Abstract

The Lagrange invariant provides a basic description of an optical imaging system. Many important conclusions can be drawn from it. We discovered that the Lagrange invariant is violated in a self-interference holography system with particular characteristics. With a proof-of-principle system, we proved this violation both theoretically and experimentally. This finding enables future exciting possibilities in optical imaging.

© 2013 Optical Society of America

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References

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2013 (1)

P. Bouchal and Z. Bouchal, J. Eur. Opt. Soc. 8, 13011 (2013).
[CrossRef]

2012 (4)

2011 (2)

2010 (1)

2008 (1)

J. Rosen and G. Brooker, Nat. Photonics 2, 190 (2008).
[CrossRef]

2007 (1)

2002 (1)

Bass, M.

M. Bass, in Handbook of Optics, 3rd ed. (McGraw-Hill, 2010), pp. 1.74–1.85.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2005), pp. 160–177, 286–308, and 412–514.

Bouchal, P.

Bouchal, Z.

Brooker, G.

Chmelik, R.

Gao, P.

Harder, I.

Kapitan, J.

Kato, J.

Katz, B.

Kelner, R.

Kim, M. K.

Lai, X. M.

Lv, X. H.

Mantel, K.

Matsumura, T.

Nercissian, V.

Rosen, J.

Siegel, N.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2005), pp. 160–177, 286–308, and 412–514.

Yamaguchi, I.

Yao, B. L.

Zeng, S. Q.

Zhao, Y.

Zhou, Z. Q.

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Figures (4)

Fig. 1.
Fig. 1.

SLM simulates two concentric lenses (with different focal length) simultaneously, to form two images of one point object.

Fig. 2.
Fig. 2.

Schematic of an SLM-based SH system.

Fig. 3.
Fig. 3.

Imaging result at d=291mm. Inset (a): USAF 1951 target. Insets (b) and (c): average intensity distributions along the arrows. Average intensity distributions for image at d=276mm (not shown) are also given.

Fig. 4.
Fig. 4.

Comparison between the theoretical predictions (curves) and measurements (symbols) of MHi and MHα1, respectively. Inset: multiplication of MHi and MHα1.

Equations (9)

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

θoho/lo.
U1(xc,yc)=P1(rc)exp[ikrc2/(2d1i)]exp(ikxcsinα1)U2(xc,yc)=P2(rc)exp[ikrc2/(2d2i)]exp(ikxcsinα2),
Pt(rc)=1,rchtc;Pt(rc)=0,else,
U(xc,yc)=P(rc)exp[ikrc2/(2dr)]exp(ikxcsinα),
U(xi,yi)=[2J1(2πrihHλdr)2πrihHλdr]δ(xiλdr+sinαλ,yiλdr),
MHi=d/lo.
MHα=hHlo/(|dr|ho).
MHα1=(lo2|f1f2|)/(f1|d(f2lo)+lof2|).
MHα2=(lo2|f1f2|)/(f2|d(f1lo)+lof1|).

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