Moving the radar and capturing data along a path are the next steps and are pretty simple, but figuring out what to do with the data is anything but. [Henrik] goes into great detail about the SAR algorithm he used, called Omega-K, a routine that makes use of the Fast Fourier Transform which he implemented for a GPU using Tensor Flow. We usually see that for neural net applications, but the code turned out remarkably detailed 2D scans of a parking lot he rode through with the bike-mounted radar. [Henrik] added an auto-focus routine as well, and you can clearly see each parked car, light pole, and distant building within range of the radar.
OK, I was thinking the accuracy can be better with higher frequency and maybe more cost effective higher resolution components. I still need to read over the math like 10 times more. I just recalled the wiki noting THz systems have made images down to sub millimeter resolution. -aperture_radar
Bike-Mounted Synthetic-Aperture Radar Makes Detailed Images
[Henrik] is at it again. Another thoroughly detailed radar project has shown up on his blog. This time [Henrik] is making some significant improvements to his previous homemade radar with the addition of Synthetic Aperture Radar (SAR) to his previous Frequency Modulated Continuous Wave (FMCW) system.
To create a SAR image, successive pulses of radio waves are transmitted to "illuminate" a target scene, and the echo of each pulse is received and recorded. The pulses are transmitted and the echoes received using a single beam-forming antenna, with wavelengths of a meter down to several millimeters. As the SAR device on board the aircraft or spacecraft moves, the antenna location relative to the target changes with time. Signal processing of the successive recorded radar echoes allows the combining of the recordings from these multiple antenna positions. This process forms the synthetic antenna aperture and allows the creation of higher-resolution images than would otherwise be possible with a given physical antenna.[2]
A synthetic-aperture radar is an imaging radar mounted on an instant moving platform.[8] Electromagnetic waves are transmitted sequentially, the echoes are collected and the system electronics digitizes and stores the data for subsequent processing. As transmission and reception occur at different times, they map to different small positions. The well ordered combination of the received signals builds a virtual aperture that is much longer than the physical antenna width. That is the source of the term "synthetic aperture," giving it the property of an imaging radar.[5] The range direction is perpendicular to the flight track and perpendicular to the azimuth direction, which is also known as the along-track direction because it is in line with the position of the object within the antenna's field of view.
FFT (Fast Fourier Transform i.e., periodogram or matched filter) is one such method, which is used in majority of the spectral estimation algorithms, and there are many fast algorithms for computing the multidimensional discrete Fourier transform. Computational Kronecker-core array algebra[16] is a popular algorithm used as new variant of FFT algorithms for the processing in multidimensional synthetic-aperture radar (SAR) systems. This algorithm uses a study of theoretical properties of input/output data indexing sets and groups of permutations.
SAMV method is a parameter-free sparse signal reconstruction based algorithm. It achieves super-resolution and is robust to highly correlated signals. The name emphasizes its basis on the asymptotically minimum variance (AMV) criterion. It is a powerful tool for the recovery of both the amplitude and frequency characteristics of multiple highly correlated sources in challenging environment (e.g., limited number of snapshots, low signal-to-noise ratio. Applications include synthetic-aperture radar imaging and various source localization.
Backprojection Algorithm has two methods: Time-domain Backprojection and Frequency-domain Backprojection. The time-domain Backprojection has more advantages over frequency-domain and thus, is more preferred. The time-domain Backprojection forms images or spectrums by matching the data acquired from the radar and as per what it expects to receive. It can be considered as an ideal matched-filter for synthetic-aperture radar. There is no need of having a different motion compensation step due to its quality of handling non-ideal motion/sampling. It can also be used for various imaging geometries.[27]
Radar waves have a polarization. Different materials reflect radar waves with different intensities, but anisotropic materials such as grass often reflect different polarizations with different intensities. Some materials will also convert one polarization into another. By emitting a mixture of polarizations and using receiving antennas with a specific polarization, several images can be collected from the same series of pulses. Frequently three such RX-TX polarizations (HH-pol, VV-pol, VH-pol) are used as the three color channels in a synthesized image. This is what has been done in the picture at right. Interpretation of the resulting colors requires significant testing of known materials.
