Use of Phase Gradient Autofocus (PGA) for Refocusing Rocking Ships in Spotlight-Mode SAR
Imagery
Dr. Charles “Jack” Jakowatz, Jr.Sandia National Laboratories
Albuquerque, NM
Purdue UniversityWest Lafayette, IN26 September, 2003
Collection Geometry for Spotlight-Mode SAR
Three-Dimensional Phase History Data for Spotlight-Mode SAR
The angular extent of the annulus is determined by the flight path. It prescribes the azimuthal resolution of the formed SAR image
This dimension of the annulus is determined by the radar bandwidth and prescribes the range resolution in the formed SAR image
The offset of the phase history data from the origin is directly proportional to the radar center frequency
Phase Errors in SAR Imagery
• Recall that for each position of the aircraftfrom which a pulse is transmitted and received, the deramp processor must “know” precisely when the returned echo arrives.
• Inevitably, there will be some uncertainty in this time, because the aircraft position is never known without some amount of error.
• For an aircraft position error in the along-line-of-sight (range) direction of only a half wavelength, a full 2 of phase error occurs.
Aircraft Position Errors Lead to Phase Errors in Collected DataUncompensated Aircraft Position Errors Lead to Phase Errors
in the Collected SAR Phase History Data
Three-Dimensional Phase History Data for Spotlight-Mode SAR
The angular extent of the annulus is determined by the flight path. It prescribes the azimuthal resolution of the formed SAR image
This dimension of the annulus is determined by the radar bandwidth and prescribes the range resolution in the formed SAR image
The offset of the phase history data from the origin is directly proportional to the radar center frequency
Cartesian raster
Image is formed by 2-D IFFT of data interpolated to the Cartesian raster
Effect of the phase error function is to blur the formed image in thecross-range (x) dimension
Defocusing Due to Phase Errors in a Spotlight-Mode SAR Image
When the interpolated samples are coherently integrated via compression (Fourier transformation), the phase errors cause defocusing of the formed
image in the cross-range dimension. The resulting blurred image is a convolution of the desired image with: IFT{exp( j phase error function)}
Removal of Phase Error Effects in SAR Imagery
• The only way to remove the residual defocus effects is to estimate the phase errors from the blurred image itself.
• Such a technique is known as a “data driven” algorithm.
• It amounts to “blind” deconvolution of the degrading phase error function.
• Sandia Laboratories developed the Phase Gradient Autofocus algorithm (PGA) in 1989 as a solution to this problem (Jakowatz, Eichel, and Ghiglia)
Processing Steps in Phase Gradient Autofocus (PGA)Processing Steps in Phase Gradient Autofocus (PGA)
PGA Results
Image defocused from uncompensated aircraft position
errors
Image refocused using PGA
Official Use Only
Autofocus by PGA of 2-inch Resolution Sandia Labs
Twin Otter Spotlight-Mode SAR Imagery
Vehicles at National Guard Armory
Defocus of Ships from Rocking Motion
Attempt to Refocus Image of Rocking Ship from LYNX Spotlight-Mode SAR (16 GHz) Using PGA
Original Global PGA
Space-Variant PGA
Note: Vertical Lines IndicatingOSA Boundaries
Before PGA After PGA
Attempt to Refocus Image of Rocking Ship from LYNX Spotlight-Mode SAR (16 GHz) Using PGA
Original Global PGA
Space-Variant PGA
Note: Vertical Lines IndicatingOSA Boundaries
Attempt to Refocus Image of Rocking Ship from LYNX Spotlight-Mode SAR (16 GHz) Using Spatially-Varying
Version of PGA
Original Global PGA
Space-Variant PGA
Note: Vertical Lines IndicatingOSA Boundaries
Ship Motion (Rocking) CorrectionLynx20030302220035
Space-Variant PGAPhase Error Function
Refocused Image of Rocking Ship from LYNX Spotlight-Mode SAR (16 GHz) Using Space-Varying PGA
Original Global PGA
Space-Variant PGA
Note: Vertical Lines IndicatingOSA Boundaries
Before PGA After Space-Varying PGA
Foliage Penetration (FOPEN)
• SAR is all-weather, day/night capable• Typical SAR frequencies have difficulties
penetrating foliage– Use different radar frequencies (VHF) to achieve
penetration• Typically, resolution suffers with these lower frequencies
– Use high resolution systems, coupled with a 3-D approach
3-D tomography from multiple data collects can be used to address the problem of foliage penetration