Abstract

The theoretical and experimental analysis of SNR in frequency-translated holography that is applied to the detection of small vibration amplitude is presented in this paper. The feature of the experiments lies on the usage of acoustic surface waves as the vibrating test object, since the acoustic surface waves give the reliable vibration amplitude and the easiness of the measurement of SNR. Furthermore the detectable smallest amplitude is estimated as 2.7 × 10−4 λ, which is several tenths smaller than the previously presented estimations, and the dependences of the detectable smallest vibration amplitude on the experimental arrangements are also made clear.

© 1976 Optical Society of America

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References

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  1. C. C. Aleksoff, Appl. Opt. 10, 1329 (1971).
    [CrossRef] [PubMed]
  2. T. Nakajima, Jpn. J. Appl. Phys. 13, 471 (1974).
    [CrossRef]
  3. S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Jpn. J. Appl. Phys. 13, 1907 (1974).
    [CrossRef]
  4. W. G. Mayer, G. B. Lamers, D. C. Auth, J. Acoust. Soc. Am. 42, 1255 (1967).
    [CrossRef]
  5. S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Proc. IEEE 63, 1259 (1975).
    [CrossRef]
  6. K. Biedermann, Optik 31, 367 (1970).
  7. R. Adler, A. Korpel, P. Desmares, IEEE Trans. Ionics Ultrason. SU-15, 157 (1968).
    [CrossRef]
  8. R. Dandliker, B. Ineichem, F. M. Mottier, Opt. Commun. 9, 412 (1973).
    [CrossRef]

1975 (1)

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Proc. IEEE 63, 1259 (1975).
[CrossRef]

1974 (2)

T. Nakajima, Jpn. J. Appl. Phys. 13, 471 (1974).
[CrossRef]

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Jpn. J. Appl. Phys. 13, 1907 (1974).
[CrossRef]

1973 (1)

R. Dandliker, B. Ineichem, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

1971 (1)

1970 (1)

K. Biedermann, Optik 31, 367 (1970).

1968 (1)

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Ionics Ultrason. SU-15, 157 (1968).
[CrossRef]

1967 (1)

W. G. Mayer, G. B. Lamers, D. C. Auth, J. Acoust. Soc. Am. 42, 1255 (1967).
[CrossRef]

Adler, R.

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Ionics Ultrason. SU-15, 157 (1968).
[CrossRef]

Aleksoff, C. C.

Auth, D. C.

W. G. Mayer, G. B. Lamers, D. C. Auth, J. Acoust. Soc. Am. 42, 1255 (1967).
[CrossRef]

Biedermann, K.

K. Biedermann, Optik 31, 367 (1970).

Dandliker, R.

R. Dandliker, B. Ineichem, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

Desmares, P.

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Ionics Ultrason. SU-15, 157 (1968).
[CrossRef]

Ineichem, B.

R. Dandliker, B. Ineichem, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

Korpel, A.

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Ionics Ultrason. SU-15, 157 (1968).
[CrossRef]

Lamers, G. B.

W. G. Mayer, G. B. Lamers, D. C. Auth, J. Acoust. Soc. Am. 42, 1255 (1967).
[CrossRef]

Mayer, W. G.

W. G. Mayer, G. B. Lamers, D. C. Auth, J. Acoust. Soc. Am. 42, 1255 (1967).
[CrossRef]

Moriizumi, T.

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Proc. IEEE 63, 1259 (1975).
[CrossRef]

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Jpn. J. Appl. Phys. 13, 1907 (1974).
[CrossRef]

Mottier, F. M.

R. Dandliker, B. Ineichem, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

Nakajima, T.

T. Nakajima, Jpn. J. Appl. Phys. 13, 471 (1974).
[CrossRef]

Sato, T.

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Proc. IEEE 63, 1259 (1975).
[CrossRef]

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Jpn. J. Appl. Phys. 13, 1907 (1974).
[CrossRef]

Shiokawa, S.

