Abstract

The van Cittert–Zernike theorem can be used to evaluate visibility at the exit of an amplitude-division interferometer with two-beam interferences. If the source illuminating the interferometer is a periodic array of slits, at the exit there is a sequence of localization surfaces. The formulas for the position and fringe spacing of the principal localization surfaces are applied to a Wollaston quartz prism, and there is good agreement between theoretical and experimental results. Moreover, the fringe localization depth and the intermediate localization surfaces obtained experimentally coincide with those predicted by theory.

© 2000 Optical Society of America

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References

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  1. S. A. Comastri, “Multilocalization of fringes and the van Cittert–Zernike theorem. 1. Theory,” J. Opt. Soc. Am. A 17, 1265–1276 (2000).
    [CrossRef]
  2. J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
    [CrossRef]
  3. M. C. Simon, “Ray tracing formulas for monoaxial optical components,” Appl. Opt. 22, 354–360 (1983).
    [CrossRef] [PubMed]
  4. M. C. Simon, R. M. Echarri, “Ray tracing formulas for monoaxial optical components: vectorial formulation,” Appl. Opt. 25, 1935–1939 (1986).
    [CrossRef] [PubMed]
  5. M. C. Simon, “Wollaston prism with large split angle,” Appl. Opt. 25, 369–376 (1986).
    [CrossRef] [PubMed]
  6. E. Hecht, A. Zajac, Optica (Addison-Wesley, Reading, Mass., 1974).

2000 (1)

1998 (1)

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

1986 (2)

1983 (1)

Comastri, S. A.

Echarri, R. M.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

M. C. Simon, R. M. Echarri, “Ray tracing formulas for monoaxial optical components: vectorial formulation,” Appl. Opt. 25, 1935–1939 (1986).
[CrossRef] [PubMed]

Garea, M. T.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

Hecht, E.

E. Hecht, A. Zajac, Optica (Addison-Wesley, Reading, Mass., 1974).

Simon, J. M.

J. M. Simon, M. C. Simon, R. M. Echarri, M. T. Garea, “Fringe localization in interferometers illuminated by a succession of incoherent line sources,” J. Mod. Opt. 45, 2245–2254 (1998).
[CrossRef]

Simon, M. C.

Zajac, A.

E. Hecht, A. Zajac, Optica (Addison-Wesley, Reading, Mass., 1974).

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Figures (8)

Fig. 1
Fig. 1

Experimental device: σ, light source consisting of a sodium source and a mask grating; E1 and E2, optical axes of the two wedges that compose the Wollaston prism; P1 and P2, polaroids; B, optical system consisting of a CCD camera and a microscope objective; T, reference to measure distances G.

Fig. 2
Fig. 2

Interferograms at Σ0: (a) without filter, (b) with filter.

Fig. 3
Fig. 3

Mask grating.

Fig. 4
Fig. 4

Interferograms: The calibration grating is at the top, and below it are the images of orders -2 to 2 between intermediate images with no fringes.

Fig. 5
Fig. 5

Images of the mask grating and of the interferogram at Σ0 between images of the calibration grating.

Fig. 6
Fig. 6

Theoretical plot μI,II versus Z and interferograms for N=69.

Fig. 7
Fig. 7

Fringe localization depth for m=2 and N=17: Sequence of images, the expected plot for the degree of coherence (solid curve), and a plot displaced 1 mm (dotted curve).

Fig. 8
Fig. 8

Source illuminating a Wollaston prism: (x, y, z): orthogonal coordinate system with origin at the central source point O and with z perpendicular to the source plane, x perpendicular to the source slits, and y perpendicular to (x, z); κ, angle of the quartz wedges that constitute the prism; O, image of O through the prism; OO, ray from O incident normally on the front face of the prism.

Tables (1)

Tables Icon

Table 1 Longitudinal Distance and Fringe Spacing in Σm

Equations (31)

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μI,II(P)=1N sin ζζ sin(ϑN)sin(ϑ)
ϑ=πq1δxE(0) Z(F+Z,ζ=πq1bE(0) Z(F+Z),
Z=PlocP,F=OPloc,q1=H cos βIIH
χ(P)=2[I(I)(P)I(II)(P)]1/2[I(I)(P)+I(II)(P)] |μI,II(P)|.
Zm=Fq1δx/(E(0)m)-1,
E(m)E(0)1+ZmF=E(0)1-mE(0)/(q1δx),
LD+|m=Zm+1/N-Zm=Fq˜(q˜-m)(N(q˜-m)-1),
LD-|m=Zm-Zm-1/N=Fq˜(q˜-m)(N(q˜-m)+1).
Ncal=184.1±1.35 pixels.
Zexp=Go-G.
GF=(208.99±0.12) mm,
Go=(122.66±0.20) mm,
G2=(75.19±0.32) mm.
E(m)|exp=cal NmNcal,ΔE(m)E(m) |expΔE(0)E(0) |exp.
F=(86.3±0.3) mm,2H=(24.5±0.1) mm.
F=(80.6±0.6) mm,q1=H cos βIIH=1,
Δq1<0.008.
δx=(0.356±0.004) mm,b=(0.107±0.005) mm,
E(0)=(67.3±0.8) μm,ΔE(0)E(0)=0.012,
N=17±1.
h=(15.0±0.1) mm,hP=(1.6±0.1) mm,
κ=(26.6°±0.3°).
no=1.5443,ne=1.5534,
α=17°±1°,F=(86.3±0.3) mm,
2H=(24.5±0.1) mm.
F=(80.6±0.6) mm,
H/H=1,Δ(H/H)<0.001.
s=s+(h+hP)(1-1/no).
F=F-OO cos α=F-(h+hP)(1-1/no)cos α=80.7 mm,
q1=H cos βIIH=1,
Δq1q1=Δ(H/H)H/H+Δ cos βIIcos βII<0.008.

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