Abstract

This paper presents a method for organizing computations in phase-step interferometry for irregular shapes that is straightforward to program. In addition to data files, which are recorded with incremental phase steps between the interfering beams, this method requires a mask file where the valid pixels can be distinguished from invalid pixels. For example, they may lie above a known threshold. By means of a simple edge-following routine, the program moves around the perimeter of the undone portion of the shape, doing the phase calculations and changing the mask pixels to mark them done. This allows the program to move contiguously from pixels that have been done to those that have not. Modulo 2π ambiguities are avoided by computing the phase differences between neighboring pixels and summing them to obtain individual pixel values.

© 1992 Optical Society of America

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References

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  1. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), pp. 349–393.
    [CrossRef]
  2. K. A. Stetson, W. R. Brohinsky, “Fringe-shifting technique for numerical analysis of time-average holograms of vibrating objects,” J. Opt. Soc. Am. A 5, 1472–1476 (1988).
    [CrossRef]
  3. R. J. Prypucniewicz, K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” in Laser Interferometry. Quantitative Analysis of Interferograms, R. J. Prypucniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 456–467 (1989).
  4. W. Osten, R. Höfling, “The inverse modulo process is automatic fringe analysis—problems and approaches,” in Proceedings of the Society for Experimental Mechanics Conference on Hologram Interferometry and Speckle Metrology (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 301–309.
  5. K. A. Stetson, “An electronic system for real-time display and quantitative analysis of hologram interference fringes,” Proc. Laser Inst. Am. 70, 78–85 (1989).

1989

K. A. Stetson, “An electronic system for real-time display and quantitative analysis of hologram interference fringes,” Proc. Laser Inst. Am. 70, 78–85 (1989).

1988

Brohinsky, W. R.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), pp. 349–393.
[CrossRef]

Höfling, R.

W. Osten, R. Höfling, “The inverse modulo process is automatic fringe analysis—problems and approaches,” in Proceedings of the Society for Experimental Mechanics Conference on Hologram Interferometry and Speckle Metrology (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 301–309.

Osten, W.

W. Osten, R. Höfling, “The inverse modulo process is automatic fringe analysis—problems and approaches,” in Proceedings of the Society for Experimental Mechanics Conference on Hologram Interferometry and Speckle Metrology (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 301–309.

Prypucniewicz, R. J.

R. J. Prypucniewicz, K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” in Laser Interferometry. Quantitative Analysis of Interferograms, R. J. Prypucniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 456–467 (1989).

Stetson, K. A.

K. A. Stetson, “An electronic system for real-time display and quantitative analysis of hologram interference fringes,” Proc. Laser Inst. Am. 70, 78–85 (1989).

K. A. Stetson, W. R. Brohinsky, “Fringe-shifting technique for numerical analysis of time-average holograms of vibrating objects,” J. Opt. Soc. Am. A 5, 1472–1476 (1988).
[CrossRef]

R. J. Prypucniewicz, K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” in Laser Interferometry. Quantitative Analysis of Interferograms, R. J. Prypucniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 456–467 (1989).

J. Opt. Soc. Am. A

Proc. Laser Inst. Am.

K. A. Stetson, “An electronic system for real-time display and quantitative analysis of hologram interference fringes,” Proc. Laser Inst. Am. 70, 78–85 (1989).

Other

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), pp. 349–393.
[CrossRef]

R. J. Prypucniewicz, K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” in Laser Interferometry. Quantitative Analysis of Interferograms, R. J. Prypucniewicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 456–467 (1989).

W. Osten, R. Höfling, “The inverse modulo process is automatic fringe analysis—problems and approaches,” in Proceedings of the Society for Experimental Mechanics Conference on Hologram Interferometry and Speckle Metrology (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 301–309.

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Figures (8)

Fig. 1
Fig. 1

Path of a contiguous trade through the points of an irregularly shaped object. The crosshatched area is the object, and the heavy lines show six successive transits around the edge of the undone area. A raster scan was used to find the starting point, and it continued to find each successive start.

Fig. 2
Fig. 2

Paths through which phase differences were calculated to each point because of the 90-deg offset.

Fig. 3
Fig. 3

Electronic holography system image of a plate with no vibration. This image was used as a mask to define valid object pixels.

Fig. 4
Fig. 4

Electronic holography system image of the plate vibrating in its lowest mode. No bias vibration was applied to the object illumination beam.

Fig. 5
Fig. 5

Electronic holography system image of the plate with a positive bias vibration.

Fig. 6
Fig. 6

Electronic holography system image of the plate with a negative bias vibration.

Fig. 7
Fig. 7

Computer screen display of the vibration amplitude coded on 16 gray levels.

Fig. 8
Fig. 8

Computer screen display of the static deformation coded on 16 gray levels.

Equations (8)

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θ = arctan ( n / d ) ,
n = A sin ( θ ) ,             d = A cos ( θ ) .
A = ( n 2 + d 2 ) 1 / 2 .
Δ θ 21 = θ 2 - θ 1 = arctan [ ( n 2 d 1 - n 1 d 2 ) / ( n 1 n 2 + d 1 d 2 ) ] .
θ 2 = θ 1 + Δ θ 21 .
to ignore Δ θ > π / 2 , set Δ θ = 0 if n 1 n 2 + d 1 d 2 < 0.
N = ( I 3 - I 2 ) / ( sin 2 π / 3 ) ,
D = ( 2 I 1 - I 2 - I 3 ) / ( 1 - cos 2 π / 3 ) ,

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