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Abstract
High-resolution and hyperspectral imaging has long been a goal for multi-dimensional data fusion sensing applications – of interest for autonomous vehicles and environmental monitoring. In the long wave infrared regime this quest has been impeded by size, weight, power, and cost issues, especially as focal-plane array detector sizes increase. Here we propose and experimentally demonstrated a new approach based on a metamaterial graphene spatial light modulator (GSLM) for infrared single pixel imaging. A frequency-division multiplexing (FDM) imaging technique is designed and implemented, and relies entirely on the electronic reconfigurability of the GSLM. We compare our approach to the more common raster-scan method and directly show FDM image frame rates can be 64 times faster with no degradation of image quality. Our device and related imaging architecture are not restricted to the infrared regime, and may be scaled to other bands of the electromagnetic spectrum. The study presented here opens a new approach for fast and efficient single pixel imaging utilizing graphene metamaterials with novel acquisition strategies.
© 2017 Optical Society of America
1. Introduction
In the visible light regime, megapixel cameras are mature technology and it is not uncommon to find two such devices on a modern cellular smart phone. However outside the optical region, high resolution cameras with high pixel density remain challenging to fabricate and produce on a large scale. For example, the Abbe diffraction limit places a lower bound on pixel size – hence array dimensions and cost – in addition to the lack of available photoconductive materials that are easily fabricated, and integrated into large-format detectors. Various approaches have been used over the last several decades in order to achieve large format infrared focal plane arrays (FPAs) [1,2], including thermal based FPAs (thermopile [3], bolometric [4], pyroelectric [5]), and photon detection based FPAs (photoconductive [6], photovoltaic [7]). One notable example consists of 35 separate FPAs, each with 2048×2048 pixels, combined together to achieve an IR imager with 147 megapixels [8]. However, this brute-force approach to increase the field of view (FOV) with large format FPAs inevitably increases the volume, weight, and cost of the systems, thus making it impractical for many general applications. An alternative approach using computational imaging methods, can overcome the above described limitations to achieve large FOV and high resolution imaging through image plane coding schemes, allowing for single pixel or sparse detector arrays [9,10].
Over the last few decades spatial light modulators (SLMs), such as digital micromirror devices [11] and liquid crystal modulators [12,13], have been used for computational imaging in the visible and infrared regimes. However, slow modulation speeds, and the lack of spectral and polarization selectivity limits their application for hyper-/multi-spectral, polarized, multidimensional, and high speed computational imaging. More recently, single pixel imaging using all-electronic metamaterial based SLMs with different coding schemes have shown great potential to overcome conventional SLM limitations [14–17]. Additionally, metamaterial based SLM designs can be scaled across the electromagnetic spectrum thus enabling significant impact to modern imaging systems [15,18–20].
Graphene has drawn significant interest for applications in optoelectronic devices owing to its unique optical and electronic properties [21,22]. In the mid-infrared range, the occurrence of both interband and intraband transitions dominates, and the ability to modify graphene conductivity for light modulation is significantly reduced compared to longer wavelengths [23,24]. However, the flexibility enabled through a metamaterial design approach allows one to overcome the this limitation by allowing significant modulation through use of the imaginary portion of the conductivity. For example, recent work on all-electronic graphene based metamaterial modulators have demonstrated modulation speeds up to several GHz at infrared wavelengths, with peak modulation depths of 80% [25]. Here we demonstrate single pixel multiplexed infrared imaging using a reconfigurable 8×8 array based on graphene metamaterials. Our electronically reconfigurable GSLM enabled implementation and comparison of two imaging schemes – a conventional raster scanning method, and a novel frequency-division multiplexed coding approach. As we demonstrate below, both achieved similar high signal-to-noise-ratios (SNRs), but our FDM imaging scheme provided a decrease in imaging time by over an order of magnitude – a factor of 64× faster.
2. Metamaterial SLM design and optical properties
In Fig. 1(a) we show an optical image of the GSLM device used as the basis for our IR imaging system. The GSLM is an 8 × 8 metamaterial pixel array bonded to a chip carrier. The metamaterial unit-cell geometry is similar to that studied elsewhere [25], and consists of a top metamaterial layer and ground plane spaced by a 300-nm thick Al2O3 film (Fig. 1(b)). A single layer of graphene was transferred and placed between the metamaterial top layer and the dielectric spacer. The top metamaterial pattern is electrically continuous, with a total area of (296μm)2, and each pixel is defined through a pixelated ground plane. The size of each ground plane pixel is (35μm)2 with a 2-μm gap in-between. Electrical control lines run to each pixel ground plane (lying underneath) and are connect by vias through a 400-nm PECVD SiNx thin film.
Fig. 1 (a) Optical image of the 8×8 GSLM in a chip carrier. (b) zoomed-in view of the SLM. (c) Scanning electron microscope (SEM) image of the patterned metamaterial on graphene by electron beam lithography (EBL).The scale bar is 5 μm. (d) a close-up view of the metamaterial with dimensions px = 2 μm, py = 1.2 μm, l = 1.3 μm, w1 = 200 nm, w2 = 300 nm, g = 100 nm.
The wavelength dependent reflectivity was characterized with an infrared Fourier transform spectrometer with various bias voltages applied between the metamaterial and ground plane layers. The metamaterial layer was grounded, while the bottom ground planes were initially connected together, in order to be biased uniformly for characterization. The reflectivity R was referenced with respect to a gold mirror, and Fig. 2(a) shows the measured absorption spectra (A = 1 − R) with voltage values of −20V (red curve) and 20V (blue curve). As can be seen, when the voltage is increased, the absorption peak shifts from 7.45 μm to 7.72 μm, while the peak amplitude remains largely unchanged. We operate the GSLM by applying a square wave with bias levels from −20V to 20V, and thus our detected IR signal is proportional to the differential absorptivity, shown in Fig. 2(b), which achieves a maximum of 16% at 7.35 μm. Although the modulation shown in Fig. 2(b) realizes both positive and negative values – which may be limiting for broad-band sources – the integrated modulation depth across the range of 5–10 μm is relatively strong, owing to the positive modulation region between 8.6–10 μm, which largely cancels the negative modulation values.
Fig. 2 (a) Measured absorption for various gate voltages applied to the graphene. (b) Differential absorption spectrum between −20 V and 20 V.(c) Illustration of the imaging setup. GSLM: Graphene spatial light modulator; BS: beam splitter; WG: Wire-grid polarizer; OAP: off-axis parabolic mirror; MCT: Mercury cadmium telluride single pixel detector. (i) Oscilloscope is used for FDM imaging, and (ii) a Lock-in amplifier is used for raster scan imaging.
3. Spatial light modulator characterization
Figure 2(c) shows a schematic of the optical setup used in order to characterize the metamaterial SLM pixels, as well as for single pixel imaging. The GSLM was mounted on the stage of a Bruker Hyperion 3000 microscope. An unmodulated IR globar source provided the illumination energy which was split by a half-mirror beamsplitter before being projected onto the GSLM by a 15×0.4 NA reflective Schwarzschild objective. The reflected and modulated light then passes back through the beamsplitter and impinges upon an object placed in the microscope’s aperture plane, then continuing on through a wire-grid polarizer before being focused onto an MCT detector with a concentrating off-axis parabolic mirror. We used two computer controlled 32-channel USB digital I/O boards to modulate the GSLM using TTL logic at frequencies up to 4 MHz. The digital signals were converted to higher voltages – necessary for the GSLM – by a custom modulator board using a transistor in a common-emitter configuration. A custom software program was developed and used both for modulation of the GSLM and data acquisition from the LIA. The cooled detector was near-background limited with a detectivity of , indicating that source photon statistics dominates detector noise.
In order to evaluate the modulation performance of each pixel of the GSLM, we applied a static pattern with −20 V or 20 V on each pixel, and a MCT based focal plane array (128×128 pixels) was used in order to image modulated IR light from the surface. Figure 3(a) shows the spatial map of the measured modulation depth of the GSLM, integrated over the spectral range of 6 μm to 7.6 μm, as a colormap in 3D perspective, top of Fig. 3(a), and a 2D plane (bottom). The modulation depth of most of the pixels is larger than 0.05 except for one defective pixel located in the lower left corner. The variation in modulation depth is due to two factors: inhomogeneous grain size of chemical-vapor deposited graphene and nonuniform metamaterial geometry fabricated by electron-beam lithography. In order to quantify the ability of our graphene metamaterial architecture to provide independent pixel control with minimal cross talk, we performed imaging of a static pattern displayed on the GSLM. In this case we displayed the letters ’Ir’ through application of a −20 V bias, while all other pixels had a bias of 20 V. Figure 3(b) is an image acquired with the FPA, and Fig. 3(c) is the FPA image normalized by the values displayed in Fig. 3(a).
Fig. 3 (a) Spatial map of the modulation depth of the spatial light modulator integrated from 6 μm to 7.6 μm. Top is the 3D map and the bottom is the corresponding 2D map. The colormapo shows the range of the modulation. (b) Experimentally measured ’Ir’ pattern statically displayed on the GSLM. The pixels with pattern ’Ir’ were applied with −20 V and other pixels were with 20 V. (c) Normalized display of a pattern of ’Ir’ based on the spatial map of the modulation depth in (a).
