Abstract

Based on the characteristic of a confocal microscope (CM) that the offset of a pinhole along an optical axis changes the axial intensity response phase, a novel tri-heterodyne confocal microscope is built up by dividing the CM measurement light path into three paths, and using three sets of focusing lenses, detectors and pinholes placed behind, on and before the focal plane to form three detection systems, thereby achieving the axial superresolution imaging and high Signal Noise Ratio (SNR) through pairwise heterodyne subtraction of three intensity signals with given phases received by the three detection systems and data processing. Simulation and experimental results indicate that the new tri-heterodyne confocal microscope reduces the full width at the half maximum of CM axial response curve by more than 50%, results in the significant improvement of CM anti-interference capability, and enables CM to be more suitable for high accuracy bipolar absolute measurement of 3D microstructures and surface contours.

©2004 Optical Society of America

1. Introduction

Confocal microscopes(CM) are widely used for imaging measurement in the fields of microelectronics, material, industrial precision measurement, biomedicine and life sciences for their good 3D chromatographic imaging capabilities[1–5],but further improvement of their chromatographic imaging capabilities is limited by diffractive effect although chromatographic capability can be improved by conventional methods of increasing the numerical aperture of a microscope objective and decreasing light wave length. In order to exceed the diffractive limitation and improve CM chromatographic imaging capability, many unconventional confocal microscopy imaging principles and superresolution methods have been recently proposed[1–14]. In the CM research field, 4PI CM, θ CM, confocal interference microscope, fiber-optic confocal scanning microscope(FOCSM), and dual-and multi-photons CM based on optical nonlinear property, etc. are proposed [1–4], and these new CM imaging methods further expand the scopes of CM application and make chromatographic imaging of transparent, semitransparent and opaque samples possible, so that CM can be used for measurement of both highly reflective industrial samples and highly scattering biological samples [2–4]. In the superresolution imaging technique field, pupil filtering, phase shift mask technique and superresolution techniques based on nonlinear variation of optical characteristics[3,6–9] and illumination superresolution techniques which reduce the main lobe of Airy spot in the optical system by changing the spatial frequency distribution of the incidence beam, etc. are proposed, and the illumination superresolution techniques include the recent orthogonal polarized light illumination and interferometric approach in addition to off-axis illumination, transfiguration illumination, and annular beam illumination [12–15].

In general, the new CMs and superresolution methods and techniques improved the CM axial resolution and made many CM superresolution imaging measurement possible [1–14]. However, all existing CMs directly use the intensity signals received for image processing, and they are subject to the influence of such factors as disturbance in intensity, ambient light disturbance and drift of ambient temperature, and so, the CM image system has a lower Signal Noise Ratio (SNR); the axial chromatographic accuracy of CM is limited by the nonlinearity of its axial intensity curve; the new CMs and existing superresolution techniques achieve superresolution imaging by sharpening the main lobe of CM Airy spot, but their side lobes and nonlinear errors of the axial response curves increase in the process of sharpening the main lobe, for instance, in the dual- and multi- photons CM based on optical nonlinear property and pupil filter superresolution approach. In order to further improve SNR and axial superresolution, a tri-heterodyne confocal microscope(TCM) totally different from superresolution approaches mentioned above is proposed. In addition, the TCM proposed makes high accuracy bipolar absolute measurement of 3D contours and surfaces possible.

2. TCM principle

TCM uses the offset of a pinhole in optical axis to change the CM axial intensity response phase and divide the CM receiving light path into three paths which are separately focused by the same three collecting lenses, and the CM three confocal photoelectric detecting systems consist of three pinholes and detectors placed behind, at and before the focus, and improve the CM axial resolution and anti-interference capability through pairwise heterodyne subtraction and processing of three signals with given phases received. As shown in Fig. 1, the light coming from a laser passes through an extender and a polarized beam splitter(PBS), and it is then converted into p light with polarization direction parallel to the paper surface, which passes through 1/4 wave plate and is focused on the surface of the object by a microscope objective, the light reflected by the object passes through 1/4 wave plate again and is converted into s light with polarization direction perpendicular to the paper surface, which is reflected by the PBS onto beam splitter 1(BS1). The measurement light is split into two beams by BS1, the measurement light reflected by BS1 is focused by collecting lens C, and it passes through a pinhole placed at the focus of collecting lens C and is received by detector C; the light passing through BS1 is split again into two beams by BS2, the measurement light reflected by BS2 is focused by collecting lens B, and it passes through pinhole B at distance M from the focus of collecting lens B and is received by detector B; the measurement light passing through BS2 is focused by collecting lens A, and it passes through pinhole A at distance M from collecting lens A and is received by detector A; heterodyne subtraction processing systems A,B and C cause the pairwise heterodyne subtractions of the three signals with given phases, and they are processed by a computer to achieve the axial superresolution confocal microscopy imaging detection.

