Simulation of holographic interferogram and phase reconstruction of Fourier transform based on MATLAB

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 ：

Object light phase

Simulate the generation of plane reference light , Its phase is shown in the figure below ：

Reference light phase

The hologram obtained after the superposition of reference light and object light is as follows ：

Holographic interferogram

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 ：

$g\left(x,y\right)=c\left(x,y\right)\exp (2\pi i{f}_{0}x)+c^{\ast }\left(x,y\right)\exp (-2\pi i{f}_{0}x)$ (1)

among ,

$c\left(x,y\right)=\frac{1}{2}\exp \left(i\psi (x,y)\right)$ （2）

$\psi (x,y)$ Contains object information ,$f_{0}x$ Describes the wavefront tilt . After Fourier transform of the above formula , Available ：

$G\left(f,y\right)=A\left(f,y\right)+C(f+f_0,y)+C^{\ast }(f-f_0,y)$ （3）

In which the capital letters A and C Denotes Fourier spectrum ,f Represents spatial frequency . We can start from two side lobe spectra $C(f+f_0,y)$ or $C^{\ast }(f-f_0,y)$ 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 $\psi (x,y)$：

$i\psi (x,y)=\log \left[c\left(x,y\right)\right]$ （4）

phase $\psi (x,y)$ 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

Reconstruction phase

3、 ... and 、 The resource acquisition

The above simulation program can be obtained from the following link ：

https://download.csdn.net/download/qq_36584460/80431355