Holography of Wi-Fi radiation

Wireless data transmission systems such as WiFi or Bluetooth emit coherent light - electromagnetic waves with precisely known amplitude and phase. Propagating in space, this radiation forms a hologram - a two-dimensional wavefront encoding a three-dimensional view of all objects traversed by the light beam. Here we demonstrate a scheme to record this hologram in a phase-coherent fashion across a meter-sized imaging region. We recover three-dimensional views of objects and emitters by feeding the resulting data into digital reconstruction algorithms. Employing a digital implementation of dark field propagation to suppress multipath reflection we significantly enhance the quality of the resulting images.


Introduction
Holography -three-dimensional imaging by phase-coherent recording of a two-dimensional wavefront -is one of the most intriguing concepts of 20 th century physics 1 . While most practical implementations have employed laser light, the concept itself is applicable to any kind of coherent radiation and has actually been invented to improve electron microscopy. Other demonstrations have since been performed with sound waves 2 , x-rays 3 , gamma rays 4 , neutrons 5 and cold atoms 6 .
It is an interesting question whether the omnipresent stray radiation of wireless devices forms holograms that encode threedimensional views of the device and its surrounding. So far, holography of microwave radiation with similar (GHz) frequency has been demonstrated for the localization of radiofrequency emitters in a two-dimensional plane 7,8 and near-field imaging with custombuilt emitters 9,10 . However, efforts to obtain images from the stray radiation of unmodified wireless devices have remained limited to onedimensional ranging 11 .
Beyond its fundamental interest, indoor imaging by arbitrary wireless signals appears attractive for a variety of applications. These range from localization of radio-frequency tags in internet-of-things settings 7,8,[12][13][14] over 3D motion capture for gaming [15][16][17] to through-wallimaging of moving targets for security enforcement 11,[18][19][20][21] . Unfortunately, it is complicated by one major challenge: multipath reflections -radiation scattered from walls and other surrounding objects outside the viewing area -blur radar signals and their echoes in indoor environments 14 . Existing approaches deal with this problem by producing or receiving short-pulse ultra-wideband signals for timedomain ranging [22][23][24]  Our approach is presented in Figure 1.  We obtain the complex amplitude ⋅ ': | ),* by a homodyne scheme, which is presented in Fig.   2a+b. In Fourier space, the propagation of the The amplitude modulation has a standing wave ratio of SWR=9.7. It creates artefacts in the recovered phases, which correlate with peaks and valleys of the amplitude.

(a) A commercial Router is used to illuminate a cross-shaped phantom object. (b) Back-propagation into the emitter plane reliably reveals the router as a single bright spot. (c) Multipath reflections create a speckle pattern that (d) can be cancelled by incoherently averaging over holograms obtained at different transmission frequencies.
We now turn to the three-dimensional reconstruction of images from this holographic data. All following analysis is based on a dataset, which has been recorded in the setting of Figure  , , Here, ℱ, ℱ GH denote the spatial Fourier transform of the light field and its inverse and

Analysis and Results
The most prominent feature in the recovered    Recording of incoherent-object hologram as complex spatial coherence function using Sagnac radial shearing interferometer and a Pockels cell. Opt.

Data acquisition and electronics
All electronic components are listed in table 1. Devices used for mixing and amplifying are from Mini Circuits UK. As the oscilloscopes used in this experiment cannot resolve the high-frequency Wi-Fi radiation directly, we down-convert the signals using a high frequency oscillator as shown in figure 5.
Depending on the antenna type and cable length, the incoming signals may be too weak to obtain a reasonable voltage resolution. We therefore amplify the high-frequency signals before they are sent to the mixing stage. The signal distortions introduced by this setup are negligibly small and do not impact later analysis.
The mixing stage consists of a high-frequency local oscillator set to approximately 2.4 and 5 GHz, respectively. Its output is split and then fed into two equal mixers, one for each antenna. We have chosen the cables in this step to be identical for both paths. The arbitrary relative phase introduced this way is irrelevant for the later analysis.
Data recorded by the oscilloscope are then transferred to the on-board PC via USB. As the USB interface is not fast enough to deliver the data in real time, a trigger is set on the reference signal whose amplitude is constant during the scanning process. The trigger setup limits the data acquisition rate to about two points per second on average.

White light reconstruction
We suppress multipath interference by white light holography as presented in Fig. 6. In this scheme, the final reconstructed image (Fig 6  "combined") is an incoherent sum of reconstructions obtained at different frequencies within the Wi-Fi transmission band (illustrated in the remaining subplots in Figure  6). We can generate separate holograms for arbitrary frequency windows within the transmission band, since our acquisition scheme (Fig. 2) records a frequency-resolved three-dimensional (x,y,f) dataset.
Multipath reflection adds unpredictable noise to the recording, which transforms to speckle patterns in the frequency-windowed holograms. Crucially, these patterns vary randomly between different frequency bands and combine to a homogeneous background in the combined image. Multipath suppression and image clarity improve for increasing bandwidth. This is similar to time-domain ranging, where shorter pulses achieve the same goal [1].
We note that our approach does not suffer from artefacts frequently observed in other white light holography schemes, such as a reduced depth of field [2]. The key difference is that our scheme preserves phase information for each frequency and therefore enables fully coherent back-propagation, while other techniques perform incoherent averaging already upon recording. In this way, our work is conceptually more similar to holographic imaging with filtered white light [3].

FDTD simulation
To validate our method and show the reconstruction limits, we simulate several scenarios, both with 5 GHz and 2.4 GHz Wi-Fi, using the commercially available Lumerical finite differences time domain (FDTD) toolkit. The storage hall is the most complex model simulated here.
The limiting factor for our type of FDTD simulation is the system memory requirement. We therefore simulate 2.4 GHz Wi-Fi instead of the higher-bandwidth 5 GHz which is used for the experimental results. The meshing size of 1.6 to 2.4 cm (homogeneous in space but different per axis) is set as large as possible while keeping the necessary precision for reconstruction, making sure the meshing size stay under 20% of the shortest occurring wavelength. With these settings, the simulation requires just under 80 GB of memory.
For the source, we use a dipole emitter producing a single wave packet with a bandwidth of 22 MHz centered around the carrier frequency in accordance with the 802.11 standard. For the different source positions, also the Wi-Fi channels are varied. The simulation time of 300 ns ensures that any non-negligible multipath reflections are received by the antenna array.
The antenna array, located in the ceiling of the building, is realized as a field time monitor with a resolution of 4.0 cm x 7.2 cm and a sampling rate of 5.7 GHz. The localization of source can be broken into finding the correct distance from the recording plane and a 2D localization in the respective plane. The 2D localization is very simple as the intensity distribution approximately forms a Gaussian near its maximum. The standard deviation of this Gaussian is of the order of a few centimeters at a depth of z=11 meters.
Finding the correct plane, however, is more difficult as the peak in intensity rapidly changes shape over the range of a few decimeters. The evolution of the peak broadness over a range of depths close to the source position is plotted in figure 7b). The variances in X and Y direction both have a minimum corresponding to the most likely z position of the emitter. With their minima at z=10.85 and z=11.2 meters, they are a few decimeters off the true source position at a depth of 10.6 meters. One possible reason for this might be the 38 cm thick ceiling, through which the waves pass before reaching the antenna array.