Investigation of third harmonic generation confocal microscopy with aberrations

Weibo Wang; Weibo Wang; Weibo Wang; Biwei Wu; Biwei Wu; Shiyi Lin; Shiyi Lin; Xiaojun Li; Xiaojun Li; Zhiqiang Zhang; Zhiqiang Zhang; Jiubin Tan; Jiubin Tan

doi:10.1364/OSAC.2.003176

1. Introduction

Third harmonic generation (THG) microscopy, a recent evolution of multiphoton microscopy, is a powerful and versatile tool for label-free imaging. Compared to second harmonic generation (SHG), which can only be observed in materials that do not possess inversion symmetry, THG is allowed for all materials. As THG is a virtual-transition-based nonlinear optical phenomenon, there is no energy absorption to the interacted specimens [1]. So phototoxicity-free imaging can be performed in THG microscopy. Due to the unique property that the signal is observed at an interface between two media with different refractive indices or third-order nonlinear susceptibilities, THG microscopy is extremely sensitive to fine structural variations [2–4]. With these superiorities, the potential of THG microscopy has been explored for lipid bodies in cells [5,6], cell and tissue morphology [2,4,7–12], label-free live brain imaging [13,14], and vivo optical biopsy [15–20]. Besides, THG microscopy begins to play an important role in archaeology [21].

THG microscopy is a coherent imaging process. The phase information of the illuminating light is transferred to the THG signal in the light-matter interaction. So the THG signal does not only depend on the distribution of the focal spot, but also the polarization state of the excitation beam. A higher resolution and an extended depth of focus can be achieved in THG microscopy when a tightly focused radially polarized light with annular illumination is used [22]. And furthermore from that, radially polarized illumination may lead to entirely different aberration characteristics from linearly or circularly polarized excitations. On the other hand, there will be an inherent “confocal effect” in harmonic generation microscopy due to the spatial characteristics of the nonlinear processes [23]. A further improvement in resolution should be obtained by adding a certain size of pinhole to the detection path of THG microscopes at the cost of reduced light efficiency. The three-dimensional (3D) point-spread function (PSF) is often used as an important indicator for the practical imaging ability in microscopy. However, due to the coherent emission feature of THG, the 3D PSF for THG confocal microscopy is still pending and has not been investigated.

The performance of microscopes under realistic experimental conditions is often affected by aberrations, which is inevitable even for the well-corrected objectives. The focal spot may be distorted due to the presence of aberrations leading to reduced focal intensity and resolution. Due to slight misalignments and tilts of individual elements, imaging system suffers small amounts of spherical aberration or small amounts of coma or astigmatism [24]. The specimen induced aberrations also affect the imaging quality of microscopes [25,26]. THG signal is usually excited by a tight focusing of near-infrared incident beam. As a third order nonlinear optical process, the THG signal intensity varies with the third power of incident illumination intensity. In consequence, THG imaging quality is dominated by the geometry of the focal spot and is particularly sensitive to the effects of aberrations. Although aberrations in THG microscopy could be corrected to a certain degree by adaptive optics [27,28], there are few researches about the demonstrations of the inﬂuence of aberrations on THG microscopy. By analyzing the aberrations in THG microscopy, the adaptive correction can be optimized further. Anisha et al. have demonstrated the inﬂuence of aberrations on THG signal from different specimen geometries [29]. However, the aberration characteristics of the 3D PSF in THG confocal microscopy under different polarized illuminations are still unclear. Besides, the effects of the size of the pinhole also need to be discussed in detail.

In this paper, the 3D PSF with primary aberrations in THG confocal microscopy under circularly or radially polarized excitations will be discussed based on the proposed 3D PSF model. The influence of aberrations on the 3D PSF distributions will be analyzed quantificationally by the transverse full width at half maximum (FWHM) and the Strehl ratio. These results are helpful to provide guidelines for the aberration correction in THG confocal microscopy and can be used to interpret THG confocal microscope images.

