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Holographic moiré in real time

Paper explains and highlights the advantages of the real-time observation greatly enhanced by the use of closed-circuit TV

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Abstract

The body of knowledge necessary to observe holographic-moiré patterns in real time is introduced. The basic factors influencing fringe visibility in holographic moiré are analyzed and expressions to evaluate fringe visibility for any given displacement and deformation are given. The application of the introduced theory in the case of real-time observation is discussed. It is shown that the maximum benefits of this technique are achieved by combining it with closed-circuit TV. Several examples of application are given.

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Abbreviations

A 0,A 1 :

total area and correlated area of the displaced pupil, respectively

a :

radius of the pupil or width of rectangular aperture

b :

depth of rectangular aperture

[C] Rot ,[C] Trans :

transformation matrices for rotation and translation components

D :

distance between the pupil and image plane

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{d} \) :

displacement vector at a point on the object

\(\overline E (X)\) :

amplitude of the wavefront along the x-axis

E M :

amplitude of the object and reconstructed wavefronts

f :

focal length of lens

<I 1>, <I 2>:

average intensities corresponding to the interfering wavefront

<I>:

resulting average intensity during superposition of holographic and auxiliary fringes

<I(P)>:

average intensity of a generic pointP

I ′ o ,I o :

background intensity of the object under double illumination

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k} _1 , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k} '_1 \) :

symmetric illumination direction of the object in double illumination. These vectors include a factor 2π/λ

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k} _0 \) :

direction of observation

L o :

distance of the object to the observation plane

L :

distance between the lens and object

l e ,m e ,n e ,l o ,n o ,n o :

angular coordinates of the illuminating source and observation direction, respectively

m v ,m m :

magnification ratio of vidicon and between vidicon and monitor

N H ,N T ,N TM :

total number of elements or pixels in scanning, its perpendicular direction and monitor total, respectively

R H ,R v :

tilts introduced to the illuminating source to generate carrier fringes

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{R} _{ T} , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{R} _{ R} , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{R} _{ D} , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{R} _{ F} \) :

rotation vectors: total, due to rigid body, due to deformation of the body and due to the carrier-fringe generation, respectively

r :

resolution of the vidicon tube

r c :

correlation radius of the speckle

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{T} , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{T} '\) :

displacement vector of the interfering wavefronts ∑1 and ∑2 at the pupil plane and image plane

T′‖,T′⊥,T ‖,T ⊥ :

components of\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{T} '\) and\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{T} \) parallel and perpendicular to the longest side of rectangular aperture

t :

period of scanning frequency of TV camera

u, v, w :

displacement components along x, y, z directions

V :

visibility of the carrier fringes

W o ,W v ,W d :

object width, useful width of vidicon and monitor width

x o :

distance between the object and front focal length of lens

θ:

angle between the illumination direction and observation direction in o-x-z plane

θ R :

angle between reference beam and normal to holographic plate

△θ R :

rotation angle introduced to reference beam

Δθ:

angle between the two wavefronts used to generate carrier fringes

φ1, φ2 :

phases of the fringes corresponding to illumination beams 1 and 2

ϕ:

change of phase corresponding to in-plane displacements

ψ:

change of phase corresponding to out-of-plane displacements

ψ R :

change of phase due to optical-path change under applied loads and auxiliary fringes

β:

phase term corresponding to the auxiliary fringes introduced=2π×Δθ/λ

∑1, ∑2 :

two interfering wavefronts of light

<>:

mean value over the ensemble

λ:

wavelength of light used

❘⌈❘ , ❘⌈1❘ , ⌈⌈2❘:

degree of coherence between interfering wavefronts, total, due to displacements at the pupil plane and observations plane, respectively

ϱ , ϱ// , ϱ ⊥:

mean speckle size, ϱ along parallel and perpendicular direction of rectangular aperture

△u, △v, △w :

speckle displacements or shifts introduced in the observation plane

δ f :

actual fringe spacing observed on the object using TV imaging system

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Authors and Affiliations

  1. Experimental Stress Analysis Laboratory, Illinois Institute of Technology, 60616, Chicago, IL

    C. A. Sciammarella (Professor and Director)

  2. Swiss Federal Institute of Technology, CH-1015, Lausanne, Laboratory of Stress Analysis, Switzerland

    P. K. Rastogi & P. Jacquot

  3. Department of Mechanics, Mechanical and Aerospace Engineering, Illinois Institute of Technology, 60616, Chicago, IL

    R. Narayanan (Research Assistant)

Authors
  1. C. A. Sciammarella
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  2. P. K. Rastogi
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  3. P. Jacquot
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  4. R. Narayanan
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Sciammarella, C.A., Rastogi, P.K., Jacquot, P. et al. Holographic moiré in real time. Experimental Mechanics 22, 52–63 (1982). https://doi.org/10.1007/BF02326077

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