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Abstract
The optical parameters of temporal-focusing multiphoton excitation microscopy (TFMPEM), which is capable of achieving varying wavelength excitation for multiple fluorophore measurement, was systematically examined to have good excitation performance. For this purpose, the approaches were adopted to quantitatively evaluate the grating groove density, focal length of the collimating lens and objective, and different excitation wavelengths. A grating with a groove density of 830 lines/mm enables the TFMPEM system to achieve a wavelength range of 700–1000 nm by adjusting the incident angle of the ultrafast laser on the grating; a diffraction efficiency of 81 ± 3% was obtained at this wavelength range. By using the 830 lines/mm grating, a collimating lens with a 500 mm focal length and a 60× water immersion objective, we achieved a large excitation area and a better filling effect of the spectrum band of the pulse on the back focal plane of the objective; these parameters ensure high optical sectioning and small variation in the illumination power density within this wavelength range. The variation ranges of the excitation area, optical sectioning, and illumination power density of 4272 ± 798 μm2, 2.6 ± 0.3 μm, and 71 ± 29%, respectively, were obtained in two-photon excitation fluorescence imaging at 700–1000 nm excitation wavelengths.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Multiphoton excitation (MPE) microscopy is a well-established technique for in vivo imaging of fluorescence-labelled biospecimens at subcellular resolution. [1–6] To further expand the scope of application for living biospecimens, the temporal resolution of MPE fluorescence imaging has been improved by combining the method with other approaches such as resonant scanning, line scanning, multifocal scanning, and temporal focusing. [7] These approaches adopt two strategies. One approach increases the scanning speed to reduce the acquisition time for mapping an entire MPE image. The other approach considers MPE as a parallelisation process for simultaneous excitation of fluorophores on the focal plane and imaging the entire MPE image at a high frame rate. Compared with step-by-step scanning, the scan-less temporal focusing generates wide-field MPE with sectioning excitation. Furthermore, temporal-focusing MPE microscopy (TFMPEM) obtains fast 3D MPE fluorescence images at a temporal resolution of 10 ms using axially resolved plane-by-plane excitation and camera-based imaging. [8–14] Consequently, TFMPEM has been widely used in emerging biomedical applications such as 3D particle tracking [15], optogenetic control [14,16], superresolution imaging [17–21], depth-resolved imaging [22,23], and high-throughput microfabrication [24–27].
The signal-to-noise ratio (SNR) of MPE images is highly dependent on the MPE efficiency of fluorophores. Therefore, many studies have investigated methods for increasing the MPE efficiency and improving imaging of the distribution of molecules and cells labelled with fluorophores in biomedical applications. [7,8,28] The spectra of multiphoton absorption for different fluorophores and fluorescent proteins have been demonstrated in many studies. [29–35] Biological processes involve interaction between various molecules, and for detecting these molecules using MPE imaging, multiple fluorophores need to be excited effectively. Therefore, by adjusting the excitation wavelength of MPE microscopy to achieve a high SNR of the multicolor MPE images, the limitation of fluorophore selection can be reduced.
Tunable wavelength excitation in spatial-focusing MPE microscopy combined with a scanning approach can be achieved by adjusting the incident wavelength of the ultrafast pulse laser. [36] However, in a conventional TFMPEM system, fast adjustment of the incident wavelength according to the fluorophores is difficult because of the diffraction component and the 4f configuration involved in this technique. Furthermore, the multicolor MPE images exhibiting multiple fluorophores with different absorption spectra obtained using a conventional TFMPEM system with an illumination configuration of a fixed wavelength of the ultrafast pulse laser will have low SNR. Therefore, the previous study was demonstrated that by adopting an optical configuration where the incident angle at the diffraction component is automatically adjusted, optimal TPE absorption of fluorophores can be obtained for multicolor TPE images using a TFMPEM system with tunable wavelength excitation. [37] The excitation area, illumination power, and optical sectioning of temporal-focusing MPE imaging are also changed at different excitation wavelengths. [7,38] However, these properties of temporal-focusing MPE imaging have not been simultaneously investigated at varying excitation wavelengths. Therefore, this study aims to quantitatively evaluate the diffraction efficiency, excitation area, illumination power, and optical sectioning of a TFMPEM system using different diffraction gratings, collimating lenses, and excitation wavelengths to provide an optical setup, that have the better excitation area and axial sectioning of multicolor TFMPEM imaging with tunable wavelength excitation for multiple fluorophore measurement.
