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Abbreviations
- a r , b r :
-
weights of a linear filter
- f :
-
spatial frequency
- f o :
-
central frequency in a signal
- f c :
-
cut-off frequency in a signal
- f s :
-
sampling frequency
- f t :
-
termination frequency
- f i (nΔx), f o (nΔx):
-
input and output function of a linear filter
- h(x) :
-
weight function of a linear filter
- H(f) :
-
transfer function of a linear filter equal to the Fourier transform ofh(x)
- h n :
-
weights in the Ormsby filters
- I :
-
light-intensity amplitude in the image plane (subscripts indicate the corresponding harmonic)
- I 1 :
-
light-intensity vector corresponding to the first harmonic
- k e :
-
parameter defining the extent of the parabolic transition in an Ormsby filter
- p 1,p 2 :
-
pitches of the master and the model grids, respectively
- T(x) :
-
in-quadrature component of the vectorI 1
- u :
-
displacement in the direction of thex-axis
- U(x) :
-
complex function equal toV(x)+iT(x)
- V(x) :
-
in-phase component of the vectorI 1
- ω:
-
angular frequency
- 쏉 o :
-
central angular frequency of a signal
- δ:
-
fringe spacing
- δ(x/Δr−r):
-
unit impulse function
- ε:
-
strain
- θ:
-
total angle rotated by the vector representing light intensity from a given origin
- λ o ,λ c ,λ t :
-
center, cut-off, and termination wave-length in the filter weighth m
- ρ:
-
relative dimensionless displacement equal tox/p 1−x/p 2
- ϕ(x):
-
phase modulation equal to ∝ψ(x)dx
- ϕ c :
-
phase of the light-intensity vector
- ψ(x):
-
frequency-modulating function
References
Sciammarella, C. A., “Basic Optical Law in the Interpretation of Moiré Patterns Applied to the Analysis of Strains, Part I,”Experimental Mechanics,5 (5),154–160 (1965).
Ross, B. E., Sciammarella, C. A., andSturgeon, D., “Basic Optical Law in the Interpretation of Moiré Patterns Applied to the Analysis of Strains, Part II,”Ibid.,5 (6),161–166 (1965).
Sciammarella, C. A., “Techniques of Fractional Fringe Interpolation,” 2nd. Int. Cong. Exp. Mech., Sept. 27–Oct. 1, Washington, D. C. (1965).
Sciammarella, C. A., and Sturgeon, D., “Substantial Improvements in the Process of Moiré Data by Optical and Digital Filtering,” Proc. 3rd Int. Cong. Exp. Stress Anal., West Berlin (March 1966).
Sciammarella, C. A., and Durelli, A. J., “Moiré Fringes as a Means of Analyzing Strains,” Trans. ASCE, Pt. I, 127, 582–603 (1962).
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Lighthill, M., “Introduction to Fourier Analysis and Generalized Functions,” Cambridge University Press (1958).
Papoulis, A., “The Fourier Integral and Its Applications,” Chap. III, McGraw-Hill Book Co., Inc. (1962).
Anders, E. B. et al., “Digital Filters,” NASA Report, NASA-5164 (1964).
Goodman, N. R., “Measuring Amplitude and Phase,” Jnl. Franklin Inst. (December 1960).
Ormsby, J. T. A., “Design of Numerical Filters with Applications to Missile Data Processing,” Jnl. Assoc. Computing Mach.,8 (3) (1961).
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Additional information
C. A. Sciammarella and D. L. Sturgeon were Professor and Research Assistant, respectively, Department of Engineering Science and Mechanics University of Florida, Gainesville, Fla., at the time this paper was prepared.
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Sciammarella, C.A., Sturgeon, D.L. Digital-filtering techniques applied to the interpolation of Moiré-fringes data. Experimental Mechanics 7, 468–475 (1967). https://doi.org/10.1007/BF02326261
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DOI: https://doi.org/10.1007/BF02326261