Image polar to cartesian and back script issues

I'm writing a script to take an image, convert it to polar form about its center, and then convert it back to cartesian. I have a working code to go to polar, and a working code to get to cartesian (except it does not cover all angles). It only seems to cover half of the original image. I can work around this by flipping the polar image and adding the results of the two, but it leaves a line artifact going through the image. I'm wondering how can I make the cartesian conversion cover every angle in the polar image. Here is the code:

img = imread('moon.tif');

%% Cart2pol

[m,n]=size(img);
m0=floor(m/2);
n0=floor(n/2);

% [idx,mp]=gray2double(img,32);

x=(1:n)-(n/2);
y=(1:m)-(m/2);

[xp,yp]=meshgrid(linspace(0,2*pi,1000),linspace(0,400,1000));

[xx,yy]=pol2cart(xp,yp);

img=double(img);
out=interp2(x,y,img,xx,yy);

figure(1)
imshow(out,[])

%% pol 2 cart

x=(1:n)-(n/2);
y=(1:m)-(m/2);
r=linspace(0,-2*pi,1000);
t=linspace(0,400,1000);

[xc,yc]=meshgrid(x,y);
[xx,yy]=cart2pol(xc,yc);

out1=interp2(r,t,out,xx,yy);
out1(isnan(out1))=0;
out1=flipud(out1);


out2=interp2(r,t,fliplr(out),xx,yy);
out2(isnan(out2))=0;

done = out1+out2;

figure(2)
imshow(out1,[])
figure(3)
imshow(out2,[])
figure(4)
imshow(img,[])
figure(5)
imshow(done,[])

Answer 1

[Gustavo De Camargo]

Try this in your %% pol 2 cart:

x=linspace(n,1,n)-floor(n/2);

y=linspace(m,1,m)-floor(m/2);

r=linspace(-pi,pi,M);

t=linspace(0,400,N);

[xc,yc]=meshgrid(x,y);

[xx,yy]=cart2pol(xc,yc);

out1=interp2(r,t,out,xx,yy);

out1(isnan(out1))=0;

[Bray Falls]

Works perfect! Thank you