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Abstract
We experimentally demonstrate the use of a large-scale silicon-photonic optical phased array (OPA) chip as a compact, low-cost, and potentially high-speed light illuminating device for ghost imaging (GI) applications. By driving 128 phase shifters of a newly developed silicon OPA chip using rapidly changing random electrical signals, we successfully retrieve a slit pattern with over 90 resolvable points in one dimension. We then demonstrate 2D imaging capability by sweeping the wavelength. With the potential of integrating high-speed phase modulators, tunable lasers, grating couplers, and CMOS driver circuit on the same silicon platform, this work paves the way towards realizing ultrahigh-speed and low-cost single-chip GI devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ghost imaging (GI), or more generally, computational single-pixel imaging, has gained interest in recent years as an alternative scheme to image a scene by using a single-pixel detector [1,2]. Unlike conventional methods, where pixelated detector arrays are employed, the GI scheme computationally reconstructs the spatial information of the object by collecting the total light intensities reflected from or transmitted through the object under pseudo-random or structured illuminations. Since one can employ lower-cost single-pixel detector with higher sensitivity and faster temporal response, this scheme is particularly beneficial at non-visible wavelength ranges, where high-speed detector arrays are not always available or are expensive. In addition, by using compressed sensing (CS) techniques, image acquisition is possible with far fewer measurements than the total number of pixels [3], which offers distinctive advantage over beam-scanning approaches. As a result, GI has been successfully applied in various applications, such as multi-spectral imaging [3,4], time-resolved three-dimensional (3D) imaging [5–7], ophthalmoscope [8], and flow cytometry [9].
On the other hand, there remain several challenges for GI to be implemented in more practical systems. First, the bulky spatial light modulator (SLM) required for GI generally makes the entire system large and complicated. Second, under a sufficient level of received optical power, the relatively slow reconfiguration time of currently available SLMs would set a limit to the achievable frame rate. Even with the state-of-the-art fastest digital micro-mirror device (DMD) used as SLM, the frame rate would typically be in the range of few fps for 64 × 64 resolution imaging [10]. In order to solve these problems, it was recently proposed to employ a high-speed light-emitting diode (LED) array instead of SLM [11]. By using a 32 × 32 LED array, high-frame-rate imaging was demonstrated successfully. However, the need for a large number of LEDs, corresponding to desired pixel size of the image, may set a challenge for increasing the pixel size.
In this Letter, we demonstrate the use of large-scale silicon photonic optical phased-array (OPA) chip as a compact, low-cost, and potentially high-speed light illuminating device for GI applications. OPA has received increasing interest in recent years as a non-mechanical beam-steering device [12–16]. Using the complementary metal-oxide-semiconductor (CMOS) process, large-scale OPA can be fabricated on a tiny silicon chip and potentially integrated with the CMOS driver circuit [13,14]. Moreover, with the recent advancement of III-V heterogeneous integration technologies, laser diodes (LDs) and optical amplifiers could also be integrated on the same silicon platform to realize ultra-low-cost single-chip light emitter [16].
Here, we newly develop a silicon photonic OPA chip with 128 phase shifters densely integrated on a 4 mm × 4 mm footprint to demonstrate GI with over 90 resolvable points in one dimension. We then demonstrate 2D imaging capability by using an off-chip diffraction grating and adopting the wavelength sweeping scheme to cover another axis. Unlike the conventional beam-scanning operation of OPA, which requires precise phase tuning and iterative calibration processes [14,15], the GI scheme enables calibration-free robust imaging, which is extremely important for practical applications. While a preliminary experiment on OPA-based 1D GI has been reported by ourselves, where we used a small-scale InP-based OPA with only 10 effective phase shifters to demonstrate 8 resolvable points [17], this work is, to our knowledge, the first experimental demonstration of high-resolution GI using large-scale chip-scale OPA with over 100 integrated phase shifters.
