Abstract

Apodized annular-aperture logarithmic axicons that form uniform-intensity axial line images with coherent light are studied in Gaussian-correlated illumination. Diffractive assessment of the line-image distributions and spatial coherence properties involves a highly oscillating double two-dimensional integral. The on-axis behavior depends only on radial integrals that can be computed with special-purpose routines. We show that at all correlation levels the images at off-axis points can be evaluated by using a technique based on spline approximations. We also demonstrate that the method of stationary phase can be sequentially applied to the four-dimensional diffraction integral, yielding accurate three-dimensional closed-form results. The stationary-phase formulas find applications in fast image evaluation, in intensity balancing by varying the irradiance, and in designing axicon phase profiles. The results complement our earlier study of partially coherent axicon images by radiometric transport techniques.

© 1999 Optical Society of America

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  34. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995), Chap. 4.
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    [CrossRef] [PubMed]
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    [CrossRef]
  44. F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
    [CrossRef]
  45. S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
    [CrossRef]
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1998 (3)

S. Yu. Popov, A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, B. Schnabel, “Apodized annular-aperture diffractive axicons fabricated by continuous-path-control electron beam lithography,” Opt. Commun. 154, 359–367 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, “Design of diffractive axicons for partially coherent light,” Opt. Lett. 23, 1639–1641 (1998).
[CrossRef]

1997 (1)

1996 (3)

1995 (2)

V. P. Koronkevich, I. A. Mikhaltsova, E. G. Churin, Yu. I. Yurlov, “Lensacon,” Appl. Opt. 34, 5761–5772 (1995).
[CrossRef] [PubMed]

S. Yu. Popov, A. T. Friberg, “Linear axicons in partially coherent light,” Opt. Eng. 34, 2567–2573 (1995).
[CrossRef]

1994 (2)

1993 (2)

1992 (7)

1991 (2)

R. Gase, “The multimode laser radiation as a Gaussian Schell-model beam,” J. Mod. Opt. 38, 1107–1115 (1991).
[CrossRef]

N. Davidson, A. A. Friesem, E. Hasman, “Holographic axilenses: high resolution and long focal depth,” Opt. Lett. 16, 523–525 (1991).
[CrossRef] [PubMed]

1990 (1)

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

1989 (1)

1988 (4)

1986 (1)

M. V. Perez, C. Gomez-Reino, J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

1982 (2)

R. C. Fairchild, J. R. Fienup, “Computer-originated aspheric holographic optical elements,” Opt. Eng. 21, 133–140 (1982).
[CrossRef]

A. T. Friberg, R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun. 41, 383–387 (1982).
[CrossRef]

1978 (1)

1976 (2)

E. Wolf, “New theory of radiative energy transfer in free electromagnetic fields,” Phys. Rev. D 13, 869–886 (1976).
[CrossRef]

L. Mandel, E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66, 529–535 (1976).
[CrossRef]

1975 (1)

W. T. Welford, “A vector raytracing equation for hologram lenses of arbitrary shape,” Opt. Commun. 14, 322–323 (1975).
[CrossRef]

1967 (1)

A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. AP-15, 187–188 (1967).
[CrossRef]

Aye, T.

Bara, S.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Sec. 3.1 and App. III.

Churin, E. G.

Cox, A. J.

Cuadrado, J. M.

M. V. Perez, C. Gomez-Reino, J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

D’Anna, J.

Davidson, N.

N. Davidson, A. A. Friesem, E. Hasnam, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

N. Davidson, A. A. Friesem, E. Hasman, “Holographic axilenses: high resolution and long focal depth,” Opt. Lett. 16, 523–525 (1991).
[CrossRef] [PubMed]

De Boor, C.

C. De Boor, A Practical Guide to Splines (Springer-Verlag, New York, 1978).

De Silvestri, S.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Erdelyi, A.

A. Erdelyi, Asymptotic Expansions (Dover, New York, 1956).

Erwin, D. A.

Fairchild, R. C.

R. C. Fairchild, J. R. Fienup, “Computer-originated aspheric holographic optical elements,” Opt. Eng. 21, 133–140 (1982).
[CrossRef]

Fienup, J. R.

R. C. Fairchild, J. R. Fienup, “Computer-originated aspheric holographic optical elements,” Opt. Eng. 21, 133–140 (1982).
[CrossRef]

Friberg, A. T.

