Abstract

In this paper the coherence requirement for different holographic setups (Fresnel hologram, Fourier hologram, and image-plane hologram) is compared. This analysis is based on the investigation of the recorded interference pattern from the superposition of reference wave and object wave in in-line and off-axis mode. The outcome of this investigation can support the choice of light source needed for certain digital holographic setups, as well as the selection of the best applicable setup to take advantage of new short coherence light sources. Moreover, as a byproduct of this investigation, the minimum required recording distance (focal length) to enable Nyquist sampling of the recorded hologram is obtained.

© 2012 Optical Society of America

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    [CrossRef]
  16. U. Schnars and W. Jueptner, Digital Holography (Springer, 2005).
  17. G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Laser Eng. 43, 1039–1055 (2005).
    [CrossRef]
  18. J. Watson, “Submersible digital holographic cameras and their application to marine science,” Opt. Eng. 50, 091313 (2011).
    [CrossRef]
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2012 (1)

K. Körner, G. Pedrini, I. Alexeenko, T. Steinmetz, R. Holzwarth, and W. Osten, “Short temporal coherence digital holography with a femtosecond frequency comb laser for multi-level optical sectioning,” Opt. Express 20, 3977–3984 (2012).
[CrossRef]

2011 (5)

2008 (1)

S. Stürwald, B. Kemper, C. Remmersmann, P. Langehanenberg, and G. von Bally, “Application of light emitting diodes in digital holographic microscopy,” Proc. SPIE 6995, 699507 (2008).
[CrossRef]

2007 (1)

2006 (1)

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

2005 (2)

L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt. 44, 3977–3984 (2005).
[CrossRef]

G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Laser Eng. 43, 1039–1055 (2005).
[CrossRef]

2004 (1)

2003 (1)

1997 (1)

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

1994 (2)

1971 (1)

S. Mallick and M. L. Robin, “Fourier transform holography using a quasimonochromatic incoherent source,” Appl. Opt. 10, 580–596 (1971).
[CrossRef]

1967 (1)

Alexeenko, I.

K. Körner, G. Pedrini, I. Alexeenko, T. Steinmetz, R. Holzwarth, and W. Osten, “Short temporal coherence digital holography with a femtosecond frequency comb laser for multi-level optical sectioning,” Opt. Express 20, 3977–3984 (2012).
[CrossRef]

Bertoletti, M.

Bryanston-Cross, P.

Charriere, F.

Claus, D.

Colomb, T.

Cuche, E.

Demoli, N.

Depeursinge, C.

Dubois, F.

Emery, Y.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, 1996).

Gori, F.

Guattari, G.

Haist, T.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical Holography (Cambridge University, 1984).

Holzwarth, R.

K. Körner, G. Pedrini, I. Alexeenko, T. Steinmetz, R. Holzwarth, and W. Osten, “Short temporal coherence digital holography with a femtosecond frequency comb laser for multi-level optical sectioning,” Opt. Express 20, 3977–3984 (2012).
[CrossRef]

Iliescu, D.

Istasse, E.

Jueptner, W.

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

Jüptner, W. P. O.

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Kemper, B.

S. Stürwald, B. Kemper, C. Remmersmann, P. Langehanenberg, and G. von Bally, “Application of light emitting diodes in digital holographic microscopy,” Proc. SPIE 6995, 699507 (2008).
[CrossRef]

Körner, K.

K. Körner, G. Pedrini, I. Alexeenko, T. Steinmetz, R. Holzwarth, and W. Osten, “Short temporal coherence digital holography with a femtosecond frequency comb laser for multi-level optical sectioning,” Opt. Express 20, 3977–3984 (2012).
[CrossRef]

Kreis, T. M.

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

Kühn, J.

Langehanenberg, P.

S. Stürwald, B. Kemper, C. Remmersmann, P. Langehanenberg, and G. von Bally, “Application of light emitting diodes in digital holographic microscopy,” Proc. SPIE 6995, 699507 (2008).
[CrossRef]

Leith, E. N.