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Proc. IEEE 63, 1259 (1975).
[CrossRef]

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Jpn. J. Appl. Phys. 13, 1907 (1974).
[CrossRef]

Ueda, M.

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Proc. IEEE 63, 1259 (1975).
[CrossRef]

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Jpn. J. Appl. Phys. 13, 1907 (1974).
[CrossRef]

Yasuda, T.

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Proc. IEEE 63, 1259 (1975).
[CrossRef]

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Jpn. J. Appl. Phys. 13, 1907 (1974).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Ionics Ultrason. (1)

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Ionics Ultrason. SU-15, 157 (1968).
[CrossRef]

J. Acoust. Soc. Am. (1)

W. G. Mayer, G. B. Lamers, D. C. Auth, J. Acoust. Soc. Am. 42, 1255 (1967).
[CrossRef]

Jpn. J. Appl. Phys. (2)

T. Nakajima, Jpn. J. Appl. Phys. 13, 471 (1974).
[CrossRef]

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Jpn. J. Appl. Phys. 13, 1907 (1974).
[CrossRef]

Opt. Commun. (1)

R. Dandliker, B. Ineichem, F. M. Mottier, Opt. Commun. 9, 412 (1973).
[CrossRef]

Optik (1)

K. Biedermann, Optik 31, 367 (1970).

Proc. IEEE (1)

S. Shiokawa, M. Ueda, T. Moriizumi, T. Yasuda, T. Sato, Proc. IEEE 63, 1259 (1975).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic arrangement for frequency-translated holography: M, modulator; V, vibrating object; L1, lens; P1, hologram; HM, half-mirror.

Fig. 2
Fig. 2

Separation of the signal and the unwanted image in the reconstruction process: P1, hologram; RC, reconstruction light; P2, Fourier transform plane; L2 and L3, lenses; PH, pinhole; P3, reconstructed image.

Fig. 3
Fig. 3

Configuration of the SAW excitor.

Fig. 4
Fig. 4

The reconstructed images of the SAW field: (a) images obtained by using the +1st and 0th order lights; (b) images obtained by using the +1st order light; (c) images obtained by using the 0th order light.

Fig. 5
Fig. 5

The relation between the SNR and the vibration amplitude.

Equations (20)

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O 0 exp ( j ω t ) + O 1 exp [ j ( ω + Ω ) t ] ,
S 0 = O 1 2 / O 0 2 = J 1 2 ( 4 π a cos ϕ / λ ) 1 ,
R 0 exp ( j ω t ) + R 1 exp [ j ( ω + Ω ) t ] ,
β = R 0 2 / R 1 2 1.
B 2 + O 1 R 1 * + O 0 R 0 * + O 1 * R 1 + O 0 * R 0 ,
B 2 = O 0 2 + O 1 2 + R 0 2 + R 1 2 ,
c ( O 1 R 1 * + O 0 R 0 * ) R c / B 2 + n R c 2 ,
c O 1 R 1 * R c 2 / B 4 ,
c O 0 R 0 * R c 2 / B 4 + n R c 2 .
S h = O 1 2 R 1 2 / ( O 0 2 R 0 2 R 0 2 + n 2 B / 4 c 2 ) .
O 0 2 + O 1 2 = 2 = R 0 2 + R 1 2 .
S h = S 0 / [ β + 4 n 2 ( 1 + S 0 ) ( 1 + β ) / c 2 ] S 0 / ( β + 4 n 2 / c 2 ) .
γ O 0 2 R 0 2 + O 1 2 R 1 2 ,
S h = S 0 / β ( 2 π a cos ϕ ) 2 / λ 2 β ,
n 2 = π ( p / d λ ) 2 N ,
t ( ) = t ( 0 ) + t ( 0 ) ( - 0 ) ,
( - 0 ) = 0 ( O 0 R 0 * + O 1 R 1 * ) / B 2 .
c = 0 t ( 0 ) .
S h = ( 2 π cos ϕ ) 2 / { β + 4 π N [ p / d λ 0 t ( 0 ) ] 2 } ,
β 7.90 ( a cos ϕ / λ ) 2 .

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