The spurious spikes in the interferogram, as shown in figure 4, appear at those positions in the signal where the amplitude is extremely low. The signal to noise ratio at these interpolation points is therefore dominated by the interpolation noise. This makes a sudden phase jump at low amplitude areas likely to occur. Due to the small amplitude, multi-looking suppresses these spikes, and considerably diminishes the phase noise.
The cubic spline interpolation kernels used here can be referred to as Parametric
Cubic Convolution (PCC)[4]. The parameters 
and 
for the 4-point and 6-point
kernels chosen here have
proved to be close to optimal for this particular configuration.
Optimization for specific purposes
can be performed by evaluating equation (1).
A comparison of cubic splines and truncated sincs underlines the necessity of careful interpolator design: note that the cubic splines used here are special cases of weighted truncated sincs. The 6-point cubic convolution kernel showed better quality than an 8-point unweighted truncated sinc.
Interpolation errors are due to the
aliasing of repeated signal spectra and the
cut-off of the signal spectra's corners.
Hence, the choice of an optimal interpolator will always depend on the
correlation properties of the signal. However, a subjective
recommendation can be given for ERS conditions, where temporal
decorrelation dominates the interferogram quality anyway. In
these cases, a 4-point cubic convolution with
proved to be sufficient. For high resolution applications of
high coherence single-pass interferometers, where multi-looking is not
desirable, longer interpolation kernels like the optimized 6-point cubic
convolution presented here are recommended.