4. Single-pixel imaging results
4.1. Raster scan imaging
Single pixel imaging was demonstrated using the experimental setup shown in Fig. 2(a). The object was a transmission mask formed by laser cutting acrylic, which was covered by a layer of evaporated gold and black paint, with the clear areas forming the letter “d” – see Fig. 4(a). In order to demonstrate the advantages our single pixel imaging approach gains over a more standard technique we first demonstrated raster-scanned single-pixel imaging. This was achieved by individually modulating each pixel at 2.27 kHz with a 4 second integration time, resulting in a total acquisition time of 256 seconds. The chopping served to allow AC-coupled detection, reducing the 1/f noise of the MCT detector and amplifiers. The modulated light then was transmitted through the object and was focused onto a single-pixel MCT detector for measurement. The signal from the MCT detector preamplifier was then sent to a lock-in amplifier. The assembled raster scanned image is shown in Fig. 4(b) and it can be observed it is nearly identical to the original object.
Fig. 4 (a) An object – “d” mask – used for single pixel imaging. The object is binary with the yellow areas corresponding to open portions, and opaque portions denoted by blue colors. (b) Reconstructed image via raster scanning with the GSLM modulated at 2.27 kHz. (c) Reconstructed image via the frequency-division multiplexing method. (d) Frequency map used for FDM imaging. (e) The measured normalized power spectrum as a function of the modulation frequency – obtained by Fourier transforming the time-domain signal recorded by the infrared detector. The inset shows the measured modulation depth for pixels with corresponding modulation frequencies. The modulation depth is normalized to the average modulation measured with raster scanning.
4.2. Frequency-division multiplexed imaging
We next turn toward demonstration of a computational single pixel imaging approach. The particular technique we implement here is frequency-division multiplexing (FDM), which can exploit the fast response of the GSLM and wide readout bandwidth of cooled single-pixel IR detectors. In contrast to the raster scanning approach, all pixels of the GSLM are continuously modulated with a square wave of different frequencies. Ideally, the pixel Fourier components would be orthogonal, i.e. the frequencies used in frequency-division multiplexing (FDM) [26]. A true orthogonal frequency map requires narrow and precise frequency spacing (0.1% at 7.5 kHz), which is difficult without analog circuitry such as phase-locked loops. Instead, we utilized a near-orthogonal scheme which placed subsequent frequencies at even multiples, avoiding the odd harmonics generated by ideal square waves.
In Fig. 4(a) we show the object used for both raster-scanned imaging (Fig. 4(b)), and FDM imaging (Fig. 4(c)). The experimental IR single pixel images shown in Figs. 4(b) and 4(c) are false color, where the intensity is linear and represented using the colormap shown to the right. We find that both the raster-scanned and FDM approaches reproduce the object accurately. The reconstructed images shown in Figs. 4(b) and 4(c) use a continuous colormap shown in an isometric view, but – since our object is binary – both images may be made binary by choosing a suitable threshold level. That is, both images may be reconstructed to look identical to the input binary object with no false positives. A map of the modulation frequencies used for each pixel in FDM imaging is shown in Fig. 4(d) in units of kHz. The optical configuration was identical to the previous single-pixel imaging setup except each pixel was modulated at a unique frequency in the range of 1.17–75 kHz, shown in 4(d). The signal from the detector preamplifier was fed to an oscilloscope, which digitized a 4 second time record and performed a fast-Fourier transform (FFT). In Fig. 4(e) we show the FFT of the time-domain signal obtained with our IR detector for FDM imaging. The inset to Fig. 4(e) shows modulation depth, normalized with respect to that obtained in the raster-scanned case, at 2.27 kHz. The detector signal, compared to that obtained with raster-scanned imaging, now consists of the modulated intensities of all pixels simultaneously, i.e. we have implemented the multiplexing (Fellgett’s) advantage. Therefore, each pixel has an equivalent integration time equal to the chosen frame rate of our imaging system. For an ideal GSLM, our multiplexing approach only degrades the SNR by – compared to over that of an FPA – due to the duty cycle of the square wave modulation. The inset to Fig. 4(e) shows the modulation depth of the GSLM as a function of modulation frequency. As can be observed, the modulation is relatively constant for frequencies of approximately 2.5 to 75 kHz.
