├── DEM_imaging_OPFA_demo.m ├── LICENSE ├── README.md ├── db20.m ├── geotiffread_modified.m ├── getdem.m ├── opfaw.m ├── opfawo.m ├── result1.pdf ├── result1.png ├── result2.pdf ├── result2.png └── result3.pdf /DEM_imaging_OPFA_demo.m: -------------------------------------------------------------------------------- 1 | close all;clear all;clc; 2 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 3 | % This program performs reading Gotcha large scene data and imaging on DEM via OPFA & RZPFA% 4 | % following fields need to be populated: % 5 | % % 6 | % data.Nfft: Size of the FFT to form the range profile in bp % 7 | % data.deltaF: Step size of frequency data (Hz) % 8 | % data.minF: Vector containing the start frequency of each pulse (Hz) % 9 | % data.x mat: The x position of each pixel (m) % 10 | % data.y mat: The y position of each pixel (m) % 11 | % data.z mat (DEM): The z position of each pixel (m) % 12 | % data.AntX: The x_a position of the sensor at each pulse (m) % 13 | % data.AntY: The y_a position of the sensor at each pulse (m) % 14 | % data.AntZ: The z_a position of the sensor at each pulse (m) % 15 | % data.R0: The range to scene center (m) % 16 | % data.phdata: Phase history data (frequency domain) % 17 | % Fast time in rows, slow time in columns % 18 | % % 19 | % The output is: % 20 | % data.im_opfa: The complex OPFA image value at each pixel 21 | % data.im_opfawo : The complex RZPFA image value at each pixel 22 | 23 | % Written by Ruizhi Hu, Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg % 24 | % Email: fred9076@gmail.com % 25 | % Date Released: 12 Aug 2020 % 26 | % % 27 | % Part of this code is adapted from the code in .. 28 | % Gorham, L.A. and Moore, L.J., "SAR image formation toolbox for % 29 | % MATLAB," Algorithms for Synthetic Aperture Radar Imagery XVII % 30 | % 7669, SPIE (2010). % 31 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 32 | 33 | %%%%%%%%%%%%%%%%%%%% ROI parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 34 | % location = 'Buildings'; % Imaging area to choose 35 | % location = 'Center'; 36 | location = 'Uhill'; 37 | switch location 38 | case 'Flyover' 39 | Xi = 667; % Flyover 40 | Yi = -787; 41 | case 'Center' 42 | Xi = 0; 43 | Yi = 0; 44 | case 'Uhill' 45 | Xi = 713; 46 | Yi = 431; 47 | end 48 | 49 | %Choose Imaging Methods% 50 | Opw = 1; % OPFA 51 | Opwo = 1; % RZPFA 52 | 53 | rsize = 512;% The extent of the image 2rsize m x 2rsize m 54 | Nr = 512;% output pixel size in a ROI Nr x Nr 55 | 56 | %%%%%%%%%%%%%%%%%%% Read Data %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 57 | C = 299792458; 58 | fileName = 'subData0'; % Make sure file names are: subData01, subData02,...,subData010 59 | fileSt = 1;% DataStart 60 | fileEn = 2; %DataEnd 61 | 62 | %Read data and parameters 63 | data.phdata= []; 64 | % Airplane Trajetory 65 | data.R0 = []; 66 | data.AntX = []; 67 | data.AntY = []; 68 | data.AntZ = []; 69 | data.Np = 0;% Samples in Slow time 70 | for ii = (fileSt:fileEn) 71 | 72 | load([fileName,num2str(ii),'.mat']); 73 | data.phdata = [data.phdata subData.phdata]; 74 | data.R0 = [data.R0;subData.R0]; 75 | data.AntX = [data.AntX;subData.AntX]; 76 | data.AntY = [data.AntY;subData.AntY]; 77 | data.AntZ = [data.AntZ;subData.AntZ]; 78 | if ii == fileEn 79 | data.K = subData.K; % Number of Samples in range 80 | data.deltaF = subData.deltaF; 81 | data.minF = subData.minF; 82 | data.freq = (0:data.K-1)*data.deltaF + data.minF; 83 | data.Fc = mean(data.freq); 84 | end 85 | data.Np = data.Np + length(subData.Np);% Total number in slow time 86 | clear subData; 87 | end 88 | data.freq = data.freq.'; 89 | 90 | 91 | [data.x_mat,data.y_mat,data.z_mat,Zi] = getdem(Xi,Yi,rsize,Nr); % get the DEM of ROI, already subtracted Z0 92 | data.xaxis = data.x_mat(1,:); 93 | data.yaxis = data.y_mat(:,1); 94 | 95 | figure 96 | colormap(jet) 97 | imagesc(data.xaxis,data.yaxis,data.z_mat); 98 | axis image 99 | title('DEM','fontsize',16); 100 | xlabel('X (m)','fontsize',16); 101 | ylabel('Y (m)','fontsize',16); 102 | set(gca,'ydir','normal'); 103 | c=colorbar; 104 | set(get(c,'label'),'string','Elevation (m)','fontsize',16) 105 | saveas(gcf,[location,'_DEM.jpeg']) 106 | 107 | 108 | %Imaging via different algorithms%% 109 | tol = 1e-6; 110 | 111 | 112 | if Opw == 1 113 | 114 | data = opfaw(data,Xi,Yi,Zi,tol,'fgg'); 115 | 116 | figure; 117 | colormap(jet) 118 | imagesc(data.xaxis,data.yaxis,db20(data.im_opfaw),[-70,0]); 119 | axis image 120 | title('OPFA (w/ DEM)','fontsize',16); 121 | xlabel('X (m)','fontsize',16); 122 | ylabel('Y (m)','fontsize',16); 123 | set(gca,'ydir','normal'); 124 | saveas(gcf,[location,'_OPFA_w_DEM.jpeg']) 125 | end 126 | 127 | if Opwo == 1 128 | data.z_mat = zeros(size(data.z_mat)); 129 | Zi = 0; 130 | data = opfawo(data,Xi,Yi,tol,'fgg'); 131 | 132 | figure; 133 | colormap(jet) 134 | imagesc(data.xaxis,data.yaxis,db20(data.im_opfawo),[-70,0]); 135 | axis image 136 | title('OPFA (w/o DEM)','fontsize',16); 137 | xlabel('X (m)','fontsize',16); 138 | ylabel('Y (m)','fontsize',16); 139 | set(gca,'ydir','normal'); 140 | saveas(gcf,[location,'_OPFA_wo_DEM.jpeg']) 141 | end 142 | 143 | 144 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # RZPFA_matlab 2 | A demo of Gotcha Large Scene data orthorectified imaging with DEM via Orthorectified Polar Format Algorithm (OPFA) 3 | 4 | ## When using this code please cite the relevant papers below: 5 | 6 | [1] Hu, Ruizhi, et al. "Orthorectified Polar Format Algorithm for Generalized Spotlight SAR Imaging With DEM." IEEE Transactions on Geoscience and Remote Sensing (2020). 7 | [2] Hu, Ruizhi, et al. "Refocusing and Zoom-In Polar Format Algorithm for Curvilinear Spotlight SAR Imaging on Arbitrary Region of Interest." IEEE Transactions on Geoscience and Remote Sensing 57.10 (2019): 7995-8012 8 | [3] Hu, Ruizhi, et al. "Curvilinear Video-SAR Persistent Imaging with Distortion Correction Based on Nufft-3." IGARSS 2019-2019 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2019 9 | 10 | ## Contents: 11 | 1) DEM_imaging_OPFA_demo.m : main program for DEM imaging 12 | 2) getdem.m ： get the DEM for any ROI 13 | 3) geotiffread_modified.m : a modified function to read DEM data to avoid error 14 | 4) opfaw.m : Imgaing function with DEM (OPFA in [1]) 15 | 5) opfawo.m : Imgaing function without DEM (RZPFA-3 in [2]) 16 | 6) db20.m : a simple function to show image in Decibel 17 | 18 | ## Dependencies: 19 | 1) Gotcha Large Scene data (Disc1.zip and Disc2.zip) are available on 20 | https://www.sdms.afrl.af.mil./content/public-data/s3_scripts/index.php?file=GotchaLargeSceneData-Disc1.zip 21 | with registration 22 | 23 | 2) The DEM data "USGS_13_n40w085.tif", ~~avaiable on https://www.sciencebase.gov/catalog/item/5deb329ae4b02caea0f0ea8f~~ (link expired) 24 | https://drive.google.com/file/d/1nNERs5p1hNhjOm359Um7jEMKlOGqqTI_/view?usp=sharing 25 | 26 | 2) NuFFT-3 code in this program is provided on: https://cims.nyu.edu/cmcl/nufft/nufftall-1.3.3.tar.gz 27 | 28 | Mexfile should be built for Matlab to call. 29 | 30 | Please also cite their papers below if you are using their codes. 