上一次最後給出了一個成像算法的示例，下面是它對應的代碼，裏面已經有了初步的註釋。
當然這個是個簡單情況，但已經大概說明了流程。代碼具體的解釋，我打算先放一放，畢竟it is a long story，我們需要從長計議。後續章節將結合代碼逐漸講解一下成像的步驟。在合適的時間，我會具體講解這些代碼的意義，以及他忽略的部分。
代碼來源已經註明，在此表示感謝！
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clear all; close all; clc;
% Tutorial: Focusing of SAR raw data
% Programmed by Diana Weihing & Stefan Auer
% Remote Sensing Technology
% Technische Universit鋞 M黱chen
% 2011
%--------------------------------------------------------------------------
% A.) Load raw data
% Dummy image ('Test_Image')
%raw = load('Test_Image'); % type: field
%max_power = 2.1807e+008;
% Real SAR data ('ERS')
raw = load('ERS'); % type: field
max_power = 10000;
% Multilooking on/off?
multilook = 1; % 0: no; 1: yes
ml_factor = 5; % multilooking factor (spatial)
% Get image size
fn = fieldnames(raw);
Raw_data = getfield(raw,fn{1});
size_azimuth = size(Raw_data,1);
size_range = size(Raw_data,2);
%--------------------------------------------------------------------------
% B.) Sensor parameters (ERS satellite)
fs=18.962468*10^6; % Range Sampling Frequency [Hz]
K_r=4.18989015*10^(11); % FM Rate Range Chirp [1/s^2] --> up-chirp
tau_p=37.12*10^(-6); % Chirp duration [s]
V=7098.0194; % Effective satellite velocity [m/s]
lambda=0.05656; % Length of carrier wave [m]
R_0=852358.15; % Range to center of antenna footprint [m]
ta=0.6; % Aperture time [s]
prf=1679.902; % Pulse Repitition Frequency [Hz]
%--------------------------------------------------------------------------
% C.) Display raw data
figure;
imagesc(abs(Raw_data));colormap('gray');
title('Raw data (unfocused)'); xlabel('Range pixels'); ylabel('Azimuth pixels');
axis equal; axis off;
%--------------------------------------------------------------------------
% D.) Define correlation chirp in range
% Basic definitions
range_chirp=zeros(1,size_range); % empty vector to be filled with chirp values
tau=-tau_p/2:1/fs:tau_p/2; % time axis in range
omega = -fs/2:1/tau_p:fs/2; % frequency axis in range ?
% Define chirp in range
ra_chirp_temp = exp(1i.*pi.*K_r.*tau.^2);
% Get size of chirp
size_chirp_r = length(tau);
%--------------------------------------------------------------------------
% Display range chirp (time + frequency domain)
figure;
subplot(2,1,1); plot(tau,real(ra_chirp_temp),'b'); hold on;
plot(tau,imag(ra_chirp_temp),'r');
title('Range chirp'); xlabel('Time axis [sec]'); ylabel('Amplitude');
xlim([min(tau) max(tau)]);
subplot(2,1,2); plot(omega, abs(fftshift(fft(ra_chirp_temp))));
title('Spectrum of range chirp'); xlabel('Frequency [Hz]'); ylabel('Absolute');
xlim([min(omega) max(omega)]);
%--------------------------------------------------------------------------
% Position chirp in range vector (centered)
% --> used for correlation procedure
range_chirp(ceil((size_range-size_chirp_r)/2):size_chirp_r+ceil((size_range-size_chirp_r)/2)-1)=ra_chirp_temp;
% Transform vector in frequency domain (fourier transform)
RANGE_CHIRP=fft(range_chirp);
% Define chirp for correlation
% --> conjugate complex of signal chirp
CON_RANGE_CHIRP=conj(RANGE_CHIRP);
%--------------------------------------------------------------------------
% E.) Define correlation chirp in azimuth
% Basic definitions
azimuth_chirp=zeros(1,size_azimuth); % empty vector to be filled with chirp values
t=-ta/2:1/prf:ta/2; % time axis in azimuth
v=-prf/2:1/ta:prf/2; % frequency axis in azimuth??