2. GI scheme using OPA
Figure 1 shows the schematic of the GI system using an integrated OPA chip. The details about the chip are depicted in the inset. Input light is first split into M waveguides, phase-controlled by M independent phase shifters, and finally emitted out from the output edge into free space. By setting the amount of phase shift at respective phase shifters randomly, we can generate rapidly changing 1D speckle at the far field, which can be used as series of illumination patterns for GI. The optical power transmitted through an object, which is placed at the far-field plane, is then detected by a single-pixel photo detector (PD).
Fig. 1 Schematic of GI system using an integrated OPA chip. Inset shows details of the OPA chip, having only 8 waveguides for the sake of clarity. The actual fabricated device has 128 waveguides (M = 128). The off-chip diffraction grating could be integrated on the OPA chip in future to realize single-chip 2D GI module.
After repeating the measurement for N different illumination patterns generated by the OPA chip, we can retrieve the image of the object O(x, y) through the iterative reconstruction method as [3]
where Ir(x, y) (r = 1, 2, ..., N) represent N different illumination patterns, Sr are the detected signals by the single-pixel PD for respective patterns, and is the ensemble average of Sr over all measurements.Alternatively, the inverse method could be used instead of Eq. (1) to achieve generally better resolution at higher computational cost. In this case, O(x, y) is obtained by numerically solving [3]
where I ≡ [I1, I2, ... IN]T is the N × P matrix (P is the number of pixels) representing the set of illumination patterns, S ≡ [S1, S2, ... SN]T is the N × 1 column vector representing the detected power, and O ≡ [O1, O2, ... OP]T is the image that we want to retrieve.Although the OPA chip with 1D waveguide array as shown in inset of Fig. 1 is capable of generating speckle patterns only in x direction, we could extend to 2D imaging by integrating grating couplers at the output waveguides and employ the wavelength dimension to steer the beam in another axis [12,15,16]. In this Letter, for simplicity, we test this feasibility by using an off-chip diffraction grating as shown in Fig. 1. Alternatively, we could also achieve 2D GI at a single wavelength by integrating vertically emitting nanoantennas in 2D array [13,14].
3. Si photonic OPA chip
A large-scale 1D OPA chip with 128 phase shifters (M = 128) is fabricated by using 8-inch silicon-on-insulator (SOI) multi-project wafer foundry service provided by Institute of Microelectronics (IME). The SOI wafer consists of 210-nm-thick silicon and 2-μm-thick buried oxide layers. The waveguide width is set to 0.4 μm to assure single-mode operation for the transverse-electric (TE) mode. The light is edge-coupled into the input waveguide and split to 128 waveguides via cascaded 1 × 2 multi-mode interference (MMI) couplers. Although carrier-injection or carrier-depletion-based phase modulators could be used to enable high-speed switching beyond 100 MHz [14], we employ thermo-optic (TO) phase tuners in this work for simplicity; 5-μm-wide 200-μm-long TiN heater with the approximate electrical resistance of 1 kΩ is inserted at each waveguide to control the optical phase independently. The separation between the adjacent heaters is set to 12 μm. To increase the phase tuning efficiency and reduce thermal crosstalks, 4-μm-wide heat-insulating grooves are introduced between the heaters. The 128 waveguides are then aligned to a 1D array with a constant pitch (d) of 2 μm at the output edge, where the light is emitted out to free space. The free-spectral range (FSR) of far-field pattern (FFP) is thus ± 22.8 deg ( = sin−1 (λ/2d)) at 1550-nm wavelength.
The microphotograph of the fabricated chip is shown in Fig. 2. The entire chip, including the electrode pads, fits inside a compact footprint of 4 mm × 4 mm. The chip is mounted on an AlN chip carrier. All 128 electrodes and the ground line are wire-bonded and electrically connected to a multi-channel driver circuit for the experiment. In Fig. 2(d), we show the measured optical transmission through a test Mach-Zehnder interferometer with a heater attached in one arm. We can confirm that the 2π optical phase shift is obtained at an electrical driving power of around 37 mW (6.1 V, 6.1 mA). Total optical insertion loss of the OPA is measured to be 10.9 dB, which includes the fiber-to-chip coupling loss of around 3 dB.
