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
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 is suggested theoretically for assuring high-quality sectioning images [1,2]. 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 . 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 [4,5]. 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 . Simultaneously, the refractive-index mismatch in a specimen induces spherical aberration and defocus  and the specimen-induced spherical aberration severely degrades the axial resolution and the intensity distribution at the focal point . 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  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 . 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 [8,9]. 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)  in which a low NA objective is adapted for tomographic imaging. In addition, Kempe and Rudolph  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 . 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) , 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 . 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 . 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  and Sheppard  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 . 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 .
In this study, we focus on the ability of Zeeman laser scanning confocal microscope (ZLSCM) on spherical aberration reduction both theoretically and experimentally. The theory of image formation in ZLSCM was developed and analyzed. Our previous research [5,18,19] reported that ZLSCM can reduce the scattering effect of specimens based on spatial coherence gating (via optical heterodyne), polarization gating (via a polarizer) and spatial filtering gating (via a pinhole) simultaneously. A linearly polarized photon-pairs (LPPP) laser beam is generated by using a Zeeman He-Ne laser, which contains orthogonal linear polarized p and s waves with 1.6MHz frequency difference . Only LPPP preserving their coherence and polarization properties contribute to the heterodyne signal in ZLSCM via a polarizer of 45° azimuth angle . In addition to provide the ability on reducing the scattering effect, ZLSCM theoretically can reduce the spherical aberration at the same time because of the features of common-path propagation of LPPP and the heterodyne detection. The wavefront distortions of p and s waves caused by the occurrence of spherical aberration are cancelled theoretically because the paired photons encounter similar distortions in their journey. Therefore, reducing the spherical aberration and the scattering effect of specimens is anticipated according to the developed image formation in ZLSCM and the previous experimental results about scattering . Based on the inherent properties of common-path propagation of LPPP and the gating effects, it is anticipated that ZLSCM is implemental with a high NA objective and can produce high performance on axial and lateral resolutions simultaneously particularly for biological specimens. In addition, the contrast of sectioning images can be improved too by suppressing background noise through heterodyne detection . In the experiments, we demonstrate the ability that ZLSCM is able to reduce the spherical aberration induced by single piece of glass plate or water medium. These results were compared with CLSM experimentally. Finally, the advantages of ZLSCM by integrating CLSM and the polarized photon-pairs interferometer are discussed in this study.
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 [12,22]. 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 ,Fig. 1 . 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
Here, the coordinate (x′1, y′1) of Eq. (5) is different from (x 1, y 1) of Eq. (2) for a generalized case. In Eq. (4), is the angular spectrum of the specimen illuminated by s-polarized light wave, and 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
Then, the output heterodyne signal is expressed as
C.C. is the complex conjugate in Eq. (8) and . If the specimen under imaging is a perfect mirror, the angular spectrum satisfies the condition m = n = 0 . 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
If an optical system suffers from aberration, the wavefront is distorted and the effect of aberration can be incorporated into the pupil function as , where Φ is the wave aberration function . 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) 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 [18,19]. 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 [1,2]. 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 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 and u = 3 [1,2]. 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 . 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 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 and 6 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 . 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 . 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  of which the Michelson interferometer is constructed while DC signal is detected.
Figure 8(a) 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  and . In contrast, the axial responses of CLSM and ZLSCM are [sin(u/2)/(u/2)]2 . 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
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 is25], 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) 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 .
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 .
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 = x′1 and y1 = y′1) 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. .
Moreover, ZLSCM is able to reduce spherical aberration in a scattering medium [5,18,19]. 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 . 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 . 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.
This research was supported by the National Science Council of Taiwan through grant # NSC 95-2215-E-010-001.
References and links
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]
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]
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.
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.
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).