Abstract

This paper presents an illustration of mathematical refocusing of images obtained by the HoloFringe300K electronic holography program. The purpose is to demonstrate that this form of electronic holography is equivalent to image-plane, phase-stepped digital holography. The mathematical refocusing method used here differs from those in common use and may have some advantages.

© 2009 Optical Society of America

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References

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  1. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
    [CrossRef]
  2. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179-181 (1994).
    [CrossRef] [PubMed]
  3. J. N. Butters and J. A. Leendertz, “Holographic and video techniques applied to engineering measurements,” Meas. Control 4, 349-354 (1971).
  4. A. Macovski, S. D. Ramsey, and L. F. Schaefer, “Time-lapse interferometry and contouring using television systems,” Appl. Opt. 10, 2722-2727 (1971).
    [CrossRef] [PubMed]
  5. K. A. Stetson, W. R. Brohinsky, J. Wahid, and T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69-76 (1989).
    [CrossRef]
  6. I. Yamaguchi and T. Zhang, “Phase shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).
    [CrossRef] [PubMed]
  7. G. Pedrini and H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 337-362.
  8. W. Osten and P. Ferraro, “Digital holography and its application in MEMS/MOEMS inspection,” in Optical Inspection of Microsystems, Vol. 109 of Optical Science and Engineering Series, W. Osten, ed. (CRC Press, 2006), pp. 351-425.
    [CrossRef]
  9. E. Lalor, “Conditions for the validity of the angular spectrum of plane waves,” J. Opt. Soc. Am. 58, 1235-1237(1968).
    [CrossRef]

1997 (1)

1994 (1)

1989 (1)

K. A. Stetson, W. R. Brohinsky, J. Wahid, and T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69-76 (1989).
[CrossRef]

1971 (2)

J. N. Butters and J. A. Leendertz, “Holographic and video techniques applied to engineering measurements,” Meas. Control 4, 349-354 (1971).

A. Macovski, S. D. Ramsey, and L. F. Schaefer, “Time-lapse interferometry and contouring using television systems,” Appl. Opt. 10, 2722-2727 (1971).
[CrossRef] [PubMed]

1968 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Brohinsky, W. R.

K. A. Stetson, W. R. Brohinsky, J. Wahid, and T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69-76 (1989).
[CrossRef]

Bushman, T.

K. A. Stetson, W. R. Brohinsky, J. Wahid, and T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69-76 (1989).
[CrossRef]

Butters, J. N.

J. N. Butters and J. A. Leendertz, “Holographic and video techniques applied to engineering measurements,” Meas. Control 4, 349-354 (1971).

Ferraro, P.

W. Osten and P. Ferraro, “Digital holography and its application in MEMS/MOEMS inspection,” in Optical Inspection of Microsystems, Vol. 109 of Optical Science and Engineering Series, W. Osten, ed. (CRC Press, 2006), pp. 351-425.
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Jüptner, W.

Lalor, E.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Leendertz, J. A.

J. N. Butters and J. A. Leendertz, “Holographic and video techniques applied to engineering measurements,” Meas. Control 4, 349-354 (1971).

Macovski, A.

Osten, W.

W. Osten and P. Ferraro, “Digital holography and its application in MEMS/MOEMS inspection,” in Optical Inspection of Microsystems, Vol. 109 of Optical Science and Engineering Series, W. Osten, ed. (CRC Press, 2006), pp. 351-425.
[CrossRef]

Pedrini, G.

G. Pedrini and H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 337-362.

Ramsey, S. D.

Schaefer, L. F.

Schnars, U.

Stetson, K. A.

K. A. Stetson, W. R. Brohinsky, J. Wahid, and T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69-76 (1989).
[CrossRef]

Tiziani, H. J.

G. Pedrini and H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 337-362.

Wahid, J.

K. A. Stetson, W. R. Brohinsky, J. Wahid, and T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69-76 (1989).
[CrossRef]

Yamaguchi, I.

Zhang, T.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Nondestruct. Eval. (1)

K. A. Stetson, W. R. Brohinsky, J. Wahid, and T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69-76 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Control (1)

J. N. Butters and J. A. Leendertz, “Holographic and video techniques applied to engineering measurements,” Meas. Control 4, 349-354 (1971).

Opt. Lett. (1)

Other (2)

G. Pedrini and H. J. Tiziani, “Digital holographic interferometry,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 337-362.

W. Osten and P. Ferraro, “Digital holography and its application in MEMS/MOEMS inspection,” in Optical Inspection of Microsystems, Vol. 109 of Optical Science and Engineering Series, W. Osten, ed. (CRC Press, 2006), pp. 351-425.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Component layout for the holographic optical head.

Fig. 2
Fig. 2

Image of two pins where the camera is focused between them.

Fig. 3
Fig. 3

Mechanical focusing of two pins: (a) shows the rear pin in focus while (b) shows the front pin in focus.

Fig. 4
Fig. 4

Mathematical focusing of the two pins: (a) shows mathematical focusing of the left pin and (b) of the right pin.

Fig. 5
Fig. 5

Coordinate system for a digitized optical field. The circles mark the locations of the camera pixels in the x - y plane.

Fig. 6
Fig. 6

Wavefronts propagating relative to the camera pixels.

Equations (13)

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S ( k x , k y ) = - - - + S ( x , y ) exp ( i k r ) d x d y .
S ( x , y , z ) = - + - + S ( k x , k y ) exp ( i k r ) d k x d k y .
k r = k x x + k y y + k z z = ( 2 π / λ ) ( x cos θ x + y cos θ y + z cos θ z ) .
F ( j , k ) = m = 0 m = M - 1 n = 0 n = N - 1 f ( m , n ) exp [ i 2 π ( j m M + k n N ) ] .
2 π λ cos θ x x = 2 π j m C M ,
2 π λ cos θ y y = 2 π k n C N .
cos θ max = λ / p .
cos θ max = j m C / M = k n C / N .
C = 2 λ / p .
cos θ x = 2 j λ / p M , cos θ y = 2 k λ / p N .
k z = 4 π p [ ( p 2 λ ) 2 ( j M ) 2 ( k N ) 2 ] 1 / 2 .
exp ( i k z ( j , k ) z ) = exp { i z 4 π p [ ( p 2 λ ) 2 - ( j M ) 2 - ( k N ) 2 ] 1 / 2 } .
S ( x , y , z ) = IFFT { FFT [ S ( x , y ) ] exp ( i k z ( j , k ) z ) } .

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