 

Fig. 1. Tri-heterodyne CM with axial superresolution.

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In TCM, BS1 has a splitter beam ratio of 2:1 between transmission and reflection, and BS2 has a ratio of 1:1, intensity adjustors PA, PB and PC are used to adjust the three measurement beams and equalize their transmitting intensity.

When the object is scanned with the workbench in the axial or lateral direction, the light source, extender, PBS, 1/4 wave plate, microscope objective, collecting lens A, pinhole A and photoelectric detector A form a para-CM with a detector placed before the focus, and intensity response I 1(v,u,+uM) received by photoelectric detector A is:

I1vu,+uM=[201P(ρ)·exp(juρ22)J0(ρv)ρdρ]2×[201P(ρ)·exp(jρ2(u+uM)2)J0(ρv)ρdρ]2

where J 0 is a first order Bessel function, ρ is a normalized radial radius, u and v are axial and lateral normalized optical coordinates, and

u=(8πλ)zsin2(α02),v(2πλ)rsinα0

where z is the axial movement of the object, r is the radial coordinate of the object lens, α 0 is the numerical aperture angle, and uM is the optical normalized coordinate corresponding to distance M of the detector in the axial direction from the focus of a collecting lens.

The light source, extender, PBS, 1/4 wave plate, the microscope objective, collecting lens B, pinhole B and photoelectric detector B form a para-CM with a detector placed behind the focus, and intensity response I 2(v,u,-uM) received by photoelectric detector B is:

I2vu,uM=[201P(ρ)·exp(juρ22)J0(ρv)ρdρ]2×[201P(ρ)·exp(jρ2(uuM)2)J0(ρv)ρdρ]2

The light source, extender, PBS, 1/4 wave plate, microscope objective, collecting lens C, pinhole C and photoelectric detector C form a CM, and intensity response l 3(v,u,0) received by photoelectric detector C is:

I3vu,0=[201P(ρ)·exp(juρ22)J0(ρv)ρdρ]2×[201P(ρ)·exp(juρ22)J0(ρv)ρdρ]2

After pairwise heterodyne subtractions of signals I 3(v,u,0), I 2(v,u,-uM) and I 1(v,u,+uM) received by photoelectric detectors A, B and C,

{IAvu=I3vu0I2vuuMIBvu=I3vu0I1vu+uMICvu=I2vuuMI1vu+uM

A computer is used to do the real-time processing of IA(v,u), IB(v,u) and IC(v,u), and the intensity response of TCM is:

Ivu={IAvu,whenICvu0IBvu,whenICvu<0

The magnitude of intensity response I(v,u) corresponds to the knaggy change of the object, and it is used to reconstruct the surface contour and microdimensions of the object. Figure 2(a) shows normalized intensity response I(v,u) of TCM obtained using (6), Fig. 2(b) shows normalized intensity response I 3(v,u,0) of conventional CM, and in comparison with I 3(v,u,0), the main lobe of I(v,u) is sharpened, the linearity of I(v,u) in the axial direction is improved, and the side lobe of I(v,u)>0 is suppressed.

 

Fig. 2. Simulated curved surfaces of TCM and CM intensity

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For such given system parameters as numerical aperture of objective, pinhole size and detector sensitivity, the sensitivities of the slope linear intervals in axial intensity curves IA(0,u), IB(0,u) and IC(0,u) depend on uM, and there is an uM in reality to optimize the TCM axial resolution and chromatographic capability.