S. Yu. Popov, A. T. Friberg, “Design of diffractive axicons for partially coherent light,” Opt. Lett. 23, 1639–1641 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, B. Schnabel, “Apodized annular-aperture diffractive axicons fabricated by continuous-path-control electron beam lithography,” Opt. Commun. 154, 359–367 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
[CrossRef]

W. Wang, A. T. Friberg, E. Wolf, “Focusing of partially coherent light in systems of large Fresnel numbers,” J. Opt. Soc. Am. A 14, 491–497 (1997).
[CrossRef]

A. T. Friberg, “Stationary-phase analysis of generalized axicons,” J. Opt. Soc. Am. A 13, 743–750 (1996).
[CrossRef]

A. T. Friberg, S. Yu. Popov, “Radiometric description of intensity and coherence in generalized holographic axicon images,” Appl. Opt. 35, 3039–3046 (1996).
[CrossRef] [PubMed]

S. Yu. Popov, A. T. Friberg, “Linear axicons in partially coherent light,” Opt. Eng. 34, 2567–2573 (1995).
[CrossRef]

A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988).
[CrossRef] [PubMed]

Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67, 245–250 (1988).
[CrossRef]

A. T. Friberg, J. Turunen, “Imaging of Gaussian Schell-model sources,” J. Opt. Soc. Am. A 5, 713–720 (1988).
[CrossRef]

A. T. Friberg, R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun. 41, 383–387 (1982).
[CrossRef]

A. T. Friberg, S. Yu. Popov, “Partially coherently illuminated uniform-intensity holographic axicons,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 224–227.

Friesem, A. A.

N. Davidson, A. A. Friesem, E. Hasnam, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

N. Davidson, A. A. Friesem, E. Hasman, “Holographic axilenses: high resolution and long focal depth,” Opt. Lett. 16, 523–525 (1991).
[CrossRef] [PubMed]

Gase, R.

R. Gase, “The multimode laser radiation as a Gaussian Schell-model beam,” J. Mod. Opt. 38, 1107–1115 (1991).
[CrossRef]

Gomez-Reino, C.

M. V. Perez, C. Gomez-Reino, J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

Gori, F.

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

Hasman, E.

Hasnam, E.

N. Davidson, A. A. Friesem, E. Hasnam, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

He, Q.

Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67, 245–250 (1988).
[CrossRef]

Herman, R. M.

Honkanen, M.

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, B. Schnabel, “Apodized annular-aperture diffractive axicons fabricated by continuous-path-control electron beam lithography,” Opt. Commun. 154, 359–367 (1998).
[CrossRef]

Jannson, T.

Jaroszewicz, Z.

Keren, E.

Kolodziejczyk, A.

Koronkevich, V. P.

Lautanen, J.

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, B. Schnabel, “Apodized annular-aperture diffractive axicons fabricated by continuous-path-control electron beam lithography,” Opt. Commun. 154, 359–367 (1998).
[CrossRef]

Lavi, S.

Magni, V.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Mandel, L.

L. Mandel, E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66, 529–535 (1976).
[CrossRef]

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995), Chap. 4.

Marcuse, D.

D. Marcuse, Principles of Optical Fiber Measurements (Academic, New York, 1981), Sec. 4.7.

Mikhaltsova, I. A.

Perez, M. V.

M. V. Perez, C. Gomez-Reino, J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

Popov, S. Yu.

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, B. Schnabel, “Apodized annular-aperture diffractive axicons fabricated by continuous-path-control electron beam lithography,” Opt. Commun. 154, 359–367 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, “Design of diffractive axicons for partially coherent light,” Opt. Lett. 23, 1639–1641 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
[CrossRef]

A. T. Friberg, S. Yu. Popov, “Radiometric description of intensity and coherence in generalized holographic axicon images,” Appl. Opt. 35, 3039–3046 (1996).
[CrossRef] [PubMed]

S. Yu. Popov, A. T. Friberg, “Linear axicons in partially coherent light,” Opt. Eng. 34, 2567–2573 (1995).
[CrossRef]

A. T. Friberg, S. Yu. Popov, “Partially coherently illuminated uniform-intensity holographic axicons,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 224–227.

Prochaska, R.

Schell, A. C.

A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. AP-15, 187–188 (1967).
[CrossRef]

Schnabel, B.

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, B. Schnabel, “Apodized annular-aperture diffractive axicons fabricated by continuous-path-control electron beam lithography,” Opt. Commun. 154, 359–367 (1998).
[CrossRef]

Sochacki, J.

Soroko, L. M.

L. M. Soroko, “Axicons and meso-optical imaging devices,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1989), Vol. 27, pp. 109–160.

Staronski, L. R.

Sudol, R. J.

A. T. Friberg, R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun. 41, 383–387 (1982).
[CrossRef]

Svelto, O.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Tengara, I.

Turunen, J.

