Abstract

The transport-of-intensity equation (TIE) is applied in the reconstruction of two interfering wavefronts by analyzing the interference patterns and their derivatives along their common propagation directions. The TIE is extended from one wave to two waves and is then applied to calculate the phase of the interference field. Finally, the phase shift concept is applied to reconstruct the phase distribution of two waves. The consistency of the method is verified by simulation.

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2014 (1)

2012 (1)

R. Shomali, A. Darudi, and S. Nasiri, Optik 123, 1282 (2012).
[CrossRef]

2011 (1)

2008 (1)

A. Darudi, R. Shomali, and M. T. Tavassoly, Opt. Laser Technol. 40, 850 (2008).
[CrossRef]

2007 (1)

2006 (1)

2005 (2)

V. Orlav, E. Luna, and E. Orlova, Appl. Opt. 44, 5169 (2005).
[CrossRef]

K. Ishizuka and B. Allman, J. Electron Microsc. 54, 191 (2005).
[CrossRef]

2002 (1)

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).
[CrossRef]

2000 (2)

M. T. Tavassoly and A. Darudi, Opt. Commun. 175, 43 (2000).
[CrossRef]

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef]

1998 (1)

1996 (2)

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef]

T. E. Gureyev and K. A. Nugent, J. Opt. Soc. Am. A 13, 1670 (1996).
[CrossRef]

1991 (1)

1988 (1)

1984 (1)

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

1983 (1)

1982 (1)

Akhlaghi, E. A.

Allman, B.

K. Ishizuka and B. Allman, J. Electron Microsc. 54, 191 (2005).
[CrossRef]

Arjona, M.

Bajt, S.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef]

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef]

Barty, A.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
[CrossRef]

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef]

Darudi, A.

R. Shomali, A. Darudi, and S. Nasiri, Optik 123, 1282 (2012).
[CrossRef]

E. A. Akhlaghi, A. Darudi, and M. T. Tavassoly, Opt. Express 19, 15976 (2011).
[CrossRef]

A. Darudi, R. Shomali, and M. T. Tavassoly, Opt. Laser Technol. 40, 850 (2008).
[CrossRef]

M. T. Tavassoly and A. Darudi, Opt. Commun. 175, 43 (2000).
[CrossRef]

De Graef, M.

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).
[CrossRef]

Diaz-Douton, F.

Dorrer, C.

Fallah, H. R.

Gureyev, T. E.

T. E. Gureyev and K. A. Nugent, J. Opt. Soc. Am. A 13, 1670 (1996).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef]

Hajimahmoodzadeh, M.

Ichikawa, K.

Ishizuka, K.

K. Ishizuka and B. Allman, J. Electron Microsc. 54, 191 (2005).
[CrossRef]

Lohmann, A. W.

Luna, E.

Luque, S. O.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 2007), Vol. 3.

McCartney, M.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef]

Nasiri, S.

R. Shomali, A. Darudi, and S. Nasiri, Optik 123, 1282 (2012).
[CrossRef]

Nugent, K. A.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef]

T. E. Gureyev and K. A. Nugent, J. Opt. Soc. Am. A 13, 1670 (1996).
[CrossRef]

Orlav, V.

Orlova, E.

Paganin, D.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef]

Pujol, J.

Roberts, A.

Roddier, C.

Roddier, F.

Shomali, R.

R. Shomali, A. Darudi, and S. Nasiri, Optik 123, 1282 (2012).
[CrossRef]

A. Darudi, R. Shomali, and M. T. Tavassoly, Opt. Laser Technol. 40, 850 (2008).
[CrossRef]

Streibl, N.

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

Takeda, M.

Tavassoly, M. T.

E. A. Akhlaghi, A. Darudi, and M. T. Tavassoly, Opt. Express 19, 15976 (2011).
[CrossRef]

A. Darudi, R. Shomali, and M. T. Tavassoly, Opt. Laser Technol. 40, 850 (2008).
[CrossRef]

M. T. Tavassoly and A. Darudi, Opt. Commun. 175, 43 (2000).
[CrossRef]

Teague, M. R.

