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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 12 — Dec. 19, 2012
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Laser divided-aperture differential confocal sensing technology with improved axial resolution

Weiqian Zhao, Chao Liu, and Lirong Qiu  »View Author Affiliations


Optics Express, Vol. 20, Issue 23, pp. 25979-25989 (2012)
http://dx.doi.org/10.1364/OE.20.025979


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Abstract

In this study, we found that the axial response curve of divided-aperture confocal microscopy has a shift while the point detector has a transverse offset from the optical axis. Based on this, a novel laser divided-aperture differential confocal sensing technology (LDDCST) with absolute zero and high axial resolution, as well as an LDDCST-based sensor, is proposed. LDDCST sets two micro-regions as virtual pinholes that are symmetrical to the optical axis along the xd direction on the focal plane of the divided-aperture confocal system to achieve the spot-division detection and to simplify the detection system, uses differential subtraction of two intensity responses simultaneously detected from the two micro-regions to achieve high axial resolution absolute measurement and low noise, and considers both resolution and measurement range by adjusting virtual pinholes in software. Theoretical analyses and packaged LDDCST sensor experiments indicate that LDDCST has high axial resolution as well as strong anti-interference and sectioning detection capability.

© 2012 OSA

1. Introduction

Confocal microscopy (CM) is widely used in microelectronics, materials, industrial precision measurements, and biomedicine for its unique optical sectioning capability and high resolution [1

1. Z. Li, K. Herrmann, and F. Pohlenz, “Lateral scanning confocal microscopy for the determination of in-plane displacements of microelectromechanical systems devices,” Opt. Lett. 32(12), 1743–1745 (2007). [CrossRef] [PubMed]

4

4. C. L. Arrasmith, D. L. Dickensheets, and A. Mahadevan-Jansen, “MEMS-based handheld confocal microscope for in-vivo skin imaging,” Opt. Express 18(4), 3805–3819 (2010). [CrossRef] [PubMed]

]. Koester et al. proposed a CM-based confocal slit divided-aperture microscope for applications in ophthalmology and otology. The microscope used separate portions of the objective aperture for illumination as well as imaging rays that achieve a high degree of optical sectioning [5

5. C. J. Koester, “Scanning mirror microscope with optical sectioning characteristics: applications in ophthalmology,” Appl. Opt. 19(11), 1749–1757 (1980). [CrossRef] [PubMed]

, 6

6. C. J. Koester, S. M. Khanna, H. D. Rosskothen, R. B. Tackaberry, and M. Ulfendahl, “Confocal slit divided-aperture microscope: applications in ear research,” Appl. Opt. 33(4), 702–708 (1994). [CrossRef] [PubMed]

]. Dwyer et al. developed a confocal theta line-scanning microscope with divided aperture for applications in human skin and oral mucosa imaging in vivo. The obtained lateral resolution was 1.7 μm, and the optical section thickness was 9.2 μm [7

7. P. J. Dwyer, C. A. DiMarzio, J. M. Zavislan, W. J. Fox, and M. Rajadhyaksha, “Confocal reflectance theta line scanning microscope for imaging human skin in vivo,” Opt. Lett. 31(7), 942–944 (2006). [CrossRef] [PubMed]

, 8

8. P. J. Dwyer, C. A. DiMarzio, and M. Rajadhyaksha, “Confocal theta line-scanning microscope for imaging human tissues,” Appl. Opt. 46(10), 1843–1851 (2007). [CrossRef] [PubMed]

]. Sheppard, Si, and Gong et al. proposed a confocal microscope with D-shaped apertures in a comparatively systemic theoretical study. The study included the effects of divider parameters and pinhole size, as well as the three-dimensional coherent transfer function [9

9. C. J. R. Sheppard, W. Gong, and K. Si, “The divided aperture technique for microscopy through scattering media,” Opt. Express 16(21), 17031–17038 (2008). [CrossRef] [PubMed]

12

12. W. Gong, K. Si, and C. J. R. Sheppard, “Improvements in confocal microscopy imaging using serrated divided apertures,” Opt. Commun. 282(19), 3846–3849 (2009). [CrossRef]

].

