Abstract

Speckle shear interferometry is used for measuring the tilt of diffuse objects with high sensitivity. The theory of tilt measurement using rotational, inversion, and folding shears is given, and experimental results are presented. Experimental configurations to achieve both inversion and folding shears simultaneously are given.

© 1986 Optical Society of America

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References

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  1. E. Archbold, A. E. Ennos, “Displacement Measurement from Double Exposure Laser Photographs,” Opt. Acta 19, 253 (1972).
    [Crossref]
  2. D. A. Gregory, “Basic Physical Principles of Defocussed Speckle Photography: a Tilt Topology Inspection Technique,” Opt. Laser Technol. 8, 201 (1976).
    [Crossref]
  3. D. A. Gregory, “Analysis of Topological Information from Defocussed Speckle Photograph,” Opt. Laser Technol. 9, 17 (1977).
    [Crossref]
  4. H. Tiziani, “A Study of the Use of Laser Speckle to Measure Small Tilts of Optically Rough Surface Accurately,” Opt. Commun. 5, 271 (1972).
    [Crossref]
  5. R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and its Engineering Applications,” Optik 67, 85 (1984).
  6. R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Measurement of Tilt with Speckle Shear Interferometry,” J. Opt. India 12, 118 (1983).
  7. R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
    [Crossref]
  8. R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Interferometric Method of Measuring Small out-of-plane Displacements,” Opt. Lett. 9, 475 (1984).
    [Crossref] [PubMed]
  9. C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” Opt. Acta 31, 681 (1984)and erratum 31, 1327 (1984).
    [Crossref]
  10. C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On the Methods of Multiplexing in Speckle Shear Interferometry,” Optik 69, 8 (1984).

1984 (4)

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and its Engineering Applications,” Optik 67, 85 (1984).

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” Opt. Acta 31, 681 (1984)and erratum 31, 1327 (1984).
[Crossref]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On the Methods of Multiplexing in Speckle Shear Interferometry,” Optik 69, 8 (1984).

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Interferometric Method of Measuring Small out-of-plane Displacements,” Opt. Lett. 9, 475 (1984).
[Crossref] [PubMed]

1983 (2)

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Measurement of Tilt with Speckle Shear Interferometry,” J. Opt. India 12, 118 (1983).

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[Crossref]

1977 (1)

D. A. Gregory, “Analysis of Topological Information from Defocussed Speckle Photograph,” Opt. Laser Technol. 9, 17 (1977).
[Crossref]

1976 (1)

D. A. Gregory, “Basic Physical Principles of Defocussed Speckle Photography: a Tilt Topology Inspection Technique,” Opt. Laser Technol. 8, 201 (1976).
[Crossref]

1972 (2)

E. Archbold, A. E. Ennos, “Displacement Measurement from Double Exposure Laser Photographs,” Opt. Acta 19, 253 (1972).
[Crossref]

H. Tiziani, “A Study of the Use of Laser Speckle to Measure Small Tilts of Optically Rough Surface Accurately,” Opt. Commun. 5, 271 (1972).
[Crossref]

Archbold, E.

E. Archbold, A. E. Ennos, “Displacement Measurement from Double Exposure Laser Photographs,” Opt. Acta 19, 253 (1972).
[Crossref]

Ennos, A. E.

E. Archbold, A. E. Ennos, “Displacement Measurement from Double Exposure Laser Photographs,” Opt. Acta 19, 253 (1972).
[Crossref]

Gregory, D. A.

D. A. Gregory, “Analysis of Topological Information from Defocussed Speckle Photograph,” Opt. Laser Technol. 9, 17 (1977).
[Crossref]

D. A. Gregory, “Basic Physical Principles of Defocussed Speckle Photography: a Tilt Topology Inspection Technique,” Opt. Laser Technol. 8, 201 (1976).
[Crossref]

Joenathan, C.

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Interferometric Method of Measuring Small out-of-plane Displacements,” Opt. Lett. 9, 475 (1984).
[Crossref] [PubMed]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” Opt. Acta 31, 681 (1984)and erratum 31, 1327 (1984).
[Crossref]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On the Methods of Multiplexing in Speckle Shear Interferometry,” Optik 69, 8 (1984).

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Measurement of Tilt with Speckle Shear Interferometry,” J. Opt. India 12, 118 (1983).

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[Crossref]

Kothiyal, M. P.

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and its Engineering Applications,” Optik 67, 85 (1984).

Krishnamurthy, R.

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and its Engineering Applications,” Optik 67, 85 (1984).

Mohanty, R. K.

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and its Engineering Applications,” Optik 67, 85 (1984).

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Interferometric Method of Measuring Small out-of-plane Displacements,” Opt. Lett. 9, 475 (1984).
[Crossref] [PubMed]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On the Methods of Multiplexing in Speckle Shear Interferometry,” Optik 69, 8 (1984).

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” Opt. Acta 31, 681 (1984)and erratum 31, 1327 (1984).
[Crossref]

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[Crossref]

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Measurement of Tilt with Speckle Shear Interferometry,” J. Opt. India 12, 118 (1983).

Sirohi, R. S.

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and its Engineering Applications,” Optik 67, 85 (1984).