2. Theory

As shown in Fig. 1, a rigorous model of a THG microscope consists of three subsystems: focusing of incident light, interaction of focal field with the specimen structures, and imaging of THG signal. It should be noted that the signal conversion is coherent in THG process. This makes THG microscopy distinguish from multi-photon fluorescence excitation microscopy [30]. Based on the vector diffraction theory [31], the circularly polarized focusing light with aberrations is given by

(1-a)$$\begin{aligned} {E_{cir - x}} &= \frac{{ - iA}}{\pi }\int_0^{{\alpha _1}} {\int_0^{2\pi } {p({r,\phi } ){{\cos }^{1/2}}{\theta _1}\sin {\theta _1}[{\cos {\theta_1}{{\cos }^2}\phi + {{\sin }^2}\phi + i\sin \phi \cos \phi ({\cos {\theta_1} - 1} )} ]} } \\ & \quad \times \exp [{i{k_1}({{z_s}\cos {\theta_1} + {\rho_s}\sin {\theta_1}\cos ({\phi - {\phi_s}} )} )} ]d{\theta _1}d\phi , \end{aligned}$$

(1-b)$$\begin{aligned} {E_{cir - y}}& = \frac{{ - iA}}{\pi }\int_0^{{\alpha _1}} {\int_0^{2\pi } {p({r,\phi } ){{\cos }^{1/2}}{\theta _1}\sin {\theta _1}[{\cos \phi \sin \phi ({\cos {\theta_1} - 1} )+ i({\cos {\theta_1}{{\sin }^2}\phi + {{\cos }^2}\phi } )} ]} } \\ & \quad \times \exp [{i{k_1}({{z_s}\cos {\theta_1} + {\rho_s}\sin {\theta_1}\cos ({\phi - {\phi_s}} )} )} ]d{\theta _1}d\phi , \end{aligned}$$

(1-c)$$\begin{aligned}{E_{cir - z}}& = \frac{{ - iA}}{\pi }\int_0^{{\alpha _1}} {\int_0^{2\pi } {p({r,\phi } ){{\cos }^{1/2}}{\theta _1}\sin {\theta _1}[{ - \sin {\theta_1}({\cos \phi + i\sin \phi } )} ]} } \\ & \quad \times \exp [{i{k_1}({{z_s}\cos {\theta_1} + {\rho_s}\sin {\theta_1}\cos ({\phi - {\phi_s}} )} )} ]d{\theta _1}d\phi , \end{aligned}$$

where ρ_s, z_s are the radial coordinate and axial coordinate of an observation point near the focal region respectively. A is a constant. k₁ is the wavevector amplitude of the excitation ﬁeld, and k₁ = 2πn₁/λ₀. n₁ is the refractive index of the immersion medium. λ₀ is the vacuum excitation wavelength. α₁ is the convergence semi-angle of the illumination, and is given as α₁= arcsin(NA/n₁). NA is the numerical aperture of the objective lens. The pupil function, p(r, ϕ) describes the complex ﬁeld distribution in the pupil plane of the objective lens. It is deﬁned in terms of a normalized radial coordinate r such that the pupil has a radius equal to 1, where r = sinθ₁/sinα₁. The pupil function is a useful way of representing aberrations introduced into the imaging system. In this paper, we only analyze the aberrations introduced in the excitation path. When aberrations are present in the excitation path, p(r, ϕ) can be represented as

(2)$$p({r,\phi } )= \exp [{i\Phi ({r,\phi } )} ].$$

Φ(r, ϕ) describes the phase aberrations and we assume that no amplitude aberrations are present in the system [27]. The phase function, Φ(r,ϕ) can be described as a series of Zernike polynomials Z_j (r, ϕ) as

(3)$$\Phi ({r,\phi } )= \sum\limits_j {{a_j}{Z_j}({r,\phi } )} ,$$

where a_j are the Zernike mode amplitudes. In this paper, three lower order Zernike aberration modes are considered. Astigmatism (Z₆), coma (Z₇) and ﬁrst order spherical aberration (Z₁₁) are deﬁned as [32,33]

(4-a)$${Z_6}({r,\phi } )= \sqrt 6 {r^2}\cos (2\phi ),$$

(4-b)$${Z_7}({r,\phi } )= 2\sqrt 2 ({3{r^3} - 2r} )\cos \phi ,$$

(4-c)$${Z_{11}}({r,\phi } )= \sqrt 5 ({6{r^4} - 6{r^2} + 1} ).$$

Fig. 1. Schematic diagram of a complete model of THG confocal microscopy system. This numerical model consists of focusing of incident light, interaction of focal field with the specimen structures, and imaging of THG signal. CP, circular polarization; RP, radial polarization; OL, objective lens; CL, collector lens; OF, optical filter; DL, detector lens; PD, confocal pinhole detector.

