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References

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  1. R. Crane, Appl. Opt. 8, 538 (1969).
  2. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 17 and 32.

1969 (1)

R. Crane, Appl. Opt. 8, 538 (1969).

1941 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 17 and 32.

Crane, R.

R. Crane, Appl. Opt. 8, 538 (1969).

Jones, R. C.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 17 and 32.

Appl. Opt. (1)

R. Crane, Appl. Opt. 8, 538 (1969).

J. Opt. Soc. Am. (1)

Other (1)

M. Born and E. Wolf, Principles of Optics, 3rd ed. (Pergamon, New York, 1965), pp. 17 and 32.

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Figures (2)

FIG. 1
FIG. 1

Up/down frequency shifter. The polarizations are shown for a fixed position and varying time.

FIG. 2
FIG. 2

Incorporation of the up/down frequency shifter with common interferometers: (a) Mach–Zehnder interferometer, (b) Twyman–Green interferometer, and (c) cyclic interferometer. FS is the up/down frequency shifter, TO is the test object, and M is a mirror. Note that the two quarter-wave plates in (b) are needed to rotate the linear polarization of the returning beams by 90° so that they pass through PB to OP.

Equations (14)

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V = [ 1 0 ] e - i ω t ,
T HWP = - i [ cos 2 θ sin 2 θ sin 2 θ - cos 2 θ ] ,
V = T HWP V = - i [ cos 2 ω t sin 2 ω t ] e - i ω t ,
V = - i 2 { [ 1 i ] e - i ( ω + 2 ω ) t + [ 1 - i ] e - i ( ω - 2 ω ) t } ,
T QWP = 1 2 [ 1 - i - i 1 ] .
V = T QWP V = - 1 2 { i [ 1 0 ] e - i ( ω + 2 ω ) t + [ 0 1 ] e - i ( ω - 2 ω ) t } ,
T PBT = [ 1 0 0 0 ]
T PBR = [ 0 0 0 1 ] .
V T = T PBT V = - i 2 [ 1 0 ] e - i ( ω + 2 ω ) t ,
V R = T PBR V = - 1 2 [ 0 1 ] e - i ( ω - 2 ω ) t .
V I = 1 2 { [ 1 0 ] e - i ( ω + 2 ω ) t + A e i ϕ [ 0 1 ] e - i ( ω - 2 ω ) t } ,
T LP = 1 2 [ 1 1 1 1 ] ,
V OP = T LP V I = 1 2 2 { e - i ( ω + 2 ω ) t + A e i ϕ e - i ( ω - 2 ω ) t } [ 1 1 ] ,
I OP = V OP V OP = 1 4 { 1 + A 2 + 2 A cos ( 4 ω t + ϕ ) } .