ALOS Data Users Handbook

ALOS Data Users Handbooka) Range Migration CorrectionIt rearranges the data after FFT according to the range migration function calculated.The range migration correction coefficient calculated is the amount of movements of a range sample (RS).Based on the amount of movements the value of A(I), which is the I th data, is moved as the value of (I-RS) thdata. Since RS is a real numerical value, I of A(I) does not always coincide with its range sampling position.Therefore, it interpolates the value of A(I) using a total of four points in the range direction, which are backtwo points and forth two points of A(I), by cubic convolution. The interpolated value is regarded as the valueat the position shifted only by RS.b) Azimuth CompressionThe azimuth compression is executed by multiplying X(f) after the range migration correction in thefrequency domain by Y(f) which converted y(t) into complex conjugate (y(t); azimuth compression referencefunction) as well as the range compression.2y(t)= exp(2πjFt )Equation 7.3-5ddY ( f ) = ∫ y(t)*⋅exp(−2π jft)dtEquation 7.3-6Z( f ) = X ( f ) ⋅Y( f )Equation 7.3-7c) 1-look ProcessingChirp band (f W ) is calculated using F dd and synthetic aperture time (T d ) by the following equation.fw= F ⋅TEquation 7.3-8dddWhere synthetic aperture distance (R d ) of 1-look and synthetic aperture time (T d ) is determined using satellitealtitude (H), off-nadir angle (O f ), azimuth beam width (B W ) and ground speed of imaging (V E ) by thefollowing equation.H ⎛ Bw⎞R d = 2⋅⋅ tan⎜⎟Equation 7.3-9cos O f ⎝ 2 ⎠RdT d = Equation 7.3-10VEIn 1-look processing, when the number of sampling points (size of FFT) is N, the number of chirp points infrequency space (M; reference function length) is represented by the following equation.7-31