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, B. Schnabel, “Apodized annular-aperture diffractive axicons fabricated by continuous-path-control electron beam lithography,” Opt. Commun. 154, 359–367 (1998).
[CrossRef]

A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
[CrossRef] [PubMed]

Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67, 245–250 (1988).
[CrossRef]

A. T. Friberg, J. Turunen, “Imaging of Gaussian Schell-model sources,” J. Opt. Soc. Am. A 5, 713–720 (1988).
[CrossRef]

J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988).
[CrossRef] [PubMed]

Valentini, G.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

Vasara, A.

Wang, W.

Welford, W. T.

W. T. Welford, “A vector raytracing equation for hologram lenses of arbitrary shape,” Opt. Commun. 14, 322–323 (1975).
[CrossRef]

Wiggins, T. A.

Wolf, E.

Yurlov, Yu. I.

Appl. Opt. (6)

IEEE J. Quantum Electron. (1)

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, “Lasers with super-Gaussian mirrors,” IEEE J. Quantum Electron. 26, 1500–1509 (1990).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. C. Schell, “A technique for the determination of the radiation pattern of a partially coherent aperture,” IEEE Trans. Antennas Propag. AP-15, 187–188 (1967).
[CrossRef]

J. Mod. Opt. (1)

R. Gase, “The multimode laser radiation as a Gaussian Schell-model beam,” J. Mod. Opt. 38, 1107–1115 (1991).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (7)

Opt. Acta (1)

M. V. Perez, C. Gomez-Reino, J. M. Cuadrado, “Diffraction patterns and zone plates produced by thin linear axicons,” Opt. Acta 33, 1161–1176 (1986).
[CrossRef]

Opt. Commun. (6)

A. T. Friberg, R. J. Sudol, “Propagation parameters of Gaussian Schell-model beams,” Opt. Commun. 41, 383–387 (1982).
[CrossRef]

W. T. Welford, “A vector raytracing equation for hologram lenses of arbitrary shape,” Opt. Commun. 14, 322–323 (1975).
[CrossRef]

N. Davidson, A. A. Friesem, E. Hasnam, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Q. He, J. Turunen, A. T. Friberg, “Propagation and imaging experiments with Gaussian Schell-model beams,” Opt. Commun. 67, 245–250 (1988).
[CrossRef]

S. Yu. Popov, A. T. Friberg, M. Honkanen, J. Lautanen, J. Turunen, B. Schnabel, “Apodized annular-aperture diffractive axicons fabricated by continuous-path-control electron beam lithography,” Opt. Commun. 154, 359–367 (1998).
[CrossRef]

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

Opt. Eng. (2)

S. Yu. Popov, A. T. Friberg, “Linear axicons in partially coherent light,” Opt. Eng. 34, 2567–2573 (1995).
[CrossRef]

R. C. Fairchild, J. R. Fienup, “Computer-originated aspheric holographic optical elements,” Opt. Eng. 21, 133–140 (1982).
[CrossRef]

Opt. Lett. (6)

Opt. Quantum Electron. (1)

Special issue on laser beam quality, Opt. Quantum Electron. 24, S861–S1135 (1992).

Phys. Rev. D (1)

E. Wolf, “New theory of radiative energy transfer in free electromagnetic fields,” Phys. Rev. D 13, 869–886 (1976).
[CrossRef]

Pure Appl. Opt. (1)

S. Yu. Popov, A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
[CrossRef]

Other (13)

L. M. Soroko, “Axicons and meso-optical imaging devices,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1989), Vol. 27, pp. 109–160.

Z. Jaroszewicz, Axicons: Design and Propagation Properties, Vol. 5 of Research & Development Treatises (Society of Photo-Optical Instrumentation Engineers Polish Chapter, Warsaw, 1997).

A. T. Friberg, ed., Selected Papers on Coherence and Radiometry, Vol. 69 of Milestone Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993).

A. Giesen, M. Morin, eds., Proceedings of the 4th International Workshop on Laser Beam and Optics Characterization, Munich, June 16–18, 1997 (Institut für Strahlwerkzeuge, Stuttgart, 1997).

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Figures (8)

Fig. 1
Fig. 1

Geometry and notation associated with line-image formation by diffractive axicons. The element has an annular aperture of inner and outer radii r1 and r2, respectively. A uniform-intensity axial image is shown schematically.

Fig. 2
Fig. 2

On-axis intensity profiles produced in coherent light by a circular diffractive axicon of radius r2=12.5 mm, designed for parameters d1=1220 mm, δz=60 mm, and λ=0.633 µm. The three (practically indistinguishable) solid curves are obtained with phase functions φ(ρ) in Eqs. (7) and (8) and relation (9), respectively, and the dashed curve results from phase φL(ρ) in relation (10).

