Abstract

A method of optical frequency shifting for heterodyne interferometry based on counterrotating wave plates is described. It is possible with this technique to obtain a higher-frequency shift with fewer components.

© 1984 Optical Society of America

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References

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  1. R. Crane, Appl. Opt. 8, 538 (1969).
  2. G. E. Sommargren, J. Opt. Soc. Am. 65, 960 (1975).
    [CrossRef]
  3. R. N. Shagam, J. C. Wyant, Appl. Opt. 17, 3034 (1978).
    [CrossRef] [PubMed]
  4. H. Z. Hu, Appl. Opt. 22, 2052 (1983).
    [CrossRef] [PubMed]
  5. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]
  6. Note the difference in the form of the matrix of a QWP at 45° in Refs. 2–4.
  7. We omit all common factors appearing outside the matrices or vectors in our calculations.
  8. R. C. Jones, J. Opt. Soc. Am. 38, 671 (1948). We follow the vectorial representation of this paper for right- and left-handed circularly polarized light. Different representations have been used in Refs. 2–4.
    [CrossRef]

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1978 (1)

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1969 (1)

R. Crane, Appl. Opt. 8, 538 (1969).

1948 (1)

1941 (1)

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Figures (2)

Fig. 1
Fig. 1

Interferometer for heterodyne interferometry: L, light source; BS, beam splitter; TO, test object; MR, reference mirror; Q, QWP; A, analyzer; D, detector. FS1, FS2, and FS3 denote the possible locations of the frequency shifter.

Fig. 2
Fig. 2

Optical frequency shifting arrangements: (a) FS1, (b) FS2, (c) FS3. LP, linearly polarized light; H1 and H3, rotating HWP's; H2, stationary HWP; QF, fixed QWP with fast axis at 45° to the X axis; QR, rotating QWP; MR, reference mirror; OP, orthogonally polarized light components; A, analyzer; X, Y, and Z, coordinate axes.

Equations (13)

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E = [ 1 0 ] exp ( i ω t ) ,
Q ( θ ) = [ cos 2 θ i sin 2 θ sin θ cos θ ( 1 + i ) sin θ cos θ ( 1 + i ) sin 2 θ i cos 2 θ ] .
Q ( 45 ° ) = [ 1 i i 1 ] .
E 1 = Q ( 45 ° ) E = [ 1 i ] exp ( i ω t ) ,
H ( ω ) = [ cos 2 ω t sin 2 ω t sin 2 ω t cos 2 ω t ] .
E 2 = H ( ω ) E 1 = [ 1 i ] exp [ i ( ω + 2 ω ) t ] ,
H ( ω ) = [ cos 2 ω t sin 2 ω t sin 2 ω t cos 2 ω t ] .
E 3 = H ( ω ) E 2 = [ 1 i ] exp [ i ( ω + 4 ω ) t ] ,
E = Q ( 45 ° ) Q ( θ ) MQ ( θ ) Q ( 45 ° ) E .
M = [ 1 0 0 1 ] .
E = [ 1 0 ] exp [ i ( ω + 2 ω ) t ] ,
E = Q ( 45 ° ) H ( ω ) Q ( θ ) MQ ( θ ) H ( ω ) Q ( 45 ° ) E ,
E = [ 1 0 ] exp [ i ( ω 6 ω ) t ] .

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