Ma, J.

Mallick, S.

S. Mallick and M. L. Robin, “Fourier transform holography using a quasimonochromatic incoherent source,” Appl. Opt. 10, 580–596 (1971).
[CrossRef]

Marquet, P.

Martínez-León, L.

Meštrovic, J.

Minetti, C.

Monemhaghdoust, Z.

Monnom, O.

Montfort, F.

Moser, C.

Novella Requena, M.-L.

Osten, W.

K. Körner, G. Pedrini, I. Alexeenko, T. Steinmetz, R. Holzwarth, and W. Osten, “Short temporal coherence digital holography with a femtosecond frequency comb laser for multi-level optical sectioning,” Opt. Express 20, 3977–3984 (2012).
[CrossRef]

C. Yuanl, G. Situ, G. Pedrini, J. Ma, and W. Osten, “Resolution improvement in digital holography by angular and polarization multiplexing,” Appl. Opt. 50, B6–B11 (2011).
[CrossRef]

L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt. 44, 3977–3984 (2005).
[CrossRef]

Pedrini, G.

K. Körner, G. Pedrini, I. Alexeenko, T. Steinmetz, R. Holzwarth, and W. Osten, “Short temporal coherence digital holography with a femtosecond frequency comb laser for multi-level optical sectioning,” Opt. Express 20, 3977–3984 (2012).
[CrossRef]

C. Yuanl, G. Situ, G. Pedrini, J. Ma, and W. Osten, “Resolution improvement in digital holography by angular and polarization multiplexing,” Appl. Opt. 50, B6–B11 (2011).
[CrossRef]

L. Martínez-León, G. Pedrini, and W. Osten, “Applications of short-coherence digital holography in microscopy,” Appl. Opt. 44, 3977–3984 (2005).
[CrossRef]

Reicherter, M.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

Remmersmann, C.

S. Stürwald, B. Kemper, C. Remmersmann, P. Langehanenberg, and G. von Bally, “Application of light emitting diodes in digital holographic microscopy,” Proc. SPIE 6995, 699507 (2008).
[CrossRef]

Robin, M. L.

S. Mallick and M. L. Robin, “Fourier transform holography using a quasimonochromatic incoherent source,” Appl. Opt. 10, 580–596 (1971).
[CrossRef]

Rodenburg, J. M.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), p. 351.

Schnars, U.

Seifert, L.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

Shen, G.

G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Laser Eng. 43, 1039–1055 (2005).
[CrossRef]

Situ, G.

Sovic, I.

Steinmetz, T.

K. Körner, G. Pedrini, I. Alexeenko, T. Steinmetz, R. Holzwarth, and W. Osten, “Short temporal coherence digital holography with a femtosecond frequency comb laser for multi-level optical sectioning,” Opt. Express 20, 3977–3984 (2012).
[CrossRef]

Stürwald, S.

S. Stürwald, B. Kemper, C. Remmersmann, P. Langehanenberg, and G. von Bally, “Application of light emitting diodes in digital holographic microscopy,” Proc. SPIE 6995, 699507 (2008).
[CrossRef]

Sun, P.-C.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), p. 351.

von Bally, G.

S. Stürwald, B. Kemper, C. Remmersmann, P. Langehanenberg, and G. von Bally, “Application of light emitting diodes in digital holographic microscopy,” Proc. SPIE 6995, 699507 (2008).
[CrossRef]

Watson, J.

D. Claus, J. Watson, and J. M. Rodenburg, “Analysis and interpretation of the Seidel aberration coefficients in digital holography,” Appl. Opt. 50, H220–H229 (2011).
[CrossRef]

J. Watson, “Submersible digital holographic cameras and their application to marine science,” Opt. Eng. 50, 091313 (2011).
[CrossRef]

Wei, R.

G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Laser Eng. 43, 1039–1055 (2005).
[CrossRef]

Wu, M.

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

Yuanl, C.

Zeidler, E.

