Abstract

We describe designs of the multipass optical configurations of an interferometer with high spectral resolution with respect to 6, 12, and 24 times more optical passes than the conventional Michelson interferometer. In each design, a movable cube corner retroreflector is combined with a folding reflector group (FRG) as the interferometer’s moving combination to implement the multipass optical configuration with the characteristic of surface division. Analyses reveal that when there are 12 or more optical passes, the net effect of the ray’s angular deviation of the entire moving combination amounts to only the alignment error of one of the reflectors in the FRG, demonstrating the self-aligning property of the interferometer.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (1)

2008 (1)

2007 (3)

2003 (1)

2002 (1)

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

1998 (1)

1997 (1)

1996 (1)

1994 (1)

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

1992 (1)

1991 (1)

1987 (1)

1979 (1)

1977 (1)

1962 (1)

1960 (1)

1958 (1)

1948 (2)

Ahn, J.

Ai, C.

Azzam, R. M. A.

Cadotte, M.

Carli, B.

Carlotti, M.

Chung, M. S.

Eom, T. B.

Genest, J.

Gibeault, M.

Hara, S.-y.

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

Hatsuzawa, T.

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

Hong, Y. K.

Horneman, V.-M.

Hsu, V. S.

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

Iwasaki, H.

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

Kahn, J. M.

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

Kang, C. S.

Kauppinen, J.

Kim, J. A.

Kim, J. W.

Kim, S.

Kondou, K.

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

Lanoue, E.

Lei, J. F.

R. Y. Wei, J. F. Lei, K. Yang, B. S. Yin, and L. B. Zeng, “Analysis on corner cube retroreflector in FT-IR spectrometer,” Opt. Instrum. 29, 69–75 (2007).

Liu, J.

Mencaraglia, F.

Murty, M. V. R. K.

Nara, M.

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

Park, B. C.

Peck, E. R.

Pisani, M.

Rossi, E.

Segre, S. E.

Smith, K. L.

Syms, R. R. A.

Tanimura, Y.

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

Taurand, G.

Thomas, D. A.

Toyoda, K.

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

Toyonaga, S.

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

Vitushkin, A. L.

Vitushkin, L. F.

Wei, R. Y.

R. Y. Wei, J. F. Lei, K. Yang, B. S. Yin, and L. B. Zeng, “Analysis on corner cube retroreflector in FT-IR spectrometer,” Opt. Instrum. 29, 69–75 (2007).

Wyant, J. C.

Yang, K.

R. Y. Wei, J. F. Lei, K. Yang, B. S. Yin, and L. B. Zeng, “Analysis on corner cube retroreflector in FT-IR spectrometer,” Opt. Instrum. 29, 69–75 (2007).

Yin, B. S.

R. Y. Wei, J. F. Lei, K. Yang, B. S. Yin, and L. B. Zeng, “Analysis on corner cube retroreflector in FT-IR spectrometer,” Opt. Instrum. 29, 69–75 (2007).

Yoder, J. P. R.

Zanza, V.

Zeng, L. B.

R. Y. Wei, J. F. Lei, K. Yang, B. S. Yin, and L. B. Zeng, “Analysis on corner cube retroreflector in FT-IR spectrometer,” Opt. Instrum. 29, 69–75 (2007).

Zhu, X.

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

Appl. Opt. (8)

J. Kauppinen, “Working resolution of 0.010 cm−1 between 20 cm−1 and 1200 cm−1 by a Fourier spectrometer,” Appl. Opt. 18, 1788–1796 (1979).
[CrossRef] [PubMed]

B. Carli, M. Carlotti, F. Mencaraglia, and E. Rossi, “Far-infrared high-resolution Fourier transform spectrometer,” Appl. Opt. 26, 3818–3822 (1987).
[CrossRef] [PubMed]

J. Kauppinen and V.-M. Horneman, “Large aperture cube corner interferometer with a resolution of 0.001 cm−1,” Appl. Opt. 30, 2575–2578 (1991).
[CrossRef] [PubMed]

C. Ai and K. L. Smith, “Accurate measurement of the dihedral angle of a corner cube,” Appl. Opt. 31, 519–527 (1992).
[CrossRef] [PubMed]

J. Liu and R. M. A. Azzam, “Polarization properties of corner-cube retroreflectors: theory and experiment,” Appl. Opt. 36, 1553–1559 (1997).
[CrossRef] [PubMed]

B. C. Park, T. B. Eom, and M. S. Chung, “Polarization properties of cube-corner retroreflectors and their effects on signal strength and nonlinearity in heterodyne interferometers,” Appl. Opt. 35, 4372–4380 (1996).
[CrossRef] [PubMed]

A. L. Vitushkin and L. F. Vitushkin, “Design of a multipass optical cell based on the use of shifted corner cubes and right-angle prisms,” Appl. Opt. 37, 162–165 (1998).
[CrossRef]

G. Taurand, J. Genest, M. Cadotte, M. Gibeault, and E. Lanoue, “Parasitic diffuse reflection in a Fourier transform spectrometer yielding subharmonic ghosts and line-shape distortion,” Appl. Opt. 46, 533–537 (2007).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

X. Zhu, V. S. Hsu, and J. M. Kahn, “Optical modeling of MEMS corner cube retroreflectors with misalignment and nonflatness,” IEEE J. Sel. Top. Quantum Electron. 8, 26–32 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (1)

Opt. Express (2)

Opt. Instrum. (1)

R. Y. Wei, J. F. Lei, K. Yang, B. S. Yin, and L. B. Zeng, “Analysis on corner cube retroreflector in FT-IR spectrometer,” Opt. Instrum. 29, 69–75 (2007).

