, compressive sensing and adaptive coded aperture imaging [12

12. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008) [CrossRef] .

14

14. H. Shen, L. Gan, N. Newman, Y. Dong, C. Li, Y. Huang, and Y. Shen, “Spinning disk for compressive imaging,” Opt. Lett. 37, 46–48 (2012) [CrossRef] [PubMed] .

]. Although SLMs, such as digital micro-mirror (DMD) [15

15. D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003) [CrossRef] .

] and liquid crystal (LC) [16

16. K. M. Johnson, D. J. McKnight, and I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 29, 699–714 (1993) [CrossRef] .

] systems are commercially available, they do not operate at THz frequencies. Attempts to develop THz SLMs have thus far been ineffective in producing efficient and high speed devices, though there are several attractive alternatives to using mechanical masks.

Semiconductor and metamaterial / semiconductor hybrid devices can be controlled by a variety of different methods to achieve THz amplitude and frequency modulation [17

17. M. Rahm, J. Li, and W. J. Padilla, “THz wave modulators: a brief review on different modulation techniques,” J. Infrared Millim. Terahz. Waves 34, 1–27 (2012) [CrossRef] .

]. An initial study demonstrated performance of a room-temperature electronic controlled metamaterial for a 4 × 4 pixel array used to form a diffractive grating [18

18. W. L. Chan, H. -T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 213511 (2009) [CrossRef] .

]. Additionally, all-electronic dynamic metamaterials have demonstrated switching speeds up to 10 MHz [19

19. D. Shrekenhamer, S. Rout, A. C. Strikwerda, C. Bingham, R. D. Averitt, S. Sonkusale, and W. J. Padilla, “High speed terahertz modulation from metamaterials with embedded high electron mobility transistors,” Opt. Express 19, 9968–9975 (2011) [CrossRef] [PubMed] .

]. Another avenue to achieving a THz SLM has been inspired by the work initially developed at millimeter wavelengths where optically excited electron plasmas in photo-active semiconductors serve as a spatial mask in creating Fresnel lenses and reflect-arrays for beam-steering and communication based applications [20

20. G. W. Webb, W. Vernon, M. Sanchez, S. Rose, and S. Angello, “Optically controlled millimeter wave antenna,” Microw. Photon. 275–278 (1999).

, 21

21. M. R. Chaharmir, J. Shaker, M. Cuhaci, and A. Sebak, “Novel photonically-controlled reflectarray antenna,” IEEE Trans. Antennas Propag. 54, 1134–1141 (2006) [CrossRef] .

]. Early studies indicate that THz spatial modulation is also possible with sufficient optical power [22

22. X. C. Zhang and D. Auston, “Generation of steerable submillimeter waves from semiconductor surfaces by spatial light modulators,” Appl. Phys. Lett. 59, 768–770 (1991) [CrossRef] .

24

24. S. Busch, B. Scherger, M. Scheller, and M. Koch, “Optically controlled terahertz beam steering and imaging,” Opt. Lett. 37, 1391–1393 (2012) [CrossRef] [PubMed] .

]. Both electronic and optically controlled SLMs pose as a fast and efficient means to dynamically control electromagnetic radiation thus allowing for realistic methods to perform THz imaging.

In this work we demonstrate single pixel multiplex THz imaging based on an optically controlled reconfigurable THz mask in high-resistivity Silicon (ρ-Si). By utilizing a DMD to optically encode spatial patterns we are able to achieve up to 1023-pixel, high fidelity THz images with frame rates as fast as one image per two seconds - only limited by available software. The achieved signal-to-noise ratio (SNR) suggests the possibility that our technology may provide quasi real-time THz imaging with frame rates as fast as 3 frames per second (fps).

2. Theory

2.1. Imaging theory

Typical single pixel camera architectures involve four key components: a light source, imaging optics, a single element detector, and a SLM. Light from an illuminated object is focused using imaging optics onto a SLM which, for binary encoding, selectively passes portions of the image to the detector and blocks others. A sequence of known patterns is displayed on the SLM and a single value is acquired for each mask frame. Prior knowledge of these masks allows for the reconstruction of the image as schematically illustrated in Fig. 1. For example, mechanical raster scanning can be emulated by displaying a single pixel at a time on the SLM.

Fig. 1 Schematic depicting multiplex imaging process where the spatial modulation of a formed image allows for the reconstruction using a single pixel detector. Example 7 × 9 binary masks taken from rows of the 63 × 63 S-matrix are shown.

