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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 10 — Jul. 19, 2010
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Zeeman laser scanning confocal microscope and its ability on reduction of specimen-induced spherical aberration

Jheng-Syong Wu, Chien Chou, Chi-Hui Chang, Li-Ping Yu, Li-Dek Chou, Hsiu-Fong Chang, Hon-Fai Yau, and Cheng-Chung Lee  »View Author Affiliations


Optics Express, Vol. 18, Issue 12, pp. 13136-13150 (2010)
http://dx.doi.org/10.1364/OE.18.013136


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Abstract

The spherical aberration induced by refractive-index mismatch results in the degradation on the quality of sectioning images in conventional confocal laser scanning microscope (CLSM). In this research, we have derived the theory of image formation in a Zeeman laser scanning confocal microscope (ZLSCM) and conducted experiments in order to verify the ability of reducing spherical aberration in ZLSCM. A Zeeman laser is used as the light source and produces the linearly polarized photon-pairs (LPPP) laser beam. With the features of common-path propagation of LPPP and optical heterodyne detection, ZLSCM shows the ability of reducing the specimen-induced spherical aberration and improving the axial resolution simultaneously.

© 2010 OSA

1. Introduction

Generally, a conventional confocal laser scanning microscope (CLSM) is composed mainly of a single frequency laser, a high numerical aperture (NA) objective lens and a small pinhole aperture. The pinhole size in optical units vp=(rpsinα)/3 is suggested theoretically for assuring high-quality sectioning images [1

1. T. Wilson and A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12(4), 227–229 (1987). [CrossRef] [PubMed]

,2

2. T. Wilson, “The role of the pinhole in confocal imaging system,” in Handbook of Biological Confocal Microscopy, J. B. Pawley ed., (Plenum Press, 1995), pp. 167–182.

]. The r p is the radius of the pinhole aperture, sin(α) is associated with the numerical aperture, M denotes the total magnification up to the pinhole plane and λ is the wavelength of laser. The pinhole aperture in CLSM plays a role of spatial filtering gating, which is the only gating available in CLSM, able to reject out-of-focus photons reflected from specimen to present the ability of optical sectioning [3

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

]. However, there are two major causes that lead to poor-quality sectioning images, the refractive-index mismatch and scattering in a specimen. When a laser beam propagates into most of biological specimens embedded in aqueous solution, the scattering effect of specimen produces wavefront distortion seriously [4

4. J. M. Schmitt, A. Knuttel, and M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11(8), 2226–2235 (1994). [CrossRef]

,5

5. H. F. Chang, C. Chou, H. F. Yau, Y. H. Chan, J. N. Yih, and J. S. Wu, “Angular distribution of polarized photon-pairs in a scattering medium with a Zeeman laser scanning confocal microscope,” J. Microsc. 223(Pt 1), 26–32 (2006). [CrossRef] [PubMed]

]. Therefore, the out-of-focal-plane scattered photons with large scattering angles can pass the pinhole and reach the photo detector. This degrades the axial resolution of CLSM. Apparently, the pinhole aperture alone in CLSM is not sufficient to reject multiple scattered photons [4

4. J. M. Schmitt, A. Knuttel, and M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11(8), 2226–2235 (1994). [CrossRef]

]. Simultaneously, the refractive-index mismatch in a specimen induces spherical aberration and defocus [6

6. S. W. Hell, and E. H. K. Stelzer, “Lens aberrations in confocal fluorescence microscopy,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, eds. (Plenum Press, 1995), pp. 347–354.

] and the specimen-induced spherical aberration severely degrades the axial resolution and the intensity distribution at the focal point [7

7. C. J. R. Sheppard, “Confocal imaging through weakly aberrating media,” Appl. Opt. 39(34), 6366–6368 (2000). [CrossRef]

]. These indicate that the combination of two adverse effects results in poor sectioning images in CLSM. Therefore, to simultaneously reduce the scattering effect and the specimen-induced spherical aberration becomes a high priority to improve the quality of sectioning images in CLSM. A method which is able to decrease the spherical aberration and the scattering effect becomes essential to assure good sectioning images.

Kempe and Rudolph [8

8. M. Kempe and W. Rudolph, “Scanning microscopy through thick layers based on linear correlation,” Opt. Lett. 19(23), 1919–1921 (1994). [CrossRef] [PubMed]

] proposed a linear correlation scanning microscope (LCSM) in which a low-coherence laser source is introduced so that an effective synthetic pinhole is constructed. Owing to a low-coherence laser source in LCSM, the reflected photons from near focus within the distance determined by the coherence length of light source are able to produce sectioning images of a specimen. It is anticipated that LCSM is less vulnerable to the scattering effect. Therefore, the ability to suppress scattered photons in LCSM with the temporal coherence gating is superior than that in CLSM with the spatial filter gating [9

9. M. Kempe, W. Rudolph, and E. Welsch, “Comparative study of confocal and heterodyne microscopy for imaging through scattering media,” J. Opt. Soc. Am. A 13(1), 46–52 (1996). [CrossRef]

]. As a result, a better performance of LCSM over CLSM on axial resolution in a scattering specimen is apparent. However, the specimen-induced spherical aberration in the signal arm lowers the axial resolution when a biological specimen is imaged by using LCSM. Theoretically, the LCSM with a low NA objective can reduce the effect of refractive-index mismatch in a biological specimen because of the heterodyne detection and basing on interference microscope configuration [8

8. M. Kempe and W. Rudolph, “Scanning microscopy through thick layers based on linear correlation,” Opt. Lett. 19(23), 1919–1921 (1994). [CrossRef] [PubMed]

,9

9. M. Kempe, W. Rudolph, and E. Welsch, “Comparative study of confocal and heterodyne microscopy for imaging through scattering media,” J. Opt. Soc. Am. A 13(1), 46–52 (1996). [CrossRef]

