Abstract

A technique to gain depth information from an image-plane digital holographic recording of a transient phase object positioned between a diffuser and an imaging system is demonstrated. The technique produces telecentric reconstructions of the complex amplitude throughout the phase volume using numerical lenses and the complex spectrum formulation of the diffraction integral. The in-plane speckle movements as well as the phase difference between the disturbed field and a reference field are calculated in a finite number of planes using a cross-correlation formulation. It is shown that depth information about in-plane phase gradients can be determined in two planes using reconstructed speckle fields from four different depths. In addition, the plane of optimum reconstruction for calculating the phase difference with maximum contrast is detected from the technique. The method is demonstrated on a measurement of a laser ablation process.

© 2009 Optical Society of America

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References

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  1. P. Rastogi, and A. Sharma, “Systematic approach to image formation in digital holography,” Opt. Eng. 42, 1208-1214 (2003).
    [CrossRef]
  2. U. Schnars, and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
    [CrossRef]
  3. C. M. Vest, Holographic Interferometry (Wiley, 1979).
  4. D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. 43, 6536-6544(2004).
    [CrossRef]
  5. N. A. Fomin, Speckle Photography for Fluid Mechanics Measurements (Springer-Verlag, 1998).
  6. E.-L. Johansson, L. Benckert, and M. Sjödahl, “Phase object data obtained by pulsed TV holography and defocused laser speckle displacement,” Appl. Opt. 43, 3235-3240 (2004).
    [CrossRef]
  7. E.-L. Johansson, L. Benckert, and M. Sjödahl, “Improving the quality of phase maps in phase object digital holographic interferometry by finding the right reconstruction distance,” Appl. Opt. 47, 1-8 (2008).
    [CrossRef]
  8. H. Li, S. Costil, V. Barnier, R. Oltra, O. Heintz, and C. Coddet, “Surface modifications induced by nanosecond pulsed Nd:YAG laser irradiation of metallic substrates,” Surf. Coat. Technol. 201, 1383-1392 (2006).
    [CrossRef]
  9. M. A. Shannon, X. L. Mao, A. Fernandez, W.-T. Chan, and R. E. Russo, “Laser ablation mass removal versus incident power density during solid sampling for inductively coupled plasma atomic emission spectroscopy,” Anal. Chem. 67, 4522-4529 (1995).
    [CrossRef]
  10. R. Salimbeni, R. Pini, and S. Siano, “High quality cleaning in conservation of culutral heritage by optimized Nd:YAG laser induced ablative effects,” Proc. SPIE 4184, 551-554 (2001).
    [CrossRef]
  11. E. György, A. P. d. Pino, P. Serra, and J. L. Morenza, “Surface nitridation of titanium by pulsed Nd:YAG laser irradiation,” Appl. Surf. Sci. 186, 130-134 (2002).
    [CrossRef]
  12. E. Amer, P. Gren, and M. Sjödahl, “Shock wave generation in laser ablation studied using pulsed digital holographic interferometry,” J. Phys. D 41, 215502 (2008).
    [CrossRef]
  13. E. Amer, P. Gren, and M. Sjödahl, “Laser-ablation-induced refractive index fields studied using pulsed digital holographic interferometry,” Opt. Lasers Eng. 47, 793-799 (2009).
    [CrossRef]
  14. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156-160(1982).
    [CrossRef]
  15. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  16. P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).
  17. M. Sjödahl, “Electronic speckle photography: increased accuracy by nonintegral pixel shifting,” Appl. Opt. 33, 6667-6673 (1994).
    [CrossRef]
  18. M. Sjödahl, “Accuracy in electronic speckle photography,” Appl. Opt. 36, 2875-2885 (1997).
    [CrossRef]
  19. G. Besnard, F. Hild, and S. Roux, ““Finite-element” displacement fields analysis from digital images: application to Portevin-Le Chatelier bands,” Exp. Mech. 46, 789-903 (2006).
    [CrossRef]

2009

E. Amer, P. Gren, and M. Sjödahl, “Laser-ablation-induced refractive index fields studied using pulsed digital holographic interferometry,” Opt. Lasers Eng. 47, 793-799 (2009).
[CrossRef]