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Interferometric Method of Measuring Small out-of-plane Displacements,” Opt. Lett. 9, 475 (1984).
[Crossref] [PubMed]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” Opt. Acta 31, 681 (1984)and erratum 31, 1327 (1984).
[Crossref]

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On the Methods of Multiplexing in Speckle Shear Interferometry,” Optik 69, 8 (1984).

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[Crossref]

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Measurement of Tilt with Speckle Shear Interferometry,” J. Opt. India 12, 118 (1983).

Tiziani, H.

H. Tiziani, “A Study of the Use of Laser Speckle to Measure Small Tilts of Optically Rough Surface Accurately,” Opt. Commun. 5, 271 (1972).
[Crossref]

J. Opt. India (1)

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Measurement of Tilt with Speckle Shear Interferometry,” J. Opt. India 12, 118 (1983).

Opt. Acta (2)

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “Multiplexing in Speckle Shear Interferometry,” Opt. Acta 31, 681 (1984)and erratum 31, 1327 (1984).
[Crossref]

E. Archbold, A. E. Ennos, “Displacement Measurement from Double Exposure Laser Photographs,” Opt. Acta 19, 253 (1972).
[Crossref]

Opt. Commun. (2)

H. Tiziani, “A Study of the Use of Laser Speckle to Measure Small Tilts of Optically Rough Surface Accurately,” Opt. Commun. 5, 271 (1972).
[Crossref]

R. K. Mohanty, C. Joenathan, R. S. Sirohi, “Speckle Shear Interferometry by Double Dove Prism,” Opt. Commun. 47, 27 (1983).
[Crossref]

Opt. Laser Technol. (2)

D. A. Gregory, “Basic Physical Principles of Defocussed Speckle Photography: a Tilt Topology Inspection Technique,” Opt. Laser Technol. 8, 201 (1976).
[Crossref]

D. A. Gregory, “Analysis of Topological Information from Defocussed Speckle Photograph,” Opt. Laser Technol. 9, 17 (1977).
[Crossref]

Opt. Lett. (1)

Optik (2)

R. Krishnamurthy, R. K. Mohanty, R. S. Sirohi, M. P. Kothiyal, “Radial Speckle Shearing Interferometer and its Engineering Applications,” Optik 67, 85 (1984).

C. Joenathan, R. K. Mohanty, R. S. Sirohi, “On the Methods of Multiplexing in Speckle Shear Interferometry,” Optik 69, 8 (1984).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic arrangement to introduce rotational shear with a double Dove prism. Imaging lens has a focal length of 250 mm; a plate containing four apertures each of 10-mm diameter is placed in front of it. (b) Schematic diagram of the Fourier filtering setup.

Fig. 2
Fig. 2

Schematic diagram showing the tilt axis relative to the folding axis x or x″.

Fig. 3
Fig. 3

(a) Three-aperture arrangement for introducing folding and inversion shears simultaneously. (b) Diffraction halo distribution at the Fourier transform plane and the information that can be retrieved from the respective halos.

Fig. 4
Fig. 4

(a) Four-aperture arrangement to provide a speckled reference beam. (b) Diffraction halo distribution and the information that can be retrieved from the respective halos.

Fig. 5
Fig. 5

Tilt fringes obtained from the respective halos. The object was tilted by 0.05 mrad between exposures: (a) Fringe pattern with folding shear: folding axis being inclined 20° to the y axis. The information was filtered from A23 halo. (b) Fringe pattern with folding shear: folding axis being inclined 70° to the y axis. The information was filtered from A13 halo. (c) Speckle interferometric fringes filtered from A24 halo to give out-of-plane displacement. (d) Fringe pattern with inversion shear filtered from A12 halo.

Tables (1)

Tables Icon

Table I Comparison of the Values of Tilt Applied and Measurement from the Interferogram

Equations (15)

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I = 2 ( a 1 2 + a 2 2 ) + 2 a 1 a 2 cos ( δ 12 2 ) cos ( ϕ 12 + δ 12 2 ) ,
δ 12 = 4 π λ [ w ( θ + Δ θ ) w ( θ ) ] = 4 π λ w θ Δ θ = 4 π λ β x Δ θ since w = β y .
δ 12 = 4 π λ w ( θ + θ ) w ( θ ) = 4 π λ [ x sin θ y ( 1 cos θ ) ] ,
x ¯ = λ 4 β sin ( θ / 2 ) .
w = y cos γ x sin γ .
δ 12 = 4 π λ [ w ( x , y ) w ( x , y ) ] = 8 π λ β y cos γ .
y ¯ = λ 4 β | cos γ | .
x = x y = y + y 0 .
w = β [ ( y y 0 ) cos γ x sin γ ] .
δ 12 = 4 π λ [ w ( x , y ) w ( x , y ) ] = 8 π λ β y cos γ .
I = 2 ( a 1 2 + a 2 2 + a 3 2 ) + 2 a 1 a 2 cos δ 12 2 cos ( ϕ 12 + δ 12 2 ) + 2 a 2 a 3 cos δ 23 2 cos ( ϕ 23 + δ 23 2 ) + 2 a 1 a 3 cos δ 13 2 cos ( ϕ 13 + δ 13 2 ) .
y ¯ = λ 4 β cos ( δ 0 / 2 ) .
β = λ 2 y ¯
β = λ 4 y ¯
β = λ 4 y ¯ cos γ

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