The measurement principles of the aforementioned approaches are generally classified into two types. For sample measurement, the first principle uses the sharp slope of the CM response curve for depth measurement, whereas the second principle uses the peak of the CM response curve for focus tracing. However, these approaches have a number of disadvantages. The absolute displacement measurement is difficult to achieve because of having no absolute zero when the sharp slope of the CM response curve is used. Furthermore, the measurement accuracy is susceptible to the nonlinearity of the sharp slope, disturbances in light source intensity, and to the reflection and dispersion characteristics of the measured sample. The tracing accuracy of CM cannot be further improved during the application of focus tracing because the worst sensitivity arises at the peak of the CM response curve.

This paper proposes a new laser divided-aperture differential confocal sensing technology (LDDCST) based on the properties of the axial response curve of a divided-aperture confocal microscopy, which shifts with the point detector as a result of a slight transverse offset from the optical axis. LDDCST uses two micro-regions as virtual pinholes that are set symmetrically in the focus along the xd direction on the CCD imaging plane to achieve Airy spot-division detection. LDDCST also uses the differential subtraction of two intensity responses simultaneously detected from the two micro-regions to achieve low noise as well as for high axial resolution absolute measurement. Compared with the aforementioned technologies, LDDCST has an absolute zero and can be used for bipolar absolute measurement. LDDCST can mitigate the effects of the disturbances in light intensity and of the reflection and dispersion characteristics of the measured sample. LDDCST can freely adjust the position and size of pinhole through software settings. The CCD and pinhole adjustment significantly simplify the detection system and eliminate the error attributed to the dissymmetrical placement of pinholes and property difference of the detectors.

2. LDDCST principle

Figure 1
Fig. 1 LDDCST principle.
is a schematic optical diagram of the LDDCST, where the pupil plane of objective L is divided into illumination pupil S1 and collection pupil S2. The collimated parallel light is focused on the measured sample by objective L after passing through pupil S1. The measurement light reflected from the sample is focused on focal plane P by collection lens LC after passing through pupil S2. The Airy spot on plane P is magnified on the CCD imaging plane by lens LM with a magnification of β. Figure 1 shows that (x,y,z) is the coordinate of objective L in the image space, (η,ξ) is the coordinate of the pupil of objective L, (xd,yd,zd) is the coordinate of the CCD imaging plane.

The scalar paraxial theory can be applied to the theoretical deduction when N.A.<0.7. The point spread functions of the illumination and collection systems are hi(vx,vy,u) and hc(vx,vy,u,vM), respectively [14

14. M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific Publishing, 1996), chap. 3.

].
hi(vx,vy,u)=S1P(vξ,vη)exp[iu2(vξ2+vη2)]exp[i(vxvξ+vyvη)]dvξdvη,
(1)
hc(vx,vy,u,vM)=S2P(vξ,vη)exp[iu2(vξ2+vη2)]exp{i[(vx+vM)vξ+vyvη]}dvξdvη,
(2)
where vx = 2πxsinα/λ, vy = 2πysinα/λ, and u = 8πzsin2(α/2)/λ are the normalized optical coordinates of objective L in the image space. vM = 2πMsinαd/λ is the normalized optical coordinate of the transverse offset, M is the transverse offset of the detector on plane P from the optical axis, α is the semi-aperture angle of objective L in the object space, αd is the semi-aperture angle of collection lens LC, P(vη,vζ) is the pupil function of objective L, and vη and vζ are the normalized radii of objective L.

Figure 1 shows that the three identical micro-regions are set as A, O, and B with radius r on the CCD image plane. Micro-region O is set at the focus, and two micro-regions A and B are set symmetrically at the focus along the xd direction on the CCD imaging plane. The three responses IA(u,-vM), IO(u,0), and IB(u,vM) those correspond to micro-regions A, O, and B are then obtained by CCD.

Axial intensity response Ii(u,vM) that is obtained from point detector i with offset vM is

Ii(u,vM)=|hi(0,0,u)hc(0,0,u,vM)|2.
(3)

Let the wavelength of the light source λ = 632.8 nm, the numerical aperture of objective L N.A. = 0.42, and the normalized radii of pupils S1 and S2 be rd = 0.5. Figure 2
Fig. 2 Theoretical axial response curves with vM = −4, 0, and 4.
shows the normalized axial intensity response curves IA(u,-4), IO(u,0), and IB(u,4), which IO(u,0) is the normalized axial intensity response of micro-region O with an offset vM = 0, IA(u,-4) and IB(u,4) are the respective normalized axial intensity responses of micro-regions A and B with an offset vM = 4.