Rev. Sci. Instrum. (1)

T. Hatsuzawa, Y. Tanimura, K. Toyoda, M. Nara, S. Toyonaga, S.-y. Hara, H. Iwasaki, and K. Kondou, “A compact laser interferometer with a piezodriven scanner for metrological measurements in regular SEMs,” Rev. Sci. Instrum. 65, 2510–2513 (1994).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the cube corner interferometer.

Fig. 2
Fig. 2

Ray propagation through an ideal CCR and the corresponding coordinate system. The shading shows the effective areas of the CCR surfaces when the incident direction is n ^ i ( n i x , n i y , n i z ) in the case of 2 n i y > n i z > n i y > n i x .

Fig. 3
Fig. 3

Six segments in 2D form when viewed along the incident direction. (a) Segments with the same effective area when the incident direction is parallel with the axis of symmetry of the CCR. (b) The incident direction is not parallel to the axis of symmetry; the shading shows the different effective areas in the case of 2 n i y > n i z > n i y > n i x .

Fig. 4
Fig. 4

3D model of the moving combination based on the CCR’s surface division method. The direction of the incident beam is parallel to the symmetric axis of the CCR.

Fig. 5
Fig. 5

2D model of the moving combinations with segments and reflection areas in them when viewed along the incident direction. (a) The beam coming from segment IV is reflected symmetrically by retroreflector RTF1 to segment III. Then it is reflected from segment VI to segment V by RTF2. (b) The beam coming from segment IV is reflected symmetrically by retroreflector RTF1 to segment V. Then it is reflected from segment II to segment III by RTF2.

Fig. 6
Fig. 6

Schematic diagram of the sextuple-pass interferometer using only one CCR.

Fig. 7
Fig. 7

Optical configuration design for 24 passes. The FRG consists of three dihedral right-angle retroreflectors RTF1–RTF3, corresponding to segments III and IV, segments V and VI, the upper part and lower part of segment II, and a plane mirror FM corresponding to the left part of segment I, respectively.

Fig. 8
Fig. 8

Optical configuration design for 48 passes. The FRG consists of four dihedral right-angle retroreflectors RTF1–RTF4, corresponding to segments III and IV, segments V and VI, the upper part and lower part of segment II, the left part and right part of the left part of segment I, and a plane mirror FM corresponding to the left part of the right part of segment I, respectively.

Tables (1)

Tables Icon

Table 1 Corresponding Segments for Incident and Emergent Rays in the CCR

Equations (15)

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ϕ max = 2 3 a .
ϕ 2 6 3 a sin ( 2 π N ) tan ( π 4 π N ) .
I n + 1 = R i R j R k I n ( where     i , j , k = N A , N B , N C and i j k , n = 1 , 3 , 5 ) .
R = [ 1 2 N x 2 2 N x N y 2 N x N z 2 N x N y 1 2 N y 2 2 N y N z 2 N x N z 2 N y N z 1 2 N z 2 ] .
{ I 2 = R N B R N C R N A I 1 = R N A N C N B I 1 = R A C B I 1 I 4 = R N A R N B R N C I 3 = R N C N B N A I 3 = R C B A I 3 I 6 = R N C R N A R N B I 5 = R N B N A N C I 5 = R B A C I 5 .
{ I 6 = R B A C R 4 5 R C B A R 2 3 R A C B I 1 I 6 r = R 6 I 6 I 1 r = R B C A R 3 2 R A B C R 5 4 R C A B I 6 r R 3 2 = R 2 R 3 = ( R 3 R 2 ) T = ( R 2 3 ) T R 5 4 = R 4 R 5 = ( R 5 R 4 ) T = ( R 4 5 ) T .
P = R B A C R 4 5 R C B A R 2 3 R A C B ,
I 6 = P I 1 , I 1 r = P T I 6 r .
cos δ 6 , 6 r = ( I 6 r ) T I 6 , cos δ 1 , 1 r = ( I 1 r ) T I 1 .
cos δ 1 , 1 r = ( I 1 r ) T I 1 = ( P T I 6 r ) T I 1 = ( I 6 r ) T P I 1 = ( I 6 r ) T I 6 = cos δ 6 , 6 r .
{ I 12 = R B C A R 10 11 R A B C R 8 9 R C A B R 6 7 R B A C R 4 5 R C B A R 2 3 R A C B I 1 R 6 7 = R 7 R 6 R 8 9 = R 9 R 8 = ( R 4 5 ) T = ( R 5 R 4 ) T R 10 11 = R 11 R 10 = ( R 2 3 ) T = ( R 3 R 2 ) T .
I 6 = P I 1 , I 7 = R 6 7 I 6 , I 12 = P T I 7 .
cos δ 6 , 7 = ( I 7 ) T I 6 , cos δ 1 , 12 = ( I 12 ) T I 1 .
cos δ 1 , 12 = ( I 12 ) T I 1 = ( P T I 7 ) T I 1 = ( I 7 ) T P I 1 = ( I 7 ) T I 6 = cos δ 6 , 7 .
cos δ 1 , 1 r = cos δ 12 , 12 r .

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