E. Zeidler, Teubner-Taschenbuch der Mathematik (B. G. Teubner,1996).

Appl. Opt. (8)

Comput. Sci. Eng. (1)

T. Haist, M. Reicherter, M. Wu, and L. Seifert, “Using graphics boards to compute holograms,” Comput. Sci. Eng. 8, 8–13 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

J. Watson, “Submersible digital holographic cameras and their application to marine science,” Opt. Eng. 50, 091313 (2011).
[CrossRef]

Opt. Express (3)

Opt. Laser Eng. (1)

G. Shen and R. Wei, “Digital holography particle image velocimetry for the measurement of 3Dt-3c flows,” Opt. Laser Eng. 43, 1039–1055 (2005).
[CrossRef]

Proc. SPIE (1)

S. Stürwald, B. Kemper, C. Remmersmann, P. Langehanenberg, and G. von Bally, “Application of light emitting diodes in digital holographic microscopy,” Proc. SPIE 6995, 699507 (2008).
[CrossRef]

Other (6)

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

E. Zeidler, Teubner-Taschenbuch der Mathematik (B. G. Teubner,1996).

P. Hariharan, Optical Holography (Cambridge University, 1984).

J. W. Goodman, Introduction to Fourier Optics2nd ed. (McGraw-Hill, 1996).

T. Goulette, D. H. Charles, and M. W. Davidson, “Infinity optical systems,” Nikon MicroscopyU, http://www.microscopyu.com/articles/optics/cfintro.html.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991), p. 351.

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Figures (9)

Fig. 1.
Fig. 1.

Nomenclature of coordinates and projection of most extremely located three-dimensional object point onto the x axis.

Fig. 2.
Fig. 2.

Graphical representation of required lateral coherence length ΔLlat resulting from maximum object extent and inclination angle of reference wave.

Fig. 3.
Fig. 3.

Graphical representation of Fourier holographic setup (black line-object wave, gray line-reference wave).

Fig. 4.
Fig. 4.

Graphical representation of a lens-based Fourier hologram, black object wave, gray reference wave, and ε diffraction angle. α is the reference wave angle.

Fig. 5.
Fig. 5.

Graphical representation of lens-based Fourier hologram with object places between lens and hologram.

Fig. 6.
Fig. 6.

Required coherence length for Fresnel hologram, lensless Fourier hologram and the two lens-based Fourier holograms in in-line and off-axis arrangment (calculated with typical values for N=1000, Δx=10μm, λ=500nm and X=10mm). The first lens-based Fourier hologram requires a much smaller coherence length in in-line and off-axis arrangment.

Fig. 7.
Fig. 7.

Graphical representation of an image-plane hologram interfering with a plane reference wave (black line-object wave, gray line-reference wave).

Fig. 8.
Fig. 8.

Required coherence length for image-plane holograms with plane reference wave and spherical reference wave for (a) in-line and (b) off-axis geometry (N=1000, Δx=10μm, λ=500nm and D=10mm).

Fig. 9.
Fig. 9.

Coherence length ΔLlong+ΔLlat versus spectral width ΔλFWHM; the larger the required coherence length the smaller the required spectral width.

Equations (53)

