Abstract

Using standard optical shop equipment, it is possible to implement simple, low-cost, phase-shifting Newton interferometers sufficiently accurate for surface evaluation. The simplification of the phase-shifting mechanism is compensated with image-processing algorithms that can deal with vibrations and uneven, nonsequential steps. The results are cross-compared with a Fizeau phase-shifting interferometer to verify the effectiveness of the method.

© 2013 Optical Society of America

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References

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  1. E. Luna, L. Salas, E. Sohn, E. Ruiz, J. Nunez, and J. Herrera, “Deterministic convergence in iterative phase shifting,” Appl. Opt. 48, 1494–1501 (2009).
    [CrossRef]
  2. J. Xu, Q. Xu, and L. Chai, “Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts,” Appl. Opt. 47, 480–485 (2008).
    [CrossRef]
  3. M. V. Mantravadi and D. Malacara, “Newton, Fizeau, and Haidenger interferometers,” in Optical Shop Testing, D. Malacara, ed., (Wiley, 2007).
  4. L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, “Profilometry by fringe projection,” Opt. Eng. 42, 3307–3314 (2003).
    [CrossRef]

2009 (1)

2008 (1)

2003 (1)

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, “Profilometry by fringe projection,” Opt. Eng. 42, 3307–3314 (2003).
[CrossRef]

Chai, L.

Garcia, V.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, “Profilometry by fringe projection,” Opt. Eng. 42, 3307–3314 (2003).
[CrossRef]

Herrera, J.

Luna, E.

E. Luna, L. Salas, E. Sohn, E. Ruiz, J. Nunez, and J. Herrera, “Deterministic convergence in iterative phase shifting,” Appl. Opt. 48, 1494–1501 (2009).
[CrossRef]

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, “Profilometry by fringe projection,” Opt. Eng. 42, 3307–3314 (2003).
[CrossRef]

Malacara, D.

M. V. Mantravadi and D. Malacara, “Newton, Fizeau, and Haidenger interferometers,” in Optical Shop Testing, D. Malacara, ed., (Wiley, 2007).

Mantravadi, M. V.

M. V. Mantravadi and D. Malacara, “Newton, Fizeau, and Haidenger interferometers,” in Optical Shop Testing, D. Malacara, ed., (Wiley, 2007).

Nunez, J.

Ruiz, E.

Salas, L.

E. Luna, L. Salas, E. Sohn, E. Ruiz, J. Nunez, and J. Herrera, “Deterministic convergence in iterative phase shifting,” Appl. Opt. 48, 1494–1501 (2009).
[CrossRef]

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, “Profilometry by fringe projection,” Opt. Eng. 42, 3307–3314 (2003).
[CrossRef]

Salinas, J.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, “Profilometry by fringe projection,” Opt. Eng. 42, 3307–3314 (2003).
[CrossRef]

Servin, M.

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, “Profilometry by fringe projection,” Opt. Eng. 42, 3307–3314 (2003).
[CrossRef]

Sohn, E.

Xu, J.

Xu, Q.

Appl. Opt. (2)

Opt. Eng. (1)

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, “Profilometry by fringe projection,” Opt. Eng. 42, 3307–3314 (2003).
[CrossRef]

Other (1)

M. V. Mantravadi and D. Malacara, “Newton, Fizeau, and Haidenger interferometers,” in Optical Shop Testing, D. Malacara, ed., (Wiley, 2007).

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup to obtain phase shifting with a Newton-type interferometer.

Fig. 2.
Fig. 2.

Perspective phase shifting.

Fig. 3.
Fig. 3.

Six of 12 interferograms to demonstrate phase shifting. These interferograms were obtained by moving the detector mounted on a linear stage and scanning the entire test surface.

Fig. 4.
Fig. 4.

Phase-shifting layout, using three initially compressed rubber/elastomer spacers. Phase shifting is obtained as the spacers expand to their original shape.

Fig. 5.
Fig. 5.

(a) Six of 12 interferograms that show phase shifting by means of the action of gravity. (b) Demodulated three-dimensional surface.

Fig. 6.
Fig. 6.

(a) One of 12 interferograms obtained by moving the camera parallel to the fringes. (b) Corresponding recuperated phase. (c) One of 12 interferograms obtained by moving the camera perpendicular to the fringes. (d) Corresponding recuperated phase. (e) One of 15 interferograms obtained with a phase-shifting Fizeau-type interferometer. (f) Corresponding recuperated phase.

Fig. 7.
Fig. 7.

(a) Difference between recovered phases of parallel and perpendicular camera displacements. (b) Horizontal cross section of the central part of the image. (c) Difference between phases recovered by means of a parallel displacement of the camera and the shift obtained with a Fizeau-type interferometer. (d) Horizontal cross section of the central part of the image.

Equations (1)

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Ii(x,y,li)=A(x,y)+B(x,y)cos(Φ0(x,y)+αix+βiy+li),

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