Abstract

We propose to add a specific phase chessboard to the classical Hartmann mask used for wave-front sensing. By doing this we obtain a pseudoguiding of the energy issuing from this mask, allowing for an increase in the sensitivity of the Hartmann test. This property is illustrated by experiment, and a comparison between classical and new Hartmanngrams is presented.

© 2000 Optical Society of America

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References

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  1. I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.
  2. A. Zverev, S. A. Rodioniv, M. N. Sokolskii, V. V. Usoskin, “Mathematical principles of Hartmann test of the primary mirror of the Large Azimuthal Telescope,” Sov. J. Opt. Technol. 44, 78–81 (1977).
  3. F. Roddier, “Variations on a Hartmann theme,” Opt. Eng. 29, 1239–1242 (1990).
    [CrossRef]
  4. R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen (abstract),” J. Opt. Soc. Am. 61, 656 (1971).
  5. F. Merkle, “Adaptive optics,” in International Trends in Optics (Academic, New York, 1991).
    [CrossRef]
  6. J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
    [CrossRef]
  7. F. Talbot, “Facts relating to optical science. IV,” Philos. Mag. 9, 401–407 (1836).
  8. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 1–108.
    [CrossRef]
  9. R. F. Edgar, “The Fresnel diffraction images of periodic structures,” Opt. Acta 16, 281–287 (1969).
    [CrossRef]

1990

F. Roddier, “Variations on a Hartmann theme,” Opt. Eng. 29, 1239–1242 (1990).
[CrossRef]

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
[CrossRef]

1977

A. Zverev, S. A. Rodioniv, M. N. Sokolskii, V. V. Usoskin, “Mathematical principles of Hartmann test of the primary mirror of the Large Azimuthal Telescope,” Sov. J. Opt. Technol. 44, 78–81 (1977).

1971

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen (abstract),” J. Opt. Soc. Am. 61, 656 (1971).

1969

R. F. Edgar, “The Fresnel diffraction images of periodic structures,” Opt. Acta 16, 281–287 (1969).
[CrossRef]

1836

F. Talbot, “Facts relating to optical science. IV,” Philos. Mag. 9, 401–407 (1836).

Edgar, R. F.

R. F. Edgar, “The Fresnel diffraction images of periodic structures,” Opt. Acta 16, 281–287 (1969).
[CrossRef]

Fontanella, J. C.

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
[CrossRef]

Ghozeil, I.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.

Merkle, F.

F. Merkle, “Adaptive optics,” in International Trends in Optics (Academic, New York, 1991).
[CrossRef]

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 1–108.
[CrossRef]

Platt, B. C.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen (abstract),” J. Opt. Soc. Am. 61, 656 (1971).

Primot, J.

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
[CrossRef]

Roddier, F.

F. Roddier, “Variations on a Hartmann theme,” Opt. Eng. 29, 1239–1242 (1990).
[CrossRef]

Rodioniv, S. A.

A. Zverev, S. A. Rodioniv, M. N. Sokolskii, V. V. Usoskin, “Mathematical principles of Hartmann test of the primary mirror of the Large Azimuthal Telescope,” Sov. J. Opt. Technol. 44, 78–81 (1977).

Rousset, G.

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
[CrossRef]

Shack, R. V.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen (abstract),” J. Opt. Soc. Am. 61, 656 (1971).

Sokolskii, M. N.

A. Zverev, S. A. Rodioniv, M. N. Sokolskii, V. V. Usoskin, “Mathematical principles of Hartmann test of the primary mirror of the Large Azimuthal Telescope,” Sov. J. Opt. Technol. 44, 78–81 (1977).

Talbot, F.

F. Talbot, “Facts relating to optical science. IV,” Philos. Mag. 9, 401–407 (1836).

Usoskin, V. V.

A. Zverev, S. A. Rodioniv, M. N. Sokolskii, V. V. Usoskin, “Mathematical principles of Hartmann test of the primary mirror of the Large Azimuthal Telescope,” Sov. J. Opt. Technol. 44, 78–81 (1977).