5. Discussion
The graphene metamaterial spatial light modulator only realizes moderate modulation capability, but yet is able to achieve good images, i.e. Fig. 4(c) reproduces the image resulting from the “d” mask accurately with no errors. The FDM image is nearly identical to the raster scanned version. These results shows that multiplexing techniques such as FDM – when combined with the wide bandwidth of the GSLM and detector – can realize a significant increase in imaging frame rates necessary for practical single-pixel imaging, without affecting image quality. Indeed the Shannon-Hartley theorem dictates that any multiplexing scheme which exhibits a speedup over raster scanning without sacrificing SNR requires greater bandwidth. The solid-state nature of the GSLM we have demonstrated here provides the necessary high modulation bandwidth. The inset in Fig. 4(e) shows the relative modulation depth of SLM pixels as a function of frequency and exhibits good performance through the 75 kHz maximum tested. It is important to note that our FDM approach results in image acquisition 64 times faster than that possible with raster-scanning. That is, the entire image was acquired over 4 seconds versus 256 seconds required for raster-scanning.
We next calculate the imaging noise for both the raster-scanned and FDM approaches. The peak signal-to-noise ratio (SNRp) is calculated as [27],
where Ppeak = 1 and represents the highest normalized pixel intensity, Pn the measured intensity for the nth pixel, On the ideal object intensity (0 or 1) for that pixel, and var is the variance. It was found that the raster scanned image had a SNRp of 17.5 dB compared to a SNRp of 15.0 dB in the FDM case. We also found the image SNR by setting the numerator in Eq. 1 equal to the average mask value of 13/63 (accounting for one failed GSLM pixel) to obtain an image SNR of 10.6 dB and 8.2 dB for raster scan and and FDM respectively. The remaining source of noise is cross-pixel interference due to intermodulation, likely caused by the nonlinear response of the MCT detector.We attribute the 2.5 dB difference of SNRp between raster scan and FDM techniques to properties of the FFT. In particular, the window function (Blackman-Harris) and detector function used will degrade SNR by discarding useful signal energy in order to avoid sidelobes, or equivalently increase the noise bandwidth. To show this, we utilized the lock-in amplifier and while displaying the same FDM modulation on the GSLM, we set the reference of the LIA to each pixel serially. The resulting SNR difference was less than 0.7 dB between raster scan and the above described serialized FDM. The synchronous demodulator of the LIA avoids certain FFT disadvantages, and indeed a bank of software synchronous demodulators can be used in order to achieve FDM imaging with no trade-offs compared to raster-scanning.
Since the imaginary part of conductivity of graphene exhibits a larger change than the real part of the conductivity, the modulation of the absorption mainly shows a resonant frequency shift over an amplitude change, consistent with our previous results [25]. Additionally, we achieve an approximate wavelength shift of 0.3 μm using an applied voltage of only ±20 V, which is significantly lower than that shown elsewhere. This lower control voltage is achieved through use of higher quality graphene, i.e. larger mobility, and a smaller gap g between metamaterial unit cells. Therefore, by improving the quality of graphene and decreasing the gap size, the control voltage can be reduced further. The lower voltages brought forth by our device configuration, as well as the use of a silicon substrate in a reflective configuration allows integration with CMOS based application-specific integrated circuit (ASIC) technology to realize on-chip control with a small form factor. Thus our device may be easily and inexpensively scaled to large formats, such as 1 million pixels with a total area about 3.5 cm on a side. The modulation speed was limited to 75 kHz by the driver electronics. Based on scaling up the pixel size from our previous devices, we believe this GSLM to be RC-limited with a 3 dB corner of approximately 350 MHz. The broad bandwidth allows selection of many orthogonal frequencies needed for FDM imaging with large-format modulator arrays.
6. Conclusion
In this paper, we have successfully demonstrated single-pixel infrared imaging with a graphene metamaterial based spatial light modulator. We have directly compared two single pixel imaging schemes, i.e. raster scan and FDM imaging. Both methods realized similar signal-to-noise ratios, but our FDM approach achieved faster frame rates by a factor equal to the image spatial resolution – 64× in the present example. Our work is general and not limited to the case experimentally demonstrated, and our configuration may be replicated to achieve metamaterial-based SLMs for single pixel imaging at nearly any desired sub-optical wavelength range. In addition, our device architecture is CMOS compatible, and thus commercial fabrication facilities may be used to obtain high performance megapixel and compact infrared imaging devices. This new approach to infrared imaging is diverse and thus highly relevant for numerous applications ranging from detectors and imaging to communications with novel acquisition strategies.
Funding
National Science Foundation (NSF) (ECCS-1610342); Office of Naval Research (N00014-15-1-0051). Performed in part at the Duke University Shared Materials Instrumentation Facility (SMIF), a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), supported by the National Science Foundation (ECCS-1542015) as part of the National Nanotechnology Coordinated Infrastructure (NNCI).
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