Abstract

The effect of varying halo intensity in speckle photography of lateral sinusoidal vibration using Young’s fringes is discussed. An interesting new result is found that, for nonunity contrast or visibility, the relative fringe shift (or the error) for minima is always minimum for the lower-order fringes. Also the error in the fringe maxima position is lowest generally at intermediate fringe orders. However, as the visibility reduces the trend becomes similar to that for the case of minima. For maxima and minima both, the error is less for larger amplitude vibrations and higher visibility.

© 1981 Optical Society of America

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References

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  1. See, for example, R. K. Erf, Speckle Metrology (Academic, New York, 1978).
  2. G. E. Maddux, S. L. Moorman, R. R. Corwin, Technical Manuscript AFFDL-TM-78-109-FBE (1978).
  3. G. H. Kaufmann, Opt. Laser Technol. 12, 207 (1980).
    [CrossRef]

1980 (1)

G. H. Kaufmann, Opt. Laser Technol. 12, 207 (1980).
[CrossRef]

1978 (1)

G. E. Maddux, S. L. Moorman, R. R. Corwin, Technical Manuscript AFFDL-TM-78-109-FBE (1978).

Corwin, R. R.

G. E. Maddux, S. L. Moorman, R. R. Corwin, Technical Manuscript AFFDL-TM-78-109-FBE (1978).

Erf, R. K.

See, for example, R. K. Erf, Speckle Metrology (Academic, New York, 1978).

Kaufmann, G. H.

G. H. Kaufmann, Opt. Laser Technol. 12, 207 (1980).
[CrossRef]

Maddux, G. E.

G. E. Maddux, S. L. Moorman, R. R. Corwin, Technical Manuscript AFFDL-TM-78-109-FBE (1978).

Moorman, S. L.

G. E. Maddux, S. L. Moorman, R. R. Corwin, Technical Manuscript AFFDL-TM-78-109-FBE (1978).

Opt. Laser Technol. (1)

G. H. Kaufmann, Opt. Laser Technol. 12, 207 (1980).
[CrossRef]

Technical Manuscript AFFDL-TM-78-109-FBE (1)

G. E. Maddux, S. L. Moorman, R. R. Corwin, Technical Manuscript AFFDL-TM-78-109-FBE (1978).

Other (1)

See, for example, R. K. Erf, Speckle Metrology (Academic, New York, 1978).

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Figures (4)

Fig. 1
Fig. 1

Normalized intensity variation for total original five fringes (K = 16.471). Solid line represents the original J 0 2 distribution, and dashed lines represent effect of changing halo intensity for different visibilities.

Fig. 2
Fig. 2

Relative error in the last fringe maxima position against the number of fringes in the pattern.

Fig. 3
Fig. 3

Relative error in the second fringe position against visibility for total number N of the original fringes as five (K = 16.471), ten (K = 32.190), and fifteen (K = 47.902). Solid and dashed lines correspond to maxima and minima, respectively.

Fig. 4
Fig. 4

Variation of the relative error in the halo. Solid lines correspond to fringe maxima at unit visibility for total number of five (K = 16.471), ten (K = 32.190), and fifteen (K = 47.902) fringes. For the case of K = 16.471 only the effect of visibility is shown for minima and maxima by dashed and dot–dash lines, respectively.

Equations (9)

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I ( x ) = I 0 ( x ) J 0 2 ( 2 π A x m λ L ) ,
I 0 ( x ) = ( 1 - ρ ) 2 for ρ 1 , and 0 for ρ > 1 ,
I ( x ) = [ 1 - ν 1 + ν + 2 ν 1 + ν J 0 2 ( K ρ ) ] I 0 ( x ) ,
K = 2 π A x m m λ L .
RE = Actual fringe position due to I ( x ) / I 0 ( x ) - Fringe position due to I ( x ) Fringe position due to I ( x ) / I 0 ( x ) .
I ( ρ ) = [ 1 - ν 1 + ν + 2 ν 1 + ν J 0 2 ( K ρ ) ] ( 1 - ρ ) 2 ,
J 0 ( K ρ ) J 1 ( K ρ ) = - 1 + ν 2 ν · 1 2 K · 1 ( 1 - ρ ) 2 I ( ρ ) - 1 K ( 1 - ρ ) [ 1 - ν 2 ν + J 0 2 ( K ρ ) ] .
Δ 1 = | 1 K ( 1 - ρ ) · 1 - ν 2 ν · 1 J 1 ( K ρ ) |
Δ 2 = | 1 K ( 1 - ρ ) [ 1 - ν 2 ν + J 0 2 ( K ρ ) ] · 1 J 0 ( K ρ ) |

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