Zverev, A.

A. Zverev, S. A. Rodioniv, M. N. Sokolskii, V. V. Usoskin, “Mathematical principles of Hartmann test of the primary mirror of the Large Azimuthal Telescope,” Sov. J. Opt. Technol. 44, 78–81 (1977).

J. Opt. Soc. Am.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen (abstract),” J. Opt. Soc. Am. 61, 656 (1971).

J. Opt. Soc. Am. A

J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A 7, 1589–1608 (1990).
[CrossRef]

Opt. Acta

R. F. Edgar, “The Fresnel diffraction images of periodic structures,” Opt. Acta 16, 281–287 (1969).
[CrossRef]

Opt. Eng.

F. Roddier, “Variations on a Hartmann theme,” Opt. Eng. 29, 1239–1242 (1990).
[CrossRef]

Philos. Mag.

F. Talbot, “Facts relating to optical science. IV,” Philos. Mag. 9, 401–407 (1836).

Sov. J. Opt. Technol.

A. Zverev, S. A. Rodioniv, M. N. Sokolskii, V. V. Usoskin, “Mathematical principles of Hartmann test of the primary mirror of the Large Azimuthal Telescope,” Sov. J. Opt. Technol. 44, 78–81 (1977).

Other

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 367–396.

F. Merkle, “Adaptive optics,” in International Trends in Optics (Academic, New York, 1991).
[CrossRef]

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. 27, pp. 1–108.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Principle of the Hartmann test. The distorted wave front is sampled by a grid of square holes. The light beams emerging from the holes are deflected with respect to the local slopes of the wave front.

Fig. 2
Fig. 2

Orders diffracted by the Hartmann mask (one-dimensional case), for a = 2d/3. The main part of the diffracted energy is concentrated in orders -1, 0, and 1.

Fig. 3
Fig. 3

Hartmann test seen as a lateral shearing interferometer. The observed pattern corresponds essentially to three tilted replicas of the analyzed wave front, which constructively interfere in the Talbot plane.

Fig. 4
Fig. 4

Addition of the recommended phase chessboard to the Hartmann mask. The height of the phase step is equal to π (for the central wavelength).

Fig. 5
Fig. 5

Orders diffracted by the MHM (one-dimensional case), for a = 2d/3. The main part of the energy is now concentrated in the two central orders.

Fig. 6
Fig. 6

Numerically calculated intensity for the propagation of the optical field diffracted by the Hartmann mask (a) without and (b) with phase chessboard, between z = 0 and the first Talbot distance D T of the Hartmann mask (in monochromatic illumination).

Fig. 7
Fig. 7

Experimental evolution of two cells of the recorded interferogram along the propagation axis z produced by the MHM under (a) laser illumination and (b) white-light illumination.

Fig. 8
Fig. 8

Use of the MHM as a wave-front sensor. Optical setup.

Fig. 9
Fig. 9

Hartmanngrams obtained for a spherical aberration at increasing distances (from top to bottom: z = 0, 5.3, and 15.8 mm) from the Hartmann mask (a) without and (b) with phase chessboard.

Equations (13)

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

tx=Πax * combdx,
FTu=sinπuaπuacomb1/du.
tx=C0+C1 exp2iπx/d+C-1 exp-2iπx/d,
Eix=exp2iπgx/λ,
Ex, z=p=-1,0,1 Cp exp2iπλx sin θp+z cos θp+gx-z tan θp,
Ix, z=M0+M1 cos2πdx-z dgdx+M2 cos4πdx-z dgdx,
M0=C02+2C12,
M1=4C0C1 cosπλz/d2,
M2=2C12.
tpx=Πax * combdxexpiπx/d,
FTpu=sinπuaπuacomb1/du * δu-1/2d,
tpx=C1/2 expiπx/d+C-1/2 exp-iπx/d,
Ipx, z=2C1/221+cos2πdx-z dgdx.

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