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Simulation of holographic interferogram and phase reconstruction of Fourier transform based on MATLAB
2022-07-06 07:26:00 【In the wind °】
One 、 Generation of holographic interferogram
In the simplest case , Interferogram ( Hologram ) It is caused by distorted beam ( Object light ) And plane waves ( Reference light ) Produced by mixing .
First , Simulate a distorted beam ( Object light ), Its phase is shown in the figure below :
Simulate the generation of plane reference light , Its phase is shown in the figure below :
The hologram obtained after the superposition of reference light and object light is as follows :
Two 、 Phase reconstruction
In order to obtain the reconstructed phase in the holographic interferogram , This paper uses the translation and filtering processing in Fourier domain to reconstruct the wavefront phase .
The above holographic interferogram can be expressed as :
g ( x , y ) = c ( x , y ) exp ( 2 π i f 0 x ) + c ∗ ( x , y ) exp ( − 2 π i f 0 x ) g\left( x,y \right)=c\left( x,y \right)\exp (2\pi i{ {f}_{0}}x)+{ {c}^{*}}\left( x,y \right)\exp (-2\pi i{ {f}_{0}}x) g(x,y)=c(x,y)exp(2πif0x)+c∗(x,y)exp(−2πif0x) (1)
among ,
c ( x , y ) = 1 2 exp ( i ψ ( x , y ) ) c\left( x,y \right)=\frac{1}{2}\exp \left( i\psi (x,y) \right) c(x,y)=21exp(iψ(x,y)) (2)
ψ ( x , y ) \psi (x,y) ψ(x,y) Contains object information , f 0 x { {f}_{0}}x f0x Describes the wavefront tilt . After Fourier transform of the above formula , Available :
G ( f , y ) = A ( f , y ) + C ( f + f 0 , y ) + C ∗ ( f − f 0 , y ) G\left( f,y \right)=A\left( f,y \right)+C(f+{ {f}_{0}},y)+{ {C}^{*}}(f-{ {f}_{0}},y) G(f,y)=A(f,y)+C(f+f0,y)+C∗(f−f0,y) (3)
In which the capital letters A and C Denotes Fourier spectrum ,f Represents spatial frequency . We can start from two side lobe spectra C ( f + f 0 , y ) C(f+{ {f}_{0}},y) C(f+f0,y) or C ∗ ( f − f 0 , y ) { {C}^{*}}(f-{ {f}_{0}},y) C∗(f−f0,y) Choose one of , And convert it to the origin of zero spatial frequency . next , We can perform inverse Fourier transform on the converted spectrum , Get the expression (1) As defined in c(x,y). Calculation expression (2) Complex logarithm of , The phase can be obtained ψ ( x , y ) \psi (x,y) ψ(x,y):
i ψ ( x , y ) = log [ c ( x , y ) ] i\psi (x,y)=\log \left[ c\left( x,y \right) \right] iψ(x,y)=log[c(x,y)] (4)
phase ψ ( x , y ) \psi (x,y) ψ(x,y) Uncertainty is a factor 2π, Its principal value lies in -π-π Within the scope of . In order to obtain a continuous phase diagram , A special unwrapping algorithm is used for the reconstructed phase diagram , The removal amplitude is close to 2π The discontinuity of . The algorithm implementation includes the following steps :
1) Fourier transform the hologram containing only the object light field , At this time, the spectrum is composed of a central lobe and two side lobes containing phase information .
2) Take out one of them and put it into the origin .( Filter processing )
3) Inverse Fourier transform
4) Find the reconstruction phase
The reconstructed phase is shown in the figure below
3、 ... and 、 The resource acquisition
The above simulation program can be obtained from the following link :
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