31 | 32 | * Accelerating the Nonuniform Fast Fourier Transform: (L. Greengard and J.-Y. Lee) SIAM Review 46, 443 (2004). 33 | 34 | * The type 3 nonuniform FFT and its applications: (J.-Y. Lee and L. Greengard) J. Comput. Phys. 206, 1 (2005). 35 | 36 | Other NuFFT-3 schemes are applicable, such as FINUFFT on: https://finufft.readthedocs.io/en/latest/ 37 | Quite fast, but tends to crush when data or image is large. 38 | * Barnett, Alexander H., Jeremy Magland, and Ludvig af Klinteberg. "A Parallel Nonuniform Fast Fourier Transform Library Based on an “Exponential of Semicircle" Kernel." SIAM Journal on Scientific Computing 41.5 (2019): C479-C504. 39 | 40 | ## Results 41 | ![image](https://github.com/fred9076/OPFA_matlab/blob/master/result1.png) 42 | ![image](https://github.com/fred9076/OPFA_matlab/blob/master/result2.png) 43 | -------------------------------------------------------------------------------- /db20.m: -------------------------------------------------------------------------------- 1 | function dataout = db20(data) 2 | 3 | dataout = 20*log10(abs(data)/(eps+max(abs(data(:))))+eps); 4 | end -------------------------------------------------------------------------------- /geotiffread_modified.m: -------------------------------------------------------------------------------- 1 | function varargout = geotiffread_modified(filename, varargin) 2 | %GEOTIFFREAD Read GeoTIFF file 3 | % 4 | % [A, R] = GEOTIFFREAD(FILENAME) reads a georeferenced grayscale, RGB, or 5 | % multispectral image or data grid from the GeoTIFF file specified by 6 | % FILENAME into A and constructs a spatial referencing object, R. 7 | % 8 | % [X, CMAP, R] = GEOTIFFREAD(FILENAME) reads an indexed image into X and 9 | % the associated colormap into CMAP, and constructs a spatial referencing 10 | % object, R. Colormap values in the image file are rescaled into the 11 | % range [0,1]. 12 | % 13 | % FILENAME is a string scalar or character vector that specifies the name 14 | % of the GeoTIFF file. FILENAME can include the folder name. Otherwise, 15 | % the file must be in the current folder or in a folder on the MATLAB 16 | % path. If the named file includes the extension '.TIF' or '.TIFF' 17 | % (either upper or lower case), you can omit the extension from FILENAME. 18 | % 19 | % A is a two-dimensional array if the file contains a grayscale image or 20 | % data grid. A is an M-by-N-by-P array if the file contains a color 21 | % image, multispectral image, hyperspectral image, or data grid. The 22 | % class of A depends on the storage class of the pixel data in the file 23 | % which is related to the BitsPerSample property as returned by the 24 | % IMFINFO function. 25 | % 26 | % R is a geographic raster reference object if the image or data grid is 27 | % referenced to a geographic coordinate system, or a map raster reference 28 | % object if it is referenced to a projected coordinate system. 