Sensitivity kA(0,u,uM) is obtained using the differential of heterodyne signal IA(0,u) on u, and slopes kA(0,u,uM) and kA(0,0,uM) are equal in the linear interval, so the slope of IA(0,u) in the linear interval is expressed as kA(0,0,uM), then

kA0, 0uM=sinc[(uM)4π]·[(uM4)·cos(uM4)sin(uM4)]{(uM4)}2

Similarly, slope kB(0,0,uM) of IB(0,u) in the linear interval is:

kB0, 0uM=sinc[(uM)4π]·[(uM4)·cos(uM4)sin(uM4)]{(uM4)}2

Slope kB(0,0,uM) of IB(0,u) in the linear interval is:

kC0, 0uM=2sinc[(uM)4π]·[(uM4)·cos(uM4)sin(uM4)]{(uM4)}2

When uM=±5.21, the absolute values of kA(0,0,uM), kB(0,0,uM) and kC(0,0,uM) extremes obtained through calculating the extreme of Eqs. (7), (8) and (9) are the largest, they are 0.27, -0.27 and 0.54 respectively, and here, the full width at the half maximum (FWHM) of I(0,u) is the smallest, the axial resolution is the largest and the chromatographic capability is the strongest.

Intensity curves I 1(0,u,+uM), I 2(0,u,-uM), I 3(0,u,0), IC(0,u) and I(0,u) when uM=5.21 are shown in Fig. 3(a), and their normalized curves are shown in Fig. 3(b).

 

Fig. 3. Simulated axial intensity curves with uM =5.21.

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TCM works in range ab_when it is used for chromatographic imaging, and it can be seen from Fig. 3(b) that FWHM of curve I(0,u) is twice smaller than that of curve I 3(0,u,0) in the imaging range, i.e. TCM axial resolution is improved 66% better than CM axial resolution, the linearity of two slope intervals in curve I(0,u) is better than that in curve I 3(0,u,0), and the side lobe has the smallest effect on the imaging quality in imaging range ab.

As shown in Fig. 3, conventional CMs use the slopes of intensity response curves I 3(0,u,0) to measure surface contours and microstructures, the measurement accuracy is subject to the influence of the nonlinearity of the slope interval in curve I 3(0,u,0), the disturbance of light source in intensity and environmental disturbance, etc., and the system has no absolute measurement zero required for absolute measurement. In TCM, intensity curve IC(0,u) obtained through heterodyne subtraction is used for measurement of surface contours and microstructures. It can be seen from Fig. 3 that, in comparison with I 3(0,u,0), the linearity and resolution of IC(0,u) are improved, and there is in curve IC(0,u) an absolute measurement zero needed for bipolar absolute measurement and tracing and aiming. In TCM, I(0,u) and IC(0,u) are obtained through pairwise heterodyne subtraction of I 3(0,u,0) with I 2(v,u,-uM) and I 1(v,u,+uM), and the effect of TCM intensity disturbance, the surface reflectivity variation of the object and environmental factors on these heterodyne signals is dramatically reduced, and therefore, environmental anti-interference of TCM are significantly improved, and none of the existing axial superresolution CM has such a capability to achieve this.

The effect of uM on I(0,u) should be taken into account while uM of TCM is selected. Figure 4(a) shows the axial intensity curves when uM=8.0, and Fig. 4(b) shows their normalized curves. In comparison with Fig. 3(a), intensity curve I(0,u) in Fig. 4 has a smaller FWHM and a larger intensity, so, the selection of uM should take into consideration its effect on intensity, in addition to satisfy the superresolution requirement.

 

Fig. 4. Simulated axial intensity curves when uM =8.0.

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3. Experiments and analyses

TCM experimental setup is established as shown in Fig. 1, the microscope objective used is an objective of 60×0.85, the sizes of pinholes used are 10μm in diameter, and the object used is a gauge block. The gauge bolck is moved with a movable workbench in TCM axial direction and its displacement z is measured by laser heterodyne interferometer HP5529A. Figure 5(a) shows measured intensity curves I 1(0,z,+M), I 2(0,z,-M) and I 3(0, z, 0), and intensity curves IC(0,z) and I(0,z) obtained through heterodyne subtraction of I 1(0,z,+M), I 2(0,z,-M) and I 3(0,z,0). Figure 5(b) shows the normalized curves of I 3(0,z,0) and I(0,z).

 

Fig. 5. Measured intensity response curves.