For imaging systems using intensity based detectors that are not sensitive to the phase of electromagnetic radiation, binary masks that modulate the intensity are well suited. There are several different types of binary coded apertures that can be used to multiplex an image - though the field is dominated by random and Hadamard based masks. Random binary masks are comprised of 1’s and 0’s determined by standard probability distributions such as Gaussian or Bernoulli, among others. Hadamard matrices are square matrices composed of +1’s and −1’s in which each row is orthogonal to all other rows [25

25. M. Harwit and N. J. Sloane, Hadamard Transform Optics (Academic, 1979).

]. To create binary masks we can use an S-matrix, created by omitting the first row and column of the corresponding normalized Hadamard matrix, substituting all 1’s with 0’s, and all −1’s with 1’s. Each row of this matrix can then be used as a 1, 0 mask for successive measurements in a single pixel imaging system.

We define a one- or two- dimensional image by a vector X with N-elements (this can be done by concatenating the rows into a single column). We represent a single measurement yj in a multiplexing scheme by the following expression:
yj=i=1Nϕjixi
(1)
or the matrix equation Y = Φ × X. In this equation, Y is a column vector with M-elements representing the M measurements taken and Φ is the M × N measurement matrix, in which each row represents a mask displayed on the SLM. For example, Φ that corresponds to a raster scan imaging technique is the N × N identity matrix. For a well-conditioned measurement matrix [26

26. W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 6th ed. (Thompson Brooks/Cole, 2008).

] and the fully determined case, i.e. M = N, the reconstruction becomes linear and can be solved by a simple matrix equation: X = Φ−1 × Y[25

25. M. Harwit and N. J. Sloane, Hadamard Transform Optics (Academic, 1979).

]. One advantage of using S-matrices as the measurement matrix such that Φ = SN is the particularly simple decoding process given by: SN1=2N+1(2SNTJN) where SN is the S-matrix of order N, SNT is its transpose, and JN is an N × N matrix of all 1’s [25

25. M. Harwit and N. J. Sloane, Hadamard Transform Optics (Academic, 1979).

].

2.2. Dynamic THz spatial light modulators

The photoexcitation of free carriers in semiconductors is a well understood process for both CW and ultrafast optical beams [27

27. R. H. Bube, Photoelectronic Properties of Semiconductors, (Cambridge University, 1992).

]. For ρ-Si substrates a higher carrier density can be generated by CW pump beams, compared to pulsed sources of identical average power, due to the relatively long carrier lifetimes in Si [28

28. D. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16, 15123–15129 (2008) [CrossRef] [PubMed] .

]. The change in the complex dielectric constant can be described by the Drude model [28

28. D. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16, 15123–15129 (2008) [CrossRef] [PubMed] .

31

31. T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78, 1106–1109 (1997) [CrossRef] .

].
ε(ω)=εωp2ω(ω+iΓ),
(2)
where ε = 11.7 is the frequency independent dielectric permittivity due to the contribution of bound electrons, Γ = 1/τc is the damping rate (with τc = 160 fs the average collision time [28

28. D. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16, 15123–15129 (2008) [CrossRef] [PubMed] .

, 31

31. T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78, 1106–1109 (1997) [CrossRef] .

]), ωp2 is the plasma frequency defined as ωp2=nSie2/ε0m* with e the electron charge, ε0 the free-space permittivity, and m* = 0.26me the effective mass [31

31. T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78, 1106–1109 (1997) [CrossRef] .

]. If we neglect the carrier diffusion and consider only free carrier generation and linear recombination in the semiconductor, the carrier density nSi is proportional to the optical power of the pump beam and is modulated through photodoping [30

30. H. Alius and G. Dodel, “Amplitude-, phase-, and frequency modulation of far-infrared radiation by optical excitation of silicon,” Infrared Phys. 32, 1–11 (1991) [CrossRef] .

]
nSi=I0(1R)τ2Adh¯ω,
(3)
where I0 is average power, R is the reflectivity of Si at the pump wavelength, h̄ω is the photon energy, τ = 25 μs is the carrier lifetime [32

32. H. Schulenburg and H. Tributsch, “Electropassivation of silicon and bulk lifetime determination with dry polymer contact,” J. Phys. D 33, 851 (2000) [CrossRef] .

], A is the area of the laser excitation, and d is the penetration depth. At THz frequencies the photodoped charges correspond to a large increase in the absorption coefficient as a function of I0, allowing for strong attenuation of incident THz electromagnetic waves.

