How to get wrapped phase data from unwrapped phase data

Hello, I have a unwrapped phase data (like figure c)), and would like to converter to wapped phase -pi to pi (figure d)). The unwrapped data as below,

clear all
close all

x = [0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300;
0	25	50	75	100	125	150	175	200	225	250	275	300];

y = [0	0	0	0	0	0	0	0	0	0	0	0	0;
25	25	25	25	25	25	25	25	25	25	25	25	25;
50	50	50	50	50	50	50	50	50	50	50	50	50;
75	75	75	75	75	75	75	75	75	75	75	75	75;
100	100	100	100	100	100	100	100	100	100	100	100	100;
125	125	125	125	125	125	125	125	125	125	125	125	125;
150	150	150	150	150	150	150	150	150	150	150	150	150;
175	175	175	175	175	175	175	175	175	175	175	175	175;
200	200	200	200	200	200	200	200	200	200	200	200	200;
225	225	225	225	225	225	225	225	225	225	225	225	225;
250	250	250	250	250	250	250	250	250	250	250	250	250;
275	275	275	275	275	275	275	275	275	275	275	275	275;
300	300	300	300	300	300	300	300	300	300	300	300	300];

P1 = [0.00629902465548593	0	0.370360403979544	0.697952300768709	1.09498976198938	1.56870800849013	2.12395906570559	2.81585532372079	3.39866169304573	3.64253589553491	4.26484759295528	4.83926438355056	4.98002974456558;
0.137381160979757	0.246608475310334	0.592860021968966	0.796909269134396	1.17006024381228	1.61722777123652	2.09098133689549	2.49798333473697	3.27627600697244	3.76528436339437	4.27393969223159	4.69233205784296	4.82449188605027;
0.283802206311021	0.379244486555537	0.636863031608359	0.894743014026747	1.32245034405842	1.76881078704342	2.22803397844447	2.88148743448661	3.48150531224602	3.86924267707491	4.33418741403774	4.75077070610127	5.00893907178119;
0.521196529741695	0.534390705876809	0.920249592084803	1.05001285542764	1.66533802386529	2.09312319089403	2.32781805966794	2.94214425179044	3.48540934510910	3.94159355749976	4.44480140586060	4.92395859232093	5.20553404005533;
0.930727793725104	1.00047800959736	1.19722667041764	1.44486409206520	1.90284091792818	2.29410161862994	2.70298917461811	3.19572251117720	3.66103111577096	4.01087501806143	4.57994821896516	5.24967348809286	5.45832605077326;
1.45432174020560	1.52165971306495	1.65779975241850	1.85155102351230	2.41122947846562	2.65820594154887	3.14661217993624	3.59598633141906	4.03429414470343	4.40257738423707	5.11279339119620	5.48946170408643	5.72329126786549;
2.09243861721516	2.15418697359138	2.29137619939394	2.61066961130222	2.93275370878592	3.45800370014039	3.77806691806529	4.12323508596284	4.55659505933522	4.99103488622617	5.47479588652139	5.82258900961291	6.06276261255363;
2.84828226959355	2.88904349573765	2.96873285191344	3.08069203738026	3.44697966788091	4.13567533931369	4.52894098819945	4.67412567995202	5.15296324526301	5.56523852795320	5.96502602345583	6.21078028605879	6.52849691526073;
3.74002027926708	3.75993225502666	3.83411382444209	4.00456816843311	4.32926896155507	4.77622144003005	5.16736759461981	5.49836937572280	5.88647170837687	6.18271839080470	6.59759022678129	6.97084214072058	6.75170686464779;
4.78524857165206	4.74826975259759	4.81706589206119	4.97601956899259	5.27355150638661	5.63396907113975	5.99958011195912	6.36694810730541	6.77714174291766	6.70742436573057	7.25550718842670	7.26295700795507	7.25746708897833;
6.03717083993188	5.79887631698666	5.91639397495982	6.00350593883982	6.33213672950170	6.64106263587169	6.95706983158674	7.28782367961083	7.70705369497867	7.63458594897408	7.93261292601932	8.00295469770043	7.82960635002508;
7.19298190970422	7.15760814782713	7.24449095049573	7.47603016525217	7.57972831981689	7.78795195979569	8.01946233620746	8.20828974079021	8.68131635353786	8.70525487083782	8.81017351195784	8.91630723595258	8.87870649490453;
8.54520636494540	8.55348201216040	8.61726432100011	8.75404753128375	8.88337889302489	9.04996267034075	9.23602519155018	9.42482470685441	9.64993914996010	9.70203369491229	9.65289346191122	9.39722499724188	9.12721227719753];

figure(2)
pcolor(x,y,P1)
axis square, 
shading interp
colorbar
colormap((gray(256)));
set(gca,'xtick',[])
set(gca,'ytick',[])
set(gca,'FontSize',14)

