Abstract

We describe a robust interferometer with external phase-shift control that does not require moving parts. The optical architecture resembles a common-path device in which the interfering waves propagate together in one collimated beam passing through the test sample. The collimated beam is incident on a calcite plate, which produces a polarization selective lateral translation and superposition of the reference and test waves. The characteristic features of the proposed interferometer, i.e. one-beam single-element scheme combined with external phase-shift control without moving parts, make a highly vibration insensitive device. Validation experiments are presented.

© 2017 Optical Society of America

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References

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  1. H. Schreiber and J. H. Bruning, “Phase shifting Interferometry” in Optical Shop Testing, 3rd edition, D. Malacara, ed. (Wiley, 2007) Chap. 14.
  2. J. A. Ferrari, E. M. Frins, D. Perciante, and A. Dubra, “Robust one-beam interferometer with phase-delay control,” Opt. Lett. 24(18), 1272–1274 (1999).
    [PubMed]
  3. J. A. Ferrari and E. M. Frins, “One-beam interferometer by beam folding,” Appl. Opt. 41(25), 5313–5316 (2002).
    [PubMed]
  4. J. A. Ferrari and E. M. Frins, “Single-element interferometer,” Opt. Commun. 279, 235–239 (2007).
  5. R. Oldenbourg and M. Shribak, “Microscopes” in Handbook of Optics, Michael Bass, ed. (3rd ed., McGraw-Hill, 2010) Vol. I.
  6. M. Shribak, K. G. Larkin, and D. Biggs, “Mapping optical path length and image enhancement using quantitative orientation-independent differential interference contrast microscopy,” J. Biomed. Opt. 22(1), 16006 (2017).
    [PubMed]
  7. J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).
  8. G. A. Ayubi, C. D. Perciante, J. L. Flores, J. M. Di Martino, and J. A. Ferrari, “Generation of phase-shifting algorithms with N arbitrarily spaced phase-steps,” Appl. Opt. 53(30), 7168–7176 (2014).
    [PubMed]
  9. G. A. Ayubi, C. D. Perciante, J. M. Di Martino, J. L. Flores, and J. A. Ferrari, “Generalized phase-shifting algorithms: error analysis and minimization of noise propagation,” Appl. Opt. 55(6), 1461–1469 (2016).
    [PubMed]
  10. G. A. Ayubi, C. D. Perciante, J. M. Di Martino, J. L. Flores, and J. A. Ferrari, “Generalized phase-shifting algorithms: error analysis and minimization of noise propagation: erratum,” Appl. Opt. 55(28), 7763 (2016).
    [PubMed]

2017 (1)

M. Shribak, K. G. Larkin, and D. Biggs, “Mapping optical path length and image enhancement using quantitative orientation-independent differential interference contrast microscopy,” J. Biomed. Opt. 22(1), 16006 (2017).
[PubMed]

2016 (2)

2014 (1)

2013 (1)

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).

2007 (1)

J. A. Ferrari and E. M. Frins, “Single-element interferometer,” Opt. Commun. 279, 235–239 (2007).

2002 (1)

1999 (1)

Alonso, J. R.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).

Ayubi, G. A.

Biggs, D.

M. Shribak, K. G. Larkin, and D. Biggs, “Mapping optical path length and image enhancement using quantitative orientation-independent differential interference contrast microscopy,” J. Biomed. Opt. 22(1), 16006 (2017).
[PubMed]

Dalchiele, E. A.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).

Di Martino, J. M.

Dubra, A.

Fernández, A.

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).

Ferrari, J. A.

Flores, J. L.

Frins, E. M.

Larkin, K. G.

M. Shribak, K. G. Larkin, and D. Biggs, “Mapping optical path length and image enhancement using quantitative orientation-independent differential interference contrast microscopy,” J. Biomed. Opt. 22(1), 16006 (2017).
[PubMed]

Perciante, C. D.

Perciante, D.

Shribak, M.

M. Shribak, K. G. Larkin, and D. Biggs, “Mapping optical path length and image enhancement using quantitative orientation-independent differential interference contrast microscopy,” J. Biomed. Opt. 22(1), 16006 (2017).
[PubMed]

Appl. Opt. (4)

J. Biomed. Opt. (1)

M. Shribak, K. G. Larkin, and D. Biggs, “Mapping optical path length and image enhancement using quantitative orientation-independent differential interference contrast microscopy,” J. Biomed. Opt. 22(1), 16006 (2017).
[PubMed]

Opt. Commun. (2)

J. M. Di Martino, G. A. Ayubi, E. A. Dalchiele, J. R. Alonso, A. Fernández, J. L. Flores, C. D. Perciante, and J. A. Ferrari, “Single-shot phase recovery using two laterally separated defocused images,” Opt. Commun. 293, 1–3 (2013).

J. A. Ferrari and E. M. Frins, “Single-element interferometer,” Opt. Commun. 279, 235–239 (2007).

Opt. Lett. (1)

Other (2)

R. Oldenbourg and M. Shribak, “Microscopes” in Handbook of Optics, Michael Bass, ed. (3rd ed., McGraw-Hill, 2010) Vol. I.

H. Schreiber and J. H. Bruning, “Phase shifting Interferometry” in Optical Shop Testing, 3rd edition, D. Malacara, ed. (Wiley, 2007) Chap. 14.

Supplementary Material (1)

NameDescription
» Visualization 1       Interferograms vs. phase-shift

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Figures (5)

Fig. 1
Fig. 1 Proposed interferometer. L2 is an imaging lens and C is a camera. The inset shows the calcite plate (BD): OA is the optical axis, and d is the lateral displacement of the extraordinary beam.
Fig. 2
Fig. 2 Experimental calibration curve.
Fig. 3
Fig. 3 Fringe displacement due to mechanical vibrations of the Mach-Zehnder (blue curve) and the proposed interferometer (red curve).
Fig. 4
Fig. 4 (a)-(c) Interferograms showing the two replicas of the phase sample, acquired for φ( ν 1 )=0(rad), φ( ν 2 )=1.49 (rad) and φ( ν 3 )=3.17 (rad), respectively; (d)-(f) Interferograms acquired without the test sample showing spurious low-contrast interference.
Fig. 5
Fig. 5 Reconstructed phase profile of the test object (in false color). The figure on the right side show a horizontal cut of the phase profile along the dashed line.

Tables (1)

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Table 1 RMS versus No. of frames.

Equations (6)

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E 1 ( x,y )=( x ^ + y ^ exp[ iφ( ν ) ] ) E 0 ( x,y )exp[ iϕ( x,y ) ],
E 2 ( x,y )= x ^ E 0 ( xd,y )exp[ i( ϕ( xd,y )+ε ) ]+ y ^ E 0 ( x,y )exp[ i( ϕ( x,y )+φ( ν ) ) ],
E 3 ( x,y )= E 0 ( xd,y )exp[ i( ϕ( xd,y )+ε ) ]+ E 0 ( x,y )exp[ i( ϕ( x,y )+φ( ν ) ) ].
I( x,y )=a( x,y )+b( x,y )cos[ ϕ( x,y )ϕ( xd,y )+φ( ν )ε ].
I( x,y )=a( x,y )+b( x,y )cos[ ϕ( x,y )+( φ( ν )ε ) ]ford<x<2d,
I( x,y )=a( x,y )+b( x,y )cos[ ( φ( ν )ε )ϕ( xd,y ) ]for2d<x<3d.

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