2008

E. Amer, P. Gren, and M. Sjödahl, “Shock wave generation in laser ablation studied using pulsed digital holographic interferometry,” J. Phys. D 41, 215502 (2008).
[CrossRef]

E.-L. Johansson, L. Benckert, and M. Sjödahl, “Improving the quality of phase maps in phase object digital holographic interferometry by finding the right reconstruction distance,” Appl. Opt. 47, 1-8 (2008).
[CrossRef]

2006

H. Li, S. Costil, V. Barnier, R. Oltra, O. Heintz, and C. Coddet, “Surface modifications induced by nanosecond pulsed Nd:YAG laser irradiation of metallic substrates,” Surf. Coat. Technol. 201, 1383-1392 (2006).
[CrossRef]

G. Besnard, F. Hild, and S. Roux, ““Finite-element” displacement fields analysis from digital images: application to Portevin-Le Chatelier bands,” Exp. Mech. 46, 789-903 (2006).
[CrossRef]

2004

2003

P. Rastogi, and A. Sharma, “Systematic approach to image formation in digital holography,” Opt. Eng. 42, 1208-1214 (2003).
[CrossRef]

2002

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

E. György, A. P. d. Pino, P. Serra, and J. L. Morenza, “Surface nitridation of titanium by pulsed Nd:YAG laser irradiation,” Appl. Surf. Sci. 186, 130-134 (2002).
[CrossRef]

2001

R. Salimbeni, R. Pini, and S. Siano, “High quality cleaning in conservation of culutral heritage by optimized Nd:YAG laser induced ablative effects,” Proc. SPIE 4184, 551-554 (2001).
[CrossRef]

1997

1995

M. A. Shannon, X. L. Mao, A. Fernandez, W.-T. Chan, and R. E. Russo, “Laser ablation mass removal versus incident power density during solid sampling for inductively coupled plasma atomic emission spectroscopy,” Anal. Chem. 67, 4522-4529 (1995).
[CrossRef]

1994

1982

Amer, E.

E. Amer, P. Gren, and M. Sjödahl, “Laser-ablation-induced refractive index fields studied using pulsed digital holographic interferometry,” Opt. Lasers Eng. 47, 793-799 (2009).
[CrossRef]

E. Amer, P. Gren, and M. Sjödahl, “Shock wave generation in laser ablation studied using pulsed digital holographic interferometry,” J. Phys. D 41, 215502 (2008).
[CrossRef]

Barnier, V.

H. Li, S. Costil, V. Barnier, R. Oltra, O. Heintz, and C. Coddet, “Surface modifications induced by nanosecond pulsed Nd:YAG laser irradiation of metallic substrates,” Surf. Coat. Technol. 201, 1383-1392 (2006).
[CrossRef]

Benckert, L.

Besnard, G.

G. Besnard, F. Hild, and S. Roux, ““Finite-element” displacement fields analysis from digital images: application to Portevin-Le Chatelier bands,” Exp. Mech. 46, 789-903 (2006).
[CrossRef]

Carl, D.

Chan, W.-T.

M. A. Shannon, X. L. Mao, A. Fernandez, W.-T. Chan, and R. E. Russo, “Laser ablation mass removal versus incident power density during solid sampling for inductively coupled plasma atomic emission spectroscopy,” Anal. Chem. 67, 4522-4529 (1995).
[CrossRef]

Coddet, C.

H. Li, S. Costil, V. Barnier, R. Oltra, O. Heintz, and C. Coddet, “Surface modifications induced by nanosecond pulsed Nd:YAG laser irradiation of metallic substrates,” Surf. Coat. Technol. 201, 1383-1392 (2006).
[CrossRef]

Costil, S.

H. Li, S. Costil, V. Barnier, R. Oltra, O. Heintz, and C. Coddet, “Surface modifications induced by nanosecond pulsed Nd:YAG laser irradiation of metallic substrates,” Surf. Coat. Technol. 201, 1383-1392 (2006).
[CrossRef]

Fernandez, A.