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It can be seen from Fig. 5(b) that FWHM of curve I 3(0,z,0) is twice as wide as that of I(0,z) in the measurement range of I(0,z)>0, i.e.CM axial resolution is improved by about 50%, the linearity of two slope intervals in curve I(0,z) is better than that in curve I 3(0,z,0), and the side lobe has a smaller effect on the measurements in the range of I(0,z)>0. In Fig. 5(a), in comparison with I 3(0,z,0), the linear range of intensity curve IC(0,z) is expanded, the resolution and linearity of curve IC(0,z) are improved, and there is an absolute measurement zero in curve IC(0,z). All these measurements are in good agreement with the results of simulations and theoretical analyses mentioned above.

In TCM, superrolution imaging is achieved through pairwise heterodyne subtraction of three signals with different phases at the signal processing stage; in the existing superresolution filtering, superrolution imaging is achieved by changing the pupil function of a collecting or object lens by a superresolution element placed before the collecting or object lens; the comparison of TCM with CM indicates that they achieve superresolution imaging in different ways and with superresolution element in different position, so TCM can be easily combined with superresolution pupil filtering and complement each other to achieve higher superresolution imaging.

4. Conclusions

Theoretical analyses and preliminary experiments indicate that the TCM based on the characteristic that the offset of CM pinhole along the optical axis changes the axial intensity response phase has high SNR and axial superresolution imaging capability, and it can:

  1. improve CM chromatographic capability by about 50%, and improves the linearity of the axial response and CM chromatographic accuracy;
  2. suppress the common mode noise caused by environmental disturbance, the disturbance of the light source in intensity and detector’s electrical drift, and improve CM SNR;
  3. achieve bipolar measurement function of confocal measurement system, and be more suitable for high accuracy bipolar absolute measurement of 3D surface contours and 3D microstructures;
  4. satisfy the higher superresolution requirements through its easy combination with existing pupil filters.

TCM provides a new imaging approach and technique with high SNR and axial superresolution capability in the optical microscopy imaging field.

Acknowledgments

Thanks to National Science Foundation of China (No.50475035) for the support.

References

1. T. Wilson, Confocal Microscopy (Academic press limited, 1990).

2. J. Pawley, Handbook of Biological Confocal Microscopy (Plenun, New York, 1995). [CrossRef]  

3. Min Gu, Principles of three-dimensional Imaging in Confocal Microscopes (World Scientific Publishing Co.Pte.Ltd., Singapore,1996).

4. A. Diaspro (ed.) Confocal and Two-Photon Microscopy. Foundations, Applications and Advances (Wiley, New York, 2001).

5. C.H. Lee and J.P. Wang,“Noninterferometric Differential Confocal Microscopy With 2-nm Depth Resolution,” Opt. Commun. l35,233~237(1997). [CrossRef]  

6. T. Wilson and S.J. Hewlett, “Superresonlution in confocal scanning microscopy,” Opt.Lett. 16, 1062–1064 (1991). [CrossRef]   [PubMed]  

7. DanielM. de Juana, Jose E. Oti, and Vidal F. Canales, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609 (2003). [CrossRef]   [PubMed]  

8. Liu Li, Deng Xiao-qang, and Wang Gui-ying, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Physica Sinica 50, 48–51(2001).

9. Tasso R.M. Sales and Michael Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997). [CrossRef]   [PubMed]  

10. C.J. Schwarz, Y. Kuznetsova, and S.R.J. Brueck, “Imaging interferometric microscopy,” Opt. Lett. 28, 1424–1426 (2003). [CrossRef]   [PubMed]  

11. X. Chen and S.R.J Brueck, “Imaging interferometric lithography: approaching the resolution limits of optics,” Opt.Lett. 24, 124–126 (1999). [CrossRef]  

12. Vicente Mico, AIDO, and Zeev Zalevsky, “Single-step superresolution by interferometric imaging,” Opt. Express 12, 2589–2596 (2004).http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2589 [CrossRef]   [PubMed]  

13. M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and Universidad de Valencia, “Axial gain resolutionin optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 15, 1740–1745 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1740 [CrossRef]  

14. Haifeng Wang, “New approach to supperresolution,” Opt. Eng. 40, 851~855(2001). [CrossRef]  

15. Andrew I. Whiting, Ayman F. Abouraddy, Bahaa E.A. Saleh, and Malvin C. Teich, “Polarization -assisted transverse and axial optical superresolution,” Opt. Express 15, 1714–1723 (2003). [CrossRef]  

