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 University West Lafayette, IN 26 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 aircraft from 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 Data Uncompensated 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 the cross-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)

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 OriginalGlobal PGASpace-Variant PGA Note: Vertical Lines Indicating OSA Boundaries Before PGA After PGA

Attempt to Refocus Image of Rocking Ship from LYNX Spotlight-Mode SAR (16 GHz) Using PGA OriginalGlobal PGASpace-Variant PGA Note: Vertical Lines Indicating OSA Boundaries

Attempt to Refocus Image of Rocking Ship from LYNX Spotlight-Mode SAR (16 GHz) Using Spatially-Varying Version of PGA OriginalGlobal PGASpace-Variant PGA Note: Vertical Lines Indicating OSA Boundaries

Ship Motion (Rocking) Correction Lynx Space-Variant PGAPhase Error Function

Refocused Image of Rocking Ship from LYNX Spotlight- Mode SAR (16 GHz) Using Space-Varying PGA OriginalGlobal PGASpace-Variant PGA Note: Vertical Lines Indicating OSA 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