Abstract

Digital holography utilizing the optical Doppler effect is proposed in which the time variation of interference fringes is recorded using a high-speed CMOS camera. The complex amplitude diffracted from the object wave is extracted by time-domain Fourier transforming the recorded interference fringes. The method was used to measure the surface shape of a concave mirror under a disturbed environment.

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References

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  1. J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
    [CrossRef]
  2. L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, 1980).
  3. U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).
  4. T. Kreis and W. Jueptner, Opt. Eng. (Bellingham) 36, 2357 (1997).
    [CrossRef]
  5. I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
    [CrossRef] [PubMed]
  6. J. Schwider, O. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, Opt. Eng. (Bellingham) 32, 1883 (1993).
    [CrossRef]
  7. J. Schmit and K. Creath, Appl. Opt. 34, 3610 (1995).
    [CrossRef] [PubMed]
  8. Q. Hao, Q. Zhu, and Y. Hu, Opt. Lett. 34, 1288 (2009).
    [CrossRef] [PubMed]
  9. D. Barada, Y. Kikuchi, and T. Yatagai, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest CD (Optical Society of America, 2009), paper DWD4.
  10. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 57–61.

2009 (1)

1997 (2)

T. Kreis and W. Jueptner, Opt. Eng. (Bellingham) 36, 2357 (1997).
[CrossRef]

I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
[CrossRef] [PubMed]

1995 (1)

1993 (1)

J. Schwider, O. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, Opt. Eng. (Bellingham) 32, 1883 (1993).
[CrossRef]

1967 (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Barada, D.

D. Barada, Y. Kikuchi, and T. Yatagai, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest CD (Optical Society of America, 2009), paper DWD4.

Creath, K.

Falkenstoerfer, O.

J. Schwider, O. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, Opt. Eng. (Bellingham) 32, 1883 (1993).
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 57–61.

Hao, Q.

Hu, Y.

Jueptner, W.

T. Kreis and W. Jueptner, Opt. Eng. (Bellingham) 36, 2357 (1997).
[CrossRef]

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Kikuchi, Y.

D. Barada, Y. Kikuchi, and T. Yatagai, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest CD (Optical Society of America, 2009), paper DWD4.

Kreis, T.

T. Kreis and W. Jueptner, Opt. Eng. (Bellingham) 36, 2357 (1997).
[CrossRef]

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Merzlyakov, N. S.

L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, 1980).

Schmit, J.

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

Schreiber, H.

J. Schwider, O. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, Opt. Eng. (Bellingham) 32, 1883 (1993).
[CrossRef]

Schwider, J.

J. Schwider, O. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, Opt. Eng. (Bellingham) 32, 1883 (1993).
[CrossRef]

Streibl, N.

J. Schwider, O. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, Opt. Eng. (Bellingham) 32, 1883 (1993).
[CrossRef]

Yamaguchi, I.

Yaroslavskii, L. P.

L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, 1980).

Yatagai, T.

D. Barada, Y. Kikuchi, and T. Yatagai, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest CD (Optical Society of America, 2009), paper DWD4.

Zhang, T.

Zhu, Q.

Zoeller, A.

J. Schwider, O. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, Opt. Eng. (Bellingham) 32, 1883 (1993).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Opt. Eng. (Bellingham) (2)

T. Kreis and W. Jueptner, Opt. Eng. (Bellingham) 36, 2357 (1997).
[CrossRef]

J. Schwider, O. Falkenstoerfer, H. Schreiber, A. Zoeller, and N. Streibl, Opt. Eng. (Bellingham) 32, 1883 (1993).
[CrossRef]

Opt. Lett. (2)

Other (4)

L. P. Yaroslavskii and N. S. Merzlyakov, Methods of Digital Holography (Consultants Bureau, 1980).

U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).

D. Barada, Y. Kikuchi, and T. Yatagai, in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest CD (Optical Society of America, 2009), paper DWD4.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), pp. 57–61.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for Doppler phase-shifting digital holography. ND, neutral density filter; SF, spatial filter; BS, beam splitter.

Fig. 2
Fig. 2

Time variation of the intensity at a pixel of a digital hologram (a) with constant reference mirror movement and (b) with striking of the table.

Fig. 3
Fig. 3

Beat frequency spectra obtained from 500 images (a) with constant reference mirror movement and (b) with striking.

Fig. 4
Fig. 4

Surface shape of concave mirror measured (a) with constant reference mirror movement and (b) with striking.

Fig. 5
Fig. 5

RMS error versus number of images used to reconstruct surface shape (a) with constant reference mirror movement and (b) with striking.

Equations (13)

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U O ( x , y , t ) = A O ( x , y ) exp { i [ ω O ( t ) t ϕ O ( x , y ) ] } ,
U R ( t ) = A R exp { i [ ω R ( t ) t ϕ R ] } .
ω O ( t ) = ω 0 ( 1 + v O ( t ) c 1 v O ( t ) c ) 2 ,
ω R ( t ) = ω 0 ( 1 + v R ( t ) c 1 v R ( t ) c ) 2 ,
I ( x , y , t ) = | U O ( x , y , t ) + U R ( t ) | 2
= A O 2 ( x , y ) + A R 2 + 2 A O ( x , y ) A R cos [ Δ ω ( t ) t Δ ϕ ( x , y ) ] ,
Δ ϕ ( x , y ) = ϕ O ( x , y ) ϕ R ,
Δ ω ( t ) = ω O ( t ) ω R ( t ) .
F t ( I ) ( x , y , ω b ) = [ A O 2 ( x , y ) + A R 2 ] δ ( ω b ) + F ( x , y , ω b + ω b , 0 ) + F * ( x , y , ω b ω b , 0 ) ,
F ( x , y , ω b ) = A O ( x , y ) A R a ( ω b ) exp { i [ Δ ϕ ( x , y ) + b ( ω b ) ] } ,
DFT [ I ] ( x , y , ν b , m ) = n = 0 N 1 I ( x , y , t n ) exp ( i 2 π t n ν b , m ) ,
m = 0 , 1 , 2 , , N 1 ,
H ( x , y ) = λ ϕ O ( x , y ) 4 π ,

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