2. Methods
2.1 TFMPEM with tunable wavelength excitation
The crucial components of a TFMPEM system include a diffraction device, a collimating lens, and an objective, as shown in Fig. 1a. The pulse light is generated by an ultrafast laser oscillator and is diffracted by the reflection grating. The TFMPEM system uses a 4f configuration, which enables each wavelength of the pulse light to be temporally in phase at the focal plane of the objective. The dashed line in Fig. 1a indicates the Fourier plane of the 4f configuration, because the wavelengths of the pulse light source are separated by the grating and then collimated by the lens to form the spectrum of the pulse on this plane. After the pulse passes through the objective, the wavelengths are combined in phase only at the focal plane of the objective to realize temporal focusing. [8–12]
Fig. 1. (a) Schematics of the TFMPEM system with tunable wavelength excitation through adjustment of the incident angle of the excitation laser according to its wavelength. Bottom: the intensity profiles of an ultrafast pulse in the time domain at the grating, Fourier, and temporal-focusing planes. Diffraction models for (b) the Littrow and (c) TFMPEM experimental configurations.
Based on this concept, the following two aspects must be taken into consideration in developing a TFMPEM system with varying wavelengths of the excitation light source: (1) the excitation light must travel along the optical axes of the 4f system and the imaging plane must be conjugated with the diffracted surface of the diffraction device; (2) the propagation direction of the diffraction light varies as the excitation wavelength varies. Hence, in this study, the reflection blazed grating was chosen as the diffraction device for increasing the diffraction efficiency because reflection gratings usually have higher diffraction efficiency than transmission gratings. [39,40] Usually, the reflection blazed grating is used as a diffraction scheme by following the Littrow configuration shown in Fig. 1b. [40,41] However, to address the aforementioned aspects, the direction of the first-order diffraction light must be maintained along the optical axis of the 4f system, even at varying excitation wavelength. The dispersed pulse light with the central frequency for each excitation wavelength travels along the optical axis. To realize this strategy, the incident angle of the excitation light at the fixed grating should be adjusted according to the excitation wavelength. Figure 1a and 1c illustrate the diffraction scheme for the TFMPEM system with tunable wavelength excitation. From the diffraction grating equation, the incident angle ${\theta _i}$ of the excitation light at the reflection grating is given by [41]
where ${\lambda _o}$ is the wavelength of the excitation light and a is the groove density of the reflection grating. Consider the wavelength of the excitation light to range from 700 to 1000 nm. The incident angle for the different groove densities of the grating is shown in Fig. 2. Moreover, a groove density more than 1000 lines/mm at long excitation wavelengths requires an incident angle of more than 90° and cannot support excitation wavelengths of 700–1000 nm. Hence, considering the higher axial sectioning and no need to customize the grating, gratings with groove densities of 600 and 830 lines/mm are utilized for simulating the excitation performance of temporal-focusing MPE imaging at different excitation wavelengths.Fig. 2. Incident angles of the excitation light for keeping the first-order diffracted light with a diffraction angle of 0° as a function of the excitation wavelength for the different groove densities.