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For radially polarized illumination, the result can be expressed as [34]

(5)$$\begin{aligned}\left[ {\begin{array}{{c}} {{E_{ral - x}}}\\ {{E_{ral - y}}}\\ {{E_{ral - z}}} \end{array}} \right]& = \frac{{ - iA}}{\pi }\int_0^{{\alpha _1}} {\int_0^{2\pi } {p({r,\phi } ){{\cos }^{1/2}}{\theta _1}\sin {\theta _1} {l_0}({{\theta_1}} )} } \\ & \quad \times \exp [{i{k_1}({{z_s}\cos {\theta_1} + {\rho_s}\sin {\theta_1}\cos ({\phi - {\phi_s}} )} )} ]\left[ {\begin{array}{{c}} {\cos {\theta_1}\cos \phi }\\ {\cos {\theta_1}\sin \phi }\\ {\sin {\theta_1}} \end{array}} \right]d{\theta _1}d\phi . \end{aligned}$$

It is noteworthy that the azimuthal component will also be generated at the focus, when the electric field at the pupil including aberration function varies with the azimuthal angle. So this situation should be taken into account if coma and astigmatism are studied for radially polarized illumination. The function l₀(θ₁) is the apodization function in the entrance pupil of the focusing system. The azimuthal Bessel-Gauss beam is more akin to the azimuthally polarized TE₀₁ mode of the step-index optical fiber than to either the linear Bessel-Gauss or the Laguerre-Gaussian modes. So the Bessel-Gauss solution of Jordan and Hall for l₀(θ₁) is applied [34,35]:

(6)$${l_0}({{\theta_1}} )= \exp \left[ { - {\beta_0}^2{{\left( {\frac{{\sin {\theta_1}}}{{\sin {\alpha_1}}}} \right)}^2}} \right]{J_1}\left( {2{\beta_0}\frac{{\sin {\theta_1}}}{{\sin {\alpha_1}}}} \right).$$

β₀ is the ratio of the pupil radius and the beam waist, and is set to 1. J_n(x) denotes a Bessel function of the first kind, of order n.

For the interaction of focal field with the specimen, the induced THG polarization in the focal volume can be calculated by [1,36]

(7)$${{\boldsymbol P}^{(THG)}}({\textbf r}) = {\chi ^{(3)}}({\textbf r}){\boldsymbol E}({\textbf r}){\boldsymbol E}({\textbf r}){\boldsymbol E}({\textbf r}),$$

where χ⁽³⁾(r) is the third order susceptibility and r is the position vector in the focal region. For simplicity and without loss of generality, the third order susceptibility of the specimen is assumed to be oriented in all directions equally.

The THG signal emitted from the specimen is collected by a high aperture objective lens and imaged onto a ﬁnite sized confocal pinhole. In this paper, the objective lens and collector lens are assumed to possess the same numerical aperture. The electric ﬁeld in the detector plane due to a radiating THG polarization in the focal region can be expressed as [37,38]

(8-a)$${E_{dx}}({{\rho_d},{\phi_d},{z_d}} )= P_x^{(THG)}[{K_0^A + K_2^A\cos ({2{\phi_d}} )} ]+ P_y^{(THG)}K_2^A\sin ({2{\phi_d}} )+ 2iP_z^{(THG)}K_1^A\cos {\phi _d},$$

(8-b)$${E_{dy}}({{\rho_d},{\phi_d},{z_d}} )= P_x^{(THG)}K_2^A\sin ({2{\phi_d}} )+ P_y^{(THG)}[{K_0^A - K_2^A\cos ({2{\phi_d}} )} ]+ 2iP_z^{(THG)}K_1^A\sin {\phi _d},$$

(8-c)$${E_{dz}}({{\rho_d},{\phi_d},{z_d}} )={-} 2i({P_x^{(THG)}\cos {\phi_d} + P_y^{(THG)}\sin {\phi_d}} )K_1^B - 2P_z^{(THG)}K_0^B,$$

where

(9-a)$$K_0^A = \int_0^{{\alpha _2}} {\sqrt {\frac{{\cos {\theta _2}}}{{\cos {\theta _1}}}} } \sin {\theta _2}({1 + \cos {\theta_1}\cos {\theta_2}} ){J_0}({{k_2}{\rho_d}\sin {\theta_2}} )\exp ({i{k_2}{z_d}\cos {\theta_2}} )d{\theta _2},$$

(9-b)$$K_0^B = \int_0^{{\alpha _2}} {\sqrt {\frac{{\cos {\theta _2}}}{{\cos {\theta _1}}}} } {\sin ^2}{\theta _2}\sin {\theta _1}{J_0}({{k_2}{\rho_d}\sin {\theta_2}} )\exp ({i{k_2}{z_d}\cos {\theta_2}} )d{\theta _2},$$