We measured the THz transmission, shown as the solid curves in Fig. 2, through a 520 μm thick ρ-Si substrate (ρ > 10,000 ohm-cm) for increasing optical power using a 980 nm CW laser diode. We characterize the THz transmission using a Fourier Transform Infrared (FTIR) spectrometer, a mercury (Hg) arc lamp source, multi-layer mylar beamsplitter, and liquid-helium cooled silicon bolometer. The size of the THz and optical beams was 4mm and 9mm, respectively, at the plane where we placed the ρ-Si substrate. Etalons due to multiple reflections within the ρ-Si substrate were removed and the modified interferogram was Fourier transformed to obtain the sample spectrum. A similar procedure was performed for a reference with an open channel; division of the sample and reference spectra resulted in the frequency dependent absolute value transmission T(ω) and corresponding differential transmission [Tp(ω)−Tp=0(ω)]/Tp=0(ω) shown in Figs. 2(a) and 2(b), respectively. We observe broadband attenuation of the THz signal where, at our maximum fluence of p = 1 W/cm2, we measure a modulation depth of 43% at 0.7 THz. The undoped (Tp=0(ω), black curve) of Fig. 2(a) was performed in vacuum; however, due to technical limitations, transmission measurements for both photodoped cases were performed in air - leading to a reduced signal-to-noise which accounts for the large fluctuations in T(ω).

Fig. 2 (a) Solid curves show the transmission of THz radiation through ρ-Si wafer as a function of frequency for several different optical fluence values. Measurements were done in atmosphere in FTIR system. The dashed curves show the simulated fits for increasing carrier concentration nSi within the penetration depth (85 μm) of ρ-Si. (b) Dependence of the differential transmission on the optical fluence as defined in the text.

3. Experimental setup

A schematic of the THz imaging system is presented in Fig. 3(a) and consists of both an optical beam path (red lines) and a THz beam path (gray lines). As a broadband THz source we utilize a Hg-Arc lamp which emulates a 5500 K blackbody. The source is used in conjunction with a long-pass filter (LPF-065 from Lakeshore) that blocks wavelengths shorter than 65 μm (> 4.6 THz). The THz imaging optics consist of two 50.8 mm diameter 90° off-axis parabolic mirrors (OAPMs) each with an effective focal length of fL=190.6 mm. The first OAPM is fL from the source and back-illuminates the object a distance 150 mm away. The second OAPM, a distance 933 mm from the object, focuses the radiation and forms a conjugate image on the SLM 215 mm away. The system has an overall magnification of 0.23, mapping the 43.5 mm diameter object to approximately 10 mm at the SLM. An image was formed by placing a back illuminated patterned metal aperture between the OAPMs so that a THz image (10 mm in diameter) was formed at the SLM plane. The THz image is transmitted through the ρ-Si and focused using a 50.8 mm diameter TPX lens with f = 100 mm to the detector - a liquid-helium cooled silicon bolometer. The entire apparatus is enclosed and is purged by dry air at room temperature to reduce the THz absorption due to water vapor.

Fig. 3 (a) Schematic of LED and THz optical layouts. The THz beam (shown in gray) passes through the object and is imaged with the OAPMs onto a ρ-Si wafer. The collimated 980 nm wavelength optical beam (shown in red) reflects off the DMD surface and creates a spatial light pattern at the THz image plane. (b) Photograph of a 7×9 S-matrix mask pattern displayed on DMD; each mask pixel is 1.5 mm being constructed from tiling 109 × 109 DMD pixels. (c) Lock-in amplifier voltage output is displayed as a function of time in seconds for the 63 sequential S-matrix masks; the entire measurement takes approximately 2 s. Inset: reconstructed THz beam profile at image plane. (d) Zoom-in of time data shown in (c). Raw data from four consecutive S-matrix mask measurements are shown with the corresponding binary mask shown above; the averaged values used for reconstruction along with the standard deviation are shown on the right.

The DMD is computer controlled and able to change between frames up to a (software limited) time of 32 ms. Binary bitmap files are loaded into the software to be displayed on the DMD. The white portions represent light that was directed toward the ρ-Si whereas black represents light that was directed away. This corresponds to white mask regions photodoping the ρ-Si, i.e. modulating the THz transmission where black represents unmodulated regions. Since the DMD is designed for much shorter optical wavelengths, we may utilize several mirror pixels to function as a single THz-sized pixel for the S-matrix mask, thus permitting flexibility for both pixel count and pitch. We use S-matrix masks of varying complexity and change the pixel size accordingly to keep the overall mask area approximately equal. The THz image resolutions we investigated are summarized in Table 1 and the relation between physical size and DMD pixels is detailed.

