Abstract

Parallel two-step phase-shifting point-diffraction interferometry for microscopy based on a pair of cube beamsplitters is proposed. The first 45°-tilted cube beamsplitter splits object wave into two parallel copies: one copy is filtered by a pinhole in its Fourier plane to behave as reference wave, while the other one remains unchanged as object wave. The second cube beamsplitter combines the object and reference waves, and then split them together into two beams. Along with the two beams, two parallel phase-shifting interferograms are obtained in aid of polarization elements. Based on the proposed configuration, slightly-off-axis interferometry for microscopy is performed, which suppresses dc term by subtracting the two phase-shifting holograms from each other. The setup is highly stable due to its common-path configuration, and has been demonstrated to be suitable for measuring moving objects or dynamic processes.

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References

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2010 (2)

2009 (3)

2008 (2)

2007 (1)

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

2006 (3)

2005 (1)

2004 (1)

1999 (1)

1996 (1)

1992 (1)

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[Crossref]

1984 (1)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

1935 (1)

F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung,” Z. Techn. Phys. 16, 454–457 (1935).

Attwood, D.

Awatsuji, Y.

Badizadegan, K.

Bokor, J.

Brock, N.

Cai, L. Z.

Chang, C.

Dasari, R. R.

Deflores, L. P.

Dong, G. Y.

Ehlers, M. D.

Feld, M. S.

Ferrari,, J. A.

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

Frins,, E. M.

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

Gao, P.

Goldberg, K. A.

Harder, I.

Hayes, J.

Ikeda, T.

Iwai, H.

Kaneko, A.

Koliopoulos, C. L.

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[Crossref]

Koyama, T.

Kubota, T.

Lee, S. H.

Liu, J.-P.

Mantel, K.

Matoba, O.

Medecki, H.

Meneses-Fabian, C.

Meng, X. F.

Millerd, J.

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Naulleau, P. P.

Nercissian, V.

Newpher, T. M.

Nishio, K.

North-Morris, M.

Novak, M.

Park, Y.

Poon, T.-C.

Popescu, G.

Rinehart, M. T.

Robledo-Sánchez, C.

Rodriguez-Zurita, G.

Shaked, N. T.

Shen, X. X.

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Tahara, T.

Tejnil, E.

Toto-Arellano, N. I.

Ura, S.

Vaughan, J. C.

Vázquez-Castillo, J. F.

Wang, Y. R.

Wax, A.

Wyant, J.

Xu, X. F.

Yang, X. L.

Yao, B.

Zernike, F.

F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung,” Z. Techn. Phys. 16, 454–457 (1935).

Zhu, Y.

Appl. Opt. (4)

Opt. Commun. (1)

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

Opt. Eng. (1)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).

Opt. Express (3)

Opt. Lett. (7)

Proc. SPIE (1)

C. L. Koliopoulos, “Simultaneous phase shift interferometer,” Proc. SPIE 1531, 119–127 (1992).
[Crossref]

Z. Techn. Phys. (1)

F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung,” Z. Techn. Phys. 16, 454–457 (1935).

Other (1)

D. Malacara, Optical Shop Testing (John Wiley & Sons, Inc, 2007).

Supplementary Material (2)

» Media 1: AVI (4106 KB)     
» Media 2: AVI (3020 KB)     

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Figures (5)

Fig. 1
Fig. 1

Experimental setup; NF, neutral variable attenuator; P, P 1, P 2 and P 3, linear polarizers; BS 1, BS 2, non-polarizing cube beamsplitters; BE, beam expander; MO, microscope objective; L 1~L 3, achromatic lenses with focal length f 1=175mm and f 2=f 3=100mm; Pinhole, pinhole filter with diameter d=15μm; λ/4, quarter-wave plate, A, aperture. The principal axis of the quarter-wave plate has the angle π/4 with respect to the polarization direction of the object wave.

Fig. 2
Fig. 2

Schematic of cube beamsplitter for beam-splitting. (a) beam splitting for on-axis interferometry configuration; (b) beam splitting for off-axis interferometry configuration.

Fig. 3
Fig. 3

Experimental results for a specimen of rectangular phase step; (a) parallel two-step phase-shifting interferograms (phase-shift δ=π/2); (b) a part of frequency spectrum of (I 1-I 2)R D with logarithm scale; (c) reconstructed optical path difference of the phase step; the color bar represents the optical path length in unit of wavelength λ (632.8nm).

Fig. 4
Fig. 4

Experimental results for a specimen of water-suspended PMMA beads; (a) dynamic parallel two-step phase-shifting interferograms with phase-shift δ=π/2 (Media 1, AVI, 4.0MB); (b) dynamic reconstructed OPD of the specimen (Media 2, AVI, 2.9MB);

Fig. 5
Fig. 5

Stability test for the proposed setup. OPD i denotes the OPD obtained by the ith measurement; RMS{OPD i-OPD i-1} denote the standard deviation of “OPD i(x,y)-OPD i-1(x,y)”.

Equations (4)

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R ( x , y ) = O 0 exp ( i K x ) ,
{ I 1 ( x , y ) = | O t e s t | 2 + | R | 2 + O t e s t * R + O t e s t R * ; I 2 ( x , y ) = | O t e s t | 2 + | R | 2 + exp ( i δ ) O t e s t * R + exp ( i δ ) O t e s t R * ,
I 1 I 2 = [ 1 exp ( i δ ) ] O * R + [ 1 exp ( i δ ) ] O R * .
O r ( x , y ) = I F T { F T { ( I 1 I 2 ) R D } W ^ ( ξ , η ) } / [ 1 exp ( i δ ) ] ,

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