(9-c)$$K_1^A = \int_0^{{\alpha _2}} {\sqrt {\frac{{\cos {\theta _2}}}{{\cos {\theta _1}}}} } \sin {\theta _2}\sin {\theta _1}\cos {\theta _1}{J_1}({{k_2}{\rho_d}\sin {\theta_2}} )\exp ({i{k_2}{z_d}\cos {\theta_2}} )d{\theta _2},$$

(9-d)$$K_1^B = \int_0^{{\alpha _2}} {\sqrt {\frac{{\cos {\theta _2}}}{{\cos {\theta _1}}}} } {\sin ^2}{\theta _2}\cos {\theta _1}{J_1}({{k_2}{\rho_d}\sin {\theta_2}} )\exp ({i{k_2}{z_d}\cos {\theta_2}} )d{\theta _2},$$

(9-e)$$K_2^A = \int_0^{{\alpha _2}} {\sqrt {\frac{{\cos {\theta _2}}}{{\cos {\theta _1}}}} } \sin {\theta _2}({1 - \cos {\theta_1}\cos {\theta_2}} ){J_2}({{k_2}{\rho_d}\sin {\theta_2}} )\exp ({i{k_2}{z_d}\cos {\theta_2}} )d{\theta _2},$$

with α₂ being the angular aperture of the detector lens. ρ_d, ϕ_d, and z_d are the cylindrical coordinates of an observation point near the detection region. The azimuthal angle θ₂ is related to the azimuthal angle θ₁ by the relationship:

(10)$$\frac{{{k_1}\sin {\alpha _1}}}{{{k_2}\sin {\alpha _2}}} = \frac{{{k_1}\sin {\theta _1}}}{{{k_2}\sin \theta {}_2}} = M,$$

where M is the nominal magnification of the detector lens system. k₂ is the wave number for the third harmonic field in detection region, expressed as k₂= 2πn_d/λ_THG. λ_THG denotes the wavelength of THG. n_d is the refractive index of the image space.

The detected signal of a THG microscope employing a confocal pinhole detector of radius R is given by integrating the THG intensity over the area of the detector [37,39]:

(11)$${I_{THG}} = \int_0^R {\int_0^{2\pi } {{{|{{{\boldsymbol E}_d}} |}^2}{r_p}d{r_p}d{\phi _p}} } .$$

3. Results and discussions

In this paper, the excitation wavelength is set to 1230 nm, which is widely adopted in THG microscopy. We consider an oil immersion (n₁ = 1.518) objective of NA = 1.4. The nominal magnification of the detector lens system M is set to 100. In practical terms, for a traditional confocal imaging system, a pinhole diameter of one Airy units (AU) is used, which corresponds to 1.22M·λ₀/NA [40]. It is worth mentioning that in the case of THG microscopy with long (e.g., infrared) wavelengths, the size of AU is larger than in typical confocal systems with visible light. In addition, the spatial characteristics of THG processes near the focus region lead to overall resolutions similar to that of the confocal systems [23]. The cubic dependence of THG reduces the size of effective THG PSF by a factor of $\sqrt {3} $. Thus the minimum distance of two points in THG images can be clearly distinguished is 0.61λ₀/($\sqrt {3} $NA). There will be no significant apodization effect even with a 1.0 AU confocal pinhole in THG microscopy. Theoretically, the maximum resolution of a confocal microscope would be achieved with a pinhole diameter of 0.2 AU, despite the dramatic decrease in signal intensity [41]. So we considered a confocal pinhole of 1.0 or 0.2 AU for comparison.

3.1 3D PSF with spherical aberration

Figure 2 shows the PSF distributions of THG confocal microscopy with varying amounts of spherical aberration. The intensity line profiles of the PSFs are normalized by the peak intensity of the aberration-free PSF for a 1.0 AU confocal pinhole. As expected, spherical aberration does not destroy the rotational symmetry of the PSF. By adding a 0.2 AU confocal pinhole to the detection path in THG microscopes, a further improvement in resolution will be realized at the expense of the signal reaching the detector. As can be seen from Fig. 2(a1)-(a3), moderate amounts of spherical aberration hardly affect the transverse PSF distributions when the THG signal is excited by circularly polarized beams. It is noticed in Fig. 2(b1)-(b3) that, the PSF distributions at the through-focus projection are more sensitive to those in the focal plane. The axial PSF distribution gets broader and side lobes become more significant with the increment of the amounts of spherical aberration. As illustrated in Fig. 2(c1)-(c3), for radially polarized excitation, spherical aberration seems not to distort the transverse PSF distribution. There is only a slight broadening when the aberration coefficient increases. It is particularly interesting to find that the side lobe in the axial PSF distribution moves along the optical axis with varying amounts of spherical aberration according to Fig. 2(d1)-(d3). In addition, compared to circularly polarized excitation, the focal shift induced by spherical aberration under radially polarized excitation is greater. For circularly polarized excitation, the focal shifts (relative to the aberration free case) at spherical aberration coefficient of 1.2 are 80 nm and 50 nm for confocal pinholes of 1.0 AU and 0.2 AU respectively. While for radially polarized excitation, the values get to 160 nm and 100 nm respectively.

