Fuentes Normativas

This method of image reconstruction should lead to a focused image with the appropriate resolutions. However, this is not always the case as any number of factors can cause errors in the phase and amplitude measurements to degrade the image quality.

The first, and most troubling, effect of these errors is image defocusing. This is caused by the occurrence of fluctuations in the path length between the radar receiver aperture and the scene, caused by variations in the refractive index, multi-path effects, and the deviations of the sensor from the established track [CURLb-91]. This deviation from the assumed trajectory may be from a mismatch in the assumed velocity and acceleration or a displacement of the platform from the estimated position. As seen from the explanation of the echo signal and the reconstruction algorithm, SAR uses the accurately known distance for correcting of the phase delay. Any distortion of this will cause the image to defocus in that each pixel is not accurately mapped. Auto-focus techniques have been developed to help overcome these errors and improve the image quality [CURLb-91].

Geometric and radiometric distortion is the other main error that reduces the image quality. Again, this error is caused by the deviations from the assumed motion in the range and azimuth directions. This causes not only a defocusing of the image, but also distortion of the actual dimensions of the image. These distortions are proportional to the velocity deviations. Unlike defocusing, the main effect of the distortions comes from non-planar movement of the platform. This cannot be corrected with auto-focus, but rather through the measuring of the actual motion of the platform and this information is then used in the processing to correct the image. This is called motion compensation

[CURLb-91].

2.4.8.1 M otion com pensation:

Motion compensation is the method used to correct for the planar and non-planar motion deviations from the assumed trajectory [STIMc-98]. In radar applications, it is

acceptable to have deviation within a quarter of the wavelength during a single pulse, to maintain phase coherence within a small error. This deviation is reduced by another factor of two for SAR due to the two-way propagation— one eighth of a wavelength [STEI-76]. This level of control may not be possible to achieve. However, with signal processing, it has become possible to use a correction for the motion deviation with the signal echo to maintain this accuracy.

In motion compensation, an external motion sensor is used to accurately record the actual motion of the radar platform [STIMc-98]. This motion is then manipulated to determine the frequency change that accompanies the deviated motion and this is applied to the echo response as the signal is being processed. This, in effect, removes the phase error by applying a corrective function to the signal processing. While this cannot remove all errors, it can remove enough for to maintain image quality.

2.4.8.2 Auto-focus:

Auto-focusing of SAR images is a widely used signal processing strategy to compensate for the quadratic and higher level phase errors [CURLb-91]. This technique is most often applied after the original motion compensation and data formatting. Auto-focus is normally accomplished in two steps: error estimation within the signal and error compensation.

There are multiple methods of auto-focusing. Prominent point processing is used when strong point targets exist. This method allows for high performance in correcting phase errors, but requires dominant scattering elements throughout the scene. The coherent auto-focusing methods are phase gradient and phase difference [WU-00]. These techniques operate directly on the complex, d 0, received signal to correlate the phase differences or gradients between phases throughout the picture. These values are then used to estimate a correction function. Finally, incoherent methods, map drift and contrast optimization, use the intensity of compressed images and disregard the phase information [WU-00].

The most common algorithm used for auto-focusing an image is called Phase Gradient Auto-focus, PGA [WU-00]. It consists of making an estimate of the gradient of the phase error in the SAR image using four steps: centre shifting, windowing, phase gradient estimation, and iteration. The algorithm was created for spotlight SAR, due to the plausible assumption in spotlight SAR that the phase error is constant with range. This assumption is not correct for stripmap SAR until the data has been formatted further.

The auto-focus algorithm is applied after the range compression of the raw data has been completed to allow for the separation of the image into range bins. For each range bin, the strongest scatterer, an, is chosen and shifted to the origin of the image. This is done to remove the frequency offset due to the Doppler shift. This must be done in a circular manner so that samples, which are shifted off the edge may be wrapped around and shifted to the opposite side. This centre shifting attempts to align strong scatterers and subsequently improve the S/N for the phase estimation.

Once the image has been centre shifted, it is windowed, preserving the width of the dominant blur for each range bin while discarding the data that does not contribute to the phase error estimation, i.e. clutter. The window size, W, is chosen by registering the dominant blur on each range bin and averaging over all the bins. These are incoherently summed to obtain a one-dimensional function whose width, at a chosen threshold, gives the point-spread function. This is nominally given by:

■>(*) = Z | / „ « | 2 [2-71]

n

where fn(x) is the circularly shifted image data and n is the bin number [WAHL-94].

The redundancy of the blur, as assumed with a constant phase error with range, the function, s(x), will plateau at its maximum value approximately the width of the window, W, and smaller outside of W. As the image becomes more focused, W will converge until it is only a few pixels in size.

When the scene does not contain strong scatterers, i.e. images of natural landscapes, seascapes or icescapes, the above method will not work, as the range bins do not provide a strong enough scattered response to allow for windowing of s(x). The window width, W, is then chosen to span the maximum possible blur width and progressively reduce by 20% per iteration.

Once shifted and windowed, the image data is now represented by

G„ ( u ) = |G„ (M )|eJ^ '<")+l?' <“>1 [2.72]

where Gn(u)is the inverse Fourier transform of the image data, gn(x), 9n(u) is the scatterer-dependent phase function and (j)e(u)is the phase error [WAHL-94].

The linear unbiased minimum variance (LUMV) estimate for the gradient of the phase error is given by:

X l m { o ; ( « ) ( ? „ (« ) } <*Lv (« ) = - v . .2— [2.74] filu m v(« ) = 0 . ( « ) + — ---

The estimated phase gradient, <phmv ( u ) , is integrated to obtain an averaged value which is then used as the phase correction, <f>e( u ) . This is done to remove any bias and linear trend. This phase correction is then complex multiplied by the range-compressed phase history domain data by: e x p [-j^ (« )]. The process of center shifting, windowing and phase gradient estimation is repeated. As the image begins to focus, the scatterers become more compact making the circular shifting more precise and the window size smaller.

When the PGA algorithm is applied to stripmap data, the assumption of constant phase error with range is no longer valid and a conversion of the data from stripmap to spotlight, known as Stripmap Spotlight Compression (SSC) [BATE-98],

Chapter 3 SAR System Design: