Abstract

A holographic wavefront sensor based on the Talbot effect is proposed. Optical wavefronts are measured by sampling the light amplitude distribution with a two-dimensional (2D) precorrected holographic grating. The factors that allow changing an angular measurement range and a spatial resolution of the sensor are discussed. A comparative analysis with the Shack–Hartmann sensor is illustrated with some experimental results.

© 2012 Optical Society of America

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References

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  1. D. Podanchuk, V. Kurashov, A. Kovalenko, V. Dan’ko, and A. Yurchenko, “Measurement of light-phase distortions in an acousto-optical deflector with Shack–Hartmann wavefront sensor,” Proc. SPIE 3904, 311–318 (1999).
    [CrossRef]
  2. A. A. Goloborodko, V. I. Grygoruk, V. N. Kurashov, D. V. Podanchuk, and N. S. Sutyagina, “Determination of local surface defects using a Shack–Hartmann wavefront sensor,” Ukr. J. Phys. 53, 946–951 (2008).
  3. V. Molebny, V. Kurashov, D. Podanchuk, A. Kovalenko, I. Pallikaris, and L. Naoumidis, “Aberration mapping for sight correction,” Proc. SPIE 3246, 238–247 (1998).
    [CrossRef]
  4. D. M. Alloin and J.-M. Mariotti, eds., Adaptive Optics for Astronomy (Cambridge University, 2004).
  5. A. Koryakovskiy and V. Marchenko, “Wavefront detector based on the Talbot effect,” Sov. J. Tech. Phys. 26, 821–825 (1981).
  6. V. V. Lobachev and V. A. Sokolov, “Amplitude–phase light field detector based on the Talbot effect,” Opt. Spectrosc. 81, 107–113 (1996).
  7. N. Salama, D. Patrignani, L. De Pasquale, and E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
    [CrossRef]
  8. P. Zhou and J. H. Burge, “Analysis of wavefront propagation using the Talbot effect,” Appl. Opt. 49, 5351–5359 (2010).
    [CrossRef]
  9. C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
    [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

2010

2008

A. A. Goloborodko, V. I. Grygoruk, V. N. Kurashov, D. V. Podanchuk, and N. S. Sutyagina, “Determination of local surface defects using a Shack–Hartmann wavefront sensor,” Ukr. J. Phys. 53, 946–951 (2008).

2001

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

1999

N. Salama, D. Patrignani, L. De Pasquale, and E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

D. Podanchuk, V. Kurashov, A. Kovalenko, V. Dan’ko, and A. Yurchenko, “Measurement of light-phase distortions in an acousto-optical deflector with Shack–Hartmann wavefront sensor,” Proc. SPIE 3904, 311–318 (1999).
[CrossRef]

1998

V. Molebny, V. Kurashov, D. Podanchuk, A. Kovalenko, I. Pallikaris, and L. Naoumidis, “Aberration mapping for sight correction,” Proc. SPIE 3246, 238–247 (1998).
[CrossRef]

1996

V. V. Lobachev and V. A. Sokolov, “Amplitude–phase light field detector based on the Talbot effect,” Opt. Spectrosc. 81, 107–113 (1996).

1981

A. Koryakovskiy and V. Marchenko, “Wavefront detector based on the Talbot effect,” Sov. J. Tech. Phys. 26, 821–825 (1981).

Balmer, J. E.

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Burge, J. H.

Dan’ko, V.

D. Podanchuk, V. Kurashov, A. Kovalenko, V. Dan’ko, and A. Yurchenko, “Measurement of light-phase distortions in an acousto-optical deflector with Shack–Hartmann wavefront sensor,” Proc. SPIE 3904, 311–318 (1999).
[CrossRef]

De Pasquale, L.