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u(x)=exp(ikd)iλdu(x)exp[iπλd((xx)2+(yy)2)]dxdy,
Δφlong=2πλ(d2d1),
ΔLlong=Δφlongλ2π=d2d1.
u0(x)=A0exp[iπλd(xx0)2].
ur(x)=Arexp(i2πvrx),
I(x)=A02+Ar2+2A0Arcos[πλd(xx0)2+2πvrx].
φ=πλd(lΔx+xmax)2+2πvrlΔx,
ΔφΔl=πλd2(lΔx+xmax)Δx+2πvrΔx.
Δφ=2πNΔxλd(NΔx2+xmax)=πNΔxλd(NΔx+X).
ΔLlat=Δφλ2π=NΔx2d(NΔx+X).
ΔLlat=2L1withtanβ=X2d=2L1NΔxΔLc=NΔxX2d.
Δφ=2πNΔx(Δx+xmaxλd+vr).
ΔLlat=Δφλ2π=NΔx2d(2Δx+X).
dmin=(X+NΔx)Δxλ.
ΔLlat=Nλ(2Δx+X)2(X+NΔx).
ΔLlat=NΔx2d(2Δx+2X+NΔx).
dmin=2(X+NΔx)Δxλ,
ΔLlat=Nλ(2Δx+2X+NΔx)4(X+NΔx).
ur(x)=Arexp[iπλdr(xxr)2],
φ=πλd[2x(xrx0)+x02xr2]=πλd[2lΔx(xrx0)+x02xr2].
Δφ=2πNΔxλd(xr+xmax).
dmin=XΔxλ,
ΔLlat=NΔxX2d=Nλ2.
ΔLlat=NΔxXd=Nλ2,
dmin=2XΔxλ.
u(x˜)=u(x)exp[iπλd1(x˜x)2]dx.
u(x)=u(x˜)exp(iπλfx˜2)exp[iπλd1(xx˜)2]dx˜=exp(iπλdx2)u(x)exp[iπλd1(x˜x)2]dx[iπλx˜2(1d21f)]exp(i2πλd2x˜x)dx˜.
F{exp(x24a)}=2aexp(aω2),
u(x)=exp(iπλfx2)F{u(x)}exp(iπd1λf2x2)=F{u(x)}.
φ=2πx(ν0+νr),
ν0=ω2π=xλf;andνr=sinαλν0.
Δφ={4πΔx2lλfΔlforin-line8πΔx2lλfΔlforoff-axis.
fmin{2NΔx2λforin-line4NΔx2λforoff-axis.
ΔLlat=λ.
u(x)=exp(iπλfx˜2)exp[iπλd1(xx˜)2]dx˜=exp(iπλd1x2)exp[iπλx˜2(1d11f)]exp(i2πλd1xx˜)dx˜.
u(x)=u(x)A(x)exp[iπλd2(xx)2]dx,
u(x)=exp(iπλd2x2)exp[iπλ(d1f)x2]A(x)exp(iπλd2x2)exp(i2πλd2xx)dx=exp(iπλd2x2)A(x)exp[iπλx2(d2+d1f(d1f)d2)]exp(i2πλd2xx)dx.
φ=2πxν0+πλdr(2xxrxr2)=2πλd2x2+πλdr(2xxrxr2).
d2min{2NΔx2λforin-lineNΔx2λ(2+N)foroff-axis,
ΔLlat={2NΔx2d2=λforin-lineNΔx2d2(2+N)=λforoff-axis
u(x)=u(xβ)exp(iπx2λd2)exp(iπx02λd1).
ur(x)=Arexp[iπλd2(xxr)2].
φ=πλ[(2xxrxr2)d2+x02d1]=πλd2[(2xxr+x2β)xr2].
Δφ=2πΔxλd2[xr+Δxlβ]Δl.
ΔLlat=NΔxd2(xr+Δxβ).
d2min={NΔx2βλforin-line2Δxλ(xr+NΔx2β)foroff-axis.
ΔLlat=NΔx2d2β=λ.
ΔLlat=NΔx(2Δx+Dβ)2βd2=Nλ(2Δx+Dβ)2(NΔx+Dβ).
φ=πx2λd2(β+1β)+2πxνr=πΔx2l2λd2(β+1β)+πΔxlD+NΔxλd2.
Δφ=[2πΔx2lλβd2(β+1)+πΔxλd2(D+NΔx)]Δl.
d2min={NΔx2λβ(β+1)forin-lineΔxλβ[NΔx(2β+1)+Dβ]foroff-axis,
ΔLlat={NΔx2d2β(β+1)=λforin-lineNλ[2Δx(β+1)+β(D+NΔx)][NΔx(2β+1)+Dβ]foroff-axis.
ΔLlong+ΔLlat={λ20.66ΔλFWHM;Gaussianλ20.32ΔλFWHM;Lorentzianλ2ΔλFWHM;Rectangular.

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