]. However, the distorted wavefront in the signal arm produced by specimens does not well match the wavefront of the reference beam, in particular in the marginal region of the wavefront. It can be considered that the effective NA of the objective in LCSM is decreased because the marginal region of wavefront less contributes to the heterodyne signal due to low coherence length of laser. With severe refractive-index variation in biological specimens, the lateral resolution improvement of LCSM wrought by a high NA immersion lens becomes negligible when imaging in a specimen below a certain depth for tomographic images. This is true even in a non-scattering specimen in LCSM. Therefore, it becomes equivalent to a conventional optical coherence tomography (OCT) [10

10. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

] in which a low NA objective is adapted for tomographic imaging. In addition, Kempe and Rudolph [8

8. M. Kempe and W. Rudolph, “Scanning microscopy through thick layers based on linear correlation,” Opt. Lett. 19(23), 1919–1921 (1994). [CrossRef] [PubMed]

] suggested a group-velocity-dispersion compensator (GVC) in reference arm for low-coherence laser in LCSM. Theoretically, LCSM with GVC can improve the axial and lateral resolutions of tomographic images at same time. However, a prior knowledge of the refractive index of the image object is required in order to utilize GVC properly. This renders LCSM impractical on biological section imaging.

Alternately, a dynamic focusing method is suggested in optical coherence microscope (OCM) in which a high NA objective and single-mode fibers are introduced [11

11. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19(8), 590–592 (1994). [CrossRef] [PubMed]

]. OCM has the advantages including being able to reduce the scattering effect and perform a high NA objective effectively, which implies a better lateral and axial resolutions in tomographic image. OCM implemented with single-mode optical fibers as a synthetic pinhole is equivalent to a low-coherence confocal interference microscope (CIM) [12

12. C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43(7), 1493–1502 (2004). [CrossRef] [PubMed]

], and it is usually performed en-face scanning purpose. Because both LCSM and OCM lack prior-knowledge of the refractive-index variations in specimens, it is very difficult to maintain the optical path difference between the reference arm and the signal arm within the coherence length of low-coherence source [13

13. H. W. Wang, J. A. Izatt, and M. D. Kulkarni, “Optical coherence microscopy,” in Handbook of Optical Coherence Tomography, B. E. Bouma and G. J. Tearney, eds. (Marcel Dekker, 2001) , pp. 275–298.

]. As a result, CIM suffers from specimen-induced spherical aberration as well. Theoretically, CIM is able to reduce the spherical aberration only under the condition that the reference pupil is identical to the objective pupil and the object is featureless [12

12. C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43(7), 1493–1502 (2004). [CrossRef] [PubMed]

]. However, it becomes impractical to reduce the spherical aberrations by perfectly matching the wave fronts of signal and reference beams.

Several methods for reducing spherical aberration in confocal microscopy have been proposed, such as Sheppard & Gu [14

14. C. J. R. Sheppard and M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30(25), 3563–3568 (1991). [CrossRef] [PubMed]

] and Sheppard [15

15. C. J. R. Sheppard, M. Gu, K. Brain, and H. Zhou, “Influence of spherical aberration on axial imaging of confocal reflection microscopy,” Appl. Opt. 33(4), 616–624 (1994). [CrossRef] [PubMed]

] addressed that the tube length of the objective can be adjusted. This method can compensate the low-order spherical aberration but is less practical for attaining the sectioning image of different depths in a specimen. In addition, an adaptive optical microscope with high NA objective, in which the specimen-induced spherical aberration can be quantified in terms of Zernike modes, is recently proposed [16

16. M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express 12(26), 6540–6552 (2004). [CrossRef] [PubMed]

]. Their result indicates that the adaptive correction of low-order Zernike modes is applicable for many specimens. Particularly, an improvement on axial resolution can be applied to confocal fluorescence microscopy or two-photon microscopy. Nevertheless, higher-order Zernike modes cannot be corrected effectively by adaptive optical system if the wavefront is severely distorted. Besides, the refractive-index mismatch between surrounding media and a specimen induces defocus and spherical aberration at same time. One requires a high NA immersion objective integrating with appropriate immersion oil to reduce the mismatch of refractive-index and thus it reduces the spherical aberration in CLSM. This results in an improvement on axial and lateral resolutions of sectioning images only at the position close to glass/medium boundary [17

17. C. J. R. Sheppard, and D. M. Shotton, Confocal Laser Scanning Microscopy (Springer, 1997) , pp. 27–39.

].

2. Imaging formation theory in ZLSCM

The image formation theory in ZLSCM is similar to CLSM. Because ZLSCM behaves as a fully spatial coherent imaging system, in which a highly spatial and temporal correlated polarized photon-pairs laser beam and a point detector are used, the image formation in ZLSCM can be derived by use of the coherent transfer function (CTF) according to the image formation theory in confocal microscopy [12

12. C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43(7), 1493–1502 (2004). [CrossRef] [PubMed]

,22

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

]. Moreover, because the circular symmetry of this optical setup and the isotropic property of the specimen are assumed in this study, p and s waves can be treated as the same and independent along the wave propagation. Therefore, the image formation theory of ZLSCM can be described by a scalar theory.