2.2 Simulating approach for diffraction efficiency analysis
The diffraction efficiency of the grating is an important factor affecting the excitation performance of temporal-focusing MPE imaging. To achieve high MPE efficiency in TFMPEM at different excitation wavelengths, the power of the diffracted light needs to be maintained through the grating. The diffraction efficiency of the grating is determined by the incident angle and wavelength of light, grating material, groove density, diffraction order, and blaze angle of the grating. The variation in diffraction efficiency during wavelength tuning was simulated using GSolver software. GSolver conducts a rigorous coupled wave analysis to solve Maxwell’s equations in the grating structures numerically. [42]
2.3 Simulating approach for illumination area analysis
The TFMPEM technique provides a large illumination area to quickly obtain MPE fluorescence images of specimens. The illumination area of the TFMPEM system at different excitation wavelengths should not only be large but also identical. However, this configuration causes variation in the illumination area at different excitation wavelengths, mainly because of the different incident angles of the light hitting the grating. The incident angle on the grating is adjusted according to the excitation wavelengths, which results in an elliptical distribution of the projection area of the excitation light on the grating plane. Because the focal plane of the objective is the conjugate plane of the grating plane, the illumination area is considered to be varying and elliptical in shape. Hence, the size of the illumination area of the TFMPEM system at the focal plane of the objective is determined by the full width at half maximum (FWHM) size of the incident Gaussian beam of the ultrafast laser, the incident angle on the grating, and the focal length of the collimating lens and the objective. On the focal plane of the objective, the lengths of the major ($La$) and minor ($Lb$) axes of the elliptical illumination area at the excitation wavelength are
where D is the FWHM of the incident beam size; $f1$ and $f2$ are the focal length of the collimating lens and the objective, respectively; ${\lambda _o}$ is the central wavelength of the pulse; and ${\theta _i}({{\lambda_o}} )$ is the incident angle on the grating according to the excitation wavelength. The illumination area (IA) on the focal plane of the objective at different excitation wavelengths is given by2.4 Simulating approach for optical sectioning analysis
The optical sectioning of the TFMPEM imaging is regulated by the groove density of the grating and focal lengths of the collimating lens and the objective. When an ultrafast pulse passes through a grating and the collimating lens in the TFMPEM, it aligns to form a band of the spectrum on the Fourier plane, which is also the back focal plane of the objective. The optimal MPE efficiency on the temporal-focusing plane corresponds to the combination of the amplitude and phase of all frequencies of the ultrafast pulse. [9,43] Some variation may occur in the amplitude and phase of its frequencies to affect the optical sectioning of TFMPEM imaging. [44–46]
Hence, the Fourier transformation calculation was used to yielded the two-dimensional distribution of the spectra of the pulse on the Fourier plane. When an ultrafast pulse with the Gaussian distribution in beam shape passes through a grating in the TFMPEM system, the decomposition of plane waves of different frequencies and with different diffractive angles ${\theta _\omega }$ can be calculated using the diffraction grating equation. After the pulse passes through the collimated lens, the spectrum distribution of the pulse on the Fourier plane of TFMPEM can be calculated by the spatial-domain Fourier transformation based on the theory of Fourier optics; [47] it is written as
3. Results and discussion
3.1 Diffraction efficiency analysis at different excitation wavelengths
The 600 and 830 lines/mm gratings were considered as the reflective blazed gratings. The blaze angle for the 600 and 830 lines/mm grating were 13.0° and 19.38°, which are identical to the grating specifications provided by the grating manufacturers (Edmund Optics, Thorlabs). Moreover, the grating surfaces coated with the gold and aluminum layer were also investigated respectively. In this work, the diffraction efficiency is defined as the power of the first-order diffraction light relative to the power of the incident light at each excitation wavelength. The average diffraction efficiency in transverse electric and magnetic polarizations for the Littrow and TFMPEM experimental configurations was obtained as shown in Fig. 3. Because the reflectance on the gold-coated surface was higher than that on the aluminum-coated surface, the gold-coated grating had the higher average diffraction efficiency. The diffraction efficiencies for the 600 and 830 lines/mm gratings with the gold-coated surface in the TFMPEM experimental configuration at excitation wavelengths 700–1000 nm were 79 ± 6% and 81 ± 3%, which are similar to the efficiency in the Littrow configuration. Although the diffraction efficiency of the 830 lines/mm grating with the gold coating showed a slight decrease at a small range of short wavelengths, this grating presented higher average diffraction efficiency than the 600 lines/mm grating with the gold coating. Moreover, the variation in the diffraction efficiency for the 830 lines/mm grating with the gold coating was also smaller. Consequently, the 830 lines/mm grating provided high diffraction light power with small variation in the TFMPEM experimental setup.
Fig. 3. Diffraction efficiencies of the first-order diffraction light at different wavelengths for (a) the 600 and (b) the 830 lines/mm gratings with the gold and aluminum coating in the Littrow and the TFMPEM experimental configurations.
