Abstract

The dynamic signature of the subwavelength variation of a rectangular aperture has recently been shown to be determinable from far-field irradiance with a precision better than 1 nm [Opt. Lett. 29, 1045 (2004)]. We have proposed, and have theoretically shown, that detection sensitivity can be greatly enhanced with an embedded-aperture Mach–Zehnder interferometer configuration, after parameter optimization. The sensitivity, in terms of derivative intensity of observed subwavelength variations, could be enhanced approximately 2.7 times, compared with the directly detected method. Another method of detection of subwavelength variation from pattern measurement of far-field diffraction has also been proposed. The associated shifting of the dark line of the diffraction pattern had a good linear correlation to subwavelength variation, which was magnified approximately 150 times, and gave good contrast for measurement.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Jutamulia, ed., Selected Papers on Near-Field Optics (SPIE Press, Bellingham, Wash., 2002).
  2. C.-H. Lee, H.-Y. Mong, W.-C. Lin, “Noninterferometric wide-field optical profilometry with nanometer depth resolution,” Opt. Lett. 27, 1773–1775 (2002).
    [CrossRef]
  3. C.-H. Lee, H.-Y. Chiang, H.-Y. Mong, “Sub-diffraction-limit imaging based on the topographic contrast of differential confocal microscopy,” Opt. Lett. 28, 1772–1774 (2003).
    [CrossRef] [PubMed]
  4. D. Lin, Z. Liu, R. Zhang, J. Yan, C. Yin, Y. Xu, “Step-height measurement by means of a dual-frequency interferometric confocal microscope,” Appl. Opt. 43, 1472–1479 (2004).
    [CrossRef] [PubMed]
  5. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 38.
  6. S. Selci, M. Righini, “Detection of subwavelength slit-width variation with irradiance measurements in the far field,” Opt. Lett. 27, 1971–1973 (2002).
    [CrossRef]
  7. S.-C. Chu, J.-L. Chern, “Characterization of the signature of subwavelength variation from far-field irradiance,” Opt. Lett. 29, 1045–1047 (2004).
    [CrossRef] [PubMed]
  8. See http://mathworld.wolfram.com/LeibnizIntegralRule.html .
  9. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 74.
  10. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

2004 (2)

2003 (1)

2002 (2)

Chern, J.-L.

Chiang, H.-Y.

Chu, S.-C.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 38.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), p. 74.

Lee, C.-H.

Lin, D.

Lin, W.-C.

Liu, Z.

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, New York, 1992).

Mong, H.-Y.

Righini, M.

Selci, S.

Xu, Y.

Yan, J.

Yin, C.

Zhang, R.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Schematic diagram of the interferometer configuration.

Fig. 2
Fig. 2

Derivative intensity versus the half-aperture width. The maximum-sensitive-observation half-aperture was optimized at (a) 50 µm, (b) 100 µm, and (c) 150 µm.  

Fig. 3
Fig. 3

Dark-line position shift versus the half-aperture variation. The thicker lines denote the interferometer configuration, and the lighter lines denote the single aperture.

Fig. 4
Fig. 4

Diffraction patterns before and after 100-nm half-aperture variation in two situations: (a) and (b) the directly detected method and (c) and (d) the embedded-aperture interferometer configuration.

Fig. 5
Fig. 5

Diffraction patterns centered at the first dark-line position: (a) the directly detected method and (b) the embedded-aperture interferometer configuration. (c) Cross sections along the y axis of (a) and (b), where the thicker curve represents the embedded-aperture interferometer configuration, and the lighter curve represents the directly detected method.

Fig. 6
Fig. 6

Contrasts and the contrast ratio of the diffraction pattern observed. The thicker line denotes the contrast in the embedded-aperture interferometer configuration, and the lighter line denotes the directly detected method. The dotted line denotes the contrast ratio.

Equations (18)

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

U1=Aexpjkz+jπλz(x2+y2)jλz×4ab sinc(kax/z)sinc(kby/z),
U2=Aexpjkz+jπλz(x2+y2)jλz×4ab sinc(kax/z)sinc(kby/z),
I(x, y)=|U1+U2|2=16A2(λz)2sin2(kby/z)(ky/z)2sin2(kax/z)(kx/z)2+sin2(kax/z)(kx/z)2+2sin(kax/z)sin(kax/z)(kx/z)2.
Pz=-XX-YYI(x, y)dxdy=16A2(λz)2-YYsin2(kby/z)(ky/z)2dy-XXsin2(kax/z)(kx/z)2dx+-XXsin2(kax/z)(kx/z)2dx+2-XXsin(kax/z)sin(kax/z)(kx/z)2dx.
fa=16A2(λz)22zbkSi2kbYz-sin2(kbY/z)(kbY/z)2×2zkSi2kaXz+Sik(a+a)Xz-Sik(a-a)Xz,
a>ak(a+a)X/z=(2m1+1)π,k(a-a)X/z=(2m2+1)π
I(x, y)=16A2(λz)2sin2(kax/z)(kx/z)2sin2(kby/z)(ky/z)2.
xd(a)=mλz2a,(m=1, 2, 3).
xd(a)=mλz21a0-1a02(a-a0)+1a03(a-a0)2-1a04(a-a0)3+O(a-a0)4,
Δxd-mλz2a02Δa.
Ix=0,2Ix2>0.
I(x, y)=16A2(λz)2sin2(kby/z)(ky/z)21(kx/z)2{sin(ka0x/z)+sin[k(a0+Δa)x/z]}2=C{sin(ka0x/z)+sin[k(a0+Δa)x/z]}2,
sin(ka0x/z)cos(kΔax/z)+cos(ka0x/z)sin(kΔax/z).
I(x, y)=C[2 sin(ka0x/z)+(kΔax/z)cos(ka0x/z)]2.
tan(ka0xd/z)=-kΔaxd/2z.
dxdda=dxdd(a0+Δa)=dxdd(Δa).
dxdda=dxdd(Δa)=-kxd/2zkΔa2z+ka0zsec2ka0xdz-xd/2a0sec2ka0xdz,
Δxd-mλz4a02Δa.

Metrics