Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

Whole optical wavefields reconstruction by Digital Holography

S. Grilli, P. Ferraro, S. De Nicola, A. Finizio, G. Pierattini, and R. Meucci

Open Access Open Access

Abstract

In this paper, we have investigated on the potentialities of digital holography for whole reconstruction of wavefields. We show that this technique can be efficiently used for obtaining quantitative information from the intensity and the phase distributions of the reconstructed field at different locations along the propagation direction. The basic concept and procedure of wavefield reconstruction for digital in-line holography is discussed. Numerical reconstructions of the wavefield from digitally recorded in-line hologram patterns and from simulated test patterns are presented. The potential of the method for analysing aberrated wave front has been exploited by applying the reconstruction procedure to astigmatic hologram patterns.

©2001 Optical Society of America

Full Article  |  PDF Article
More Like This
Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm

Yan Zhang, Giancarlo Pedrini, Wolfgang Osten, and Hans J. Tiziani
Opt. Express 11(24) 3234-3241 (2003)

Correct-image reconstruction in the presence of severe anamorphism by means of digital holography

Sergio De Nicola, Pietro Ferraro, Andrea Finizio, and Giovanni Pierattini
Opt. Lett. 26(13) 974-976 (2001)

Optical vortex phase-shifting digital holography

Cheng-Shan Guo, Xin Cheng, Xiu-Yun Ren, Jian-Ping Ding, and Hui-Tian Wang
Opt. Express 12(21) 5166-5171 (2004)

View More...

Supplementary Material (2)

Media 1: MOV (873 KB)     
Media 2: MOV (1716 KB)     

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)
Fig. 1.
Fig. 1. Experimental setup of the Mach-Zehnder interferometer for digital in-line holography.

Download Full Size | PDF

Fig. 2.
Fig. 2. Hologram recorded under two different conditions corresponding to two settings of the CCD frame buffer: (a) (736×572); (b) (768×572).

Download Full Size | PDF

Fig. 3.
Fig. 3. Clip video presentation of the digitally reconstructed object wavefield intensity distribution obtained at different distances d’ from the hologram plane along the z-axis direction, through the evaluation of the diffraction formula (1). The left video (873 KB) is obtained using the hologram pattern in Fig. 2a and for values of d’ ranging from 170 mm to 200 mm with discrete spatial step of Δz=1 mm; the right movie (1.903 KB) is obtained from the aberrated hologram of Fig. 2b and for d’ values ranging from 181 mm to 218 mm, with Δz=1 mm. Click on the figure with mouse to see the movie (<2 Mb for each). [Media 1] [Media 2] [Media 3]

Download Full Size | PDF

Fig. 4.
Fig. 4. Recording geometry in digital holographic reconstruction of the object wavefield.

Download Full Size | PDF

Fig. 5.
Fig. 5. Intensity distributions the circular (a) and elliptical (b) fringe patterns computed by Eq.(6)

Download Full Size | PDF

Fig. 6.
Fig. 6. Digital intensity reconstruction of the simulated hologram patterns of fig. 5a-5b: (a) reconstruction of the spherical wave front at distance d’=180 mm from the hologram plane; (b) image reconstruction of the astigmatic fringe pattern at a distance d’=180 mm (c) reconstruction of the spherical wave front at the focal plane z=250 mm; (d) reconstructed tangential focal line for the astigmatic fringe pattern at distance zy =250 mm

Download Full Size | PDF

Fig. 7.
Fig. 7. Wrapped phase distributions computed by the convolution-based reconstruction method at distance d’=180 mm (a) phase reconstruction of the simulated spherical wave front; (b) phase reconstruction of the astigmatic wave front.

Download Full Size | PDF

Fig. 8.
Fig. 8. Three-dimensional representations of the unwrapped phase values from the wrapped data of fig. 7a and 7b.

Download Full Size | PDF

Fig. 9.
Fig. 9. One dimensional representation of the unwrapped phase values along the x-horizontal (straight line) and y-vertical (dashed line) directions for reconstruction distances d’ ranging from 160 mm to 220 mm, step size of 10 mm: (a) phase reconstructions of the simulated spherical wave front ; (b) phase reconstructions of the astigmatic wave front. The scale of the horizontal axis is determined by the pixel size Δx’=Δξ of the reconstructed image which does not change in the convolution-based reconstruction method. The vertical axis is the z propagation axis along which the various phase distributions are evaluated.

Download Full Size | PDF

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

b ′ ( x ′ , y ′ ; d ′ ) = exp { i π d ′ λ ( ν 2 + μ 2 ) } ∬ h ( ξ , η ) r ( ξ , η ) g ( ξ , η )
× exp { − 2 i π ( ξ ν + η μ ) } d ξ d η
g ( ξ , η ) = exp ( i 2 π d ′ ⁄ λ ) i λ d ′ exp { i π d ′ λ ( ξ 2 + η 2 ) }
Δ x ′ = d ′ λ N Δ ξ Δ y ′ = d ′ λ N Δ η
b ′ ( x ′ , y ′ ; d ′ ) = ℑ − 1 { ℑ [ h ( ξ , η ) r ( ξ , η ) ] ℑ [ g ( ξ , η ) ] }
ℑ [ g ( ξ , η ) ] = ∫ − ∞ ∞ ∫ − ∞ ∞ g ( ξ , η ) exp [ − i 2 π ( ν ξ + μ η ) ] d ξ d η
ℑ [ g ( ξ , η ) ] = exp ( i 2 π d ′ / λ ) exp ⌊ − i π λ d ′ ( ν 2 + μ 2 ) ⌋
I ( ξ , η ) = l + cos ⁡ [ π λ ( ξ 2 z x + η 2 z y ) ]
I ( ξ , η ) = 1 + 1 2 exp [ + i π λ ( ξ 2 z x + η 2 z y ) ] + 1 2 exp [ − i π λ ( ξ 2 z x + η 2 z y ) ]
h ( ξ , η ) = 1 2 exp [ + i ψ ( ξ , η ) ]
ψ ( ξ , η ) = π λ ( ξ 2 z x + η 2 z y )
Δ ψ ( x ′ , y ′ , Δ z ) = Arctan [ Re { b ( x ′ , y ′ , d ′ ) } Im { b ( x ′ , y ′ , d ′ + Δ z ) } − Re { b ( x ′ , y ′ , d ′ + Δ z ) } Im { b ( x ′ , y ′ , d ′ ) } Re { b ( x ′ , y ′ , d ′ ) } Re { b ( x ′ , y ′ , d ′ + Δ z ) } + Im { b ( x ′ , y ′ , d ′ + Δ z ) } Im { b ( x ′ , y ′ , d ′ ) } ]
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use