Figure 2 shows that the shapes of curves IA(u,-4) and IB(u,4) are almost the same as that of IO(u,0). A shift is only observed in the u direction of IO(u,0) when the point detector has slight transverse offset vM. That is, the offset of the point detector in the xd direction results in a shift of the divided-aperture confocal microscope axial intensity response. LDDCST is based on this feature.

The LDDCST intensity response ILDDCST(u,vM) is obtained through the differential subtraction of responses IA(u,-vM) and IB(u,vM), by using Eq. (1) to Eq. (3), and

ILDDCST(u,vM)=IA(u,vM)IB(u,vM).
(4)

Figure 3
Fig. 3 Theoretical response curves of LDDCST.
shows the theoretical response curves of LDDCST, which IO(u,0), IA(u,-4), and IB(u,4) are the respective axial intensity responses of micro-regions O, A, and B, and ILDDCST(u,vM) is the intensity response of LDDCST with vM.

CM axial resolution can be calculated from the slopes of the linear range of response curves. In LDDCST, the axial resolution can also be calculated from the slopes of the linear range of response curves. Gradient k(u,vM) of ILDDCST(u,vM) on u is
Δaxial=k(u,vM)=ILDDCST(u,vM)u,
(5)
where k(u,vM) is determined in the linear range, while the gradient in the linear measurement range of ILDDCST(u,vM) can be expressed in k(0,vM) at u = 0 as follows

Δaxial=k(u,vM)=k(0,vM).
(6)

Figure 4
Fig. 4 Variation of gradient curve k(0,vM) with vM.
shows the value of k(0,vM), where λ = 632.8 nm and N.A. = 0.42. The largest value is calculated at vM = 4. Thus, LDDCST has the best axial resolution when micro-regions A and B are at offset vM = 4.

Let the fluctuation factor attributed to the variations in the light source and the reflectivity of the sample is η, and the noise attributed to the environmental variation and the electrical noise is ε. The intensity responses received from micro-regions A and B are (ηIA(u,-vM) + ε) and (ηIB(u,vM) + ε). The property equation of LDDCST can be expressed as

IL(u,vM)=[ηIA(u,vM)+ε][ηIB(u,vM)+ε][ηIA(u,vM)+ε]+[ηIB(u,vM)+ε]=IA(u,vM)IB(u,vM)IA(u,vM)+IB(u,vM)+2ε/η.
(7)

LDDCST is often used for high-precision measurement where ε→0, Thus, 2ε/η is negligible relative to the sum of IA(u,-vM) and IB(u,vM). Equation (7) can be simplified as

IL(u,vM)IA(u,vM)IB(u,vM)IA(u,vM)+IB(u,vM).
(8)

Figure 5
Fig. 5 LDDCST property curves with different offset vM.
shows the LDDCST property curves with N.A. = 0.42 and different offset vM that are obtained through Eq. (8). Figure 5 shows that LDDCST sensitivity increases and its measurement range decreases when vM increases to 4, whereas LDDCST sensitivity decreases and its measurement range increases when vM further increases.

In LDDCST, vM is optional in the software. Thus, the appropriate LDDCST property curve can be selected through optimal vM to meet the different requirements of sensitivity and measurement range. In this paper, LDDCST uses the property curve with a higher sensitivity and a smaller measurement range when used for focus tracing measurement, vM = 4 is the optimum value between sensor resolution and measurement range.

Figure 6
Fig. 6 LDDCST and CM property curves.
shows LDDCST property curve IL(u,vM = 4) and CM property curve ICM(u,0) for N.A. = 0.42, where bevel intervals ab and cd with same length of ∆u in u direction are the linear areas used for measurements.