Fig. 2. The PSF distributions of THG confocal microscopy with varying amounts of spherical aberration. As, aberration coefficient of spherical aberration; CP, circular polarization; RP, radial polarization; Scale bar: 400 nm.

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3.2 3D PSF with coma

The PSF distributions of THG confocal microscopy with varying amounts of coma are shown in Fig. 3. It is clearly observed that coma destroys the rotational symmetry of the PSF distribution. As shown in Fig. 3(a1)-(a3), the transverse PSF distributions excited by circularly polarized beams are more sensitive to coma than spherical aberration. The transverse FWHM for a confocal pinholes of 0.2 AU varies from 0.287 µm to 0.304 µm, when the aberration coefficient varies from 0 to 1.2. The increment is about 6.0%. As for a 1.0 AU confocal pinhole, the increment is about 3.3%. The shapes of the transverse PSF distributions under the discussed confocal pinhole sizes degrade significantly as the aberration coefficient gets to 1.2, especially for radially polarized beams. For the axial PSF distributions excited by circularly polarized beams under a 1.0 AU confocal pinhole, the stretching increases with varying amounts of coma. In contrast, the axial PSF profiles almost remain unchanged despite the moderate enhancement of the side lobes when the size of the confocal pinhole is set to 0.2 AU, as illustrated in Fig. 3(b1)-(b3). There is a similar conclusion for the axial PSF profiles excited by radially polarized beams except for the further exaggerated side lobes enhancement. Besides, the position of the peak intensity deviates from the optical axis in the presence of coma. The maximum offsets under circularly polarized excitation which lie in the aberration coefficient of 1.2 are 100 nm and 40 nm for confocal pinholes of 1.0 and 0.2 AU respectively. In the condition of radially polarized excitation, the maximum offsets which lie in the aberration coefficient of 0.8, and the values are 70 nm and 50 nm respectively.

Fig. 3. The PSF distributions of THG confocal microscopy with varying amounts of coma. Ac, aberration coefficient of coma; CP, circular polarization; RP, radial polarization; Scale bar: 400 nm.

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3.3 3D PSF with astigmatism

Figure 4 illustrates the PSF distributions of THG confocal microscopy with varying amounts of astigmatism. Although the rotational symmetry of the PSF distribution is destroyed by astigmatism, the position of the peak intensity keeps on the optical axis. For circularly polarized excitation, the shapes of the transverse PSF distributions remain regular with increasing the aberration coefficient. The transverse FWHM for a 0.2 AU confocal pinhole varies from 0.287 µm to 0.323 µm, when the aberration coefficient varies from 0 to 1.2. The increment is about 12.6%. For a confocal pinhole of 1.0 AU, the increment is about 9.5%. As for the axial PSF distributions, there are tails present with the increment of astigmatism. It is worth emphasizing that astigmatism is usually neglected in the realistic experiments of traditional confocal microscopy. However, the PSF distributions of THG confocal microscopy excited by radially polarized beams may be affected greatly by astigmatism. The transverse FWHM for a 0.2 AU confocal pinhole varies from 0.296 µm to 0.361 µm, when the astigmatism coefficient varies from 0 to 1.0. The increment is about 22.0%. In the case of a 1.0 AU confocal pinhole, the increment is about 19.2%. Especially when a confocal pinhole of 0.2 AU is applied, the peak-centered shape of the transverse PSF distributions in the focal plane degenerates to a four-sidelobe pattern as the aberration coefficient gradually increases to 1.2.

Fig. 4. The PSF distributions of THG confocal microscopy with varying amounts of astigmatism. Aa, aberration coefficient of astigmatism; CP, circular polarization; RP, radial polarization; Scale bar: 400 nm.