References

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  1. T. Wilson, Confocal Microscopy (Academic press limited, 1990).
  2. J. Pawley, Handbook of Biological Confocal Microscopy (Plenun, New York, 1995).
    [Crossref]
  3. Min Gu, Principles of three-dimensional Imaging in Confocal Microscopes (World Scientific Publishing Co.Pte.Ltd., Singapore,1996).
  4. A. Diaspro (ed.) Confocal and Two-Photon Microscopy. Foundations, Applications and Advances (Wiley, New York, 2001).
  5. C.H. Lee and J.P. Wang,“Noninterferometric Differential Confocal Microscopy With 2-nm Depth Resolution,” Opt. Commun. l35,233~237(1997).
    [Crossref]
  6. T. Wilson and S.J. Hewlett, “Superresonlution in confocal scanning microscopy,” Opt.Lett. 16, 1062–1064 (1991).
    [Crossref] [PubMed]
  7. DanielM. de Juana, Jose E. Oti, and Vidal F. Canales, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609 (2003).
    [Crossref] [PubMed]
  8. Liu Li, Deng Xiao-qang, and Wang Gui-ying, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Physica Sinica 50, 48–51(2001).
  9. Tasso R.M. Sales and Michael Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
    [Crossref] [PubMed]
  10. C.J. Schwarz, Y. Kuznetsova, and S.R.J. Brueck, “Imaging interferometric microscopy,” Opt. Lett. 28, 1424–1426 (2003).
    [Crossref] [PubMed]
  11. X. Chen and S.R.J Brueck, “Imaging interferometric lithography: approaching the resolution limits of optics,” Opt.Lett. 24, 124–126 (1999).
    [Crossref]
  12. Vicente Mico, AIDO, and Zeev Zalevsky, “Single-step superresolution by interferometric imaging,” Opt. Express 12, 2589–2596 (2004).http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2589
    [Crossref] [PubMed]
  13. M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and Universidad de Valencia, “Axial gain resolutionin optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 15, 1740–1745 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1740
    [Crossref]
  14. Haifeng Wang, “New approach to supperresolution,” Opt. Eng. 40, 851~855(2001).
    [Crossref]
  15. Andrew I. Whiting, Ayman F. Abouraddy, Bahaa E.A. Saleh, and Malvin C. Teich, “Polarization -assisted transverse and axial optical superresolution,” Opt. Express 15, 1714–1723 (2003).
    [Crossref]

2004 (1)

2003 (4)

Andrew I. Whiting, Ayman F. Abouraddy, Bahaa E.A. Saleh, and Malvin C. Teich, “Polarization -assisted transverse and axial optical superresolution,” Opt. Express 15, 1714–1723 (2003).
[Crossref]

C.J. Schwarz, Y. Kuznetsova, and S.R.J. Brueck, “Imaging interferometric microscopy,” Opt. Lett. 28, 1424–1426 (2003).
[Crossref] [PubMed]

M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and Universidad de Valencia, “Axial gain resolutionin optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 15, 1740–1745 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1740
[Crossref]

DanielM. de Juana, Jose E. Oti, and Vidal F. Canales, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609 (2003).
[Crossref] [PubMed]

2001 (2)

Haifeng Wang, “New approach to supperresolution,” Opt. Eng. 40, 851~855(2001).
[Crossref]

Liu Li, Deng Xiao-qang, and Wang Gui-ying, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Physica Sinica 50, 48–51(2001).

1999 (1)

X. Chen and S.R.J Brueck, “Imaging interferometric lithography: approaching the resolution limits of optics,” Opt.Lett. 24, 124–126 (1999).
[Crossref]

1997 (2)

Tasso R.M. Sales and Michael Morris, “Fundamental limits of optical superresolution,” Opt. Lett. 22, 582–584 (1997).
[Crossref] [PubMed]

C.H. Lee and J.P. Wang,“Noninterferometric Differential Confocal Microscopy With 2-nm Depth Resolution,” Opt. Commun. l35,233~237(1997).
[Crossref]

1991 (1)

T. Wilson and S.J. Hewlett, “Superresonlution in confocal scanning microscopy,” Opt.Lett. 16, 1062–1064 (1991).
[Crossref] [PubMed]

Abouraddy, Ayman F.