Fig. 2 Fabricated OPA chip with 128 phase shifters. Top photographs of (a) the entire chip, (b) 1 × 2 MMI splitter, and (c) TO phase shifter array. (d) Measured optical transmission through a test Mach-Zehnder interferometer with a heater attached in one arm. Optical phase shift of 2π is obtained at a heater driving power of 37 mW.
4. Experimental results and discussion
Figure 3 shows the experimental setup for GI. A continuous-wave (CW) light at 1550-nm wavelength range with an optical power of + 10 dBm is aligned to TE mode and coupled into the OPA chip via a lensed fiber. The emitted light from the chip is collected by an objective lens (f1 = 1.8 mm, NA = 0.80, WD = 3.4 mm). In order to image in y direction, we insert a volume phase holographic grating (Wasatch Photonics WP-600/1550-25.4, 600 l/mm at 1550 nm) after the objective lens. We then employ three cylindrical lenses to create FFP at the object plane. The focal length of each lens is selected so that the FSR of the FFP in x-direction is 9.31 mm and the spatial resolution in y-direction is 0.18 mm at the object plane. By sweeping the wavelength, the FFP is steered along the y axis. The light transmitted through the object is then focused and detected by a single-pixel avalanche PD (Hamamatsu G8931-20, ϕ = 0.2 mm). For ease of experiment, the illumination pattern (i.e., FFP of the chip) is monitored by inserting a beam splitter (BS) before the object and by using an InGaAs infrared camera (Hamamatsu C12741-03, 640 × 512 pixels, 20 μm × 20 μm pixel size). While the wavelength is manually scanned in this experiment for proof-of-concept demonstration, we should note that a high-speed wavelength-tunable laser could be employed in practice to enable rapid scanning in the y direction [16].
Fig. 3 (a) Top view and (b) side view of the experimental setup. The object is placed at the Fourier plane and the transmitted light is detected by a single-pixel avalanche PD. The FFP is monitored by the infrared InGaAs camera. Random electrical signals are applied to 128 phase shifters to generate rapidly changing speckle illumination patterns. f1 = f6 = 1.8 mm, f2 = 30 mm, f3 = 200 mm, f4 = 150 mm, f5 = 175 mm.
First, to confirm the performance of the fabricated OPA device, we fix the wavelength to 1550 nm and evaluate the conventional beam-steering functionality in x-direction. Figure 4(a) shows the measured FFPs for 11 different operating conditions, demonstrating continuous beam steering along the x axis. For each of these 11 conditions, we need to optimize the driving voltages of all 128 phase shifters to create a peak at a desired steering angle. In this work, we employ an automated peak-search algorithm, which typically takes around 800 iterations to derive the condition for each angle. From Fig. 4(a), the full-width-at-the-half-maximum (FWHM) of the beam is less than 0.5 degrees, corresponding to more than 90 resolvable points inside the FSR. This is a reasonable value for a uniformly spaced OPA with 128 phase shifters, indicating that the device is operating nearly ideally. We should note that the number of resolvable points could be enhanced to around 500 by introducing non-uniformly spaced array [15].
Fig. 4 Observed intensity patterns at the object plane when the 128 phase shifters are (a) fine-tuned for beam steering, and (b) driven randomly to generate speckle patterns.
In contrast to Fig. 4(a), Fig. 4(b) shows the measured FFPs along the x axis for 11 example cases, where 128 phase shifters are driven by random voltage patterns. We see that different speckle patterns are generated inside the FSR. We should note that since the time-consuming iterative optimization is not required in this case, it is substantially easier and inherently more robust than the beam-steering operation shown in Fig. 4(a). In practical systems, we could record the FFPs only once before the measurement to be used for the succeeding GI. Alternatively, we could integrate on-chip optical phase monitor at each output waveguide of the OPA chip [16] and compute the FFP during operation.