Table 1. Relationship between THz imaging resolution and DMD pixel sizes

table-icon
View This Table

Detection of the THz signal is performed with a lock-in detection technique. The laser diode power is modulated with a square wave at a frequency of 300 Hz, which in turn modulates the THz power detected. Output voltage from the Si-bolometer is input into a lock-in amplifier which provides the measured THz signal in Volts. Figures 3(c), 3(d) show the measured lock-in voltage as a function of time for several successive masks; the corresponding binary bitmap displayed on the DMD are shown above the raw data in Fig. 3(d). The stabilization of the lock-in signal after switching between masks is close to 5 ms, with a SNR recorded for each measurement greater than 100; this is sufficient to allow us to acquire a THz measurement at the limits of the switching time of the DMD. We may estimate the total power of THz radiation used in our imaging apparatus since our bolometer has a calibrated responsivity of 2.64 × 105 V/W at 300 Hz. Our DMD may be configured to modulate all pixels on and off, from which we measure a lock-in signal of 130 mV. Thus our THz image consists of a maximum modulated THz power of 96 nW over an integrated bandwidth from 0.2 – 4.6 THz.

4. Experimental results and discussion

In order to compare our imaging system to more conventional schemes, we perform both raster scan and Hadamard imaging and highlight differences between the two methods - see Fig. 4. S-matrix masks consist of roughly 50% light throughput and it has been demonstrated that using masks created from an N × NS-matrix can increase SNR by a factor of (N+1)2NN2 over raster scan imaging with the same resolution and pixel size [25

25. M. Harwit and N. J. Sloane, Hadamard Transform Optics (Academic, 1979).

]. Figures 4(a), 4(b) show both the metallic aperture used as an object and an optical photograph of the conjugate image at the front surface of the ρ-Si wafer. It is well known that aspheric optics, such as OAPMs, produce aberrations that can distort the image plane in the form of astigmatism and coma, as seen by the image distortion in Fig. 4(b) [36

36. C. A. Bennet, Principles of Physical Optics (John Wiley & Sons, 2008).

].

Fig. 4 Comparison of THz imaging with raster scan masks and S-matrix masks. (a,b) Show the metallic aperture used as the object and the conjugate optical image on the ρ-Si wafer. (c) Spatial map of the THz power density shown for the reference beam profile with contour plots showing the intensity drop in dB. (d) – (f) Shows raster-scan images for increasing mask complexity. (g) – (i) Shows Hadamard reconstructed images of the same size and complexity as the raster scan measurements to the immediate left. Each mask was displayed for 500 ms for all above measurements.

Figures 4(c) – 4(e) show raster-scan images acquired with increasing resolution and constructed from 63, 255, and 1023 measurements respectively. The last column in Fig. 4(f) – 4(h) shows Hadamard reconstructions with the same number of measurements and resolution as the raster scan images. In order to compare different imaging techniques and resolutions, an identical time of 500 ms per mask was used, giving total acquisition times of 31.5 s for the 7 × 9 images, 127.5 s for the 15 × 17 images, and 511.5 s for the 31 × 33 images. While the image quality in the case of 7 × 9 pixel resolution is comparable between the two techniques, the rapid decrease in image quality for the raster scan images at higher resolutions is apparent - see Fig. 4(e). In contrast, the image quality is retained for increasing pixel count in the multiplexing case.

To better understand why the signal depreciated significantly for increasing pixel complexity in the case of the raster scan we investigated the measured power for each respective mask type. We calculate the spatial dependence of the power density (nW/mm2) by taking the total measured THz power (96 nW) and extracting the THz power density per pixel pi from the measured 15×17 beam profile intensity as defined by
pi=96nW(698μm)2×xii=1255xi,
(5)
where xi is the reconstructed signal from pixel i. In Fig. 4(i) we show a high quality image of the power density - sufficient to observe optical aberrations resulting from the use of OAPMs which result in an asymmetric distribution of THz power about the horizontal axis, as mentioned above. The power/pixel decreases for increasing resolution since the pixel size is reduced - in our case from 1.5 mm to 698 μm to 328 μm. The peak power density calculated in Eq. (5) is 2.5 nW/mm2 near the center of the beam. This corresponds to a total of 5.6 nW of measured power for the 1.5 mm size pixel and 0.27 nW for the 328 μm pixel, a 95% reduction of measured power proportional to the decrease in pixel area. As shown in Fig. 4(i), the power density is −9 dB lower towards the outer diameter of the images and approaches values as low as 50 pW of THz power for 328 μm sized pixels - still well above the bolometer’s specified noise-equivalent-power (NEP) of 1.57×1013W/Hz. The raster scan is unable to compensate for the loss in measured signal for each pixel due to decreasing pixel dimension. In the Hadamard case, although the signal per pixel also drops with decreasing pixel size, the increase in sampled pixels for each data acquisition offsets the reduction in signal. Consequently, the higher resolution image offers more information without sacrificing SNR. The improvement in the image quality for increasing pixel complexity is evident and allows for the aberrations of the THz image resulting from the OAPMs to be rendered.