M. A. Shannon, X. L. Mao, A. Fernandez, W.-T. Chan, and R. E. Russo, “Laser ablation mass removal versus incident power density during solid sampling for inductively coupled plasma atomic emission spectroscopy,” Anal. Chem. 67, 4522-4529 (1995).
[CrossRef]

Fomin, N. A.

N. A. Fomin, Speckle Photography for Fluid Mechanics Measurements (Springer-Verlag, 1998).

Goodman, J. W.

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

Gren, P.

E. Amer, P. Gren, and M. Sjödahl, “Laser-ablation-induced refractive index fields studied using pulsed digital holographic interferometry,” Opt. Lasers Eng. 47, 793-799 (2009).
[CrossRef]

E. Amer, P. Gren, and M. Sjödahl, “Shock wave generation in laser ablation studied using pulsed digital holographic interferometry,” J. Phys. D 41, 215502 (2008).
[CrossRef]

György, E.

E. György, A. P. d. Pino, P. Serra, and J. L. Morenza, “Surface nitridation of titanium by pulsed Nd:YAG laser irradiation,” Appl. Surf. Sci. 186, 130-134 (2002).
[CrossRef]

Heintz, O.

H. Li, S. Costil, V. Barnier, R. Oltra, O. Heintz, and C. Coddet, “Surface modifications induced by nanosecond pulsed Nd:YAG laser irradiation of metallic substrates,” Surf. Coat. Technol. 201, 1383-1392 (2006).
[CrossRef]

Hild, F.

G. Besnard, F. Hild, and S. Roux, ““Finite-element” displacement fields analysis from digital images: application to Portevin-Le Chatelier bands,” Exp. Mech. 46, 789-903 (2006).
[CrossRef]

Ina, H.

Johansson, E.-L.

Jüptner, W. P. O.

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

Kemper, B.

Kobayashi, S.

Li, H.

H. Li, S. Costil, V. Barnier, R. Oltra, O. Heintz, and C. Coddet, “Surface modifications induced by nanosecond pulsed Nd:YAG laser irradiation of metallic substrates,” Surf. Coat. Technol. 201, 1383-1392 (2006).
[CrossRef]

Mao, X. L.

M. A. Shannon, X. L. Mao, A. Fernandez, W.-T. Chan, and R. E. Russo, “Laser ablation mass removal versus incident power density during solid sampling for inductively coupled plasma atomic emission spectroscopy,” Anal. Chem. 67, 4522-4529 (1995).
[CrossRef]

Morenza, J. L.

E. György, A. P. d. Pino, P. Serra, and J. L. Morenza, “Surface nitridation of titanium by pulsed Nd:YAG laser irradiation,” Appl. Surf. Sci. 186, 130-134 (2002).
[CrossRef]

Oltra, R.

H. Li, S. Costil, V. Barnier, R. Oltra, O. Heintz, and C. Coddet, “Surface modifications induced by nanosecond pulsed Nd:YAG laser irradiation of metallic substrates,” Surf. Coat. Technol. 201, 1383-1392 (2006).
[CrossRef]

Pini, R.

R. Salimbeni, R. Pini, and S. Siano, “High quality cleaning in conservation of culutral heritage by optimized Nd:YAG laser induced ablative effects,” Proc. SPIE 4184, 551-554 (2001).
[CrossRef]

Pino, A. P. d.

E. György, A. P. d. Pino, P. Serra, and J. L. Morenza, “Surface nitridation of titanium by pulsed Nd:YAG laser irradiation,” Appl. Surf. Sci. 186, 130-134 (2002).
[CrossRef]

Rastogi, P.

P. Rastogi, and A. Sharma, “Systematic approach to image formation in digital holography,” Opt. Eng. 42, 1208-1214 (2003).
[CrossRef]

Rastogi, P. K.

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

Roux, S.

G. Besnard, F. Hild, and S. Roux, ““Finite-element” displacement fields analysis from digital images: application to Portevin-Le Chatelier bands,” Exp. Mech. 46, 789-903 (2006).
[CrossRef]

Russo, R. E.