For simplicity, c(m,n) represents the two-dimensional (2-D) distorted CTF of a reflection-mode confocal microscope in which the pupil functions of the objective lens P˜1 and the collector lens P˜2 have circular symmetry. When the refractive-index mismatch happens in a specimen under imaging, the wave deformation including defocus and primary spherical aberration is generated. The electric field of p-polarized light is parallel to the plane of incidence of the beam-splitter and that of s-polarized light is perpendicular to it. The coherent image formation can be described by the complex amplitude Up of the p-polarized light wave at temporal frequency ωp in the image plane [12

12. C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43(7), 1493–1502 (2004). [CrossRef] [PubMed]

],
Up(x4,y4,t)=1Mexp(iωpt)Tp(m,n)cp(m,n)exp[2πi(mx4+ny4)M]  dm  dn,
(1)
where
cp(m,n)=P˜1,p(x1,y1)P˜2,p(mλfx1,nλfy1)dx1dy1,
(2)
Tp(m,n)=(x2,y2)exp[2πi(mx2+ny2)]dx2dy2.
(3)
(x 1, y 1), (x 2, y 2), and (x 4, y 4) are the coordinates of the source plane, the object plane and the image plane, respectively, as shown in Fig. 1
Fig. 1 Schematic diagram and coordinate system of a reflection-mode ZLSCM. (x 1, y 1), (x 2, y 2) and (x 4, y 4) are the coordinates of the source plane, the object plane and the image plane, respectively.
. The subscript p in Eq. (2) represents the CTF and the pupil functions for the p-polarized light wave. In Eq. (1), Tp(m,n) is the angular spectrum of the specimen illuminated by p-polarized light wave. (m,n) are the coordinates of 2-D spatial frequency and M is the magnification of the lens.

Similarly, the complex amplitude of the s-polarized light wave at temporal frequency ωs in the image plane is
Us(x4,  y4,  t)=1Mexp(iωst)Ts(m,n)cs(m,n)exp[2πi(mx4+ny4)M]dmdn,
(4)
where

cs(m,n)=P˜1,s(x1,y1)P˜2,s(mλfx1,nλfy1)dx1dy1,
(5)
Ts(m,n)=t(x2,y2)exp[2πi(mx2+ny2)]dx2dy2.
(6)

Here, the coordinate (x1, y1) of Eq. (5) is different from (x 1, y 1) of Eq. (2) for a generalized case. In Eq. (4), Ts(m,n) is the angular spectrum of the specimen illuminated by s-polarized light wave, and (m,n) are the coordinates of 2-D spatial frequency. The subscript s in Eq. (5) represents the CTF and the pupil function for the s-polarized light wave. Notice that, in general, the pupil function for the p-polarized light wave is not exactly equal to that for the s-polarized light wave because optical components contribute different phase delay to different polarized light wave. Thus, the intensity of ZLSCM in the image plane becomes

I(x4,y4,t)=|U(x4,y4,t)|2       =|12Up(x4,y4,t)+12Us(x4,y4,t)|2       =12|exp(iωpt)1MTp(m,n)cp(m,n)exp[2πi(mx4+ny4)M]  dm  dn       +exp(iωst)1Mss(m,n)cs(m,n)exp[2πi(mx4+ny4)M]  dm  dn|2.
(7)

Then, the output heterodyne signal is expressed as
IAC(x4,y4,t)  =  12exp(iΔωt)1M2Tp(m,n)Ts*(m,n)cp(m,n)cs*(m,n)               ×exp{2πi[(mm)x4+(nn)y4]M}  dm  dn  dm  dn+C.C.  ,
(8)
where

cp(m,  n)cs*(m,  n)  =  P˜1,p(x1,  y1)P˜2,p(mλfx1,  nλfy1)             ×P˜1,s*(x1,  y1)P˜2,s*(mλfx1,  nλfy1)dx1dy1dx1dy1.
(9)

C.C. is the complex conjugate in Eq. (8) and Δω   =  ωpωs. If the specimen under imaging is a perfect mirror, the angular spectrum satisfies the condition m = n = 0 [12

12. C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43(7), 1493–1502 (2004). [CrossRef] [PubMed]

]. Theoretically, because the p-polarized and the s-polarized light waves propagate in ZLSCM in common optical path, then x1=x1′ and y1=y1′ are satisfied. This is equivalent to the situation where the reflected wave front of the signal beam and that of the reference beam are fully overlapped in an interference microscope. Besides, if all optical components and specimens are not birefringent, the responses of components and specimens to the p-polarized wave and the s-polarized wave are equal. As a result, the approximation P˜1,p≈P˜1,s and P˜2,p≈P˜2,s is obtained. Under these conditions above, Eq. (9) is able to be simplified as

cp(0,   0)cs*(0,   0)=P˜1(x1,y1)P˜1*(x1,y1)P˜2(x1,y1)P˜2*(x1,y1)dx1dy1.
(10)

If an optical system suffers from aberration, the wavefront is distorted and the effect of aberration can be incorporated into the pupil function as P(x 1,  y  1)exp(iΦ), where Φ is the wave aberration function [22

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

]. In Eq. (10), the wave front aberration of the pupil functions P˜1 and P˜2 is corrected automatically and it is independent of whether the objective pupil is identical to the collector pupil or not. Theoretically, this implies that ZLSCM is able to cancel the wave aberration under the condition of non-scattering specimen. However, for a scattering specimen, depolarization and decorrelation of linearly polarized photon-pairs by scattering events degrade the ability of ZLSCM on wavefront aberration cancellation apparently. For a non-scattering specimen, in practice, propagation of the p-polarized wave and the s-polarized wave does not perfectly match in ZLSCM because optical components could be polarization-dependent. As such, the pupil functions of the p-polarized wave in Eq. (2) are not equal to those of the s-polarized wave in Eq. (5). As a result, only partial wave aberration is cancelled out in ZLSCM experimentally. In addition, the degree of common-path propagation of polarized photon-pairs laser beam in a specimen also affects the ability to reduce wavefront distortion. Therefore, the ability to reduce wavefront distortion induced by refractive-index mismatch and the scattering effect through common-path propagation and optical heterodyne determines the axial resolution and the 3-D point spread function in ZLSCM.

