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References

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  1. A. W. Lohmann, D. E. Silva, “An Interferometry Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971).
    [CrossRef]
  2. S. Yokozeki, T. Suzuki, “Shearing Interferometer Using the Grating as the Beam Splitter,” Appl. Opt. 10, 1575 (1971).
    [CrossRef] [PubMed]
  3. Y. Nakano, “A Deflection Mapping of Phase Objects Using Double Gratings,” Kogaku 11, 286 (1982) (in Japanese).
  4. Y. Nakano, K. Murata, “Measurements of Phase Objects Using the Talbot Effect and Moire Techniques,” Appl. Opt. 23, 2296 (1984).
    [CrossRef] [PubMed]
  5. Y. Nakano, K. Murata, “Measurement of the Focal Length of a Lens Using a Moire Technique,” in Conference Digest, Thirteenth Congress of the International Commission for Optics (Publisher, Location, 1984), p. 308.
  6. Y. Nakano, K. Murata, “Talbot Interferometry for Measuring the Focal Length of a Lens,” Appl. Opt. 24, 3162 (1985).
    [CrossRef] [PubMed]
  7. D. W. Swift, “A Simple Moire Fringe Technique for Magnification Checking,” J. Phys. E 7, 164 (1974).
    [CrossRef]
  8. M. Takeda, S. Kobayashi, “Lateral Aberration Measurements with a Digital Talbot Interferometer,” Appl. Opt. 23, 1760 (1984).
    [CrossRef] [PubMed]

1985 (1)

1984 (2)

1982 (1)

Y. Nakano, “A Deflection Mapping of Phase Objects Using Double Gratings,” Kogaku 11, 286 (1982) (in Japanese).

1974 (1)

D. W. Swift, “A Simple Moire Fringe Technique for Magnification Checking,” J. Phys. E 7, 164 (1974).
[CrossRef]

1971 (2)

A. W. Lohmann, D. E. Silva, “An Interferometry Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971).
[CrossRef]

S. Yokozeki, T. Suzuki, “Shearing Interferometer Using the Grating as the Beam Splitter,” Appl. Opt. 10, 1575 (1971).
[CrossRef] [PubMed]

Kobayashi, S.

Lohmann, A. W.

A. W. Lohmann, D. E. Silva, “An Interferometry Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971).
[CrossRef]

Murata, K.

Y. Nakano, K. Murata, “Talbot Interferometry for Measuring the Focal Length of a Lens,” Appl. Opt. 24, 3162 (1985).
[CrossRef] [PubMed]

Y. Nakano, K. Murata, “Measurements of Phase Objects Using the Talbot Effect and Moire Techniques,” Appl. Opt. 23, 2296 (1984).
[CrossRef] [PubMed]

Y. Nakano, K. Murata, “Measurement of the Focal Length of a Lens Using a Moire Technique,” in Conference Digest, Thirteenth Congress of the International Commission for Optics (Publisher, Location, 1984), p. 308.

Nakano, Y.

Y. Nakano, K. Murata, “Talbot Interferometry for Measuring the Focal Length of a Lens,” Appl. Opt. 24, 3162 (1985).
[CrossRef] [PubMed]

Y. Nakano, K. Murata, “Measurements of Phase Objects Using the Talbot Effect and Moire Techniques,” Appl. Opt. 23, 2296 (1984).
[CrossRef] [PubMed]

Y. Nakano, “A Deflection Mapping of Phase Objects Using Double Gratings,” Kogaku 11, 286 (1982) (in Japanese).

Y. Nakano, K. Murata, “Measurement of the Focal Length of a Lens Using a Moire Technique,” in Conference Digest, Thirteenth Congress of the International Commission for Optics (Publisher, Location, 1984), p. 308.

Silva, D. E.

A. W. Lohmann, D. E. Silva, “An Interferometry Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971).
[CrossRef]

Suzuki, T.

Swift, D. W.

D. W. Swift, “A Simple Moire Fringe Technique for Magnification Checking,” J. Phys. E 7, 164 (1974).
[CrossRef]

Takeda, M.

Yokozeki, S.

Appl. Opt. (4)

J. Phys. E (1)

D. W. Swift, “A Simple Moire Fringe Technique for Magnification Checking,” J. Phys. E 7, 164 (1974).
[CrossRef]

Kogaku (1)

Y. Nakano, “A Deflection Mapping of Phase Objects Using Double Gratings,” Kogaku 11, 286 (1982) (in Japanese).

Opt. Commun. (1)

A. W. Lohmann, D. E. Silva, “An Interferometry Based on the Talbot Effect,” Opt. Commun. 2, 413 (1971).
[CrossRef]

Other (1)

Y. Nakano, K. Murata, “Measurement of the Focal Length of a Lens Using a Moire Technique,” in Conference Digest, Thirteenth Congress of the International Commission for Optics (Publisher, Location, 1984), p. 308.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram for measuring small tilt angle variation using Talbot interferometry: (a) g1, grating of the period p; g2, second grating of the same period with g1, M, test surface; OS, observing screen, (b) Magnified Talbot image g 1 of the period p′ on the second grating g2 (x axis).

Fig. 2
Fig. 2

Moire fringes generated by two gratings of unequal period.

Fig. 3
Fig. 3

Relationship between the tilt angle δ of the test surface and the inclination angle α of the moire fringes.

Fig. 4
Fig. 4

Moire fringe patterns observed before (a) and after (b) the variation of the tilt angle: (a) α = 12°; (b) α′ = 25°.

Equations (5)

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p p = cos α cos ( α + θ ) .
sin 2 δ = cos ( α + β ) cos α .
p = P sin 2 ( δ + Δ δ ) .
sin 2 ( δ + Δ δ ) = cos ( α + θ ) cos α .
Δ δ = 1 2 { sin - 1 [ cos ( α + θ ) cos α ] - sin - 1 [ cos ( α + θ ) cos α ] } .

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