29 | % 30 | % [A, REFMAT, BBOX] = GEOTIFFREAD(FILENAME) reads a georeferenced 31 | % grayscale, RGB, or multispectral image or data grid into A; the 32 | % corresponding referencing matrix into REFMAT; and the bounding box into 33 | % BBOX. 34 | % 35 | % [X, CMAP, REFMAT, BBOX] = GEOTIFFREAD(FILENAME) reads an indexed image 36 | % into X, the associated colormap into CMAP, the referencing matrix into 37 | % REFMAT, and the bounding box into BBOX. The referencing matrix must 38 | % be unambiguously defined by the GeoTIFF file, otherwise it and the 39 | % bounding box are returned empty. 40 | % 41 | % [...] = GEOTIFFREAD(FILENAME, IDX) reads one image from a multi-image 42 | % GeoTIFF file. IDX is an integer value that specifies the order that the 43 | % image appears in the file. For example, if IDX is 3, GEOTIFFREAD reads 44 | % the third image in the file. If you omit this argument, GEOTIFFREAD 45 | % reads the first image in the file. 46 | % 47 | % [...] = GEOTIFFREAD(URL, ...) reads the GeoTIFF image from a URL. The 48 | % URL must include the protocol type (e.g., "http://"). 49 | % 50 | % Note 51 | % ---- 52 | % GEOTIFFREAD imports pixel data using the TIFF-reading capabilities of 53 | % the MATLAB function IMREAD and likewise shares any limitations of 54 | % IMREAD. Consult the IMREAD documentation for specific information on 55 | % TIFF image support. 56 | % 57 | % Example 58 | % ------- 59 | % % Read and display the Boston GeoTIFF image. 60 | % % Includes material (c) GeoEye, all rights reserved. 61 | % [boston, R] = geotiffread('boston.tif'); 62 | % figure 63 | % mapshow(boston, R) 64 | % axis image off 65 | % 66 | % See also GEOSHOW, GEOTIFFINFO, GEOTIFFWRITE, IMREAD, MAPSHOW 67 | 68 | % Copyright 1996-2017 The MathWorks, Inc. 69 | 70 | % Verify the input and output argument count. 71 | narginchk(1,2); 72 | nargoutchk(0,4); 73 | 74 | % Parse the inputs. 75 | filename = convertStringsToChars(filename); 76 | [filename, url, idx] = parseInputs(filename, varargin); 77 | 78 | % Read the info fields from the filename. 79 | info = geotiffinfo(filename); 80 | 81 | % Read the image from the filename. 82 | [A, cmap] = imread(filename,idx); 83 | 84 | % If the RefMatrix is empty, try to obtain the spatial information from a 85 | % corresponding worldfile. 86 | if isempty(info.RefMatrix) 87 | worldfilename = getworldfilename(filename); 88 | info = getSpatialInfoFromWorldfile(worldfilename, info, size(A)); 89 | end 90 | 91 | % Delete temporary file from Internet download. 92 | if (url) 93 | deleteDownload(filename); 94 | end 95 | 96 | % Assign output arguments. 97 | varargout = assignOutputArguments(A, cmap, info, nargout); 98 | 99 | %-------------------------------------------------------------------------- 100 | 101 | function [filename, url, idx] = parseInputs(filename, inputs) 102 | % Parse the inputs from the cell array, INPUTS. 103 | 104 | % Verify the filename and obtain the full pathname. 105 | extensions = {'tif', 'tiff'}; 106 | [filename, url] = internal.map.checkfilename(filename, extensions, mfilename, 1, true); 107 | 108 | % Check and set the image index number. 109 | if ~isempty(inputs) 110 | idx = inputs{1}; 111 | attributes = {'real' 'scalar' 'positive'}; 112 | validateattributes(idx, {'numeric'}, attributes, mfilename, 'IDX', 2); 113 | else 114 | idx = 1; 115 | end 116 | 117 | %-------------------------------------------------------------------------- 118 | 119 | function info = getSpatialInfoFromWorldfile(worldfilename, info, rasterSize) 120 | % Obtain the referencing matrix from a world file, if it exits. If so, 121 | % compute the bounding box and construct a spatial referencing object from 122 | % the referencing matrix and update the fields of the INFO structure. 