Andrew I. Whiting, Ayman F. Abouraddy, Bahaa E.A. Saleh, and Malvin C. Teich, “Polarization -assisted transverse and axial optical superresolution,” Opt. Express 15, 1714–1723 (2003).
[Crossref]

AIDO,

Brueck, S.R.J

X. Chen and S.R.J Brueck, “Imaging interferometric lithography: approaching the resolution limits of optics,” Opt.Lett. 24, 124–126 (1999).
[Crossref]

Brueck, S.R.J.

Canales, Vidal F.

Chen, X.

X. Chen and S.R.J Brueck, “Imaging interferometric lithography: approaching the resolution limits of optics,” Opt.Lett. 24, 124–126 (1999).
[Crossref]

de Juana, DanielM.

de Valencia, Universidad

M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and Universidad de Valencia, “Axial gain resolutionin optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 15, 1740–1745 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1740
[Crossref]

Gu, Min

Min Gu, Principles of three-dimensional Imaging in Confocal Microscopes (World Scientific Publishing Co.Pte.Ltd., Singapore,1996).

Gui-ying, Wang

Liu Li, Deng Xiao-qang, and Wang Gui-ying, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Physica Sinica 50, 48–51(2001).

Hewlett, S.J.

T. Wilson and S.J. Hewlett, “Superresonlution in confocal scanning microscopy,” Opt.Lett. 16, 1062–1064 (1991).
[Crossref] [PubMed]

Ibáñez-López, C.

M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and Universidad de Valencia, “Axial gain resolutionin optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 15, 1740–1745 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1740
[Crossref]

Kuznetsova, Y.

Lee, C.H.

C.H. Lee and J.P. Wang,“Noninterferometric Differential Confocal Microscopy With 2-nm Depth Resolution,” Opt. Commun. l35,233~237(1997).
[Crossref]

Li, Liu

Liu Li, Deng Xiao-qang, and Wang Gui-ying, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Physica Sinica 50, 48–51(2001).

Martinez-Corral, M.

M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and Universidad de Valencia, “Axial gain resolutionin optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 15, 1740–1745 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1740
[Crossref]

Mico, Vicente

Morris, Michael

Oti, Jose E.

Pawley, J.

J. Pawley, Handbook of Biological Confocal Microscopy (Plenun, New York, 1995).
[Crossref]

Saavedra, G.

M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and Universidad de Valencia, “Axial gain resolutionin optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 15, 1740–1745 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1740
[Crossref]

Saleh, Bahaa E.A.

Andrew I. Whiting, Ayman F. Abouraddy, Bahaa E.A. Saleh, and Malvin C. Teich, “Polarization -assisted transverse and axial optical superresolution,” Opt. Express 15, 1714–1723 (2003).
[Crossref]

Sales, Tasso R.M.

Schwarz, C.J.

Teich, Malvin C.

Andrew I. Whiting, Ayman F. Abouraddy, Bahaa E.A. Saleh, and Malvin C. Teich, “Polarization -assisted transverse and axial optical superresolution,” Opt. Express 15, 1714–1723 (2003).
[Crossref]

Wang, Haifeng

Haifeng Wang, “New approach to supperresolution,” Opt. Eng. 40, 851~855(2001).
[Crossref]

Wang, J.P.

C.H. Lee and J.P. Wang,“Noninterferometric Differential Confocal Microscopy With 2-nm Depth Resolution,” Opt. Commun. l35,233~237(1997).
[Crossref]

Whiting, Andrew I.

Andrew I. Whiting, Ayman F. Abouraddy, Bahaa E.A. Saleh, and Malvin C. Teich, “Polarization -assisted transverse and axial optical superresolution,” Opt. Express 15, 1714–1723 (2003).
[Crossref]

Wilson, T.

T. Wilson and S.J. Hewlett, “Superresonlution in confocal scanning microscopy,” Opt.Lett. 16, 1062–1064 (1991).
[Crossref] [PubMed]

T. Wilson, Confocal Microscopy (Academic press limited, 1990).

Xiao-qang, Deng

Liu Li, Deng Xiao-qang, and Wang Gui-ying, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Physica Sinica 50, 48–51(2001).

Zalevsky, Zeev

Acta Physica Sinica (1)

Liu Li, Deng Xiao-qang, and Wang Gui-ying, “Phase-only optical pupil filter for improving axial resolution in confocal microscopy,” Acta Physica Sinica 50, 48–51(2001).