In order to explore our imaging technique for possible use in screening applications, in Fig. 5 we show various examples of high-fidelity THz images. The top row displays photographs of all the objects imaged: crosses with 8 mm and 4.5 mm wide arms at the object plane (Fig. 5(a), 5(b)) and two razor blades imaged in manila envelopes (Fig. 5(c), 5(d)). As stated above, we can program the S-matrix masks to allow for several different functions and mask complexities. We achieved high resolution images containing 31× 33 pixels with each mask pixel measuring 328 μm across; this was acquired with 1023 sequential measurements. Like the images shown in Fig. 4, the masks were displayed for 500 ms each, giving a total image acquisition time of 511.5 s. The reconstructed THz images are shown in Fig. 5(e) – 5(h). Due to the magnification of the system, the crosses are imaged down to have 2.5 mm and 1.5 mm wide arms, respectively. The minimum feature size of the images that we can resolve for these crosses is limited by diffraction. The Rayleigh criterion suggests we achieve a diffraction limited spot size of approximately 1.4 mm at 1 THz, although the inherently broadband nature of detected radiation presented here generates a more complex diffraction pattern than that for use of a monochromatic source [35

35. E. L. Shirley, “Diffraction effects on broadband radiation: formulation for computing total irradiance,” Appl. Opt. 43, 2609–2620 (2004) [CrossRef] [PubMed] .

]. The razor blades are placed within manila envelopes and are, obviously, not visible in the optical, however are clearly identified in the THz images, demonstrating the potential for THz imaging to be used in security applications.

Fig. 5 THz imaging with high-resolution S-matrix masks (31 × 33 pixels with each pixel measuring 328 μm on a side). (a,b) Show metallic apertures used as the object of two differently sized crosses, with arm widths of approximately 8 mm and 4.5 mm in the object plane mapping to 2.5 mm and 1.5 mm on the image plane. (c,d) Two different types of metal razor blades that were placed in manila envelopes for imaging. (e) – (h) Shows the THz images of the corresponding objects shown immediately above. Each mask was displayed for 500 ms for all measurements above, giving a total acquisition time of 511.5 s for each image.

5. Metamaterial SLMs

Results presented in Figs. 4, 5 demonstrate the ability to perform THz imaging using a single pixel detector. For many potential applications it would be desirable to obtain spectral information, rather than integrating across a portion of the THz range. As discussed in the introduction, metamaterials have shown an ability to modulate THz electromagnetic radiation with demonstrated advantages over conventional materials, including spectral selectivity, amplitude modulation [37

37. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006) [CrossRef] [PubMed] .

], and phase modulation [38

38. H. -T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3, 148–151 (2009) [CrossRef] .

]. We computationally explore a metamaterial based SLM which is optically controlled - schematically shown Fig. 6(a). Our metamaterial SLM is modeled similar to that for the ρ-Si and we add a complimentary electric split ring resonator [39

39. H. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15, 1084–1095 (2007) [CrossRef] [PubMed] .

] to the top of the substrate. The optically excited charge carriers shunt the resonant response of the metamaterial, effectively modulating the transmission at the operational frequency as shown in Figs. 6(b) and 6(c). The metamaterial has been designed to yield a band-pass response centered at 1 THz and achieves a simulated modulation depth of 67% for a maximum fluence of 1 W/cm2 - see Fig. 6(b).

Fig. 6 Optically reconfigurable THz masks with metamaterials. (a) Schematic showing optical pump beam overlapped with THz incident onto complimentary electric split ring resonators (cESRRs) where the photoexcited carriers in Si underneath metamaterial dynamically tune the EM response of the MM. (b) Simulation showing the modulation in THz transmission as a function of carrier excitation. (c) Simulated current density in the cESRR and the electric field magnitude plotted in plane for the case of maximum transmission at 1 THz.

The advantage in THz imaging provided by adding resonant metamaterials, as demonstrated in Fig. 6, is an increase in modulation depth at selected frequencies over bare silicon (67% as compared to 37% at 1 THz). The modulation depth could be further improved by optimizing the geometry of ρ-Si within the metamaterial unit cell, as well as the photodoping wavelength - both of which could potentially maximize the carrier density closer to the surface. Obtaining spectral information with conventional instruments can be challenging, requiring complex high cost equipment and instrumentation with significantly limited acquisition speeds [40

40. R. A. DeVerse, R. R. Coifman, A. C. Coppi, W. G. Fateley, F. Geshwind, R. M. Hammaker, S. Valenti, F. J. Warner, and G. L. Davis, “Application of spatial light modulators for new modalities in spectrometry and imaging,” Proc. SPIE 4959, 12–22 (2003) [CrossRef] .

]. By arranging the pixels of metamaterial arrays to have uniquely designed operating frequencies we can create multi-color SLMs that could be used to perform high speed THz spectral imaging offering significant improvement over current systems.