N. Salama, D. Patrignani, L. De Pasquale, and E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Goloborodko, A. A.

A. A. Goloborodko, V. I. Grygoruk, V. N. Kurashov, D. V. Podanchuk, and N. S. Sutyagina, “Determination of local surface defects using a Shack–Hartmann wavefront sensor,” Ukr. J. Phys. 53, 946–951 (2008).

Goodman, J. W.

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

Grygoruk, V. I.

A. A. Goloborodko, V. I. Grygoruk, V. N. Kurashov, D. V. Podanchuk, and N. S. Sutyagina, “Determination of local surface defects using a Shack–Hartmann wavefront sensor,” Ukr. J. Phys. 53, 946–951 (2008).

Koryakovskiy, A.

A. Koryakovskiy and V. Marchenko, “Wavefront detector based on the Talbot effect,” Sov. J. Tech. Phys. 26, 821–825 (1981).

Kovalenko, A.

D. Podanchuk, V. Kurashov, A. Kovalenko, V. Dan’ko, and A. Yurchenko, “Measurement of light-phase distortions in an acousto-optical deflector with Shack–Hartmann wavefront sensor,” Proc. SPIE 3904, 311–318 (1999).
[CrossRef]

V. Molebny, V. Kurashov, D. Podanchuk, A. Kovalenko, I. Pallikaris, and L. Naoumidis, “Aberration mapping for sight correction,” Proc. SPIE 3246, 238–247 (1998).
[CrossRef]

Kurashov, V.

D. Podanchuk, V. Kurashov, A. Kovalenko, V. Dan’ko, and A. Yurchenko, “Measurement of light-phase distortions in an acousto-optical deflector with Shack–Hartmann wavefront sensor,” Proc. SPIE 3904, 311–318 (1999).
[CrossRef]

V. Molebny, V. Kurashov, D. Podanchuk, A. Kovalenko, I. Pallikaris, and L. Naoumidis, “Aberration mapping for sight correction,” Proc. SPIE 3246, 238–247 (1998).
[CrossRef]

Kurashov, V. N.

A. A. Goloborodko, V. I. Grygoruk, V. N. Kurashov, D. V. Podanchuk, and N. S. Sutyagina, “Determination of local surface defects using a Shack–Hartmann wavefront sensor,” Ukr. J. Phys. 53, 946–951 (2008).

Lobachev, V. V.

V. V. Lobachev and V. A. Sokolov, “Amplitude–phase light field detector based on the Talbot effect,” Opt. Spectrosc. 81, 107–113 (1996).

Loewenthal, F.

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Marchenko, V.

A. Koryakovskiy and V. Marchenko, “Wavefront detector based on the Talbot effect,” Sov. J. Tech. Phys. 26, 821–825 (1981).

Molebny, V.

V. Molebny, V. Kurashov, D. Podanchuk, A. Kovalenko, I. Pallikaris, and L. Naoumidis, “Aberration mapping for sight correction,” Proc. SPIE 3246, 238–247 (1998).
[CrossRef]

Naoumidis, L.

V. Molebny, V. Kurashov, D. Podanchuk, A. Kovalenko, I. Pallikaris, and L. Naoumidis, “Aberration mapping for sight correction,” Proc. SPIE 3246, 238–247 (1998).
[CrossRef]

Pallikaris, I.

V. Molebny, V. Kurashov, D. Podanchuk, A. Kovalenko, I. Pallikaris, and L. Naoumidis, “Aberration mapping for sight correction,” Proc. SPIE 3246, 238–247 (1998).
[CrossRef]

Patrignani, D.

N. Salama, D. Patrignani, L. De Pasquale, and E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Podanchuk, D.

D. Podanchuk, V. Kurashov, A. Kovalenko, V. Dan’ko, and A. Yurchenko, “Measurement of light-phase distortions in an acousto-optical deflector with Shack–Hartmann wavefront sensor,” Proc. SPIE 3904, 311–318 (1999).
[CrossRef]

V. Molebny, V. Kurashov, D. Podanchuk, A. Kovalenko, I. Pallikaris, and L. Naoumidis, “Aberration mapping for sight correction,” Proc. SPIE 3246, 238–247 (1998).
[CrossRef]

Podanchuk, D. V.