Fig. 3
Fig. 3

Axial intensity distributions produced by an apodized annular-aperture logarithmic axicon in spatially uniform illumination of different degrees of coherence: (a) σg= (upper curve) and σg=7.5 mm (lower curve), (b) σg=1.0 mm (upper curve) and σg=0.25 mm (lower curve). The dashed curve in (b) corresponds to a radially linearly increasing intensity of illumination. The system parameters are r1=2.5 mm, r2=5.0 mm, d1=100 mm, d2=200 mm, and λ=0.633 µm.

Fig. 4
Fig. 4

Real parts of kernel C numerically integrated from Eq. (3) at ρ=0.05 mm, z=120 mm, and λ=0.633 µm as a function of ρ1 and ρ2. The correlation width is (a) σg=, (b) σg=7.5 mm, (c) σg=1.0 mm, and (d) σg=0.25 mm.

Fig. 5
Fig. 5

3D intensity distributions of line images formed by an annular-aperture diffractive axicon in partially coherent light. The profiles are calculated with a spline-approximation technique for (a) σg=, (b) σg=7.5 mm, (c) σg=1.0 mm, and (d) σg=0.25 mm. The system parameters are as in Fig. 3.

Fig. 6
Fig. 6

3D intensity profile generated by an apodized annular-aperture logarithmic axicon in illumination with σg=0.1 mm. The plot is computed from the asymptotic formula, Eqs. (4) and (17), with S0=1. Other parameters are as in Fig. 3.

Fig. 7
Fig. 7

1D prism configuration and notation. The separation between the (fictitious) input and output planes is d.

Fig. 8
Fig. 8

Change in the angle at which the far-zone intensity distribution peaks (solid curve) and the width of the intensity distribution (HWHM, marked by dashed curves) as a function of the coherence width kσg of the incident light. The parameters are α=17.2°, n=1.5, and λ=0.633 µm.

Equations (23)

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Win(ρ1, ρ2)=S0 exp[-(ρ1-ρ2)2/2σg2],
W(ρ1, z1, ρ2, z2)
=k2π2 exp[-ik(z1-z2)]z1z2AWin(ρ1, ρ2)t(ρ1)t(ρ2)×exp{-ik[φ(ρ1)-φ(ρ2)]}×exp{-ik[(ρ1-ρ1)2/2z1-(ρ2-ρ2)2/2z2]}d2ρ1d2ρ2,
I(ρ, z)=S0(k/2πz)2At(ρ1)t(ρ2)C(ρ1, ρ2; ρ, z; σg)×exp[-ik(ρ12-ρ22)/2z]×exp{-ik[φ(ρ1)-φ(ρ2)]}ρ1ρ2 dρ1dρ2,
C(ρ1, ρ2; ρ, z; σg)
=exp[-(ρ12+ρ22)/2σg2]×02π exp[ρ1ρ2 cos(ϕ1-ϕ2)/σg2]×exp[-ikρ(ρ1 cos ϕ1-ρ2 cos ϕ2)/z]dϕ1dϕ2
μ(ρ1, z1, ρ2, z2)
=W(ρ1, z1, ρ2, z2)/[I(ρ1, z1)I(ρ2, z2)]1/2.
C(ρ1, ρ2; ρ, z; )=(2π)2J0(kρρ1/z)J0(kρρ2/z),
φ(ρ)=-12alog{2a[a2ρ4+(1+2ad1)ρ2+d12]1/2+2a2ρ2+1+2ad1},
φ(ρ)=-(2a)-1 log(1+aρ2/d1),
φ(ρ)-ρ2(2d1+aρ2)-1.
φL(ρ)-ρ2(2d1+2aρ2)-1.
C(ρ1, ρ2; 0, z; σg)=(2π)2I0(ρ1ρ2/σg2)×exp[-(ρ12+ρ22)/2σg2],
φ(ρ)=-(2a)-1 log[1+a(ρ2-r12)/d1],
t(ρ)={0.5+arctan[Δ(ρ-r1)]/π}×{0.5+arctan[Δ(r2-ρ)]/π},
ρc=[r12+(z-d1)/a]1/2,
ψ1(2)(ρc)=-ψ2(2)(ρc)=-ψ(2)(ρc)=-2(z-d1+ar12)/z2=-2aρc2/z2.
Isp(ρ, z)=S0(k/2πz2)T(ρc)C(ρc, ρc; ρ, z; σg)×ρc2[ψ(2)(ρc)]-1,
Isp(ρ, z)=S0(k/4πa)T(ρc)C(ρc, ρc; ρ, z; σg).
Wout(ρ1, ρ2)=Win(ρ1, ρ2)exp[ikβ(y1-y2)],
Win(ρ1, ρ2)=S0 exp[-(y1-y2)2/2σg2],
I()(rs)=DS0 (kσg)22πcos2 θr2exp-12(kσg)2(sin θ-β)2,

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