M. A. Shannon, X. L. Mao, A. Fernandez, W.-T. Chan, and R. E. Russo, “Laser ablation mass removal versus incident power density during solid sampling for inductively coupled plasma atomic emission spectroscopy,” Anal. Chem. 67, 4522-4529 (1995).
[CrossRef]

Salimbeni, R.

R. Salimbeni, R. Pini, and S. Siano, “High quality cleaning in conservation of culutral heritage by optimized Nd:YAG laser induced ablative effects,” Proc. SPIE 4184, 551-554 (2001).
[CrossRef]

Schnars, U.

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

Serra, P.

E. György, A. P. d. Pino, P. Serra, and J. L. Morenza, “Surface nitridation of titanium by pulsed Nd:YAG laser irradiation,” Appl. Surf. Sci. 186, 130-134 (2002).
[CrossRef]

Shannon, M. A.

M. A. Shannon, X. L. Mao, A. Fernandez, W.-T. Chan, and R. E. Russo, “Laser ablation mass removal versus incident power density during solid sampling for inductively coupled plasma atomic emission spectroscopy,” Anal. Chem. 67, 4522-4529 (1995).
[CrossRef]

Sharma, A.

P. Rastogi, and A. Sharma, “Systematic approach to image formation in digital holography,” Opt. Eng. 42, 1208-1214 (2003).
[CrossRef]

Siano, S.

R. Salimbeni, R. Pini, and S. Siano, “High quality cleaning in conservation of culutral heritage by optimized Nd:YAG laser induced ablative effects,” Proc. SPIE 4184, 551-554 (2001).
[CrossRef]

Sjödahl, M.

Takeda, M.

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, 1979).

von Bally, G.

Wernicke, G.

Anal. Chem.

M. A. Shannon, X. L. Mao, A. Fernandez, W.-T. Chan, and R. E. Russo, “Laser ablation mass removal versus incident power density during solid sampling for inductively coupled plasma atomic emission spectroscopy,” Anal. Chem. 67, 4522-4529 (1995).
[CrossRef]

Appl. Opt.

Appl. Surf. Sci.

E. György, A. P. d. Pino, P. Serra, and J. L. Morenza, “Surface nitridation of titanium by pulsed Nd:YAG laser irradiation,” Appl. Surf. Sci. 186, 130-134 (2002).
[CrossRef]

Exp. Mech.

G. Besnard, F. Hild, and S. Roux, ““Finite-element” displacement fields analysis from digital images: application to Portevin-Le Chatelier bands,” Exp. Mech. 46, 789-903 (2006).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. D

E. Amer, P. Gren, and M. Sjödahl, “Shock wave generation in laser ablation studied using pulsed digital holographic interferometry,” J. Phys. D 41, 215502 (2008).
[CrossRef]

Meas. Sci. Technol.

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

Opt. Eng.

P. Rastogi, and A. Sharma, “Systematic approach to image formation in digital holography,” Opt. Eng. 42, 1208-1214 (2003).
[CrossRef]

Opt. Lasers Eng.

E. Amer, P. Gren, and M. Sjödahl, “Laser-ablation-induced refractive index fields studied using pulsed digital holographic interferometry,” Opt. Lasers Eng. 47, 793-799 (2009).
[CrossRef]

Proc. SPIE

R. Salimbeni, R. Pini, and S. Siano, “High quality cleaning in conservation of culutral heritage by optimized Nd:YAG laser induced ablative effects,” Proc. SPIE 4184, 551-554 (2001).
[CrossRef]

Surf. Coat. Technol.

H. Li, S. Costil, V. Barnier, R. Oltra, O. Heintz, and C. Coddet, “Surface modifications induced by nanosecond pulsed Nd:YAG laser irradiation of metallic substrates,” Surf. Coat. Technol. 201, 1383-1392 (2006).
[CrossRef]

Other

C. M. Vest, Holographic Interferometry (Wiley, 1979).

N. A. Fomin, Speckle Photography for Fluid Mechanics Measurements (Springer-Verlag, 1998).

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

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

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Figures (5)

Fig. 1
Fig. 1

Top view of the experimental setup: M 1 , M 2 , mirrors; NL, negative lens; L 1 , focusing lens; L 2 , collimation lens; L, lens system for imaging; A, aperture; D, diffuser; BS 1 , BS 2 , beam splitters; R, reference beam; O, object beam.