123 | % WORLDFILENAME is a string denoting the name of the world file. 124 | 125 | if exist(worldfilename,'file') 126 | % Obtain the referencing matrix from the world file. 127 | refmat = worldfileread(worldfilename); 128 | 129 | % Calculate the spatial referencing object and bounding box from the 130 | % referencing matrix if it is not empty. 131 | if ~isempty(refmat) 132 | if strcmp(info.ModelType, 'ModelTypeGeographic') 133 | R = refmatToGeoRasterReference(refmat, rasterSize); 134 | elseif strcmp(info.ModelType, 'ModelTypeProjected') 135 | R = refmatToMapRasterReference(refmat, rasterSize); 136 | else 137 | R = []; 138 | end 139 | info.BoundingBox = mapbbox(refmat, rasterSize); 140 | info.RefMatrix = refmat; 141 | info.SpatialRef = R; 142 | end 143 | end 144 | 145 | %-------------------------------------------------------------------------- 146 | 147 | function outputs = assignOutputArguments(A, cmap, info, numOutputs) 148 | % Assign the output arguments based on the number of arguments requested. 149 | 150 | outputs{1} = A; 151 | switch numOutputs 152 | case 2 153 | if strcmp(info.ColorType, 'indexed') 154 | % [X, CMAP] = GEOTIFFREAD(...) 155 | outputs{2} = cmap; 156 | else 157 | % [A, R] = GEOTIFFREAD(...) 158 | outputs{2} = info.SpatialRef; 159 | end 160 | 161 | case 3 162 | if strcmp(info.ColorType, 'indexed') 163 | % [X, CMAP, R] = GEOTIFFREAD(...) 164 | outputs{2} = cmap; 165 | outputs{3} = info.SpatialRef; 166 | else 167 | % [A, REFMAT, BBOX] = GEOTIFFREAD(...) 168 | outputs{2} = info.RefMatrix; 169 | outputs{3} = info.BoundingBox; 170 | end 171 | 172 | case 4 173 | % [X, CMAP, REFMAT, BBOX] = GEOTIFFREAD(...) 174 | outputs{2} = cmap; 175 | outputs{3} = info.RefMatrix; 176 | outputs{4} = info.BoundingBox; 177 | end 178 | -------------------------------------------------------------------------------- /getdem.m: -------------------------------------------------------------------------------- 1 | function [XX,YY,ZZ,Zi] = getdem(xr,yr,rsize,Nr) 2 | % Interpolation to get DEM for any ROI 3 | % (xr,yr) is the center of the ROI 4 | % rsize is the size of ROI rsize(m) x rsize(m) 5 | % Nr is the number of pixels Nr x Nr 6 | % Zi is the elevation of the ROI center 7 | % XX, YY are imaging grid 8 | % ZZ is the output DEM of ROI 9 | 10 | [DEMa,~] = geotiffread_modified('USGS_13_n40w085.tif'); % read the whole DEM data, modified from the geotiffread function in the map toolbox 11 | DEMa = double(flipud(DEMa)); % latitude value vary from large to small. 12 | Z0 = 244; 13 | 14 | NI = size(DEMa,1); 15 | 16 | LonMin = -85.0005559296; % from the DEM data 17 | LonMax = -83.9993522214; 18 | LatMin = 38.9993520234; 19 | LatMax = 40.0005557316; 20 | 21 | Lo = linspace(LonMin,LonMax,NI); 22 | La = linspace(LatMin,LatMax,NI); 23 | 24 | xxr = linspace(xr - rsize, xr + rsize, Nr); 25 | yyr = linspace(yr - rsize, yr + rsize, Nr); 26 | 27 | LonC = -84.098365; % calibrated value 28 | LatC = 39.779721; 29 | 30 | OneLat = 111132.92 - 559.82*cosd(2*LatC)+ 1.175*cosd(4*LatC)-0.0023*cosd(6*LatC); 31 | OneLon = 111412.84*cosd(LatC) - 93.5*cosd(3*LatC) + 