Opt. Commun. (1)

C.H. Lee and J.P. Wang,“Noninterferometric Differential Confocal Microscopy With 2-nm Depth Resolution,” Opt. Commun. l35,233~237(1997).
[Crossref]

Opt. Eng. (1)

Haifeng Wang, “New approach to supperresolution,” Opt. Eng. 40, 851~855(2001).
[Crossref]

Opt. Express (3)

Andrew I. Whiting, Ayman F. Abouraddy, Bahaa E.A. Saleh, and Malvin C. Teich, “Polarization -assisted transverse and axial optical superresolution,” Opt. Express 15, 1714–1723 (2003).
[Crossref]

Vicente Mico, AIDO, and Zeev Zalevsky, “Single-step superresolution by interferometric imaging,” Opt. Express 12, 2589–2596 (2004).http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2589
[Crossref] [PubMed]

M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and Universidad de Valencia, “Axial gain resolutionin optical sectioning fluorescence microscopy by shaded-ring filters,” Opt. Express 15, 1740–1745 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1740
[Crossref]

Opt. Lett. (3)

Opt.Lett. (2)

X. Chen and S.R.J Brueck, “Imaging interferometric lithography: approaching the resolution limits of optics,” Opt.Lett. 24, 124–126 (1999).
[Crossref]

T. Wilson and S.J. Hewlett, “Superresonlution in confocal scanning microscopy,” Opt.Lett. 16, 1062–1064 (1991).
[Crossref] [PubMed]

Other (4)

T. Wilson, Confocal Microscopy (Academic press limited, 1990).

J. Pawley, Handbook of Biological Confocal Microscopy (Plenun, New York, 1995).
[Crossref]

Min Gu, Principles of three-dimensional Imaging in Confocal Microscopes (World Scientific Publishing Co.Pte.Ltd., Singapore,1996).

A. Diaspro (ed.) Confocal and Two-Photon Microscopy. Foundations, Applications and Advances (Wiley, New York, 2001).

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Figures (5)

Fig. 1.
Fig. 1. Tri-heterodyne CM with axial superresolution.
Fig. 2.
Fig. 2. Simulated curved surfaces of TCM and CM intensity
Fig. 3.
Fig. 3. Simulated axial intensity curves with uM =5.21.
Fig. 4.
Fig. 4. Simulated axial intensity curves when uM =8.0.
Fig. 5.
Fig. 5. Measured intensity response curves.

Equations (9)

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I 1 v u , + u M = [ 2 0 1 P ( ρ ) · exp ( ju ρ 2 2 ) J 0 ( ρv ) ρdρ ] 2 × [ 2 0 1 P ( ρ ) · exp ( j ρ 2 ( u + u M ) 2 ) J 0 ( ρv ) ρdρ ] 2
u = ( 8 π λ ) z sin 2 ( α 0 2 ) , v ( 2 π λ ) r sin α 0
I 2 v u , u M = [ 2 0 1 P ( ρ ) · exp ( ju ρ 2 2 ) J 0 ( ρv ) ρdρ ] 2 × [ 2 0 1 P ( ρ ) · exp ( j ρ 2 ( u u M ) 2 ) J 0 ( ρv ) ρdρ ] 2
I 3 v u , 0 = [ 2 0 1 P ( ρ ) · exp ( ju ρ 2 2 ) J 0 ( ρv ) ρdρ ] 2 × [ 2 0 1 P ( ρ ) · exp ( ju ρ 2 2 ) J 0 ( ρv ) ρdρ ] 2
{ I A v u = I 3 v u 0 I 2 v u u M I B v u = I 3 v u 0 I 1 v u + u M I C v u = I 2 v u u M I 1 v u + u M
I v u = { I A v u , when I C v u 0 I B v u , when I C v u < 0
k A 0, 0 u M = sin c [ ( u M ) 4 π ] · [ ( u M 4 ) · cos ( u M 4 ) sin ( u M 4 ) ] { ( u M 4 ) } 2
k B 0, 0 u M = sin c [ ( u M ) 4 π ] · [ ( u M 4 ) · cos ( u M 4 ) sin ( u M 4 ) ] { ( u M 4 ) } 2
k C 0, 0 u M = 2 sin c [ ( u M ) 4 π ] · [ ( u M 4 ) · cos ( u M 4 ) sin ( u M 4 ) ] { ( u M 4 ) } 2

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