3.2 Illumination area analysis at different excitation wavelengths
Consider the FWHM of Gaussian beam size and the pulse width of the ultrafast pulse light source to be 10 mm and 140 fs, respectively, and $f2$ to be 3 mm for a water immersion objective (60× PlanApo, Olympus). The illumination area and optical sectioning of the TFMPEM imaging are also modified by the different objectives. To simplify, we considered an objective to investigate the illumination area and optical sectioning changed by the collimating lens and excitation wavelengths in this study. However, the presented approach is also used to evaluate the excitation performance for the different objectives. The illumination areas with different focal lengths of the collimating lens for the 600 and 830 lines/mm gratings are shown in Fig. 4. When the focal length of the collimating lens was 300 mm and the grating groove density was 600 lines/mm, the illumination area decreased as the excitation wavelength decreased, as shown in Fig. 4a. Because the incident angle should be lower for a shorter wavelength, according to Eq. (1), the small incident angle caused a decrease in $La$, with $Lb$ remaining the same. Moreover, the illumination area decreased in size as the focal length was increased. When the grating groove density was increased to 830 lines/mm, the response tendency of the illumination area was similar to that for the 600 lines/mm grating, as shown in Fig. 4b. The decrease in the illumination area using the 830 lines/mm grating was more than that using the 600 lines/mm grating. The illumination area using the 830 lines/mm grating showed greater variation than that using the 600 lines/mm grating for excitation wavelengths 700–1000 nm. However, the variation in the illumination area using the 830 lines/mm grating was not considerable at longer focal lengths. In addition, the illumination area for the 830 lines/mm grating was larger than that for the 600 lines/mm grating. Therefore, a large groove density can be considered to slightly increase the size of the illumination area. Furthermore, a shorter focal length of the collimating lens can be used to enlarge the illumination area, but the variation in the illumination area for excitation wavelengths 700–1000 nm also increases. These effects should be considered together to decide the focal length of the collimating lens.
Fig. 4. Illumination area of the TFMPEM system with an ultrafast pulse laser at different excitation wavelengths and focal lengths of the collimating lens: (a) 600 lines/mm grating and (b): 830 lines/mm grating.
3.3 Optical sectioning analysis at different excitation wavelengths
According to Eq. (5), Fig. 5a-c presents the two-dimensional distribution of the spectrum on the Fourier plane considering the grating groove density as 600 lines/mm and the focal length of the collimating lens as 700 mm and using excitation wavelengths 700, 850, and 1000 nm. The sectioning size of TFMPEM imaging at the three excitation wavelengths, as shown in Fig. 5d. The spectrum size at an excitation wavelength of 700 nm was 4.3 mm, which is smaller than the back aperture of the objective, indicated by the red circle in Fig. 5a; the optical sectioning was 2.8 μm. For an excitation wavelength of 850 nm, the spectrum size was large at approximately 6.4 mm. Only a small fraction of the spectrum was blocked by the back aperture of the objective, and an optical sectioning of 2.3 μm was obtained. For an excitation wavelength of 1000 nm, the spectrum size was 8.8 mm, which is larger than the back aperture of the objective; this decreased the optical sectioning to 2.4 μm. These results indicate that if the spectrum band of the pulse on the Fourier plane fills the entire back aperture of the objective, the optical sectioning of TFMPEM imaging is higher. By contrast, a broad spectrum band does not allow the spectrum to completely pass through the back aperture of the objective, thereby reducing the optical sectioning.
Fig. 5. (a) Spectrum distribution of the pulse on the back focal plane of the objective for the 600 lines/mm grating, the same focal length of the collimating lens, and excitation wavelengths of 700, 850, and 1000 nm. The red circle indicates the back aperture of the objective, having a diameter of 5.4 mm. (b) Intensity profiles of the two-photon excitation fluorescence along the z-axis at excitation wavelengths of 700, 850, and 1000 nm.
Further, differences in the optical sectioning for the two grating grooves and varying focal lengths of the collimating lenses were determined, as shown in Fig. 6. For the 600 lines/mm grating, the variation in the optical sectioning at excitation wavelengths of 700–1000 nm decreases from 9.7 to 2.1 μm for the focal lengths from 300 to 900 mm. For the 830 lines/mm grating, the corresponding variation decreases from 5.4 to 1.9 μm. The results illustrate that a short focal length increases the size of the optical sectioning and its variation range for both gratings. The long focal length has better optical sectioning. The longer the focal length of the collimating lens, the broader the spectrum size. Therefore, the optical sectioning of the TFMPEM imaging is regulated by the filling effect of the spectrum band on the back focal plane of the objective.
