Abstract

A Doppler velocimeter using a diffraction grating and white light is proposed. Using the theory of Fourier optics and fringe model, the principle of operation of this Doppler velocimeter, its performance, and advantages over other arrangements are discussed.

© 1974 Optical Society of America

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References

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  1. S. S. Penner, T. Jerskey, Ann. Rev. Fluid Mech. 5, 9 (1973).
    [CrossRef]
  2. H. Z. Cummins, H. L. Swinney, Progress in Optics (North-Holland, Amsterdam, 1970), Vol. 8, p. 135.
    [CrossRef]
  3. C. P. Wang, Appl. Phys. Lett. 18, 522 (1971).
    [CrossRef]
  4. C. P. Wang, J. Phys. E 5, 763 (1972).
    [CrossRef]
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  6. M. J. Rudd, J. Phys. E 2, 55 (1969).
    [CrossRef]
  7. L. Lading, Opto-Electron. 4, 385 (1972).
    [CrossRef]
  8. A. Lohmann, Opt. Acta 9, 1 (1962).
    [CrossRef]
  9. S. S. Penner, N. Davidor, F. Bien, Am. J. Phys. 38, 1413 (1970).
    [CrossRef]
  10. M. J. R. Schwar, Nature 229, 621 (1971).
    [CrossRef] [PubMed]
  11. M. J. R. Schwar, F. J. Weinberg, Proc. Roy. Soc. A311, 469 (1969).

1973

S. S. Penner, T. Jerskey, Ann. Rev. Fluid Mech. 5, 9 (1973).
[CrossRef]

1972

C. P. Wang, J. Phys. E 5, 763 (1972).
[CrossRef]

L. Lading, Opto-Electron. 4, 385 (1972).
[CrossRef]

1971

M. J. R. Schwar, Nature 229, 621 (1971).
[CrossRef] [PubMed]

C. P. Wang, Appl. Phys. Lett. 18, 522 (1971).
[CrossRef]

1970

S. S. Penner, N. Davidor, F. Bien, Am. J. Phys. 38, 1413 (1970).
[CrossRef]

1969

M. J. Rudd, J. Phys. E 2, 55 (1969).
[CrossRef]

M. J. R. Schwar, F. J. Weinberg, Proc. Roy. Soc. A311, 469 (1969).

1962

A. Lohmann, Opt. Acta 9, 1 (1962).
[CrossRef]

Bien, F.

S. S. Penner, N. Davidor, F. Bien, Am. J. Phys. 38, 1413 (1970).
[CrossRef]

Cummins, H. Z.

H. Z. Cummins, H. L. Swinney, Progress in Optics (North-Holland, Amsterdam, 1970), Vol. 8, p. 135.
[CrossRef]

Davidor, N.

S. S. Penner, N. Davidor, F. Bien, Am. J. Phys. 38, 1413 (1970).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Jerskey, T.

S. S. Penner, T. Jerskey, Ann. Rev. Fluid Mech. 5, 9 (1973).
[CrossRef]

Lading, L.

L. Lading, Opto-Electron. 4, 385 (1972).
[CrossRef]

Lohmann, A.

A. Lohmann, Opt. Acta 9, 1 (1962).
[CrossRef]

Penner, S. S.

S. S. Penner, T. Jerskey, Ann. Rev. Fluid Mech. 5, 9 (1973).
[CrossRef]

S. S. Penner, N. Davidor, F. Bien, Am. J. Phys. 38, 1413 (1970).
[CrossRef]

Rudd, M. J.

M. J. Rudd, J. Phys. E 2, 55 (1969).
[CrossRef]

Schwar, M. J. R.

M. J. R. Schwar, Nature 229, 621 (1971).
[CrossRef] [PubMed]

M. J. R. Schwar, F. J. Weinberg, Proc. Roy. Soc. A311, 469 (1969).

Swinney, H. L.

H. Z. Cummins, H. L. Swinney, Progress in Optics (North-Holland, Amsterdam, 1970), Vol. 8, p. 135.
[CrossRef]

Wang, C. P.

C. P. Wang, J. Phys. E 5, 763 (1972).
[CrossRef]

C. P. Wang, Appl. Phys. Lett. 18, 522 (1971).
[CrossRef]

Weinberg, F. J.

M. J. R. Schwar, F. J. Weinberg, Proc. Roy. Soc. A311, 469 (1969).

Am. J. Phys.

S. S. Penner, N. Davidor, F. Bien, Am. J. Phys. 38, 1413 (1970).
[CrossRef]

Ann. Rev. Fluid Mech.

S. S. Penner, T. Jerskey, Ann. Rev. Fluid Mech. 5, 9 (1973).
[CrossRef]

Appl. Phys. Lett.

C. P. Wang, Appl. Phys. Lett. 18, 522 (1971).
[CrossRef]

J. Phys. E

C. P. Wang, J. Phys. E 5, 763 (1972).
[CrossRef]

M. J. Rudd, J. Phys. E 2, 55 (1969).
[CrossRef]

Nature

M. J. R. Schwar, Nature 229, 621 (1971).
[CrossRef] [PubMed]

Opt. Acta

A. Lohmann, Opt. Acta 9, 1 (1962).
[CrossRef]

Opto-Electron.

L. Lading, Opto-Electron. 4, 385 (1972).
[CrossRef]

Proc. Roy. Soc.

M. J. R. Schwar, F. J. Weinberg, Proc. Roy. Soc. A311, 469 (1969).

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

H. Z. Cummins, H. L. Swinney, Progress in Optics (North-Holland, Amsterdam, 1970), Vol. 8, p. 135.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Differential heterodyne arrangement using double slit.

Fig. 2
Fig. 2

Differential heterodyne arrangement using grating system.

Fig. 3
Fig. 3

Symmetric heterodyne arrangement using double slit.

Fig. 4
Fig. 4

Symmetric heterodyne arrangement using grating system.

Equations (12)

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ν = U / d ,
d = λ / 2 sin ϕ ,
ν = ( 2 U / λ ) sin ϕ ,
I ( x , z ) = A + 2 + A - 2 + 2 γ A + A - cos ( 2 k h x / f ) ,
A + = sinc { k a [ ( x / f ) - ( h z / f 2 ) ] } , A - = sinc { k a [ ( x / f ) + ( h z / f 2 ) ] } , γ = sinc ( 2 k h b / f ) ,
A + = sinc { k 0 a [ ( x / f ) - ( h z / f 2 ) ] } , A - = sinc { k 0 a [ ( x / f ) + ( h z / f 2 ) ] } , γ = sinc [ 2 Δ k ( h x / f ) ] ,
- c n exp ( i 2 π n x / d ) = { 1 if x + N d d / 4 , 0 if x + ( d / 2 ) + N d d / 4 , N = 0 , ± 1 , ± 2 , ,
I ( x , z ) = B + 2 + B 2 + 2 B + B - cos [ 4 π ( x - z x 0 / f ) / m d ]
B ± = B ± ( x 0 ) = { 1 if x 0 h / 2 , 0 if x 0 > h / 2 ,
V = ( I max - I min ) / ( I max + I min ) ,
b d / 4 π ,             2 Δ λ / λ 0 1 / 4 π ,
b 0.58 h ,             2 Δ λ / λ 0 2.

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