SAR polarimetry is a technique used for deriving qualitative and quantitative physical information for land, snow and ice, ocean and urban applications based on the measurement and exploration of the polarimetric properties of man-made and natural scatterers. Terrain and land use classification is one of the most important applications of polarimetric synthetic-aperture radar (PolSAR).[34]
For PolSAR image analysis, there can be cases where reflection symmetry condition does not hold. In those cases a four-component scattering model[34][38] can be used to decompose polarimetric synthetic-aperture radar (SAR) images. This approach deals with the non-reflection symmetric scattering case. It includes and extends the three-component decomposition method introduced by Freeman and Durden[36] to a fourth component by adding the helix scattering power. This helix power term generally appears in complex urban area but disappears for a natural distributed scatterer.[34]
Although some references to SARs have characterized them as "radar telescopes", their actual optical analogy is the microscope, the detail in their images being smaller than the length of the synthetic aperture. In radar-engineering terms, while the target area is in the "far field" of the illuminating antenna, it is in the "near field" of the simulated one. Careful design and operation can accomplish resolution of items smaller than a millionth of the range, for example, 30 cm at 300 km, or about one foot at nearly 200 miles (320 km).
The two dimensions of a radar image are range and cross-range. Radar images of limited patches of terrain can resemble oblique photographs, but not ones taken from the location of the radar. This is because the range coordinate in a radar image is perpendicular to the vertical-angle coordinate of an oblique photo. The apparent entrance-pupil position (or camera center) for viewing such an image is therefore not as if at the radar, but as if at a point from which the viewer's line of sight is perpendicular to the slant-range direction connecting radar and target, with slant-range increasing from top to bottom of the image.
When viewed as specified above, fine-resolution radar images of small areas can appear most nearly like familiar optical ones, for two reasons. The first reason is easily understood by imagining a flagpole in the scene. The slant-range to its upper end is less than that to its base. Therefore, the pole can appear correctly top-end up only when viewed in the above orientation. Secondly, the radar illumination then being downward, shadows are seen in their most-familiar "overhead-lighting" direction.
Surfaces that we usually consider rough will, if that roughness consists of relief less than the radar wavelength, behave as smooth mirrors, showing, beyond such a surface, additional images of items in front of it. Those mirror images will appear within the shadow of the mirroring surface, sometimes filling the entire shadow, thus preventing recognition of the shadow.
Besides measuring the distances, radar can also be used to generatetwo-dimensional images of the scene. This can be done by measuring severaldistance profiles while radar is moved on a straight line with antenna lookingsideways from the direction of travel. If the antenna radiation pattern is verynarrow, range profiles can be stacked to make image of the scene. Issue withthis method is that assumption about the narrow beam width can't often befulfilled. Antennas I'm using have beam width of about 40 degrees and resolutionin direction that radar was moved (cross-range or azimuth) would be horrible.
This post is continuation of my previous synthetic-aperture imagingexperiments. In the previous post I used omega-kfrequency domain algorithm for the image formation and automatic differentiationbased autofocusing with Tensorflow. I managed to get pretty well focused imagesfrom bicycle mounted radar considering the total lack of any motion recordingdata. The autofocus algorithm managed to improve it slightly, but it wasn'tperfectly focused.
I also redid the other scene I measured the last time. The improvement from autofocus in that scene is also huge especially for objects farther away. Theobjects farther away are still spread, but I'm not sure if they should be muchbetter than what they are now. There are lot of issues with occlusions in thisscene and some far away objects are visible for the radar only for a very shorttime. See the images in the previous post for thesame data focused with Omega-k algorithm. 2ff7e9595c
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