A. A. Goloborodko, V. I. Grygoruk, V. N. Kurashov, D. V. Podanchuk, and N. S. Sutyagina, “Determination of local surface defects using a Shack–Hartmann wavefront sensor,” Ukr. J. Phys. 53, 946–951 (2008).

Salama, N.

N. Salama, D. Patrignani, L. De Pasquale, and E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Sicre, E.

N. Salama, D. Patrignani, L. De Pasquale, and E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Siegel, C.

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Sokolov, V. A.

V. V. Lobachev and V. A. Sokolov, “Amplitude–phase light field detector based on the Talbot effect,” Opt. Spectrosc. 81, 107–113 (1996).

Sutyagina, N. S.

A. A. Goloborodko, V. I. Grygoruk, V. N. Kurashov, D. V. Podanchuk, and N. S. Sutyagina, “Determination of local surface defects using a Shack–Hartmann wavefront sensor,” Ukr. J. Phys. 53, 946–951 (2008).

Yurchenko, A.

D. Podanchuk, V. Kurashov, A. Kovalenko, V. Dan’ko, and A. Yurchenko, “Measurement of light-phase distortions in an acousto-optical deflector with Shack–Hartmann wavefront sensor,” Proc. SPIE 3904, 311–318 (1999).
[CrossRef]

Zhou, P.

Appl. Opt.

Opt. Commun.

C. Siegel, F. Loewenthal, and J. E. Balmer, “A wavefront sensor based on the fractional Talbot effect,” Opt. Commun. 194, 265–275 (2001).
[CrossRef]

Opt. Laser Technol.

N. Salama, D. Patrignani, L. De Pasquale, and E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31, 269–272 (1999).
[CrossRef]

Opt. Spectrosc.

V. V. Lobachev and V. A. Sokolov, “Amplitude–phase light field detector based on the Talbot effect,” Opt. Spectrosc. 81, 107–113 (1996).

Proc. SPIE

D. Podanchuk, V. Kurashov, A. Kovalenko, V. Dan’ko, and A. Yurchenko, “Measurement of light-phase distortions in an acousto-optical deflector with Shack–Hartmann wavefront sensor,” Proc. SPIE 3904, 311–318 (1999).
[CrossRef]

V. Molebny, V. Kurashov, D. Podanchuk, A. Kovalenko, I. Pallikaris, and L. Naoumidis, “Aberration mapping for sight correction,” Proc. SPIE 3246, 238–247 (1998).
[CrossRef]

Sov. J. Tech. Phys.

A. Koryakovskiy and V. Marchenko, “Wavefront detector based on the Talbot effect,” Sov. J. Tech. Phys. 26, 821–825 (1981).

Ukr. J. Phys.

A. A. Goloborodko, V. I. Grygoruk, V. N. Kurashov, D. V. Podanchuk, and N. S. Sutyagina, “Determination of local surface defects using a Shack–Hartmann wavefront sensor,” Ukr. J. Phys. 53, 946–951 (2008).

Other

D. M. Alloin and J.-M. Mariotti, eds., Adaptive Optics for Astronomy (Cambridge University, 2004).

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

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Figures (10)

Fig. 1.
Fig. 1.

Experimental setup for testing the sensor based on Talbot effect.

Fig. 2.
Fig. 2.

(a) Calculated and (b) experimental intensity distribution on the grating image. The grating is limited by 13×13 periods and has the period d=200μm and sub-aperture diameter b=75μm. Dotted lines show the borders of original grating.

Fig. 3.
Fig. 3.

One-dimensional intensity distribution in the Talbot plane for gratings with different aperture size: 4, 8 and 12 periods (d=200μm, b=75μm).

Fig. 4.
Fig. 4.