3. Experimental setup and results

The setup of ZLSCM is shown in Fig. 2(a)
Fig. 2 Experimental setup of (a) ZLSCM and (b) CLSM. ZL, Zeeman He-Ne laser; M1-M6, mirrors; BS, beam-splitter; O1, objective lens; GP, glass plate; P, polarizer; A, attenuator; O2, collector lens; PMT, photomultiplier tube; LA, linear amplifier; SA, spectrum analyzer; DVM, digital voltmeter; PC, personal computer; LMS, linear motor stage. (c) The experimental setup of focusing into a water medium to introduce spherical aberration.
in which a Zeeman He-Ne laser (Agilent 5517A) produces a highly correlated LPPP laser beam with 1.6 MHz beat frequency. The azimuth angle of the polarizer is set at 45° to the horizontal axis in order to generate maximum heterodyne signal [18

18. C. Chou, L. C. Peng, Y. H. Chou, Y. H. Tang, C. Y. Han, and C. W. Lyu, “Polarized optical coherence imaging in turbid media by use of a Zeeman laser,” Opt. Lett. 25(20), 1517–1519 (2000). [CrossRef]

,19

19. L. C. Peng, C. Chou, C. W. Lyu, and J. C. Hsieh, “Zeeman laser-scanning confocal microscopy in turbid media,” Opt. Lett. 26(6), 349–351 (2001). [CrossRef]

]. The long-working-distance imaging objective lens O1 (LMPLFL Olympus, 100X, NA = 0.8, WD = 3.4mm) and the collector lens O2 (Lightpath Gradium lenses, EFL = 60mm, f/# = 2.6) are used in this setup. The diameter of the pinhole is 25μm to match the objective lens O1 and the collector lens O2 for high collection efficiency [1

1. T. Wilson and A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12(4), 227–229 (1987). [CrossRef] [PubMed]

,2

2. T. Wilson, “The role of the pinhole in confocal imaging system,” in Handbook of Biological Confocal Microscopy, J. B. Pawley ed., (Plenum Press, 1995), pp. 167–182.

]. First, in this experiment, a perfect mirror as the object is moved axially through the focal point of O1 for calibrating the axial resolution of ZLSCM under aberration-free and non-scattering condition. The heterodyne signal is detected by a photomultiplier tube (Hamamatsu, R928) and measured by use of a spectrum analyzer (Advantest R3132).

In Fig. 2(b), the polarizer is removed and the spectrum analyzer is replaced by a digital voltmeter (Agilent 34401A) at DC mode, such that only DC signal is detected and polarization gating and spatial coherence gating are inactive simultaneously. It is equivalent to a CLSM in which only the intensity of the signal is measured. Therefore, the pinhole aperture becomes the only active gating in this setup that is able to reject the scattered and out-of-focus photons for sectioning images.

During the measurements, an optical attenuator is used, as shown in Figs. 2(a) and 2(b), in order to confine the detected intensity into the linear response region of the PMT to avoid saturation of the signal. When the PMT is operated within its linear response region, it is clearly observed that the axial resolution is independent of the output voltage of the PMT. This calibration step is critical to directly compare the axial responses of ZLSCM and CLSM under the same condition.

Figure 3
Fig. 3 Axial responses were measured by ZLSCM and CLSM with a mirror as object. The blue line and the red line represent the normalized signal of ZLSCM and CLSM, respectively. The crosses and the solid circles represent the experimental data of ZLSCM and CLSM, respectively. The measured interval is 0.125μm.
shows the axial responses of ZLSCM and CLSM with a mirror as object. The blue line and the red line represent the responses of ZLSCM and CLSM, respectively. The detected signals of ZLSCM and CLSM were normalized to their peak value of intensity at the focal point in order to compare them analytically. The axial resolutions of ZLSCM and CLSM, defined in term of full-width-at-half-maximum (FWHM) of the curve, are 0.91μm and 1.15μm respectively under aberration-free and non-scattering condition. This result agrees with the theoretical calculation (FWHM = 0.76μm) based on the normalized axial distance u  =  [zsin2(α/2)]/λ and u = 3 [1

1. T. Wilson and A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12(4), 227–229 (1987). [CrossRef] [PubMed]

,2

2. T. Wilson, “The role of the pinhole in confocal imaging system,” in Handbook of Biological Confocal Microscopy, J. B. Pawley ed., (Plenum Press, 1995), pp. 167–182.

]. Notice that the axial response of a symmetrical (major) peak and the diffraction region (peaks and valleys) results from a slight system-dependent aberration which depends on lens quality and system alignment, and is acceptable in a confocal microscope [23

23. R. M. Zucker, “Confocal microscopy system performance: axial resolution,” Microscopy Today 12, 38–40 (2004).

]. The axial response of ZLSCM is similar to that of CLSM under the same condition of alignment.

In order to reveal the ability of ZLSCM on spherical aberration reduction, single piece of cover glass (170μm in thickness), that is able to produce spherical aberration, was placed directly on the mirror M5 as shown in Figs. 2(a) and 2(b). Figure 4
Fig. 4 Axial responses of ZLSCM and CLSM under the condition that single piece of cover glass was placed directly on mirror M5. The blue line and the red line represent the normalized signal of ZLSCM and CLSM respectively, and the solid circles represent the experimental data. The measured interval is 0.2μm.
shows the axial responses of ZLSCM and CLSM in which the detected signals were normalized independently to their peak value of intensity at the focal point. The blue line and the red line represent the axial responses of ZLSCM and CLSM respectively, and the solid circles represent the experimental data. Because of introducing spherical aberration, Fig. 4 shows that the major peak becomes broad and the axial response is asymmetric whereas the side lobes on one side are generated in comparison with Fig. 3. Besides cover glass, focusing into a water medium as shown in Fig. 2(c) also introduces spherical aberration. The mirror M5 is scanned axially through the focal point of O1 in the water medium. Figures 5
Fig. 5 Axial responses of ZLSCM and CLSM under the condition of focusing into a water medium at the depth of 540μm from the air/water interface. The blue line and the red line represent the normalized signal of ZLSCM and CLSM respectively, and the solid circles represent the experimental data. The measured interval is 0.5μm.
and 6
Fig. 6 Axial responses of ZLSCM and CLSM under the condition of focusing into a water medium at the depth of 884μm from the air/water interface. The blue line and the red line represent the normalized signal of ZLSCM and CLSM respectively, and the solid circles represent the experimental data. The measured interval is 0.5μm.
show the axial responses of ZLSCM and CLSM at the depth of 540μm and 884μm from the air/water interface, respectively. In Figs. 5 and 6, the detected signals were normalized independently to their peak value of intensity at the focal point. The axial resolutions (defined in terms of FWHM of the main peak), the peak value of the first side lobe and the peak value of the second side lobe of ZLSCM and CLSM under the three condition of introducing spherical aberration are shown in Table 1

