Abstract

Improved quality of phase maps in pulsed digital holographic interferometry is demonstrated by finding the right reconstruction distance. The objective is to improve the optical phase information when the object under study is a phase object and when it is out of focus, leading to low contrast fringes in the phase map. A numerical refocusing is performed by introducing an ideal lens as a multiplication by a phase field in the Fourier domain, and then a region of maximum speckle correlation is found by comparing undisturbed and disturbed subimages in different refocused imaging planes. After finding the right reconstruction distance, a phase map of high visibility is constructed. By this technique a 30% reduction of the phase error for a flow of helium gas and a 50% reduction of the phase error for a weak thin lens were obtained, which resulted in a significant improvement of the visual appearance of the phase maps.

© 2008 Optical Society of America

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References

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2004 (5)

2003 (1)

2002 (1)

U. Schnars and W. P. O. Jüptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

1999 (1)

1997 (1)

1992 (1)

1979 (1)

1970 (2)

N.-E. Molin and K. A. Stetson, "Measurement of fringe loci and localization in hologram interferometry for pivot motion, in-plane rotation, and in-plane translation, Part I," Optik 31, 157-177 (1970).

N.-E. Molin and K. A. Stetson, "Measurement of fringe loci and localization in hologram interferometry for pivot motion, in-plane rotation, and in-plane translation, Part II," Optik 31, 281-291 (1970).

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Jüptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Opt. Lasers Eng. (1)

N.-E. Molin, M. Sjödahl, P. Gren, and A. Svanbro, "Speckle photography combined with speckle interferometry," Opt. Lasers Eng. 41, 673-686 (2004).
[CrossRef]

Opt. Lett. (3)

Optik (2)

N.-E. Molin and K. A. Stetson, "Measurement of fringe loci and localization in hologram interferometry for pivot motion, in-plane rotation, and in-plane translation, Part I," Optik 31, 157-177 (1970).

N.-E. Molin and K. A. Stetson, "Measurement of fringe loci and localization in hologram interferometry for pivot motion, in-plane rotation, and in-plane translation, Part II," Optik 31, 281-291 (1970).

Other (6)

I. Yamaguchi, "Fringe formations in deformation and vibration measurements using laser light," in Progress in Optics, E. Wolf, ed. (Elsevier Science, 1985), Vol. XXII.
[CrossRef]

L. Yaroslavsky, Digital Holography and Digital Image Processing, Principles, Methods, Algorithms (Kluwer Academic, 2004).

T. Kreis, Holographic Interferometry, Principles and Methods (Akademie Verlag, 1996).

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1975), pp. 9-75.
[CrossRef]

K. J. Gåsvik, Optical Metrology, 2nd ed. (Wiley, 1995).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup. Nd:YAG, pulsed laser; CCD, CCD camera; M, mirror; NL1 and NL2, negative lenses; L1, collimation lens; L2–L4, lens system for imaging; D, diffuser; PO, phase object; A, quadratic aperture; CA, circular aperture; BS, beam splitter; O, object beam; R, reference beam.

Fig. 2
Fig. 2

Configuration used for the calculation in ZEMAX. The ideal lens is put in the exit pupil plane. When the object plane is chosen closer to the imaging system (a dashed line), the focal length of the ideal lens has to be chosen to maintain a constant magnification and as a consequence the image plane is moved closer to the imaging system (a dashed line).

Fig. 3
Fig. 3

(a) Calibration curve for the numerical lens to use in the exit pupil of Fig. 2. (b) The reimaging distance as a function of refocus distance. These curves are obtained from ZEMAX by optimizing for a constant magnification for a given refocus distance.

Fig. 4
Fig. 4

Correlation coefficient versus distance from the diffuser for subimage pairs, without and with the helium gas present. The dashed line represents the distance 165 mm , which is in the middle of the gas nozzle.

Fig. 5
Fig. 5

Wrapped phase maps obtained from a flow of helium gas surrounded by air and placed 165 mm in front of a diffuser. The flow enters from below. (a) Wrapped phase map obtained from the plane of the diffuser. Low contrast fringes are seen. (b) Wrapped phase map obtained from a plane in the middle of the gas after numerical refocusing. High contrast fringes are seen.

Fig. 6
Fig. 6

Correlation coefficient versus distance from the diffuser for subimage pairs, without and with the thin lens present. The dashed line represents the distance 78 mm , which is the localization of the principal planes of the thin lens.

Fig. 7
Fig. 7

Wrapped phase maps obtained from a thin lens as a phase object and placed with its principal planes 78 mm in front of a diffuser. (a) Wrapped phase map obtained from the plane of the diffuser. Low contrast fringes are seen. (b) Wrapped phase map obtained by refocusing at the principal planes of the lens. High contrast fringes are seen.

Equations (7)

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U ( ξ , η ) = exp ( i k f 2 + ξ 2 + η 2 )
Δ x i 2 = Δ x i 1 z 2 z 1 ,
γ = i p j p ( I 1 ( i , j ) I ¯ 1 ) ( I 2 ( i , j ) I ¯ 2 ) { [ i p j p ( I 1 ( i , j ) I ¯ 1 ) 2 ] [ i p j p ( I 2 ( i , j ) I ¯ 2 ) 2 ] } 1 / 2
Δ ϕ = arctan [ Re ( s ) Im ( s ) Im ( s ) Re ( s ) Im ( s ) Im ( s ) + Re ( s ) Re ( s ) ] ,
σ Δ ϕ = π 2 3 π arcsin | μ | + arcsin 2 | μ | 1 2 n = 1 μ 2 n n 2 ,
γ ( q ) = | P ( b ) P * ( b + A p ) exp [ i k L b ( q A ) ] exp [ i k 2 L 2 | b | 2 ( α A Z ) d 2 b ] | P ( b ) | 2 d 2 b | 2 .
A = m L k ϕ r ,

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