Modified convolution method to reconstruct particle hologram with an elliptical Gaussian beam illumination

Xuecheng Wu,Yingchun Wu,Zhihua Wang,Jing Yang,Kefa Cen,Binwu Zhou,Gérard Gréhan

doi:10.1364/oe.21.012803

Abstract

Application of the modified convolution method to reconstruct digital inline holography of particle illuminated by an elliptical Gaussian beam is investigated. Based on the analysis on the formation of particle hologram using the Collins formula, the convolution method is modified to compensate the astigmatism by adding two scaling factors. Both simulated and experimental holograms of transparent droplets and opaque particles are used to test the algorithm, and the reconstructed images are compared with that using FRFT reconstruction. Results show that the modified convolution method can accurately reconstruct the particle image. This method has an advantage that the reconstructed images in different depth positions have the same size and resolution with the hologram. This work shows that digital inline holography has great potential in particle diagnostics in curvature containers.

Highlights

Digital holography, as a real 3D imaging technique, can simultaneously provide the size [1, 2] and 3D position [1, 3] of the particle, and thereafter retrieve the 3D motion of the particle [4, 5]
The interrogated objects are usually illuminated by the collimated plane wave or spherical wave to avoid aberration during the recording process, and the object can be reconstructed by numerical diffraction of the hologram [1, 14]
The interrogated objects might be held in a complex container with curvature surface, and the collimated plane wave is transformed into a shaped beam after passing through the surface, such as elliptical Gaussian beam [15, 16]

Summary

Introduction

As a real 3D imaging technique, can simultaneously provide the size [1, 2] and 3D position [1, 3] of the particle, and thereafter retrieve the 3D motion of the particle [4, 5]. The interrogated objects might be held in a complex container with curvature surface, and the collimated plane wave is transformed into a shaped beam after passing through the surface, such as elliptical Gaussian beam [15, 16]. This might cause aberration, such as the astigmatism in the optical system [15, 17,18,19]. The astigmatism distorts the recorded hologram, and hinder reconstructing the clear image with the classical method, such as Fresnel integral [1] and wavelet method [24]

Objectives

Methods

Conclusion