Table 1. Axial Resolution, Peak Value of First Side Lobe, and Peak Value of Second Side Lobe of ZLSCM and CLSM Under Three Conditions of Introducing Spherical Aberration

table-icon
View This Table
. Because the axial resolution value and the peak values of side lobes in ZLSCM are all smaller than that in CLSM under the three condition of introducing spherical aberration, it is obvious that ZLSCM shows the ability to reduce the specimen-induced spherical aberration.

Furthermore, in order to verify that the common-path propagation of LPPP is critical to the spherical aberration reduction in ZLSCM, we conducted another experiment in which a CIM is set up, as shown in Fig. 7
Fig. 7 Experimental setup of CIM. PBS, polarized beam-splitter; HWP, half wave plate.
. This setup is analogous to ZLSCM without common-path configuration and can be compared directly with the performance of ZLSCM. The major difference between these two setups is that, only p-polarized wave is incident into the specimen, while s-polarized wave is not. Then, the two waves are combined by the beam-splitter BS2 and detected by PMT with a collector lens. An attenuator placed between the mirror M6 and beam-splitter BS2 is in order to confine the detected intensity in the linear response region of PMT to prevent saturation of the signal. This is similar to ZLSCM in which the heterodyne signal is generated in PMT and measured by use of a spectrum analyzer. Notice that CIM is based on Mach-Zehnder interferometer and detects heterodyne signal. It is in contrast to conventional CIM [24

24. D. K. Hamilton and C. J. R. Sheppard, “A confocal interference microscope,” Opt. Acta (Lond.) 29, 1573–1577 (1982).

] of which the Michelson interferometer is constructed while DC signal is detected.

Figure 8(a)
Fig. 8 Axial responses of ZLSCM, CLSM and CIM under the condition that (a) a mirror as object, and (b) single piece of cover glass was placed directly on mirror M5. The blue line, the red line and the green line represent the normalized signal of ZLSCM, CLSM and CIM, respectively. The measured interval is 0.1μm and 0.2μm in Fig. 8(a) and Fig. 8(b), respectively.
shows the axial responses of ZLSCM, CLSM and CIM under the condition of using the mirror M5 as object. The intensities of ZLSCM, CLSM and CIM were normalized independently to its maximum value in the z-scan range in order to compare the axial response of three systems. The detected signal in CIM belongs to interference term, and the pattern of the axial response can be theoretically derived whereas the envelope of the fringes is sin(u/2)/(u/2) under aberration-free and non-scattering condition according to [24

24. D. K. Hamilton and C. J. R. Sheppard, “A confocal interference microscope,” Opt. Acta (Lond.) 29, 1573–1577 (1982).

] and [25

25. C. J. R. Sheppard and Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik (Stuttg.) 87, 129–132 (1991).

]. In contrast, the axial responses of CLSM and ZLSCM are [sin(u/2)/(u/2)]2 [22

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

]. In Fig. 8(a), it is obvious that the performance of axial response of CIM is worse than CLSM and ZLSCM due to non-common-path configuration. However, the background noise of CIM is higher than CLSM and ZLSCM. This is due to the polarization leakage in both arms by imperfect polarized beam-splitter (PBS) in Fig. 7. The complex amplitude of the signal beam and reference beam can be expressed by

Esig(z,t)  =  Ap(z)exp[i(ωpt+ϕsig)]+As(z)exp[i(ωst+ϕsig)],
(11)
Eref(t)=Αs exp[i(ωst+ϕref)]+Αp exp[i(ωpt+ϕref)].
(12)

The subscripts p and s in Eqs. (11) and (12) represent p-polarized and s-polarized, respectively. φsig and φref are the phase terms of the signal beam and reference beam, accordingly. In Eqs. (11) and (12), the second terms represent the polarization leakage due to PBS and is smaller than the first term. Thus, the detected heterodyne signal is
ΙAC=2Αp(z)Αs(z)cos(Δωt)+2ΑpΑscos(Δωt)+2Αp(z)Αscos(Δωt+Δϕ)+2Αs(z)Αpcos(ΔωtΔϕ),
(13)
where the beat frequency Δω=ωp−ωs and the phase difference Δφ=φsig−φref. The first and the second terms represent the heterodyne signal contributed by the leakage from signal and reference beams. The third term represents the signal of CIM. Note that the leakage from the signal beam (the first term) depends upon the axial distance while the reference beam (the second term) doesn’t. Therefore, the background noise will increase when z approach z = 0. According to [25

25. C. J. R. Sheppard and Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik (Stuttg.) 87, 129–132 (1991).

], even though the background noise is reduced, CIM still suffers from a series of side lobes.

Figure 8(b) shows that the axial responses of ZLSCM, CLSM and CIM under the condition where one cover glass (170μm in thickness) was placed directly on the top of mirror M5. In Fig. 8(b), the performance of CIM is worse than that in CLSM and ZLSCM apparently, because of the combination of spherical aberration. From these experimental results, they show that ZLSCM can effectively reduce spherical aberration compared with CLSM and CIM. As a result, the common-path propagation of LPPP in ZLSCM is confirmed critically to the ability of spherical aberration reduction.

