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### Fourier transform profilometry of fringe pattern

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```Hi,

I want to realize the 1D Fourier Transform Profilometry based on the article of Takeda:
"Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and
profilometry: An overview".

Assuming that the signal has the next form:
g(x,y)=a(x,y)+b(x,y)cos(2*pi*f0*x+phase(x,y))

the purpose is to extract the phase(x,y).

The steps are:

1. FFT => G(fx,y)=A(fx,y)+C(fx-f0,y)+C*(-(f+f0),y);
when C is FT of c(x,y)=0.5b(x,y)ep(i*phase(x,y))
2. Filter out C(fx,y):
C(fx, y) = H(fx, y)G(fx +fo, Y).
when H(fx,y)=sinc(pi*delta_x*fx), delta_x=1/f0
4. IFFT on C(fx,y)=> c(x,y) =(l/2)b(x,y)exp[i*phase(x,y)]
5. Phase extraction: using log or  arctan(real/image)
6. phase unwrapping

The problem is that after step 5, the wrapped phase does not look like expected (is not wrapped and doesn't fit the height profile).

Can anybody explain me, where is my mistake? Thanks a lot.

The code is:

% 1D - FFT =>G(fx)

G=fftshift(fft(g));
Fs=100;  %sampling
N=length(G);

% this part of the code generates frequency axis
if mod(N,2)==0
k=-N/2:N/2-1; % N even
else
k=-(N-1)/2:(N-1)/2; % N odd
end
T=N/Fs;
X_freq=k/T;  % frequency axis

%%G(fx-f0)

f0= 6;    %example of f0
X_freq_f0=X_freq+f0;

% H(fx)

delta_x=1/f0;
sinc_argument=pi*delta_x*(X_freq_f0);
H=sinc(sinc_argument);

% C(fx)=G(fx-f0)H(fx)

C_freq=H.*y_last_fft_norm_shifted;

% IFFT

G_ifft=ifft(ifftshift(C_freq));

% phase extraction using arctan(real/imag)

G_ifft_real=real(G_ifft);
G_ifft_imag=imag(G_ifft);
phase=atan(G_ifft_real./G_ifft_imag);

phase_unwrapped=unwrap(phase);

Thanks
J
```
 0

See related articles to this posting

```Hello!
I have similar problem in MathCad. Try to find this article: X. Liang, X. Su. Computer Simulation of a 3-D Sensing System with Structured Illumination // Optics and Lasers in Engineering. Vol. 27. 1997. Pp. 379-393.
Best regards,
Dmitry.
```
 0
Reply stepd (1) 10/9/2011 5:12:28 AM

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