Abstract

We investigated the optical properties of a homodyne scanning optical microscope (HSOM) with phase-diversity detection. We found that an HSOM is a coherent imaging system and has the same coherent transfer function as a confocal scanning optical microscope (CSOM). In addition, the depth discrimination ability of an HSOM is the same as that of a CSOM. The resolution of an HSOM can be improved by inserting an annular aperture in the optical path of either the signal or reference beams without reducing the signal intensity.

© 2012 Optical Society of America

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References

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  1. T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).
  2. X. S. Gan and C. J. R. Sheppard, “Imaging in a confocal microscope with one circular and one annular lens,” Opt. Commun. 103, 254–264 (1993).
    [CrossRef]
  3. H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
    [CrossRef]
  4. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16, 674–676(2004).
    [CrossRef]
  5. C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility χ(3) for vibrational microscopy,” Opt. Lett. 29, 2923–2925(2004).
    [CrossRef]
  6. E. Hecht and A. Zajak, Optics (Addison-Wesley, 1974).
  7. S. Kimura and T. Wilson, “Effect of axial pinhole displacement in confocal microscopes,” Appl. Opt. 32, 2257–2261(1993).
    [CrossRef]
  8. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

2009 (1)

H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
[CrossRef]

2004 (2)

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16, 674–676(2004).
[CrossRef]

C. L. Evans, E. O. Potma, and X. S. Xie, “Coherent anti-Stokes Raman scattering spectral interferometry: determination of the real and imaginary components of nonlinear susceptibility χ(3) for vibrational microscopy,” Opt. Lett. 29, 2923–2925(2004).
[CrossRef]

1993 (2)

X. S. Gan and C. J. R. Sheppard, “Imaging in a confocal microscope with one circular and one annular lens,” Opt. Commun. 103, 254–264 (1993).
[CrossRef]

S. Kimura and T. Wilson, “Effect of axial pinhole displacement in confocal microscopes,” Appl. Opt. 32, 2257–2261(1993).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Evans, C. L.

Gan, X. S.

X. S. Gan and C. J. R. Sheppard, “Imaging in a confocal microscope with one circular and one annular lens,” Opt. Commun. 103, 254–264 (1993).
[CrossRef]

Hashizume, J.

H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
[CrossRef]

Hecht, E.

E. Hecht and A. Zajak, Optics (Addison-Wesley, 1974).

Ide, T.

H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
[CrossRef]

Kimura, S.

Kurokawa, T.

H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
[CrossRef]

Mikami, H.

H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
[CrossRef]

Miyamoto, H.

H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
[CrossRef]

Potma, E. O.

Sheppard, C.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Sheppard, C. J. R.

X. S. Gan and C. J. R. Sheppard, “Imaging in a confocal microscope with one circular and one annular lens,” Opt. Commun. 103, 254–264 (1993).
[CrossRef]

Shimano, T.

H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
[CrossRef]

Taylor, M. G.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16, 674–676(2004).
[CrossRef]

Watanabe, K.

H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
[CrossRef]

Wilson, T.

S. Kimura and T. Wilson, “Effect of axial pinhole displacement in confocal microscopes,” Appl. Opt. 32, 2257–2261(1993).
[CrossRef]

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

Xie, X. S.

Zajak, A.

E. Hecht and A. Zajak, Optics (Addison-Wesley, 1974).

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (1)

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16, 674–676(2004).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Mikami, T. Shimano, T. Kurokawa, T. Ide, J. Hashizume, K. Watanabe, and H. Miyamoto, “Amplification of optical disk readout signals by homodyne detection,” Jpn. J. Appl. Phys. 48, 03A014 (2009).
[CrossRef]

Opt. Commun. (1)

X. S. Gan and C. J. R. Sheppard, “Imaging in a confocal microscope with one circular and one annular lens,” Opt. Commun. 103, 254–264 (1993).
[CrossRef]

Opt. Lett. (1)

Other (3)

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

E. Hecht and A. Zajak, Optics (Addison-Wesley, 1974).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of the HSOM optical system.

Fig. 2.
Fig. 2.

Coherent transfer functions of the HSOM with aperture parameter of inner radius r. The inset shows the annular aperture used in the calculation.

Fig. 3.
Fig. 3.

Intensity variation versus optical units (u) when using flat mirror moved in the z direction.

Equations (20)

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vx=2πλxsinα,vy=2πλysinα,andu=2πλzsin2α,
vxd=2πλxsinβ,vyd=2πλysinβ,andud=2πλzsin2β,
a(vxd,vyd,ud;vxs,vys,us)=+h1(vx,vy,u)t(vxvxs,vyvys,uus)×h2(vxdvx,vydvy,udu)dvxdvydu.
(D1D2)=12(1,11,1)(ar).
|D1|2=12(aa*+rr*+ar*+a*r),|D2|2=12(aa*+rr*ar*a*r),},
Ih(ud;vxs,vys,us)=+|D1|2dvxddvyd+|D2|2dvxddvyd=+(ar*+a*r)dvxddvyd.
(D3D4)=12eiπ4(1,11,1)(1,00,i)(1,11,1)(ar)=12eiπ4(a+r+i(ar)a+ri(ar)).
|D3|2=14[(a+r)(a+r)*+(ar)(ar)*+2i(ar*a*r)],|D4|2=14[(a+r)(a+r)*+(ar)(ar)*2i(ar*a*r)].}.
Iq(ud;vxs,vys,us)=+|D3|2dvxddvyd+|D4|2dvxddvyd=i+(ar*a*r)dvxddvyd.
I(ud;vxs,vys,us)=Ih2+Iq2=(+ar*dvxddvyd)(+a*rdvxddvyd)=|+ar*dvxddvyd|2.
i(ud;vxs,vys,us)=+h1(vx,vy,u)t(vxvxs,vyvys,uus)h2(vxdvx,vydvy,udu)×h3*(vxd,vyd,ud)dvxdvydudvxddvyd.
hn(vx,vy,u)=+P(x0,y0)An(x0,y0)exp{i[vxx0+vyy0+12u(x02+y02)]}dx0dy0,
P(x0,y0)={1,(x02+y021)0,(x02+y02>1).
i(vxs,vys,us;ud)=h1(vxs,vys,us)+h2(vxdvxs,vydvys,udus)h3*(vxd,vyd,ud)dvxddvyd.
i(vxs,vys,us;ud)=h1(vxs,vys,us)[h2(vxs,vys,udus)h3*(vxs,vys,ud)],
C(s,t,us;ud)=(2π)4{P(s,t)A1(s,t)exp[i2us(s2+t2)]}{P(s,t)A2(s,t)A3(s,t)exp[i2us(s2+t2)]},
i(ud;vxs,vys,us)=+h(vx,vy,u)t(vxvxs,vyvys,uus)h(vxdvx,vydvy,ud+u)×h*(vxd,vyd,ud)dvxdvydudvxddvyd=+h(vx,vy,us)h(vxdvx,vydvy,ud+us)×h*(vxd,vyd,ud)dvxdvydvxddvyd.
+h(vx,vy,us)h(vxdvx,vydvy,ud+us)dvxdvy=(2π)2h(vxd,vyd,ud+2us),
i(ud;vxs,vys,us)=(2π)2+h(vxd,vyd,ud+2us)h*(vxd,vyd,ud)dvxdvy=(2π)4+P(x0,y0)exp[i2(ud+2us)(x02+y02)]×P*(x0,y0)exp[i2ud(x02+y02)]dx0dy0=(2π)4+P(x0,y0)exp[ius(x02+y02)]dx0dy0=(2π)4h(0,0,2us).
I(us)=(sinus2/us2)2.

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