In order to further demonstrate the capability of ZLSCM to reduce the specimen-induced spherical aberration, we choose an optical grating as the image object with grooves 21.3μm wide and 13μm deep. The period of it is 40μm. These parameters of the grating are obtained by using a scanning electron microscope (SEM).

The grating was scanned by ZLSCM and CLSM under two different conditions, one with single piece of cover glass placed right on the grating and the other without cover glass. The surface profile scanned by ZLSCM and CLSM are shown in Fig. 9(a)
Fig. 9 1-D scanning profiles of the optical grating under the condition (a) of aberration-free (b) that single piece of cover glass (170μm in thickness) was placed directly on the grating. The laser beam was focused on the upper surface of the grating. The blue line and the red line represent the experimental data measured by ZLSCM and CLSM, respectively. The measured interval is 1μm and 0.1μm in Fig. 9(a) and Fig. 9(b), respectively.
under the condition where the laser beam was focused on the upper surface of the grating and no cover glass was placed on the top of grating. In other words, this experiment is under aberration-free and non-scattering condition. The blue line and the red line represent the experimental data measured by ZLSCM and CLSM, respectively. The detected signals of ZLSCM and CLSM were normalized to their maximum intensity independently in order to compare them to each other. The performance of ZLSCM on 1-D surface profile scan is similar to that of CLSM. This result can be predicted by the axial responses of ZLSCM and CLSM under aberration-free and non-scattering condition as shown in Fig. 3.

In the second part of the experiments, single piece of cover glass (170μm in thickness) was placed directly on optical grating in order to produce spherical aberration. Figure 9(b) shows the result of 1-D surface profiles scanned by ZLSCM and CLSM independently in the interval of 0.1μm under the condition where the laser beam was focused on the upper surface of the grating. The detected signals were normalized to their maximum intensity in the scanning range. Notice that the normalized signal level in the valley of optical grating (see Fig. 9(b)) is higher than that in Fig. 9(a). This result is caused by the spherical aberration the cover glass introducing. By comparing the surface scanning profile (Fig. 9(b)) and the axial response (Fig. 4) under the same condition by using single piece of cover glass to produce spherical aberration, the difference of normalized signal in the valley of optical grating shown in Fig. 9(b) agrees with the response at z = -13μm in depth of Fig. 4. It is the depth of grooves of the grating. As shown in Fig. 9(b), the maximum (normalized) signals of CLSM and ZLSCM in the valley of optical grating are 0.132 (location at x = 23.8) and 0.049 (location at x = 23.5μm) respectively. While in Fig. 4, the normalized signal of CLSM is 0.127 and that of ZLSCM is 0.094 at z = -13μm. These experimental results verify that ZLSCM can effectively reduce the spherical aberration from refractive-index mismatch apparently. In addition, the edge effect is observed in Fig. 9(b) due to spherical aberration [26

26. M. Gu and C. J. R. Sheppard, “Effects of defocus and primary spherical aberration on images of a straight edge in confocal microscopy,” Appl. Opt. 33(4), 625–630 (1994). [CrossRef] [PubMed]

].

4. Discussion and conclusions

In this research, we have developed the theory of image formation in ZLSCM and conducted experiments to verify the ability of spherical aberration reduction in ZLSCM. Theoretically, the wave aberration generated in one polarized wave of the polarized photon-pairs laser beam is identical to that in other polarized wave at the same time. This implies that the wavefront distortion of LPPP can be cancelled effectively by heterodyne interference. According to the developed theory of image formation in ZLSCM, it is able to cancel spherical aberration regardless of whether the objective pupil is identical to the collector pupil or not (see Eq. (10)). This is different from the conclusion that the spherical aberration cancellation in an interference microscope is only limited under the condition that the reference pupil and the object pupil are identical [12

12. C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43(7), 1493–1502 (2004). [CrossRef] [PubMed]

].

In experiment, we verify that ZLSCM is able to reduce the specimen-induced spherical aberrations and improves the axial resolution under the condition of introducing spherical aberration. In Fig. 3, the axial resolution of ZLSCM is comparable with that of CLSM and agrees with the theoretical calculation under aberration-free and non-scattering condition. Figures 4-6 show that all side lobes in ZLSCM are smaller than that in CLSM and the axial resolutions of ZLSCM is improved in contrast to CLSM. These represent that all orders of spherical aberration are reduced simultaneously in ZLSCM. These advantages are also verified in the experiments of surface profiling of an optical grating as shown in Fig. 9. Moreover, the feature of common-path propagation of LPPP is critical to the ability of spherical aberration reduction. It is verified by the experimental results as shown in Fig. 8. This corresponds to the requirement of image formation theory (x1 = x1 and y1 = y1) of ZLSCM. As a result, ZLSCM is able to image a specimen tomographically without caring the refractive-index mismatch. To reduce the spherical aberration dynamically is applicable in a biological specimen because of the intrinsic properties of the distorted wave front cancellation due to common-path propagation of LPPP in a specimen. In addition, ZLSCM also performs the ability to reject background noise because of the heterodyne detection that enhances the image contrast significantly. This result is similar to the research of Potma et al. [21

21. E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31(2), 241–243 (2006). [CrossRef] [PubMed]

].

