Abstract

An improved type of Dammann grating (DG) that could generate an equal-intensity spot array which has only three phases is proposed. Numerical solutions of 1×4 and 1×5 such DGs are given. A 4×4 two-phase DG manufactured by very-large-scale integration (VLSI) techniques is presented. A phase-shift-interferometry-based technique that measures the intensity and sub-beam phases of beam splitting gratings is proposed. The performance measurements of the manufactured 4×4 two-phase DG using the proposed technique is carried out.

© 2013 Optical Society of America

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References

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  1. H. Dammann and K. Görtler, Opt. Commun. 3, 312 (1971).
    [CrossRef]
  2. C. Zhou and L. Liu, Appl. Opt. 34, 5961 (1995).
    [CrossRef]
  3. A. Yan, L. Liu, E. Dai, J. Sun, and Y. Zhou, Opt. Lett. 35, 1251 (2010).
    [CrossRef]
  4. D. Pabeuf, F. Emaury, S. de Rossi, R. Mercier, G. Lucas-Leclin, and P. Georges, Opt. Lett. 35, 1515 (2010).
    [CrossRef]
  5. B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
    [CrossRef]
  6. B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
    [CrossRef]
  7. D. Malacara, Optical Shop Testing (Wiley-Interscience, 2007).

2013 (1)

B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
[CrossRef]

2011 (1)

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

2010 (2)

1995 (1)

1971 (1)

H. Dammann and K. Görtler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Dai, E.

B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
[CrossRef]

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

A. Yan, L. Liu, E. Dai, J. Sun, and Y. Zhou, Opt. Lett. 35, 1251 (2010).
[CrossRef]

Dammann, H.

H. Dammann and K. Görtler, Opt. Commun. 3, 312 (1971).
[CrossRef]

de Rossi, S.

Emaury, F.

Georges, P.

Görtler, K.

H. Dammann and K. Görtler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Li, B.

B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
[CrossRef]

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

Liu, L.

B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
[CrossRef]

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

A. Yan, L. Liu, E. Dai, J. Sun, and Y. Zhou, Opt. Lett. 35, 1251 (2010).
[CrossRef]

C. Zhou and L. Liu, Appl. Opt. 34, 5961 (1995).
[CrossRef]

Lucas-Leclin, G.

Lv, X.

B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
[CrossRef]

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley-Interscience, 2007).

Mercier, R.

Pabeuf, D.

Shen, B.

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

Sun, J.

B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
[CrossRef]

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

A. Yan, L. Liu, E. Dai, J. Sun, and Y. Zhou, Opt. Lett. 35, 1251 (2010).
[CrossRef]

Wu, Y.

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

Yan, A.

B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
[CrossRef]

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

A. Yan, L. Liu, E. Dai, J. Sun, and Y. Zhou, Opt. Lett. 35, 1251 (2010).
[CrossRef]

Zhi, Y.

B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
[CrossRef]

Zhou, C.

Zhou, Y.

Appl. Opt. (1)

J. Opt. (1)

B. Li, A. Yan, L. Liu, E. Dai, J. Sun, B. Shen, X. Lv, and Y. Wu, J. Opt. 13, 055706 (2011).
[CrossRef]

Opt. Commun. (2)

B. Li, E. Dai, A. Yan, X. Lv, Y. Zhi, J. Sun, and L. Liu, Opt. Commun. 290, 126 (2013).
[CrossRef]

H. Dammann and K. Görtler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Opt. Lett. (2)

Other (1)

D. Malacara, Optical Shop Testing (Wiley-Interscience, 2007).

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Figures (6)

Fig. 1.
Fig. 1.

One period of a binary phase (0, π) three-phase DG, where {xk,k=1,2,,K}, are the normalized phase transition points.

Fig. 2.
Fig. 2.

Surface profile of the fabricated 4×4 three-phase DG measured with Taylor-Hobson Talysurf (S3F) equipment.

Fig. 3.
Fig. 3.

Camera image of beam spots when the fabricated 4×4 three-phase DG is illuminated by a He–Ne laser.

Fig. 4.
Fig. 4.

Scheme for the measurement of the intensity and phases of the sub-beams of beam splitting gratings.

Fig. 5.
Fig. 5.

(a) Method of dividing and (b) the beam spots of the upper-right corner of the 2×2 sub-array without a reference beam.

Fig. 6.
Fig. 6.

Interference patterns of the upper-right corner of the 2×2 sub-array spots with four phase delays.

Tables (2)

Tables Icon

Table 1. Numerical Solutions of Binary-Phase (0, π) Three-Phase DG

Tables Icon

Table 2. Experimental and Theoretical (in the Brackets) Sub-Beam Phases of the 4×4 Two-Phase DG (rad/π)

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

{A0=k=0K(1)k(xk+1xk),An=12nπk=0K(1)k{[sin(2nπxk+1)sin(2nπxk+1)]+i[cos(2nπxk+1)cos(2nπxk)]},
uniθ=max(θ+n)min(θ+n)max(θ+n)+min(θ+n).
φsub-beams(x,y)=arctan(I4(x,y)I2(x,y)I1(x,y)I3(x,y)).

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