Volkov, V. V.

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).
[CrossRef]

Wall, M.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef]

Yazdani, R.

Zhu, Y.

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).
[CrossRef]

Zuegel, J. D.

Appl. Opt. (3)

J. Electron Microsc. (1)

K. Ishizuka and B. Allman, J. Electron Microsc. 54, 191 (2005).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Micron (1)

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).
[CrossRef]

Opt. Commun. (2)

M. T. Tavassoly and A. Darudi, Opt. Commun. 175, 43 (2000).
[CrossRef]

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

Opt. Express (2)

Opt. Laser Technol. (1)

A. Darudi, R. Shomali, and M. T. Tavassoly, Opt. Laser Technol. 40, 850 (2008).
[CrossRef]

Opt. Lett. (3)

Optik (1)

R. Shomali, A. Darudi, and S. Nasiri, Optik 123, 1282 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, Phys. Rev. Lett. 77, 2961 (1996).
[CrossRef]

Ultramicroscopy (1)

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicroscopy 83, 67 (2000).
[CrossRef]

Other (1)

D. Malacara, Optical Shop Testing (Wiley, 2007), Vol. 3.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Phase distributions for Φ1 and (b) Φ2.

Fig. 2.
Fig. 2.

(a) Simulated IIP and (b) simulated PIF.

Fig. 3.
Fig. 3.

Simulated derivative of the IIP with respect to z for Δz=5mm.

Fig. 4.
Fig. 4.

Dotted and solid lines indicate the simulated and calculated PIFs, respectively; the profiles are taken from row #35 of their corresponding matrices.

Fig. 5.
Fig. 5.

(a) Profiles of the IIPs in arbitrary units (A.U.) are given for four phase shifts and (b) the corresponding derivatives of the IIPs with respect to z.

Fig. 6.
Fig. 6.

(a) Profiles of the calculated PIFs and (b) the error of the reconstructed phase distributions.

Equations (26)

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U=U1+U2=Iexp(iθ),
Ui(x,y,z)=Ii(x,y,z)exp[iΦi(x,y,z)],i=1,2,
I=I1+I2+2I1I2cos(Φ2Φ1),
tan(θ)=asin(Φ1)+sin(Φ2)acos(Φ1)+cos(Φ2),
a=I1I2.
.(IiΦi)=0,i=1,2.
.(IiΦi)=kIiz,i=1,2,
=xi^+yj^
.(Iθ)=kIz.
j,kθ˜j,kSm,nj,k=abF˜m,n.
θ˜j,k=1MNp,qM,Nθ(p,q)exp(i2πpjM)exp(i2πqkN),
F˜m,n=1MNu,vM,NkIz(u,v)exp(i2πumM)exp(i2πvnN),
Sm,nj,k=(2π)2(jmba+knab)I˜mj,nk,
I˜mj,nk=1MNlfMNI(l,f)exp(i2πl(mj)M)exp(i2πf(nk)N).
θ˜j,k=abm,n[Sm,nj,k]1F˜m,n.
tan(θn)=asin(Φ1)+sin(Φ2+δn)acos(Φ1)+cos(Φ2+δn).
b+c=T1d+T1e,
b+e=T2d+T2c,
bc=T3d+T3e,
be=T4d+T4c,
b=asin(Φ1),c=sin(Φ2),d=acos(Φ1),e=cos(Φ2),T1=tan(θ1),T2=tan(θ2),T3=tan(θ3),T4=tan(θ4).
Φ2=arctan(T3M1T1+T1M112M1+T21),
Φ1=arctan(T1+T3[M2(T2+T4)]/tan(Φ2)22M2/tan(Φ2)),
M1=T1T2T1T3,M2=T1T3T4T2.
I±Δz=I|Δz|k.(Iθ),
IzI+ΔzIΔz2Δz.

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