6. Conclusion

We have performed high fidelity THz single pixel imaging and various scenes have been rendered. An optically controlled spatial light modulator was implemented through photodoping in high resistivity silicon and controlled by a DMD. We use S-matrix masks of varying resolution ranging from 63 to 1023 pixels and were able to obtain THz images as fast as one per two seconds. We directly compared Hadamard imaging to the raster-scan technique and highlighted the advantages of the multiplexing method. At THz frequencies dynamically reconfigurable semiconducting device technology provides significant advantages over traditional masks due to the benefit of adaptability and real-time control. This work demonstrates a new path for construction of THz imaging systems. Future work will realize real time imaging of more complex scenes as well as incorporating metamaterials to add additional functionalities applicable to sensing, imaging, and dynamic scene projectors.

Acknowledgment

References and links

1.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999) [CrossRef] .

2.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. on Prog. in Phys. 70, 1325–1379 (2007) [CrossRef] .

3.

T. M. Korter and D. F. Plusquellic, “Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared,” Chem. Phys. Lett. 385, 45–51 (2004) [CrossRef] .

4.

N. Karpowicz, H. Zhong, C. Zhang, K. -I. Lin, J. -S. Hwang, J. Xu, and X. -C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett. 86, 054105 (2005) [CrossRef] .

5.

K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11, 2549 (2003) [CrossRef] [PubMed] .

6.

G. P. Williams, “Filling the THz gap – high power sources and applications,” Rep. Prog. Phys. 69, 301–326 (2005) [CrossRef] .

7.

A. W. Lee and Q. Hu, “Real-time, continuous-wave terahertz imaging by use of a microbolometer focal-plane array,” Opt. Lett. 30, 2563–2565 (2005) [CrossRef] [PubMed] .

8.

N. R. Butler, R. J. Blackwell, R. Murphy, R. J. Silva, and C. A. Marshall, “Low-cost uncooled microbolometer imaging system for dual use,” Proc. SPIE 2552583–591 (1995) [CrossRef] .

9.

Q. Wu, T. D. Hewitt, and X. -C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996) [CrossRef] .

10.

B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett. 20, 1716–1718 (1995) [CrossRef] [PubMed] .

11.

M. C. Nuss, “Chemistry is right for T-ray imaging,” IEEE Circ. Dev. Mag. , 12, 25–30 (1996) [CrossRef] .

12.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008) [CrossRef] .

13.

O. Furxhi, E. L. Jacobs, and C. Preza, “Image plane coded aperture for terahertz imaging,” Opt. Eng. 51, 091612 (2012) [CrossRef] .

14.

H. Shen, L. Gan, N. Newman, Y. Dong, C. Li, Y. Huang, and Y. Shen, “Spinning disk for compressive imaging,” Opt. Lett. 37, 46–48 (2012) [CrossRef] [PubMed] .

15.

D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE 4985, 14–25 (2003) [CrossRef] .

16.

K. M. Johnson, D. J. McKnight, and I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron. 29, 699–714 (1993) [CrossRef] .

17.

M. Rahm, J. Li, and W. J. Padilla, “THz wave modulators: a brief review on different modulation techniques,” J. Infrared Millim. Terahz. Waves 34, 1–27 (2012) [CrossRef] .

18.

W. L. Chan, H. -T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett. 94, 213511 (2009) [CrossRef] .

19.

D. Shrekenhamer, S. Rout, A. C. Strikwerda, C. Bingham, R. D. Averitt, S. Sonkusale, and W. J. Padilla, “High speed terahertz modulation from metamaterials with embedded high electron mobility transistors,” Opt. Express 19, 9968–9975 (2011) [CrossRef] [PubMed] .

20.

G. W. Webb, W. Vernon, M. Sanchez, S. Rose, and S. Angello, “Optically controlled millimeter wave antenna,” Microw. Photon. 275–278 (1999).

21.

M. R. Chaharmir, J. Shaker, M. Cuhaci, and A. Sebak, “Novel photonically-controlled reflectarray antenna,” IEEE Trans. Antennas Propag. 54, 1134–1141 (2006) [CrossRef] .

22.

X. C. Zhang and D. Auston, “Generation of steerable submillimeter waves from semiconductor surfaces by spatial light modulators,” Appl. Phys. Lett. 59, 768–770 (1991) [CrossRef] .

23.

T. Okada and K. Tanaka, “Photo-designed terahertz devices,” Sci. Rep. 1, 121 (2011) [CrossRef] .

24.

S. Busch, B. Scherger, M. Scheller, and M. Koch, “Optically controlled terahertz beam steering and imaging,” Opt. Lett. 37, 1391–1393 (2012) [CrossRef] [PubMed] .