Answer 1

[Star Strider]

According to the unwrap documentation, unwrapping takes the original and adds radians to phase angles that originally go from .

Unwrapped:

P1 = [0.00629902465548593	0	0.370360403979544	0.697952300768709	1.09498976198938	1.56870800849013	2.12395906570559	2.81585532372079	3.39866169304573	3.64253589553491	4.26484759295528	4.83926438355056	4.98002974456558;
0.137381160979757	0.246608475310334	0.592860021968966	0.796909269134396	1.17006024381228	1.61722777123652	2.09098133689549	2.49798333473697	3.27627600697244	3.76528436339437	4.27393969223159	4.69233205784296	4.82449188605027;
0.283802206311021	0.379244486555537	0.636863031608359	0.894743014026747	1.32245034405842	1.76881078704342	2.22803397844447	2.88148743448661	3.48150531224602	3.86924267707491	4.33418741403774	4.75077070610127	5.00893907178119;
0.521196529741695	0.534390705876809	0.920249592084803	1.05001285542764	1.66533802386529	2.09312319089403	2.32781805966794	2.94214425179044	3.48540934510910	3.94159355749976	4.44480140586060	4.92395859232093	5.20553404005533;
0.930727793725104	1.00047800959736	1.19722667041764	1.44486409206520	1.90284091792818	2.29410161862994	2.70298917461811	3.19572251117720	3.66103111577096	4.01087501806143	4.57994821896516	5.24967348809286	5.45832605077326;
1.45432174020560	1.52165971306495	1.65779975241850	1.85155102351230	2.41122947846562	2.65820594154887	3.14661217993624	3.59598633141906	4.03429414470343	4.40257738423707	5.11279339119620	5.48946170408643	5.72329126786549;
2.09243861721516	2.15418697359138	2.29137619939394	2.61066961130222	2.93275370878592	3.45800370014039	3.77806691806529	4.12323508596284	4.55659505933522	4.99103488622617	5.47479588652139	5.82258900961291	6.06276261255363;
2.84828226959355	2.88904349573765	2.96873285191344	3.08069203738026	3.44697966788091	4.13567533931369	4.52894098819945	4.67412567995202	5.15296324526301	5.56523852795320	5.96502602345583	6.21078028605879	6.52849691526073;
3.74002027926708	3.75993225502666	3.83411382444209	4.00456816843311	4.32926896155507	4.77622144003005	5.16736759461981	5.49836937572280	5.88647170837687	6.18271839080470	6.59759022678129	6.97084214072058	6.75170686464779;
4.78524857165206	4.74826975259759	4.81706589206119	4.97601956899259	5.27355150638661	5.63396907113975	5.99958011195912	6.36694810730541	6.77714174291766	6.70742436573057	7.25550718842670	7.26295700795507	7.25746708897833;
6.03717083993188	5.79887631698666	5.91639397495982	6.00350593883982	6.33213672950170	6.64106263587169	6.95706983158674	7.28782367961083	7.70705369497867	7.63458594897408	7.93261292601932	8.00295469770043	7.82960635002508;
7.19298190970422	7.15760814782713	7.24449095049573	7.47603016525217	7.57972831981689	7.78795195979569	8.01946233620746	8.20828974079021	8.68131635353786	8.70525487083782	8.81017351195784	8.91630723595258	8.87870649490453;
8.54520636494540	8.55348201216040	8.61726432100011	8.75404753128375	8.88337889302489	9.04996267034075	9.23602519155018	9.42482470685441	9.64993914996010	9.70203369491229	9.65289346191122	9.39722499724188	9.12721227719753];

figure
plot((1:size(P1,1)), P1)
grid
title('Original Unwrapped')