Fig. 2
Fig. 2

Geometry of the reconstruction configuration: The distance a is the distance between the diffuser and the entrance pupil of the imaging lens system having effective focal length f 0 . The distance l is the distance between the exit pupil of the imaging lens system and the detection plane. The numerical lens f 1 is used to compensate for the curvature of the reference wave and to move a distance x in object space and x i in image space, respectively, with constant magnification.

Fig. 3
Fig. 3

Measured phase field and speckle displacement field at a reconstruction depth of (a)  1 mm , (b)  4.7 mm , and (c)  8.4 mm , respectively, in front of the diffuser screen. The three arrows in the upper right corner correspond to a speckle displacement of 1, 2, and 3 pixels, respectively. (d) The measured speckle y displacement in pixels as a function of refocusing depth x at three different y positions at z = 1.4 mm in the phase disturbance.

Fig. 4
Fig. 4

Geometry of the idealized ray-tracing model between the diffuser screen D and the recording plane RP. The unknown phase distribution is represented by the three thin phase screens, ϕ ( r 1 ) , ϕ ( r 2 ) , and ϕ ( r 3 ) , respectively, separated a distance L, where the r represent in-plane position vectors. L R is the variable distance between the last phase screen and the recording plane, and s 1 , s 2 , and s 3 , respectively, are two-component directional vectors. The vector p represents the speckle movement in the recording plane due to the phase disturbance.

Fig. 5
Fig. 5

Magnitude of the phase gradient field (a) reconstructed a distance 4.15 mm from the diffuser, (b) reconstructed a distance 5.65 mm from the diffuser, and (c) calculated by a numerical differentiation of the unwrapped phase field in Fig. 3b. The correlation values in the plane x = 7.15 mm are shown in (d); the sum of the phase gradients in (a) and (b) is shown in (e).

Equations (11)

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U ( z , y , x ) = I { U ( z , y , 0 ) } exp [ i k m x ] exp [ i k ( p z + q y ) ] d p d q ,
x i = f 1 [ l ( a x f 0 ) ( a x ) f 0 ] ( l f 1 ) ( a x f 0 ) ( a x ) f 0 ,
M = f 0 f 1 ( l f 1 ) ( a x f 0 ) ( a x ) f 0 .
M = f 1 f 0 .
J ( Δ z , Δ y , Δ x ) = U d ( z , y , x ) U r * ( z Δ z , y Δ y , x Δ x ) ,
J ( Δ z , Δ y ; x = x r ) = U d ( z , y ; x = x r ) U r * ( z Δ z , y Δ y ; x = x r )
e = σ 2 B 1 γ γ ,
s 1 ( r 1 ) = 1 k ϕ ( r 1 ) , r 2 = r 1 + s 1 ( r 1 ) L , s 2 ( r 2 ) = s 1 ( r 1 ) + 1 k ϕ ( r 2 ) , r 3 = r 2 + s 2 ( r 2 ) L , s 3 ( r 3 ) = s 2 ( r 2 ) + 1 k ϕ ( r 3 ) , r 4 = r 3 + s 3 ( r 3 ) L R , p = r 4 r 1 ,
( N 1 N 2 0 N 2 N 3 1 0 1 ( N 1 ) ) ( ϕ ( r 1 ) ϕ ( r 2 ) ϕ ( r N ) ) = k L ( p 1 p 2 p N ) ,
( N 2 N 3 1 N 3 N 4 0 1 2 ( N 2 ) ) ( ϕ ( r 2 ) ϕ ( r 3 ) ϕ ( r N 1 ) ) = k L ( p 1 p 2 p N ) .
ϕ ( r 2 ) = k L P · l , ϕ ( r 3 ) = ϕ ( r 2 ) k 2 L i = 1 4 p i ,

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