25.

M. Harwit and N. J. Sloane, Hadamard Transform Optics (Academic, 1979).

26.

W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 6th ed. (Thompson Brooks/Cole, 2008).

27.

R. H. Bube, Photoelectronic Properties of Semiconductors, (Cambridge University, 1992).

28.

D. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16, 15123–15129 (2008) [CrossRef] [PubMed] .

29.

M. Van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett. 56, 1694–1696 (1990) [CrossRef] .

30.

H. Alius and G. Dodel, “Amplitude-, phase-, and frequency modulation of far-infrared radiation by optical excitation of silicon,” Infrared Phys. 32, 1–11 (1991) [CrossRef] .

31.

T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78, 1106–1109 (1997) [CrossRef] .

32.

H. Schulenburg and H. Tributsch, “Electropassivation of silicon and bulk lifetime determination with dry polymer contact,” J. Phys. D 33, 851 (2000) [CrossRef] .

33.

C. Hutley, Diffraction Gratings, (Academic, 1982).

34.

J. P. Rice, J. E. Neira, M. Kehoe, and R. Swanson, “DMD diffraction measurements to support design of projectors for test and evaluation of multispectral and hyperspectral imaging sensors,” Proc. SPIE 7210, 72100D (2009) [CrossRef] .

35.

E. L. Shirley, “Diffraction effects on broadband radiation: formulation for computing total irradiance,” Appl. Opt. 43, 2609–2620 (2004) [CrossRef] [PubMed] .

36.

C. A. Bennet, Principles of Physical Optics (John Wiley & Sons, 2008).

37.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006) [CrossRef] [PubMed] .

38.

H. -T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3, 148–151 (2009) [CrossRef] .

39.

H. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express 15, 1084–1095 (2007) [CrossRef] [PubMed] .

40.

R. A. DeVerse, R. R. Coifman, A. C. Coppi, W. G. Fateley, F. Geshwind, R. M. Hammaker, S. Valenti, F. J. Warner, and G. L. Davis, “Application of spatial light modulators for new modalities in spectrometry and imaging,” Proc. SPIE 4959, 12–22 (2003) [CrossRef] .

OCIS Codes
(110.1085) Imaging systems : Adaptive imaging
(160.3918) Materials : Metamaterials
(110.6795) Imaging systems : Terahertz imaging
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Imaging Systems

History
Original Manuscript: March 21, 2013
Revised Manuscript: May 5, 2013
Manuscript Accepted: May 7, 2013
Published: May 14, 2013

Citation
David Shrekenhamer, Claire M. Watts, and Willie J. Padilla, "Terahertz single pixel imaging with an optically controlled dynamic spatial light modulator," Opt. Express 21, 12507-12518 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12507