0.118*cosd(5*LatC); 32 | 33 | [XX, YY] = meshgrid(xxr,yyr); 34 | 35 | RLoM = XX/OneLon + LonC; 36 | RLaM = YY/OneLat + LatC; 37 | 38 | 39 | [LoM, LaM] = meshgrid(Lo,La); 40 | 41 | DEMs = interp2(LoM,LaM,DEMa,RLoM,RLaM,'spline'); 42 | 43 | DEMs = DEMs - Z0; 44 | Zi= sum(sum(DEMs(Nr/2:Nr/2+1,Nr/2:Nr/2+1)))/4; 45 | 46 | ZZ = DEMs; 47 | 48 | return 49 | 50 | 51 | 52 | -------------------------------------------------------------------------------- /opfaw.m: -------------------------------------------------------------------------------- 1 | function data = opfaw(data,Xi,Yi,Zi,tol,meth) 2 | % OPFA Algorithm with DEM 3 | % DEM calculated by function getdem 4 | % Xi,Yi,Zi is the location of refocusing point 5 | % tol is the tolerence for nufft; 6 | % (Xi,Yi,Zi) is the refocusing point 7 | % meth can be 'fgg' or 'finufft' 8 | % 9 | C = 299792458; 10 | ic = round(data.Np/2); % center of Azimuth 11 | 12 | Xa = data.AntX'; % curve smoothing may be needed for some trajectory 13 | Ya = data.AntY'; 14 | Za = data.AntZ'; 15 | R0A = data.R0'; 16 | 17 | lambda = C/data.Fc; 18 | 19 | % 20 | %Apertuer center 21 | Xc = Xa(ic); 22 | Yc = Ya(ic); 23 | Zc = Za(ic); 24 | % 25 | %First-order derivatives 26 | dt = 2/data.Np; 27 | Xdk = diff(Xa)/dt;% 28 | Ydk = diff(Ya)/dt; 29 | Zdk = diff(Za)/dt; 30 | Xdc = Xdk(ic); % Center derivatives 31 | Ydc = Ydk(ic); 32 | Zdc = Zdk(ic); 33 | %Second-order derivative 34 | Xddk = diff(Xdk)/dt; 35 | Yddk = diff(Ydk)/dt; 36 | Zddk = diff(Zdk)/dt; 37 | Xddc = Xddk(ic); % center second-derivatives 38 | Yddc = Yddk(ic); 39 | Zddc = Zddk(ic); 40 | % clear Xdk Ydk Zdk Xddk Yddk Zddk; 41 | 42 | 43 | %%%%%%%%%%%%%%%%%%% Non-uniform Input Calculation %%%%%%%%%%%%% 44 | % 45 | Rfi = sqrt((Xa-Xi).^2 + (Ya-Yi).^2 + (Za-Zi).^2);% w.r.t Refocusing point 46 | El = asind((Za-Zi)./Rfi); 47 | Az = atan2d((Ya-Yi),(Xa-Xi)); 48 | 49 | Kx = 4*pi/C*data.freq*(cosd(Az).*cosd(El));% Kxi Kyi Non-uniform input wavenumber locations after refocusing 50 | Ky = 4*pi/C*data.freq*(sind(Az).*cosd(El)); 51 | 52 | Ac = Az(ic);%Center angles 53 | Ec = El(ic); 54 | 55 | Kxc = 4*pi/C*data.Fc*(cosd(Ac)*cosd(Ec));%center wavenumber 56 | Kyc = 4*pi/C*data.Fc*(sind(Ac)*cosd(Ec)); 57 | disp('Input Calculation finished') 58 | 59 | % %%%%%%%%%%%%%%%%%%% Refocusing %%%%%%%%%%%%% 60 | % 61 | ddi = R0A - Rfi; % differential range for refocusing 62 | sr = double(data.phdata.*exp(-1i*4*pi/C*data.freq*ddi)); % Refocusing 63 | disp('Refocusing finished') 64 | %%%%%%%%%%%%%%%%%%% Non-uniform Output Calculation %%%%%%%%%%%%% 65 | % 66 | 67 | % %Calculation of the mapping 68 | A = (Xc-data.x_mat)*Xdc + (Yc-data.y_mat)*Ydc + (Zc-data.z_mat)*Zdc;%Mat for image reconstrution 69 | Ai = (Xc-Xi)*Xdc + (Yc-Yi)*Ydc + (Zc-Zi)*Zdc;% For calculating the mapping 70 | Ri = sqrt((Xc-Xi)^2+(Yc-Yi)^2 + (Zc-Zi)^2 ); 71 | Rt = sqrt((Xc-data.x_mat).^2+(Yc-data.y_mat).^2 + (Zc-data.z_mat).^2 );%Mat 72 | Di = Ri.