Abstract
We propose using the circle polynomials to describe a particle’s transmission function in a digital holography setup. This allows both opaque and phase particles to be determined. By means of this description, we demonstrate that it is possible to estimate the digital in-line hologram produced by a spherical particle. The experimental intensity distribution due to an opaque micro-inclusion is compared to the theoretical one obtained by our new model. Moreover, the simulated hologram and reconstructed image of the particle by an optimal fractional Fourier transformation under the opaque disk, quadratic phase, and quasi-spherical phase approximation are compared with the results obtained by simulating holograms by the Lorenz–Mie Theory (LMT). The Zernike coefficients corresponding to the considered particles are evaluated using the double exponential (DE) method which is optimal in various respects.
Highlights
This work is motivated by the fact that in studies on digital holography a spherical particle is generally considered as an opaque disk, not as a spherical object or, even better, as a thin lens
It should be noted that the digital reconstruction of the image of the object does not put in evidence the spot of light at the center of the reconstructed image predicted by the Lorenz–Mie theory (LMT)
The fractional Fourier transformation is used to reconstruct the image of the particle and the optimal fractional order is deduced from the ABCD matrix formalism
Summary
We propose using the circle polynomials to describe a particle’s transmission function in a digital holography setup. This allows both opaque and phase particles to be determined. By means of this description, we demonstrate that it is possible to estimate the digital in-line hologram produced by a spherical particle. The experimental intensity distribution due to an opaque micro-inclusion is compared to the theoretical one obtained by our new model. The simulated hologram and reconstructed image of the particle by an optimal fractional Fourier transformation under the opaque disk, quadratic phase, and quasi-spherical phase approximation are compared with the results obtained by simulating holograms by the Lorenz–Mie Theory (LMT).
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