Moreover, ZLSCM is able to reduce spherical aberration in a scattering medium [5

5. H. F. Chang, C. Chou, H. F. Yau, Y. H. Chan, J. N. Yih, and J. S. Wu, “Angular distribution of polarized photon-pairs in a scattering medium with a Zeeman laser scanning confocal microscope,” J. Microsc. 223(Pt 1), 26–32 (2006). [CrossRef] [PubMed]

,18

18. C. Chou, L. C. Peng, Y. H. Chou, Y. H. Tang, C. Y. Han, and C. W. Lyu, “Polarized optical coherence imaging in turbid media by use of a Zeeman laser,” Opt. Lett. 25(20), 1517–1519 (2000). [CrossRef]

,19

19. L. C. Peng, C. Chou, C. W. Lyu, and J. C. Hsieh, “Zeeman laser-scanning confocal microscopy in turbid media,” Opt. Lett. 26(6), 349–351 (2001). [CrossRef]

]. However, a trade-off between reducing scattering effect and reducing spherical aberration in ZLSCM exists because multiple scattering events decorrelates p and s waves, which results in lower heterodyne efficiency. When entering a scattering medium, LPPP laser beam is scattered and becomes partially polarized and decorrelated spatially. Only scattered LPPP which are able to preserve their polarization and spatial coherence can contribute to heterodyne signal. Thus, the stronger scattering effect in a specimen produces lower degree of polarization (DOP) and lower degree of spatial coherence (DOC) of LPPP. This indicates the degradation of the ability to correct the distorted wavefront in ZLSCM. Therefore, for most of biological specimens which present the scattering effect and linear birefringence simultaneously, a pair of two identical polarized photons to replace p and s waves is suggested in order to avoid linear birefringent effect for biological tomographic imaging. As consequence, highly scattering effect limits the performance of ZLSCM due to the decorrelation of polarized photon-pairs. The ability of wave aberration reduction in ZLSCM is dependent upon DOP and DOC of LPPP.

Additionally, ZLSCM compares with low coherence interferometer such as LCSM and OCM. In LCSM, a low-coherence source can reduce the scattering effect and correct the specimen-induced wave aberration via a synthetic pinhole aperture only when the wavefronts of the reference beam and the signal beam are perfect matched [8

8. M. Kempe and W. Rudolph, “Scanning microscopy through thick layers based on linear correlation,” Opt. Lett. 19(23), 1919–1921 (1994). [CrossRef] [PubMed]

]. In contrast, OCM in which a high NA objective and a low-coherence source are integrated together is able to produce sectioning images of high axial and lateral resolutions by en-face image only [11

11. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19(8), 590–592 (1994). [CrossRef] [PubMed]

]. However, both LCSM and OCM are not applicable to reduce the spherical aberration induced by refractive-index mismatch in a specimen. Both LCSM and OCM rely on low coherence gating to produce sectioning images. In contrast, ZLSCM relies on polarization gating, spatial coherence gating and spatial filtering gating at the same time. In order to further investigate the ability of spherical aberration reduction in ZLSCM, a high-NA oil-immersion objective is suggested for sectioning imaging. However, the unavailability of the fluorescence signal detection which is essential to many biological specimens is the disadvantage of ZLSCM. Finally, we expect that ZLSCM is able to perform deeper penetration into specimens than CLSM based on the properties of LPPP in specimens.

Acknowledgment

This research was supported by the National Science Council of Taiwan through grant # NSC 95-2215-E-010-001.

References and links

1.

T. Wilson and A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12(4), 227–229 (1987). [CrossRef] [PubMed]

2.

T. Wilson, “The role of the pinhole in confocal imaging system,” in Handbook of Biological Confocal Microscopy, J. B. Pawley ed., (Plenum Press, 1995), pp. 167–182.

3.

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

4.

J. M. Schmitt, A. Knuttel, and M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11(8), 2226–2235 (1994). [CrossRef]

5.

H. F. Chang, C. Chou, H. F. Yau, Y. H. Chan, J. N. Yih, and J. S. Wu, “Angular distribution of polarized photon-pairs in a scattering medium with a Zeeman laser scanning confocal microscope,” J. Microsc. 223(Pt 1), 26–32 (2006). [CrossRef] [PubMed]

6.

S. W. Hell, and E. H. K. Stelzer, “Lens aberrations in confocal fluorescence microscopy,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, eds. (Plenum Press, 1995), pp. 347–354.

7.

C. J. R. Sheppard, “Confocal imaging through weakly aberrating media,” Appl. Opt. 39(34), 6366–6368 (2000). [CrossRef]

8.

M. Kempe and W. Rudolph, “Scanning microscopy through thick layers based on linear correlation,” Opt. Lett. 19(23), 1919–1921 (1994). [CrossRef] [PubMed]

9.

M. Kempe, W. Rudolph, and E. Welsch, “Comparative study of confocal and heterodyne microscopy for imaging through scattering media,” J. Opt. Soc. Am. A 13(1), 46–52 (1996). [CrossRef]

10.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]

11.

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19(8), 590–592 (1994). [CrossRef] [PubMed]

12.

C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43(7), 1493–1502 (2004). [CrossRef] [PubMed]

13.

H. W. Wang, J. A. Izatt, and M. D. Kulkarni, “Optical coherence microscopy,” in Handbook of Optical Coherence Tomography, B. E. Bouma and G. J. Tearney, eds. (Marcel Dekker, 2001) , pp. 275–298.

14.

C. J. R. Sheppard and M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30(25), 3563–3568 (1991). [CrossRef] [PubMed]

15.

C. J. R. Sheppard, M. Gu, K. Brain, and H. Zhou, “Influence of spherical aberration on axial imaging of confocal reflection microscopy,” Appl. Opt. 33(4), 616–624 (1994). [CrossRef] [PubMed]

16.

M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express 12(26), 6540–6552 (2004). [CrossRef] [PubMed]

17.

C. J. R. Sheppard, and D. M. Shotton, Confocal Laser Scanning Microscopy (Springer, 1997) , pp. 27–39.

18.

C. Chou, L. C. Peng, Y. H. Chou, Y. H. Tang, C. Y. Han, and C. W. Lyu, “Polarized optical coherence imaging in turbid media by use of a Zeeman laser,” Opt. Lett. 25(20), 1517–1519 (2000). [CrossRef]

19.

L. C. Peng, C. Chou, C. W. Lyu, and J. C. Hsieh, “Zeeman laser-scanning confocal microscopy in turbid media,” Opt. Lett. 26(6), 349–351 (2001). [CrossRef]

20.