*(Ri-Rt) ;%Mat 73 | Ei = 2*Ai - A./Rt*Ri - Ai*Rt/Ri ;% Mat 74 | Fi = (Xc-Xi)*Ydc - (Yc- Yi)*Xdc; 75 | 76 | % %Non-uniform output grids after mapping 77 | data.Xh = (Ydc*Di-(Yc-Yi)*Ei)/Fi ; 78 | data.Yh = (-Xdc*Di+(Xc-Xi)*Ei)/Fi ; 79 | disp('Output calculation finished') 80 | %%%%%%%%%%___NuFFt3_Imaging____%%%%%%%%%%%%%% 81 | nj = data.K*data.Np;% Number of Input Samples 82 | Kx = Kx(:)-Kxc; 83 | Ky = Ky(:)-Kyc; 84 | 85 | xj = Kx;% Input locations 86 | yj = Ky; 87 | iflag = 0; 88 | sk = -data.Xh(:);% Output locations 89 | tk = -data.Yh(:); 90 | nk = length(sk); % Number of output samples 91 | % tol=1e-15; % error tolerance 92 | 93 | if strcmp(meth, 'fin') % Finufft may crush for large data and large image 94 | [fk,~]=finufft2d3(xj,yj,sr(:),iflag,tol,sk,tk); % Call Nufft-3 95 | 96 | elseif strcmp(meth, 'fgg') 97 | [fk,~]=nufft2d3(nj,xj,yj,sr(:),iflag,tol,nk,sk,tk); 98 | 99 | end 100 | disp('NuFFT-3 finished') 101 | 102 | data.im_opfaw = reshape(fk,[length(data.x_mat(1,:)),length(data.x_mat(1,:))]); % Reshape to image 103 | 104 | 105 | 106 | 107 | %%%%%%%%%%% Calculating effect scene due to defocus %%%%%%%%%%%%%%% 108 | % data.rqpew = zeros(size(data.x_mat)); 109 | % Bi = (Xc - Xi)* data.Xh +(Yc - Yi)*data.Yh; %Mat 110 | % Ci = Xdc* data.Xh +Ydc*data.Yh; %Mat 111 | % Hi = Xddc* data.Xh +Yddc*data.Yh; %Mat 112 | % G = Xdc^2 + Ydc^2 + Zdc^2 + (Xc - data.x_mat)*Xddc + (Yc - data.y_mat)*Yddc + (Zc-data.z_mat)*Zddc;%Mat 113 | % Gi = Xdc^2 + Ydc^2 + Zdc^2 + (Xc - Xi)*Xddc + (Yc - Yi)*Yddc + (Zc-Zi)*Zddc; 114 | % % Rdt0 = A0./Rt0;%Mat 115 | % Rdi = Ai/Ri; 116 | % Rddt = (G.*(Rt.^2) - A.^2)./(Rt.^3);%Mat 117 | % Rddi = (Gi*(Ri^2) - Ai^2)/(Ri^3); 118 | % data.rqpew = 2*pi/lambda*abs(Rddt - Rddi - Bi*(Ri*Rddi - 2*Rdi^2)/(Ri^3)-(2*Ci*Rdi - Hi*Ri )/(Ri^2));%Mat 119 | 120 | return -------------------------------------------------------------------------------- /opfawo.m: -------------------------------------------------------------------------------- 1 | function data = opfawo(data,Xi,Yi,tol,meth) 2 | % OPFA Algorithm without DEM, ie Zi = 0, data.z_mat = 0 3 | % DEM calculated by function getdem 4 | % Xi,Yi,Zi is the location of refocusing point 5 | % tol is the tolerence for Nufft 6 | % (Xi,Yi,Zi) is the refocusing point 7 | % meth can be 'fgg' or 'finufft' 8 | C = 299792458; 9 | ic = round(data.Np/2); % center of Azimuth 10 | Xa = data.AntX'; 11 | Ya = data.AntY'; 12 | Za = data.AntZ'; 13 | R0A = data.R0'; 14 | lambda = C/data.Fc; 15 | 16 | 17 | % 18 | %Apertuer center 19 | Xc = Xa(ic); 20 | Yc = Ya(ic); 21 | Zc = Za(ic); 22 | % 23 | %First-order derivatives 24 | dt = 2/data.Np; 25 | Xdk = diff(Xa)/dt;% 26 | Ydk = diff(Ya)/dt; 27 | Zdk = diff(Za)/dt; 28 | Xdc = Xdk(ic); % Center derivatives 29 | Ydc = Ydk(ic); 30 | Zdc = Zdk(ic); 31 | %Second-order derivative 32 | Xddk = diff(Xdk)/dt; 33 | Yddk = diff(Ydk)/dt; 34 | Zddk = diff(Zdk)/dt; 35 | Xddc = Xddk(ic); % center second-derivatives 36 | Yddc = Yddk(ic); 37 | Zddc = Zddk(ic); 38 | % clear Xdk Ydk Zdk Xddk Yddk Zddk; 39 | 40 | 41 | %%%%%%%%%%%%%%%%%%% Non-uniform Input Calculation %%%%%%%%%%%%% 42 | % 43 | Rfi0 = sqrt((Xa-Xi).^2 + (Ya-Yi).^2 + Za.^2);% w.r.t Refocusing point 44 | El = asind(Za./Rfi0); 45 | Az = atan2d((Ya-Yi),(Xa-Xi)); 46 | 47 | Kx0 = 4*pi/C*data.freq*(cosd(Az).*cosd(El));% Kxi Kyi Non-uniform input wavenumber locations after refocusing 48 | Ky0 = 4*pi/C*data.freq*(sind(Az).*cosd(El)); 49 | 50 | Ac = Az(ic);%Center angles 51 | Ec = El(ic); 52 | 53 | Kxc0 = 4*pi/C*data.Fc*(cosd(Ac)*cosd(Ec));%center wavenumber 54 | Kyc0 = 4*pi/C*data.Fc*(sind(Ac)*cosd(Ec)); 55 | disp('Input Calculation finished') 56 | 57 | % %%%%%%%%%%%%%%%%%%% Refocusing %%%%%%%%%%%%% 58 | % 59 | ddi0 = R0A - Rfi0; % differential range for refocusing 60 | srwo = double(data.phdata.