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3.4 Strehl ratio and FWHM

Strehl ratio is usually used as a merit function in adaptive optics [22,42]. In this paper, it is adopted as a key metric for the quality of the aberrated PSF of THG confocal microscopy for situations with varying amounts of aberrations. Strehl ratio can be calculated according to

(12)$$S = \frac{{{I_{ab}}}}{{{I_0}}},$$

where S is the Strehl ratio. I₀ is the maximum intensity of the unaberrated PSF distribution at the geometrical focus plane, and I_ab is the maximum intensity of the aberrated PSF distribution taken at the plane of the geometrical focus. As presented in Fig. 5, the general trend is that a larger aberration coefficient leads to a lower Strehl ratio. Under the condition of circularly polarized excitation, for the discussed three kinds of aberrations, the Strehl ratio with a 1.0 AU confocal pinhole is larger than that with a 0.2 AU confocal pinhole respectively as seen from Fig. 5(a). But it’s worth noting that the size of the confocal pinhole has a negligible effect on the relationship between the Strehl ratio and the spherical aberration coefficient. The observed result can be explained by the fact that spherical aberration is an on-axis aberration. In addition, spherical aberration has the lowest Strehl ratio compared with coma and astigmatism under circularly polarized excitation. On the other hand, for radially polarized excitation, the Strehl ratio of coma with a confocal pinhole of 1.0 AU is almost identical to that with a confocal pinhole of 0.2 AU. It also has the greatest value in the involved situations when the radially polarized beams are used, as presented in Fig. 5(b). It also can be observed that the contrast of THG confocal microscopy is significantly reduced by astigmatism when THG signal is excited by radially polarized beams.

Fig. 5. The Strehl ratio as a function of the aberration coefficients for primary aberrations. (a) Circularly polarized excitation, (b) radially polarized excitation.

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The resolution of THG confocal microscopy can be estimated by the FWHM of the PSF. As illustrated in Fig. 6, the size of the confocal pinhole does not affect overall variation trends of the FWHM relative to the aberration coefficient. Under radially polarized excitation, astigmatism significantly reduces the resolution of THG confocal microscopy. So astigmatism should be corrected primarily in THG confocal microscopy when the radially polarized illumination is utilized. Meanwhile, it is important to note that, the FWHM values of the PSF for radially polarized excitation may decrease under a certain amount of spherical aberration and coma. Besides, the FWHM values of the PSF for circularly polarized excitation remain almost unchanged with varying amounts of spherical aberration for a confocal pinhole of 1.0 AU. In spite of these, coma and spherical aberration still need to be corrected in THG confocal microscopy for contrast.

Fig. 6. The FWHM values of the PSF for THG confocal microscopy as a function of the aberration coefficients for primary aberrations. (a) For a 1.0 AU pinhole, (b) for a 0.2 AU pinhole.

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4. Conclusion

To the best of our knowledge, this is the first demonstration about the 3D PSF of THG confocal microscopy. The aberration characteristics of the 3D PSF under circularly and radially polarized excitations are compared. We also take into account situations with different sizes of confocal pinholes. Our study shows that moderate amounts of spherical aberration have a negligible effect on the transverse PSF distributions when THG signal is excited by circularly polarized beams. Furthermore, the focal shift induced by spherical aberration is also smaller than that under radially polarized illumination. Astigmatism, which is usually neglected in the realistic experiments of traditional confocal microscopy, significantly reduces the resolution and contrast of THG confocal microscopy under radially polarized excitation. So astigmatism should be concerned and be corrected primarily in THG confocal microscopy when the radially polarized illumination is utilized. At the same time, the FWHM values of the PSF for radially polarized excitation may decrease under a certain amount of spherical aberration and coma. On the whole, the Strehl ratio decreases monotonically as the aberration coefficient increases, which means that it is an applicable metric for the quality of the aberrated PSF of THG confocal microscopy. These results are important for the interpretation of THG confocal microscope images and can provide guidelines for the adaptive aberration correction in THG confocal microscopy.

Funding

National Natural Science Foundation of China (51775148); Natural Science Foundation of Heilongjiang Province (QC2018079); China Postdoctoral Science Foundation (2017T100235).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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Investigation of third harmonic generation confocal microscopy with aberrations

Abstract

1. Introduction

2. Theory

3. Results and discussions

3.1 3D PSF with spherical aberration

3.2 3D PSF with coma

3.3 3D PSF with astigmatism

3.4 Strehl ratio and FWHM

4. Conclusion

Funding

Disclosures

References

Cited By

Figures (6)

Equations (22)

OSA Continuum