Agilent Technologies, Laser and Optics User’s Manual (Agilent Technologies, 2002), Chap. 5.

21.

E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31(2), 241–243 (2006). [CrossRef] [PubMed]

22.

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

23.

R. M. Zucker, “Confocal microscopy system performance: axial resolution,” Microscopy Today 12, 38–40 (2004).

24.

D. K. Hamilton and C. J. R. Sheppard, “A confocal interference microscope,” Opt. Acta (Lond.) 29, 1573–1577 (1982).

25.

C. J. R. Sheppard and Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik (Stuttg.) 87, 129–132 (1991).

26.

M. Gu and C. J. R. Sheppard, “Effects of defocus and primary spherical aberration on images of a straight edge in confocal microscopy,” Appl. Opt. 33(4), 625–630 (1994). [CrossRef] [PubMed]

OCIS Codes
(080.1010) Geometric optics : Aberrations (global)
(110.2990) Imaging systems : Image formation theory
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(180.1790) Microscopy : Confocal microscopy

ToC Category:
Microscopy

History
Original Manuscript: March 23, 2010
Revised Manuscript: May 14, 2010
Manuscript Accepted: May 14, 2010
Published: June 3, 2010

Virtual Issues
Vol. 5, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Jheng-Syong Wu, Chien Chou, Chi-Hui Chang, Li-Ping Yu, Li-Dek Chou, Hsiu-Fong Chang, Hon-Fai Yau, and Cheng-Chung Lee, "Zeeman laser scanning confocal microscope and its ability on reduction of specimen-induced spherical aberration," Opt. Express 18, 13136-13150 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-12-13136


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References

  1. T. Wilson and A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12(4), 227–229 (1987). [CrossRef] [PubMed]
  2. T. Wilson, “The role of the pinhole in confocal imaging system,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed., (Plenum Press, 1995), pp. 167–182.
  3. T. Wilson and C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic Press, 1984).
  4. J. M. Schmitt, A. Knuttel, and M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11(8), 2226–2235 (1994). [CrossRef]
  5. H. F. Chang, C. Chou, H. F. Yau, Y. H. Chan, J. N. Yih, and J. S. Wu, “Angular distribution of polarized photon-pairs in a scattering medium with a Zeeman laser scanning confocal microscope,” J. Microsc. 223(Pt 1), 26–32 (2006). [CrossRef] [PubMed]
  6. S. W. Hell and E. H. K. Stelzer, “Lens aberrations in confocal fluorescence microscopy,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, eds., (Plenum Press, 1995), pp. 347–354.
  7. C. J. R. Sheppard, “Confocal imaging through weakly aberrating media,” Appl. Opt. 39(34), 6366–6368 (2000). [CrossRef]
  8. M. Kempe and W. Rudolph, “Scanning microscopy through thick layers based on linear correlation,” Opt. Lett. 19(23), 1919–1921 (1994). [CrossRef] [PubMed]
  9. M. Kempe, W. Rudolph, and E. Welsch, “Comparative study of confocal and heterodyne microscopy for imaging through scattering media,” J. Opt. Soc. Am. A 13(1), 46–52 (1996). [CrossRef]
  10. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). [CrossRef] [PubMed]
  11. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19(8), 590–592 (1994). [CrossRef] [PubMed]
  12. C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43(7), 1493–1502 (2004). [CrossRef] [PubMed]
  13. H. W. Wang, J. A. Izatt, and M. D. Kulkarni, “Optical coherence microscopy,” in Handbook of Optical Coherence Tomography, B. E. Bouma and G. J. Tearney, eds. (Marcel Dekker, 2001) , pp. 275–298.
  14. C. J. R. Sheppard and M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30(25), 3563–3568 (1991). [CrossRef] [PubMed]
  15. C. J. R. Sheppard, M. Gu, K. Brain, and H. Zhou, “Influence of spherical aberration on axial imaging of confocal reflection microscopy,” Appl. Opt. 33(4), 616–624 (1994). [CrossRef] [PubMed]
  16. M. Schwertner, M. Booth, and T. Wilson, “Characterizing specimen induced aberrations for high NA adaptive optical microscopy,” Opt. Express 12(26), 6540–6552 (2004). [CrossRef] [PubMed]
  17. C. J. R. Sheppard and D. M. Shotton, Confocal Laser Scanning Microscopy (Springer, 1997) , pp. 27–39.
  18. C. Chou, L. C. Peng, Y. H. Chou, Y. H. Tang, C. Y. Han, and C. W. Lyu, “Polarized optical coherence imaging in turbid media by use of a Zeeman laser,” Opt. Lett. 25(20), 1517–1519 (2000). [CrossRef]
  19. L. C. Peng, C. Chou, C. W. Lyu, and J. C. Hsieh, “Zeeman laser-scanning confocal microscopy in turbid media,” Opt. Lett. 26(6), 349–351 (2001). [CrossRef]
  20. Agilent Technologies, Laser and Optics User’s Manual (Agilent Technologies, 2002), Chap. 5.
  21. E. O. Potma, C. L. Evans, and X. S. Xie, “Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging,” Opt. Lett. 31(2), 241–243 (2006). [CrossRef] [PubMed]
  22. M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, 1996).
  23. R. M. Zucker, “Confocal microscopy system performance: axial resolution,” Microscopy Today 12, 38–40 (2004).
  24. D. K. Hamilton and C. J. R. Sheppard, “A confocal interference microscope,” Opt. Acta (Lond.) 29, 1573–1577 (1982).
  25. C. J. R. Sheppard and Y. Gong, “Improvement in axial resolution by interference confocal microscopy,” Optik (Stuttg.) 87, 129–132 (1991).
  26. M. Gu and C. J. R. Sheppard, “Effects of defocus and primary spherical aberration on images of a straight edge in confocal microscopy,” Appl. Opt. 33(4), 625–630 (1994). [CrossRef] [PubMed]

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