Editing Synthetic-aperture radar (section)

=== Backprojection algorithm ===
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.<ref name=":1">{{Cite journal|last=Duersch|first=Michael|title=Backprojection for Synthetic Aperture Radar|journal=BYU ScholarsArchive}}</ref>

==== Advantages ====
* ''It is invariant to the imaging mode'': which means, that it uses the same algorithm irrespective of the imaging mode present, whereas, frequency domain methods require changes depending on the mode and geometry.<ref name=":1" />
* Ambiguous azimuth aliasing usually occurs when the Nyquist spatial sampling requirements are exceeded by frequencies. Unambiguous aliasing occurs in [[Squint (antenna)|squinted]] geometries where the signal bandwidth does not exceed the sampling limits, but has undergone "spectral wrapping." Backprojection Algorithm does not get affected by any such kind of aliasing effects.<ref name=":1" />
* ''It matches the space/time filter:'' uses the information about the imaging geometry, to produce a pixel-by-pixel varying matched filter to approximate the expected return signal. This usually yields antenna gain compensation.<ref name=":1" />
* With reference to the previous advantage, the back projection algorithm compensates for the motion. This becomes an advantage at areas having low altitudes.<ref name=":1" />

==== Disadvantages ====
* The computational expense is more for Backprojection algorithm as compared to other frequency domain methods.
* It requires very precise knowledge of imaging geometry.<ref name=":1" />

==== Application: geosynchronous orbit synthetic-aperture radar (GEO-SAR) ====
In GEO-SAR, to focus specially on the relative moving track, the backprojection algorithm works very well. It uses the concept of Azimuth Processing in the time domain. For the satellite-ground geometry, GEO-SAR plays a significant role.<ref name=":8">{{Cite book|last1=Zhuo|first1=Li|last2=Chungsheng|first2=Li |chapter=Back projection algorithm for high resolution GEO-SAR image formation |title=2011 IEEE International Geoscience and Remote Sensing Symposium |publisher=IEEE |pages=336–339|doi=10.1109/IGARSS.2011.6048967|year=2011|isbn=978-1-4577-1003-2|s2cid=37054346}}</ref>

The procedure of this concept is elaborated as follows.<ref name=":8" /> 
# The raw data acquired is segmented or drawn into sub-apertures for simplification of speedy conduction of procedure.
# The range of the data is then compressed, using the concept of "Matched Filtering" for every segment/sub-aperture created. It is given by-<math display="inline">s(t, \tau) = \exp \left(-j \cdot \frac{4\pi}{\lambda} \cdot R(t)\right) \cdot \operatorname{sinc}\left(\tau - \frac{2}{c} \cdot R(t)\right)</math> where ''τ'' is the range time, ''t'' is the azimuthal time, ''λ'' is the wavelength, ''c'' is the speed of light.
# Accuracy in the "Range Migration Curve" is achieved by range interpolation.
# The pixel locations of the ground in the image is dependent on the satellite–ground geometry model. Grid-division is now done as per the azimuth time.
# Calculations for the "slant range" (range between the antenna's phase center and the point on the ground) are done for every azimuth time using coordinate transformations.
# Azimuth Compression is done after the previous step.
# Step 5 and 6 are repeated for every pixel, to cover every pixel, and conduct the procedure on every sub-aperture.
# Lastly, all the sub-apertures of the image created throughout, are superimposed onto each other and the ultimate HD image is generated.