Digital in-line holography assessment for general phase and opaque particle

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.

Digital in-line holography in a droplet with cavitation air bubbles

“…Otherwise, when n d < n b , total reflexion does not occur. This point has been developed in [6] in the case of a transparent particle as inclusion. In the case of [6], a general pupil function, denoted by p(s, θ), represented in the form of a Zernike series:…”

“…Then, the expansion coefficients γ m n are used to determine the expansion coefficients Γ m n (ε). The summation is over n = |m|, |m| + 2, · · · , n. This way of writing the scaled pupil function allows us to use the previous developments in [6]. Consequently, the intensity distribution I(σ) recorded by the CCD satisfies…”

“…In this paragraph, two cases have been considered: in the first case, the air bubble is approximated as a thin lens, ie, a quadratic phase approximation, and the second case, the air bubble is approximated as a quasi-spherical phase approximation. To elaborate the new expressions of the Zernike coefficients of the two cited cases, the Zernike coefficients in [6] for a transparent particle are used.…”

“…Now, if the quasi-spherical approximation is employed [6,21] to describe the pupil function p of the air bubble, recall that in the case of [6] …”

“…Probably, this impossibility is essentially due to the chosen experimental configuration. Recently, in the case of holography, we have proposed a modelisation of a droplet in the air to calculate the hologram of such an object [6]. In that study, the aperture, i.e., the ratio between the index of the air and the index of the droplet, is no more than unity.…”