% FM Rate Azimuth Chirp
K_a=-2*V^2/(lambda*R_0);
% Define chirp in azimuth
az_chirp_temp=exp(1i.*pi.*K_a.*t.^2);
% Get size of chirp
size_chirp_a = length(t);
%--------------------------------------------------------------------------
% Display azimuth chirp (time + frequency domain)
figure;
subplot(2,1,1); plot(t,real(az_chirp_temp),'b'); hold on;
plot(t,imag(az_chirp_temp),'r');
title('Azimuth chirp'); xlabel('Time axis [sec]'); ylabel('Amplitude');
xlim([min(t) max(t)]);
subplot(2,1,2); plot(v, abs(fftshift(fft(az_chirp_temp))));
title('Spectrum of azimuth chirp'); xlabel('Frequency [Hz]'); ylabel('Absolute');
xlim([min(v) max(v)]);
%--------------------------------------------------------------------------
% Position chirp in azimuth vector (centered)
% --> used for correlation procedure
azimuth_chirp(ceil((size_azimuth-size_chirp_a)/2):size_chirp_a+ceil((size_azimuth-size_chirp_a)/2)-1)=az_chirp_temp;
% Transform vector in frequency domain (fourier transform)
AZIMUTH_CHIRP=fft(azimuth_chirp);
% Define chirp for correlation
% --> conjugate complex of signal chirp
CON_AZIMUTH_CHIRP=conj(AZIMUTH_CHIRP);
%--------------------------------------------------------------------------
% F.) Focusing (= 2D correlation)
% Dummy matrix to be filled with processed data
processed=zeros(size_azimuth,size_range);
%-------------------------------------------------
% F.1) Range compression
% --> correction in azimuth time - range frequency domain
% --> result in azimuth-range domain
for k1 = 1:size_azimuth
vek = Raw_data(k1,:); % Select row in range
VEK = fft(vek); % Fourier Transform
CORR = VEK.*CON_RANGE_CHIRP; % Multiply spectra
if_vek = fftshift(ifft(CORR)); % Inverse Fourier Transform
processed(k1,:) = if_vek;
end
clear vek VEK CORR if_vek
%-------------------------------------------------
% F.2) Azimuth compression
% conducted in azimuth frequency - range time domain
for k2 = 1:size_range
vek = processed(:,k2); % select row in azimuth
VEK = fft(vek); % Fourier Transform
CORR = VEK.*CON_AZIMUTH_CHIRP.'; % Multiply spectra
if_vek = fftshift(ifft(CORR)); % Inverse Fourier Transform
processed(:,k2) = if_vek;
end
% F.1) Range compression
% --> correction in azimuth time - range frequency domain
% --> result in azimuth-range domain
clear vek VEK CORR if_vek
%--------------------------------------------------------------------------
% G.) Spatial Multilooking
% ERS: resolution in range: approx. 25 m, resolution in azimuth: approx. 5 m
% Aim: pixel should have the same size in azimuth and range
% solution: average 5 azimuth pixels to one azimuth pixel
if multilook == 1
% define size of output image
output_image=zeros(ceil(size_azimuth/ml_factor),size_range);
% Dummy index
index=1;
% Spatial averaging
for i=1:ml_factor:size_azimuth-ml_factor % jump along azimuth axis according to multilooking factor
vek=processed(i:i+(ml_factor-1),:); % select azimuth bins
m_vek=mean(abs(vek),1); % average value of azimuth bins
output_image(index,:)=m_vek;
index=index+1;
end
% Final SAR image (multi-looked)
processed = output_image;
end
%--------------------------------------------------------------------------
% H.) Display SAR image
figure;
imagesc(abs(processed));colormap('gray')
title('Processed SAR image')
xlabel('Range','FontSize',12); ylabel('Azimuth','FontSize',12);
caxis([0 max_power]);
axis equal; axis off;
%--------------------------------------------------------------------------