In Figs. 3, 5 and 6, we can observe that

  • 1) LDDCST has an absolute zero, which has the maximum sensitivity and corresponds to the LDDCST focus. Thus, LDDCST is suitable for focus tracing measurement;
  • 2) LDDCST has a slope in the bevel interval cd double as that in the bevel interval ab in comparison with CM under the same conditions. Thus, the axial resolution of LDDCST is improved;
  • 3) The linearity of LDDCST in the bevel interval cd is better than that of CM in the bevel interval ab. The linear measurement range of LDDCST is extended;
  • 4) LDDCST uses the differential detection and anti-noise process to suppress effectively the common-mode noise that results from environmental differences, disturbance in the intensity of the light source, and from electrical drift of the detector, etc.;
  • 5) LDDCST considers both resolution and measurement range. Different work modes can-meet the requirements of resolution and measurement range by adjusting vM in the software.

3. LDDCST sensor

Figure 7
Fig. 7 The LDDCST sensor we developed (a) Schematic diagram of LDDCST sensor and (b) Photo of packaged sensor.
shows the LDDCST sensor that we developed. Figure 7(a) shows the schematic diagram of the LDDCST sensor, whereas Fig. 7(b) shows the photo of packaged sensor. The laser source is a semiconductor laser CPS180 produced by Thorlabs Inc. The diameter of the laser beam is ϕ5 mm. Microscope objective L is SPAHL-50 with long work distance produced by SIGMA KOKI. The N.A. of SPAHL-50 is 0.42. The diameter of the illumination and collection pupils is ϕ2.5 mm. Collection lens LC is a convex lens with a focal length of 150 mm. Lens LM is a standard microscopic objective with magnification of β = 10 × . The CCD used as detector is a WATEC 902H2 Ultimate with effective pixels of 752(H) × 582(V), and the pixel size is 8.6 μm (H) × 8.3 μm (V). The mirrors are used to reduce the LDDCST sensor size through folding light path

Micro-regions A and B with a diameter of 6 pixels and offset C are set on the CCD imaging plane, where C = βλvM/2πMsinαd = vMC0 is the lateral offset of the point detector, based on the calculation with actual parameters, and C0≈7.5 pixels. Thus, the best offset is C≈30 pixels when vM = 4. By using u = 8πzsin2(α/2)/λ and C = vMC0, Eq. (8) can be described as

IL(z,C)IA(z,C)IB(z,C)IA(z,C)+IB(z,C)=IA(z,vMC0)IB(z,vMC0)IA(z,vMC0)+IB(z,vMC0).
(9)

4. Experiments and analyses

4.1 Axial properties

An experimental setup is established to verify the LDDCST principle and to calibrate the axial properties of the LDDCST sensor. In the experiments, the movement of the sample is achieved by using Picomotor Actuators produced by NEWFOCUS to drive the flexible hinge. The XL80 laser interferometer produced by RENISHAW is used to measure the movement displacement. The grey summations of pixels within two micro-regions A and B are respectively calculated when the measured sample moves along the z direction. The axial intensity responses IA(z,-C) and IB(z,C) are then obtained. Next, the LDDCST sensor response curve ILDDCST(z,C) and property curve IL(z,C) are respectively obtained by using Eq. (4) and Eq. (9).

Figure 8
Fig. 8 Axial properties experimental curves of LDDCST sensor (a) experimental curves of ILDDCST(z,C) with different vM and (b) experimental curves of IL(z,C) with different vM.
shows the LDDCST sensor experimental response curves ILDDCST(z,C) and property curves IL(z,C) for C = 10, 20, 30, or 40 pixels. Figure 8(a) shows that ILDDCST(z,C) has the best axial resolution of ∆axial = 5.5 nm when vM = 4 (i.e., C≈30 pixels). It agrees with the theoretical analyses in Fig. 4 and Fig. 5. Figure 8(b) shows that the measurement range of IL(z,C) decreases as C increases to 30 pixels, whereas increases as C further increases. So, the improvement of the resolution increases as C increases to 30 pixels, whereas decreases as C further increases. The results follow the theoretical analyses shown in Fig. 5.

4.2 Lateral properties

An experimental setup based on the Knife-Edge Test verifies the LDDCST principle and then calibrated the lateral properties of the LDDCST sensor. In the setup, the movement of the sample is achieved by using a high-precision electric motorized translation stage with a feed of 0.08 μm to drive the air bearing slider. The XL80 laser interferometer is used for displacement measurement. The focal point moves across the knife-edge when the measured sample moves along the x direction. The distance that corresponds to the step change of axial intensity responses IA(x,-C) and IB(x,C) can represent the LDDCST sensor lateral resolution.

