Continuous-capture microwave imaging

Abstract

Light-in-flight sensing has emerged as a promising technique in image reconstruction applications at various wavelengths. We report a microwave imaging system that uses an array of transmitters and a single receiver operating in continuous transmit-receive mode. Captures take a few microseconds and the corresponding images cover a spatial range of tens of square meters with spatial resolution of 0.1 meter. The images are the result of a dot product between a reconstruction matrix and the captured signal with no prior knowledge of the scene. The reconstruction matrix uses an engineered electromagnetic field mask to create unique random time patterns at every point in the scene and correlates it with the captured signal to determine the corresponding voxel value. We report the operation of the system through simulations and experiment in a laboratory scene. We demonstrate through-wall real-time imaging, tracking, and observe second-order images from specular reflections.

Fig. 1. Position evaluation based on time of flight.

In panel a, a diagram showing an ellipse with focal points Tx and Rx as the solution to the equation r₁ + r₂ = r and the corresponding polar coordinates (ρ, θ) description of a solution point P. In panel b, the amplitude of the field at P as it travels the θ values along the ellipse for increasing values of r defined by the arrow.

Fig. 2. Time-of-flight sampling mask.

Panels a, b, c, and d show the normalized spatiotemporal mask at different times (t_a < t_b < t_c < t_d). This mask is generated by 12 transmitters arranged in a line with the receiver in the center. Notice the several elliptical contributions adding to unique spatial patterns at each time step.

Fig. 3. Experimental setup.

Schematic showing the pseudo-random binary sequence (PRBS) generators that feed the antenna array after an amplification stage (not shown). The transmitter array comprises 12 omni-directional antennas each receiving a unique PRBS code. The generators are synchronized by the trigger source also used to time align the analog-to-digital converter (ADC). The differential receiver comprises two omini-directional antennas connected by a 180-degree transformer and amplification stage (not shown). The ADC digitizes the signal from the amplified transformer output and stores it in a local buffer. The computer (CPU) queries and transfers the digitized capture from the ADC buffer and uploads it to a graphics processing unit (GPU) that performs the image reconstruction.

Fig. 4. Numerical evaluation of image reconstruction model.

The simulated scene in panel a shows the two walls (black), the position of the transmitters (red) and the receiver (blue), and the first-order reconstructed image using Eq. (2) with its corresponding gray scale bar in panel b. In panel c, the histogram of the normalized image pixels in blue is fitted by a Gaussian in orange.

Fig. 5. Noise analysis of image reconstruction model.

Image loss (blue dots) as a function of additive white Gaussian noise (AWGN) and the AWGN prediction (orange line). Insets show the recovered images at different noise levels for comparison.

Fig. 6. Second-order reconstruction of the scene in Fig. 4a.

Panel sets (a, b, c, d), (e, f, g, h), and (i, j, k, l) correspond to threshold filter levels of 4σ, 5σ, and 6σ applied to the normalized image in Fig. 4b, respectively. Panels a, e, i correspond to the filtered first-order image, the second-order result including gray scale bars (b, f, j) and corresponding intensity distribution (c, g, k), and the combined first- and second-order masks (d, h, l) in black with the ground truth scene in red.

Fig. 7. Experimental demonstration.

Ground truth images from a camera mounted 5 m above the scene with a person (a), a wall (b), a person behind a wall and no wall background subtraction (c), and a person behind a wall with background subtraction (d). The corresponding first-order reconstructions and gray scale bars for panels a, b, c, and d set are shown, respectively, in panels e, f, g, and h.