Abstract

Two solutions are presented to the problem of unknown absolute fringe order in double exposure hologram interferometry, a problem that confronts systems that require a single view of an object. One solution determines the vectorial object displacements relative to one reference point on the object. The other employs variations of the sensitivity vectors to provide absolute displacement analysis. For absolute displacements, a minimum of four illuminations is required.

© 1990 Optical Society of America

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References

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  1. P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
    [CrossRef]
  2. K. A. Stetson, W. R. Brohinsky, “Electrooptic Holography and its Application to Hologram Interferometry,” Appl. Opt. 24, 3631–3637 (1985).
    [CrossRef] [PubMed]
  3. K. Creath, “Phase Shifting Speckle Interferometry,” Appl. Opt. 24, 3053–3058.
    [PubMed]
  4. K. A. Stetson, F. Mottier, “The Use of Microcomputers and Image Processors in Holographic Displacement and Strain Analysis,” in Proceedings, Optronic 88, International Laser Congress, Apr.1988 (Magazin Verlag, Kronberg, F.R.G.), pp. 57–63.

1985 (1)

1982 (1)

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Brohinsky, W. R.

Brown, N.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Creath, K.

Hariharan, P.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Mottier, F.

K. A. Stetson, F. Mottier, “The Use of Microcomputers and Image Processors in Holographic Displacement and Strain Analysis,” in Proceedings, Optronic 88, International Laser Congress, Apr.1988 (Magazin Verlag, Kronberg, F.R.G.), pp. 57–63.

Oreb, B. F.

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Stetson, K. A.

K. A. Stetson, W. R. Brohinsky, “Electrooptic Holography and its Application to Hologram Interferometry,” Appl. Opt. 24, 3631–3637 (1985).
[CrossRef] [PubMed]

K. A. Stetson, F. Mottier, “The Use of Microcomputers and Image Processors in Holographic Displacement and Strain Analysis,” in Proceedings, Optronic 88, International Laser Congress, Apr.1988 (Magazin Verlag, Kronberg, F.R.G.), pp. 57–63.

Appl. Opt. (2)

Opt. Commun. (1)

P. Hariharan, B. F. Oreb, N. Brown, “A Digital Phase-Measurement System for Real-Time Holographic Interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Other (1)

K. A. Stetson, F. Mottier, “The Use of Microcomputers and Image Processors in Holographic Displacement and Strain Analysis,” in Proceedings, Optronic 88, International Laser Congress, Apr.1988 (Magazin Verlag, Kronberg, F.R.G.), pp. 57–63.

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Equations (18)

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Ω = K · L + N ,
Δ Ω = K · Δ L ,
Δ Ω = Ω 1 - Ω 0 and Δ L = L 1 - L 0 .
{ Δ L } = [ K ] - 1 { Δ Ω } ,
{ Δ L } = [ K T K ] - 1 [ K T { Δ Ω } .
Δ Ω = Δ K · L 0 + K · Δ L .
Ω j = K n · L m + N n .
No . of equations = nm No . of unknowns = 3 m + n .
1 3 / n + 1 / m .
n = 3 unsolvable ; n = 4 , m 4 , solvable ; n = 5 , m 3 , solvable ; n = 6 , m 2 , solvable ; m = 1 , unsolvable .
{ Ω } = [ [ K ] 1 0 0 0 I 0 [ K ] 2 0 0 I 0 0 [ K ] 3 0 I 0 0 0 [ K ] 4 I ]     { L 1 L 2 L 3 L 4 N } .
k ^ 1 = ( R 1 - R obj ) / R 1 - R obj , k ^ 1 = ( R L - R obj ) / R L - R obj .
K = ( 2 π / λ ) ( k ^ 2 - k ^ 1 ) ,
{ L } = [ K T K ] - 1 [ K T ] { Ω + N } ,
[ A B C D E F G H L M N P Q R S T ]     [ K 0 0 0 I 0 K 0 0 I 0 0 K 0 I 0 0 0 K I ] = [ I ] .
[ AK BK CK DK [ A + B + C + D ] EK FK GK HK [ E + F + G + H ] LK MK NK PK [ L + M + N + P ] QK RK SK TK [ Q + R + S + T ] ] = [ I ] .
QK = RK = SK = TK = 0 , or [ Q + R + S + T ] K = 0 ,
[ Q + R + S + T ] = I .

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