4.3 Standard step measurement

The HS-500MG is measured as the sample by the LDDCST sensor. The movement of the sample is achieved by using a high-precision electric motorized translation stage with a feed of 0.08 μm to drive the air bearing slider. The XL80 laser interferometer is used to measure the sample movement along the x direction.

5. Conclusions

A new LDDCST is proposed in this paper. This new LDDCST uses two micro-regions as virtual pinholes on the CCD imaging plane to achieve virtual detection, can freely adjust the position and size of the pinhole. LDDCST significantly simplifies the structure and the pinhole adjustments, mitigates the error caused by pinhole adjustment, uses the differential subtraction of two intensity responses to achieve absolute measurement and low noise, has improved axial resolution and an extended measurement range, can consider both resolution and measurement range, and effectively suppresses the effects of the disturbances in light intensity and of the reflection and dispersion characteristics of the sample. An LDDCST-based sensor has been developed. Preliminary experiments indicate that the LDDCST sensor has an axial resolution of approximately 5.5 nm and a lateral resolution of approximately 0.77 μm, which follows the theoretical analyses.

Acknowledgments

The authors would like to thank the National Science Foundation of China (No. 91123014, 60927012), Nature Science Association Foundation (NSAF) (No.11076004) and major national scientific instrument and equipment development project of China (No.2011YQ040136) for supports.

References and links

1.

Z. Li, K. Herrmann, and F. Pohlenz, “Lateral scanning confocal microscopy for the determination of in-plane displacements of microelectromechanical systems devices,” Opt. Lett. 32(12), 1743–1745 (2007). [CrossRef] [PubMed]

2.

J. F. Aguilar, M. Lera, and C. J. R. Sheppard, “Imaging of spheres and surface profiling by confocal microscopy,” Appl. Opt. 39(25), 4621–4628 (2000). [CrossRef] [PubMed]

3.

H. Yu, T. Chen, and J. Qu, “Improving FRET efficiency measurement in confocal microscopy imaging,” Chin. Opt. Lett. 8(10), 947–949 (2010). [CrossRef]

4.

C. L. Arrasmith, D. L. Dickensheets, and A. Mahadevan-Jansen, “MEMS-based handheld confocal microscope for in-vivo skin imaging,” Opt. Express 18(4), 3805–3819 (2010). [CrossRef] [PubMed]

5.

C. J. Koester, “Scanning mirror microscope with optical sectioning characteristics: applications in ophthalmology,” Appl. Opt. 19(11), 1749–1757 (1980). [CrossRef] [PubMed]

6.

C. J. Koester, S. M. Khanna, H. D. Rosskothen, R. B. Tackaberry, and M. Ulfendahl, “Confocal slit divided-aperture microscope: applications in ear research,” Appl. Opt. 33(4), 702–708 (1994). [CrossRef] [PubMed]

7.

P. J. Dwyer, C. A. DiMarzio, J. M. Zavislan, W. J. Fox, and M. Rajadhyaksha, “Confocal reflectance theta line scanning microscope for imaging human skin in vivo,” Opt. Lett. 31(7), 942–944 (2006). [CrossRef] [PubMed]

8.

P. J. Dwyer, C. A. DiMarzio, and M. Rajadhyaksha, “Confocal theta line-scanning microscope for imaging human tissues,” Appl. Opt. 46(10), 1843–1851 (2007). [CrossRef] [PubMed]

9.

C. J. R. Sheppard, W. Gong, and K. Si, “The divided aperture technique for microscopy through scattering media,” Opt. Express 16(21), 17031–17038 (2008). [CrossRef] [PubMed]

10.

K. Si, W. Gong, and C. J. R. Sheppard, “Three-dimensional coherent transfer function for a confocal microscope with two D-shaped pupils,” Appl. Opt. 48(5), 810–817 (2009). [CrossRef] [PubMed]

11.

W. Gong, K. Si, and C. J. R. Sheppard, “Optimization of axial resolution in a confocal microscope with D-shaped apertures,” Appl. Opt. 48(20), 3998–4002 (2009). [CrossRef] [PubMed]

12.

