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Endoscopic pulsed digital holography for 3D measurements

A. Tonatiuh Saucedo, Fernando Mendoza Santoyo, Manuel De la Torre-Ibarra, Giancarlo Pedrini, and Wolfgang Osten

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Abstract

A rigid endoscope and three different object illumination source positions are used in pulsed digital holography to measure the three orthogonal displacement components from hidden areas of a harmonically vibrating metallic cylinder. In order to obtain simultaneous 3D information from the optical set up, it is necessary to match the optical paths of each of the reference object beam pairs, but to incoherently mismatch the three reference object beam pairs, such that three pulsed digital holograms are incoherently recorded within a single frame of the CCD sensor. The phase difference is obtained using the Fourier method and by subtracting two digital holograms captured for two different object positions.

©2006 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Experimental set up for the 3D endoscopic pulsed digital holography with simultaneous recording of three digital holograms. BS, Beam splitters; CB, Cube beam splitters; M, mirrors; O, object illumination beams; R reference beams.

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Fig. 2.
Fig. 2. Fourier spectrum consisting of three incoherently added digital holograms.

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Fig. 3.
Fig. 3. Geometry of the illuminating beams, showing the unitary vectors of illumination.

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Figs. 4.
Figs. 4. (a), (b) and (c) are wrapped phase map of three illumination directions, n̂ i1, n̂ i2 and n̂ i3 respectively.

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Fig. 5.
Fig. 5. The component of the resultant deformation normal to the cylinder surface.

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Fig. 6.
Fig. 6. The component of the resultant deformation tangent to the cylinder surface.

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Equations (16)

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

I ( ξ , η ) = ∑ k = 1 3 I k ( ξ , η )
= ∑ k = 1 3 [ ∣ R k ( ξ , η ) + O k ( ξ , η ) ∣ 2 ]
O k ( ξ , η ) = o k ( ξ , η ) exp [ i ϕ k ( ξ , η ) ]
R k ( ξ , η ) = r k ( ξ , η ) exp ⌊ − 2 π i ( f k ξ ξ + f k η η ) ⌋
I ( ξ , η ) = ∑ k = 1 3 { a k ( ξ , η )
+ c k ( ξ , η ) exp ⌊ 2 π i ( f k ξ ξ + f k η η ) ⌋
+ c k * ( ξ , η ) exp [ − 2 π i ( f k ξ ξ + f k η η ) ] }
a k ( ξ , η ) = o k 2 ( ξ , η ) + r k 2 ( ξ , η )
c k ( ξ , η ) = o k ( ξ , η ) r k ( ξ , η ) exp [ i ϕ k ( ξ , η ) ]
FT { I } = ∑ k = 1 2 [ A k ( f ξ , f n )
+ C k ( f ξ − f k ξ , f n − f kn )
+ C k * ( f ξ − f k ξ , f n − f kn ) ]
ϕ k ( ξ , η ) = arctan ⁡ Im [ c k ( ξ , η ) ] Re [ c k ( ξ , η ) ] , k = 1,2,3
Δ ϕ k ( ξ , η ) = ϕ k ′ ( ξ , η ) − ϕ k ( ξ , η ) , k = 1,2,3
Δ ϕ k = ( 2 π λ ) u → ∙ s → k
s → k = n ̂ k − n ̂ o , k = 1,2,3
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