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References

  1. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B68, 1085–1094 (1999). [CrossRef]
  2. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. on Prog. in Phys.70, 1325–1379 (2007). [CrossRef]
  3. T. M. Korter and D. F. Plusquellic, “Continuous-wave terahertz spectroscopy of biotin: vibrational anharmonicity in the far-infrared,” Chem. Phys. Lett.385, 45–51 (2004). [CrossRef]
  4. N. Karpowicz, H. Zhong, C. Zhang, K. -I. Lin, J. -S. Hwang, J. Xu, and X. -C. Zhang, “Compact continuous-wave subterahertz system for inspection applications,” Appl. Phys. Lett.86, 054105 (2005). [CrossRef]
  5. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express11, 2549 (2003). [CrossRef] [PubMed]
  6. G. P. Williams, “Filling the THz gap – high power sources and applications,” Rep. Prog. Phys.69, 301–326 (2005). [CrossRef]
  7. A. W. Lee and Q. Hu, “Real-time, continuous-wave terahertz imaging by use of a microbolometer focal-plane array,” Opt. Lett.30, 2563–2565 (2005). [CrossRef] [PubMed]
  8. N. R. Butler, R. J. Blackwell, R. Murphy, R. J. Silva, and C. A. Marshall, “Low-cost uncooled microbolometer imaging system for dual use,” Proc. SPIE2552583–591 (1995). [CrossRef]
  9. Q. Wu, T. D. Hewitt, and X. -C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett.69, 1026–1028 (1996). [CrossRef]
  10. B. B. Hu and M. C. Nuss, “Imaging with terahertz waves,” Opt. Lett.20, 1716–1718 (1995). [CrossRef] [PubMed]
  11. M. C. Nuss, “Chemistry is right for T-ray imaging,” IEEE Circ. Dev. Mag., 12, 25–30 (1996). [CrossRef]
  12. W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett.93, 121105 (2008). [CrossRef]
  13. O. Furxhi, E. L. Jacobs, and C. Preza, “Image plane coded aperture for terahertz imaging,” Opt. Eng.51, 091612 (2012). [CrossRef]
  14. H. Shen, L. Gan, N. Newman, Y. Dong, C. Li, Y. Huang, and Y. Shen, “Spinning disk for compressive imaging,” Opt. Lett.37, 46–48 (2012). [CrossRef] [PubMed]
  15. D. Dudley, W. Duncan, and J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc. SPIE4985, 14–25 (2003). [CrossRef]
  16. K. M. Johnson, D. J. McKnight, and I. Underwood, “Smart spatial light modulators using liquid crystals on silicon,” IEEE J. Quantum Electron.29, 699–714 (1993). [CrossRef]
  17. M. Rahm, J. Li, and W. J. Padilla, “THz wave modulators: a brief review on different modulation techniques,” J. Infrared Millim. Terahz. Waves34, 1–27 (2012). [CrossRef]
  18. W. L. Chan, H. -T. Chen, A. J. Taylor, I. Brener, M. J. Cich, and D. M. Mittleman, “A spatial light modulator for terahertz beams,” Appl. Phys. Lett.94, 213511 (2009). [CrossRef]
  19. D. Shrekenhamer, S. Rout, A. C. Strikwerda, C. Bingham, R. D. Averitt, S. Sonkusale, and W. J. Padilla, “High speed terahertz modulation from metamaterials with embedded high electron mobility transistors,” Opt. Express19, 9968–9975 (2011). [CrossRef] [PubMed]
  20. G. W. Webb, W. Vernon, M. Sanchez, S. Rose, and S. Angello, “Optically controlled millimeter wave antenna,” Microw. Photon.275–278 (1999).
  21. M. R. Chaharmir, J. Shaker, M. Cuhaci, and A. Sebak, “Novel photonically-controlled reflectarray antenna,” IEEE Trans. Antennas Propag.54, 1134–1141 (2006). [CrossRef]
  22. X. C. Zhang and D. Auston, “Generation of steerable submillimeter waves from semiconductor surfaces by spatial light modulators,” Appl. Phys. Lett.59, 768–770 (1991). [CrossRef]
  23. T. Okada and K. Tanaka, “Photo-designed terahertz devices,” Sci. Rep.1, 121 (2011). [CrossRef]
  24. S. Busch, B. Scherger, M. Scheller, and M. Koch, “Optically controlled terahertz beam steering and imaging,” Opt. Lett.37, 1391–1393 (2012). [CrossRef] [PubMed]
  25. M. Harwit and N. J. Sloane, Hadamard Transform Optics (Academic, 1979).
  26. W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 6th ed. (Thompson Brooks/Cole, 2008).
  27. R. H. Bube, Photoelectronic Properties of Semiconductors, (Cambridge University, 1992).
  28. D. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express16, 15123–15129 (2008). [CrossRef] [PubMed]
  29. M. Van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett.56, 1694–1696 (1990). [CrossRef]
  30. H. Alius and G. Dodel, “Amplitude-, phase-, and frequency modulation of far-infrared radiation by optical excitation of silicon,” Infrared Phys.32, 1–11 (1991). [CrossRef]
  31. T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett.78, 1106–1109 (1997). [CrossRef]
  32. H. Schulenburg and H. Tributsch, “Electropassivation of silicon and bulk lifetime determination with dry polymer contact,” J. Phys. D33, 851 (2000). [CrossRef]
  33. C. Hutley, Diffraction Gratings, (Academic, 1982).
  34. J. P. Rice, J. E. Neira, M. Kehoe, and R. Swanson, “DMD diffraction measurements to support design of projectors for test and evaluation of multispectral and hyperspectral imaging sensors,” Proc. SPIE7210, 72100D (2009). [CrossRef]
  35. E. L. Shirley, “Diffraction effects on broadband radiation: formulation for computing total irradiance,” Appl. Opt.43, 2609–2620 (2004). [CrossRef] [PubMed]
  36. C. A. Bennet, Principles of Physical Optics (John Wiley & Sons, 2008).
  37. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett.96, 107401 (2006). [CrossRef] [PubMed]
  38. H. -T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics3, 148–151 (2009). [CrossRef]
  39. H. Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, “Complementary planar terahertz metamaterials,” Opt. Express15, 1084–1095 (2007). [CrossRef] [PubMed]
  40. R. A. DeVerse, R. R. Coifman, A. C. Coppi, W. G. Fateley, F. Geshwind, R. M. Hammaker, S. Valenti, F. J. Warner, and G. L. Davis, “Application of spatial light modulators for new modalities in spectrometry and imaging,” Proc. SPIE4959, 12–22 (2003). [CrossRef]

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