MATLAB Implementation of Fresnel Digital Holography

Fresnel digital holography is a computational technique that simulates the optical holographic recording and reconstruction processes. The core principle involves simulating interference between object and reference waves through discretized Fresnel diffraction formulas.

The implementation approach consists of three key steps:

Object Wave Simulation Define an object plane (e.g., 2D image) with initial phase distribution, combined with parameters like light source wavelength and pixel size to construct the initial object wavefront. In MATLAB, this typically involves creating complex amplitude matrices using functions like exp() for phase initialization and managing spatial coordinates through meshgrid().

Fresnel Diffraction Calculation Apply discretized Fresnel diffraction formulas (such as convolution method or angular spectrum method) to propagate the object wave to the hologram plane. This step requires complex amplitude Fast Fourier Transform (FFT) operations using fft2() and ifft2() functions while adhering to sampling theorem constraints. The implementation must handle proper zero-padding and frequency domain filtering to prevent artifacts.

Hologram Generation and Reconstruction Superimpose reference waves (commonly simulated as plane or spherical waves) at the hologram plane to record interference patterns forming the hologram. During reconstruction, illuminate the hologram with conjugate reference waves and perform inverse Fresnel diffraction to reconstruct the original object wave. MATLAB's matrix operations efficiently handle complex wavefield calculations, while FFT accelerates large-scale diffraction simulations through fftshift() and ifftshift() for proper frequency domain alignment.

This technology finds wide applications in optical metrology, microscopic imaging, and 3D display systems. Practical implementation requires careful attention to prevent spectral aliasing using appropriate anti-aliasing filters, and optimal selection of propagation distances and sampling intervals based on wavelength and resolution requirements. Computational efficiency can be enhanced through MATLAB's parallel computing toolbox for large datasets.