We then place a 1D slit pattern as an object to be imaged. As shown in the second top rows of Fig. 5(a) and 5(b), the object pattern consists of apertures with the width varying from 0.5 mm to 0.1 mm (from left to right in Fig. 5). The speckle illumination pattern as shown in Fig. 4(b) is switched one after another in every 100 μs. From the detected signal, we retrieve Sr, which is then used to reconstruct the image by either Eq. (1) or (2). Figure 5(a) and 5(b) show the obtained 1D images with increasing N by using the iterative and inverse reconstruction methods, respectively. We also plot on the top row of Fig. 5 the peak signal-to-noise ratio (PSNR) of the reconstructed images as a function of N. In both cases, PSNR increases monotonically with N and starts to saturate at around N ∼400, where we see that the slit pattern is retrieved successfully. In particular, finer PSNR is obtained by the inverse method, in which case, the narrowest apertures with 0.1-mm width are also resolved. In our setup shown in Fig. 3, this spatial resolution corresponds to 0.4-deg divergence in the far-field, which is consistent with the FWHM of the beam, measured under the beam-steering condition [See Fig. 4(a)].
Fig. 5 Reconstructed 1D images of the slit pattern with increasing N by using (a) the iterative method [Eq. (1)] and (b) the inverse method [Eq. (2)]. For each method, PSNR of the reconstructed images is plotted as a function of N on the top row.
Finally, we test the capability of 2D imaging by sweeping the wavelength of the tunable laser. As an imaging object, we insert a 1951 USAF resolution target (Edmund Optics, group = −1, element = 5). The wavelength is scanned from 1498.8 nm to 1517.0 nm with 1.4-nm step to cover a total range of around 2 mm with 14 pixels in y direction. Figure 6 shows the results of 2D imaging. Similar to the case for 1D imaging, PSNR improves at large N as plotted in Fig. 6(a). For this imaging object, the PSNR saturate at N > 200, where the image is retrieved successfully as shown in Fig. 6(b).
Fig. 6 (a) PSNR of the reconstructed 2D images with increasing N, and (b) actual reconstructed images for N = 10, 100, 200, 300, 400, and 500. The wavelength is scanned from 1498.8 nm to 1517.0 nm with 1.4-nm step to cover a total range of around 2 mm with 14 pixels in y direction.
There are several factors that can be improved to enhance the performance of the OPA chip. First, the number of resolvable points could be increased to around 500 by simply adopting a non-uniformly spaced array [15]. Second, the switching speed, which is currently limited by the response time of the TO phase shifters (measured to be around 20 μs), could be enhanced to over 100 MHz if we employ carrier injection [14]. Moreover, by using carrier-depletion-type high-speed phase modulators, the bandwidth should readily exceed 10 GHz [18]. In addition, the number of measurements can be reduced significantly by using CS techniques. With all these improvements, ultra-high line scan rate beyond 10 M lines per second should be possible for around 500 pixels. Furthermore, by integrating grating couplers as well as a tunable-wavelength laser on the same chip [16], single-chip ultrahigh-speed 2D GI module can be realized.
5. Conclusion
We have demonstrated GI using a newly developed compact silicon photonic OPA chip with 128 densely integrated phase shifters. By driving all phase shifters with random electrical signals, different speckle illumination patterns were generated, which were used to image 1D slit pattern with the spatial resolution comparable to that of the conventional beam steering. We have then demonstrated 2D imaging through the combination of wavelength scanning scheme to cover another dimension. Unlike conventional beam-steering OPAs, where phase errors need to be calibrated and time-consuming iterative optimization is generally required to tune the optical phases, the demonstrated imaging scheme is much easier and more robust against fabrication errors. While the switching speed of the current device is limited to be around 20 μs by the response time of the TO phase shifters, we could employ carrier-depletion-type phase shifters to achieve ultra-high-speed switching rate exceeding 10 GHz. With the potential of integrating grating couplers and light source on the same platform, this work paves the way towards realization of high-speed single-chip 2D illumination GI module for wide ranges of applications.
Funding
Grant-in-Aid of Japan Society for the Promotion of Science (JSPS) (26000010, 18H03769).
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