The dependence of curvature of test spherical wave upon the shift of the mirror M3 from focus of the lens L5 measured by the Shack–Hartmann sensor (a) and sensor based on Talbot effect with different periodic gratings: (b) d=100μm, b=50μm; (c) d=150μm, b=75μm; (d) d=200μm, b=100μm; (e) d=200μm, b=75μm.

Fig. 5.
Fig. 5.

The image patches obtained with spherical wave front (R=1m) for different diffraction gratings: (a) d=150μm, b=75μm; (b) d=200μm, b=75μm.

Fig. 6.
Fig. 6.

Enlarged sub-areas of the hartmannogram (a) and image of the grating with d=200μm, b=75μm at planes of ZT (b) and 1.5ZT (c).

Fig. 7.
Fig. 7.

Joint hartmannogram (a), grating images (b, c, d) and corresponding reconstructed phase maps (eh) at different image planes: f=24mm (a, e); Z=ZT=127mm (b, g), Z=1.5ZT=190mm (c, g), Z=2ZT=254mm (d, h).

Fig. 8.
Fig. 8.

The Zernike coefficients for the wavefront reconstruction with the Shack–Hartmann sensor (a) and sensor based on Talbot effect (grating with d=200μm, b=75μm) for the different grating image planes: Z=ZT=127mm (b), Z=1.5ZT=190mm (c), Z=2ZT=254mm (d).

Fig. 9.
Fig. 9.

(a) Intensity distribution in the Talbot plane for a plane incident wave; (b) synthesized interferogram of the trefoil aberration; (c) intensity distribution in the Talbot plane for the wave front aberrated by trefoil.

Fig. 10.
Fig. 10.

(a) Phase map and (b) interferogram of the spherical wave front reconstructed from data of holographic Talbot sensor measurements with aberration precompensation (the contour lines on the phase map are plotted with 0.1λ interval); (c) synthesized interferogram of the spherical wavefront that added to the trefoil aberration when SDOE was recorded.

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

U(x,y)=++U0(ξ,η)h(xξ,yη)dξdη,
h(x,y)=exp[ikz]iλzexp[ik2z(x2+y2)].
U0(ξ,η)=P(ξ,η)·S(ξ,η),
P(ξ,η)=A(ξ,η)·U0·exp[iφ(ξ,η)],
A(ξ,η)={1,ξ,ησ0,if other.
S(ξ,η)=n=m=CnCmexp[i2π(nξ+mη)d].
U(x,y)=U(x)U(y)=+U0(ξ)h(xξ)dξ+U0(η)h(yη)dη,
h(x)=1iλzexp[ik2z(x2+z2)].
U(x)=Φ(x,z)n=CnP˜(ω)*T˜n(ω),
T˜n(ω)=F^{exp[i(2πnξd+kξ22z)];ω};
exp[i(Ω2ξ2+ωξ)]dξ=2πiΩexp[iω24Ω2],
T˜n(ω)=2iλzexp[i(ω24Ω2πnωdΩ2+2π2n2zkd2)],
T˜n(ω)=2iλzexp[i(ω24Ω2πnωdΩ2)],
U(x)=Ψ(x,ZT)P˜(ω)*(exp[iω24Ω2]S(ω/2Ω2)).
U(x)S(x).
U(x)S(x+zTsinθ).
zT=zTRRzT,
d=d(1zTR).
P(ξ)={1,|ξ|σ0,|ξ|>σ,
P˜(ω)=2σsinc(ωσ).
S(ξ)=n=+δ(ξnd).
U(x)n=+exp[ik2zT(x+nd)2]sinc(kzT(x+nd)σ).
U(x)n=0Nexp[iπ(2nN)d(6ndz3Ndz+4xR)2Rλz]sinc(π(2RxdzT(2nN))b2RzTNλ),
U(x)sin(2πx(N+1)dλzT)sin(2πxdλzT)sinc(πxbNλzT).
θλ4ld.

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