W. Gong, K. Si, and C. J. R. Sheppard, “Improvements in confocal microscopy imaging using serrated divided apertures,” Opt. Commun. 282(19), 3846–3849 (2009). [CrossRef]

13.

W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express 12(21), 5013–5021 (2004). [CrossRef] [PubMed]

14.

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific Publishing, 1996), chap. 3.

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(120.6660) Instrumentation, measurement, and metrology : Surface measurements, roughness
(130.6010) Integrated optics : Sensors
(180.1790) Microscopy : Confocal microscopy

ToC Category:
Microscopy

History
Original Manuscript: September 7, 2012
Revised Manuscript: October 21, 2012
Manuscript Accepted: October 23, 2012
Published: November 2, 2012

Virtual Issues
Vol. 7, Iss. 12 Virtual Journal for Biomedical Optics

Citation
Weiqian Zhao, Chao Liu, and Lirong Qiu, "Laser divided-aperture differential confocal sensing technology with improved axial resolution," Opt. Express 20, 25979-25989 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-23-25979


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References

  1. Z. Li, K. Herrmann, and F. Pohlenz, “Lateral scanning confocal microscopy for the determination of in-plane displacements of microelectromechanical systems devices,” Opt. Lett.32(12), 1743–1745 (2007). [CrossRef] [PubMed]
  2. J. F. Aguilar, M. Lera, and C. J. R. Sheppard, “Imaging of spheres and surface profiling by confocal microscopy,” Appl. Opt.39(25), 4621–4628 (2000). [CrossRef] [PubMed]
  3. H. Yu, T. Chen, and J. Qu, “Improving FRET efficiency measurement in confocal microscopy imaging,” Chin. Opt. Lett.8(10), 947–949 (2010). [CrossRef]
  4. C. L. Arrasmith, D. L. Dickensheets, and A. Mahadevan-Jansen, “MEMS-based handheld confocal microscope for in-vivo skin imaging,” Opt. Express18(4), 3805–3819 (2010). [CrossRef] [PubMed]
  5. C. J. Koester, “Scanning mirror microscope with optical sectioning characteristics: applications in ophthalmology,” Appl. Opt.19(11), 1749–1757 (1980). [CrossRef] [PubMed]
  6. C. J. Koester, S. M. Khanna, H. D. Rosskothen, R. B. Tackaberry, and M. Ulfendahl, “Confocal slit divided-aperture microscope: applications in ear research,” Appl. Opt.33(4), 702–708 (1994). [CrossRef] [PubMed]
  7. P. J. Dwyer, C. A. DiMarzio, J. M. Zavislan, W. J. Fox, and M. Rajadhyaksha, “Confocal reflectance theta line scanning microscope for imaging human skin in vivo,” Opt. Lett.31(7), 942–944 (2006). [CrossRef] [PubMed]
  8. P. J. Dwyer, C. A. DiMarzio, and M. Rajadhyaksha, “Confocal theta line-scanning microscope for imaging human tissues,” Appl. Opt.46(10), 1843–1851 (2007). [CrossRef] [PubMed]
  9. C. J. R. Sheppard, W. Gong, and K. Si, “The divided aperture technique for microscopy through scattering media,” Opt. Express16(21), 17031–17038 (2008). [CrossRef] [PubMed]
  10. K. Si, W. Gong, and C. J. R. Sheppard, “Three-dimensional coherent transfer function for a confocal microscope with two D-shaped pupils,” Appl. Opt.48(5), 810–817 (2009). [CrossRef] [PubMed]
  11. W. Gong, K. Si, and C. J. R. Sheppard, “Optimization of axial resolution in a confocal microscope with D-shaped apertures,” Appl. Opt.48(20), 3998–4002 (2009). [CrossRef] [PubMed]
  12. W. Gong, K. Si, and C. J. R. Sheppard, “Improvements in confocal microscopy imaging using serrated divided apertures,” Opt. Commun.282(19), 3846–3849 (2009). [CrossRef]
  13. W. Zhao, J. Tan, and L. Qiu, “Bipolar absolute differential confocal approach to higher spatial resolution,” Opt. Express12(21), 5013–5021 (2004). [CrossRef] [PubMed]
  14. M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific Publishing, 1996), chap. 3.

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