*exp(-1i*4*pi/C*data.freq*ddi0)); % Refocusing 61 | disp('Refocusing finished') 62 | %%%%%%%%%%%%%%%%%%% Non-uniform Output Calculation %%%%%%%%%%%%% 63 | % 64 | 65 | % %Calculation of the mapping 66 | A0 = (Xc-data.x_mat)*Xdc + (Yc-data.y_mat)*Ydc + Zc*Zdc;%Mat for image reconstrution 67 | Ai0 = (Xc-Xi)*Xdc + (Yc-Yi)*Ydc + Zc*Zdc;% For calculating the mapping 68 | Ri0 = sqrt((Xc-Xi)^2+(Yc-Yi)^2 + Zc^2 ); 69 | Rt0 = sqrt((Xc-data.x_mat).^2+(Yc-data.y_mat).^2 + Zc^2 );%Mat 70 | Di0 = Ri0.*(Ri0-Rt0) ;%Mat 71 | Ei0 = 2*Ai0 - A0./Rt0*Ri0 - Ai0*Rt0/Ri0 ;% Mat 72 | Fi0 = (Xc-Xi)*Ydc - (Yc- Yi)*Xdc; 73 | 74 | % %Non-uniform output grids after mapping 75 | data.Xh0 = (Ydc*Di0-(Yc-Yi)*Ei0)/Fi0 ; 76 | data.Yh0 = (-Xdc*Di0+(Xc-Xi)*Ei0)/Fi0 ; 77 | disp('Output calculation finished') 78 | %%%%%%%%%%___NuFFt3_Imaging____%%%%%%%%%%%%%% 79 | nj = data.K*data.Np;% Number of Input Samples 80 | Kx0 = Kx0(:)-Kxc0; 81 | Ky0 = Ky0(:)-Kyc0; 82 | 83 | xj = Kx0;% Input locations 84 | yj = Ky0; 85 | iflag = 0; 86 | sk = -data.Xh0(:);% Output locations, minus sign for distortioncompensation 87 | tk = -data.Yh0(:); 88 | nk = length(sk); % Number of output samples 89 | if strcmp(meth, 'fin') 90 | [fkwo,~]=finufft2d3(xj,yj,srwo(:),iflag,tol,sk,tk); % Call Nufft-3 91 | elseif strcmp(meth, 'fgg') 92 | [fkwo,~]=nufft2d3(nj,xj,yj,srwo(:),iflag,tol,nk,sk,tk); 93 | 94 | end 95 | disp('NuFFT-3 finished') 96 | 97 | data.im_opfawo = reshape(fkwo,[length(data.x_mat(1,:)),length(data.x_mat(1,:))]); % Reshape to image 98 | %%%%%%%%%%% Calculating effect scene due to defocus without DEM %%%%%%%%%%%%%%% 99 | % data.rqpewo = zeros(size(data.x_mat)); 100 | % Bi0 = (Xc - Xi)* data.Xh0 +(Yc - Yi)*data.Yh0; %Mat 101 | % Ci0 = Xdc* data.Xh0 +Ydc*data.Yh0; %Mat 102 | % Hi0 = Xddc* data.Xh0 +Yddc*data.Yh0; %Mat 103 | % G0 = Xdc^2 + Ydc^2 + Zdc^2 + (Xc - data.x_mat)*Xddc + (Yc - data.y_mat)*Yddc + Zc*Zddc;%Mat 104 | % Gi0 = Xdc^2 + Ydc^2 + Zdc^2 + (Xc - Xi)*Xddc + (Yc - Yi)*Yddc + Zc*Zddc; 105 | % 106 | % Rdi0 = Ai0/Ri0; 107 | % Rddt0 = (G0.*(Rt0.^2) - A0.^2)./(Rt0.^3);%Mat 108 | % Rddi0 = (Gi0*(Ri0^2) - Ai0^2)/(Ri0^3); 109 | % data.rqpewo = 2*pi/lambda*abs(Rddt0 - Rddi0 - Bi0*(Ri0*Rddi0 - 2*Rdi0^2)/(Ri0^3)-(2*Ci0*Rdi0 - Hi0*Ri0 )/(Ri0^2));%Mat 110 | 111 | 112 | return -------------------------------------------------------------------------------- /result1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/fred9076/OPFA_matlab/719b14111f44b564394b5bf1a5f980b9a6d5be81/result1.pdf -------------------------------------------------------------------------------- /result1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/fred9076/OPFA_matlab/719b14111f44b564394b5bf1a5f980b9a6d5be81/result1.png -------------------------------------------------------------------------------- /result2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/fred9076/OPFA_matlab/719b14111f44b564394b5bf1a5f980b9a6d5be81/result2.pdf -------------------------------------------------------------------------------- /result2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/fred9076/OPFA_matlab/719b14111f44b564394b5bf1a5f980b9a6d5be81/result2.png -------------------------------------------------------------------------------- /result3.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/fred9076/OPFA_matlab/719b14111f44b564394b5bf1a5f980b9a6d5be81/result3.pdf --------------------------------------------------------------------------------