Wrapped:

mf = mod(P1,2*pi);
wP1 = mf.*(mf<=pi) + (mf-2*pi).*(mf>pi)

wP1 = 13×13

0.0063 0 0.3704 0.6980 1.0950 1.5687 2.1240 2.8159 -2.8845 -2.6406 -2.0183 -1.4439 -1.3032 0.1374 0.2466 0.5929 0.7969 1.1701 1.6172 2.0910 2.4980 -3.0069 -2.5179 -2.0092 -1.5909 -1.4587 0.2838 0.3792 0.6369 0.8947 1.3225 1.7688 2.2280 2.8815 -2.8017 -2.4139 -1.9490 -1.5324 -1.2742 0.5212 0.5344 0.9202 1.0500 1.6653 2.0931 2.3278 2.9421 -2.7978 -2.3416 -1.8384 -1.3592 -1.0777 0.9307 1.0005 1.1972 1.4449 1.9028 2.2941 2.7030 -3.0875 -2.6222 -2.2723 -1.7032 -1.0335 -0.8249 1.4543 1.5217 1.6578 1.8516 2.4112 2.6582 -3.1366 -2.6872 -2.2489 -1.8806 -1.1704 -0.7937 -0.5599 2.0924 2.1542 2.2914 2.6107 2.9328 -2.8252 -2.5051 -2.1600 -1.7266 -1.2922 -0.8084 -0.4606 -0.2204 2.8483 2.8890 2.9687 3.0807 -2.8362 -2.1475 -1.7542 -1.6091 -1.1302 -0.7179 -0.3182 -0.0724 0.2453 -2.5432 -2.5233 -2.4491 -2.2786 -1.9539 -1.5070 -1.1158 -0.7848 -0.3967 -0.1005 0.3144 0.6877 0.4685 -1.4979 -1.5349 -1.4661 -1.3072 -1.0096 -0.6492 -0.2836 0.0838 0.4940 0.4242 0.9723 0.9798 0.9743

plot((1:size(P1,1)), wP1)
grid
title('Wrapped')

The Mapping Toolbox has the wrapToPi function, and while I do not have it, the online Run feature dees, and it produces:

wrapped = wrapToPi(P1)

wrapped = 13×13

0.0063 0 0.3704 0.6980 1.0950 1.5687 2.1240 2.8159 -2.8845 -2.6406 -2.0183 -1.4439 -1.3032 0.1374 0.2466 0.5929 0.7969 1.1701 1.6172 2.0910 2.4980 -3.0069 -2.5179 -2.0092 -1.5909 -1.4587 0.2838 0.3792 0.6369 0.8947 1.3225 1.7688 2.2280 2.8815 -2.8017 -2.4139 -1.9490 -1.5324 -1.2742 0.5212 0.5344 0.9202 1.0500 1.6653 2.0931 2.3278 2.9421 -2.7978 -2.3416 -1.8384 -1.3592 -1.0777 0.9307 1.0005 1.1972 1.4449 1.9028 2.2941 2.7030 -3.0875 -2.6222 -2.2723 -1.7032 -1.0335 -0.8249 1.4543 1.5217 1.6578 1.8516 2.4112 2.6582 -3.1366 -2.6872 -2.2489 -1.8806 -1.1704 -0.7937 -0.5599 2.0924 2.1542 2.2914 2.6107 2.9328 -2.8252 -2.5051 -2.1600 -1.7266 -1.2922 -0.8084 -0.4606 -0.2204 2.8483 2.8890 2.9687 3.0807 -2.8362 -2.1475 -1.7542 -1.6091 -1.1302 -0.7179 -0.3182 -0.0724 0.2453 -2.5432 -2.5233 -2.4491 -2.2786 -1.9539 -1.5070 -1.1158 -0.7848 -0.3967 -0.1005 0.3144 0.6877 0.4685 -1.4979 -1.5349 -1.4661 -1.3072 -1.0096 -0.6492 -0.2836 0.0838 0.4940 0.4242 0.9723 0.9798 0.9743

figure
plot((1:size(P1,1)), wrapped)
grid
title('wrapToPi')

.

[Tina Hsiao]

Thanks a lot!

[Star Strider]

As always, my pleasure!

.