Fig. 6. Optical sectioning at different excitation wavelengths for different focal lengths of the collimating lens (a) 600 lines/mm grating and (b) 830 lines/mm grating.
3.4 Discussion
The proposed TFMPEM system uses a 60× water immersion objective and has an adjustable range of excitation wavelength from 700 to 1000 nm. According to diffraction efficiency analysis of the TFMPEM experimental configuration, a small variation and high average in the diffraction efficiency is obtained for a grating groove density of 830 lines/mm and the gold coating. A small focal length of the collimating lens provides a large illumination area on the focal plane of the objective. However, a small focal length also results in a small spectrum size of the pulse on the back focal plane of the objective, which does not achieve the filling effect of the spectrum band on the back focal plane of the objective; thus, the optical sectioning of TFMPEM imaging is reduced. [44–46] Conversely, a long focal length of the collimating lens decreases the illumination area but enhances the optical sectioning of TFMPEM imaging. However, a spectrum size of the pulse larger than the back aperture of the objective should be avoided because this would reduce the optical sectioning of TFMPEM imaging.
The results of the illumination area and optical sectioning analyses revealed that the excitation volume can be quantitatively estimated for the evaluation of the two gratings, different excitation wavelengths, and different focal lengths of collimating lenses. The variation in the excitation volume of TFMPEM imaging is plotted in Fig. 7. The lateral direction denotes the length of the major axis of the elliptical illumination area and the axial direction denotes the sectioning size. Because a short excitation wavelength resulted in large variation of the optical sectioning for collimating lens focal lengths of 300–900 mm, the variation in the excitation volume at the excitation wavelength of 700 nm was investigated initially. The lateral and axial variation of the excitation volume with different collimating lenses for the grating groove densities of 600 and 830 lines/mm were obtained as shown in Fig. 7a and 7b, respectively. When the focal length of the collimating lens was larger than 600 mm for the 600 lines/mm grating and 500 mm for the 830 lines/mm grating, the optical sectioning of the TFMPEM imaging was less than 4 μm. For the 600 lines/mm grating, an optical sectioning of 3.6 μm and an illumination area of 2164 μm2 (La: 55 μm and Lb: 50 μm) were obtained by using a focal length of 600 mm. For the 830 lines/mm grating, an optical sectioning of 2.9 μm and an illumination area of 3474 μm2 (La: 74 μm and Lb: 60 μm) were obtained using a focal length of 500 mm. The two focal lengths for the grating groove densities of 600 and 830 lines/mm provide a resolution of optical sectioning of less than 4 μm and a large illumination area. For the 600 lines/mm grating with a focal length of 600 mm, the lateral and axial variation in the excitation volume at different excitation wavelengths are demonstrated in Fig. 7c. The variation in the optical sectioning and illumination area at excitation wavelengths 700–1000 nm was 3.1 ± 0.6 μm and 2309 ± 145 μm2, respectively. However, when the grating groove density and focal length of the collimating lens were changed to 830 lines/mm and 500 mm, respectively, the variation in the optical sectioning and illumination area in this wavelength range was improved to 2.6 ± 0.3 μm and 4272 ± 798 μm2, respectively, as shown in Fig. 7d.
Fig. 7. (a),(b) Lateral and axial variation in the excitation volume at an excitation wavelength of 700 nm and using different collimating lenses. (c),(d) Comparison of the lateral and axial variation in the excitation volume at different excitation wavelengths and using a collimating lens of (c) 600 mm focal length and (d) 500 mm focal length. (a),(c) 600 and (b),(d) 830 lines/mm gratings.
The spectrum size on the back focal plane of the objective not only regulates the optical sectioning of the imaging but also modifies the illumination power on the specimens. The spectrum size of the pulse over the back aperture of the objective causes a loss of the illumination power on the focal plane of the objective. Furthermore, the diffraction efficiency and results of illumination area analysis are considered to determine the illumination power density on the focal plane of the objective at different excitation wavelengths. The power loss of the excitation light in the $4f$ system ($P{R_{4f}}$) can then be obtained by comparing the power of the excitation light on the temporal-focusing plane and that of the excitation light after being diffracted by the grating; it is expressed as
Fig. 8. Illumination power density on the focal plane of the objective at different excitation wavelengths using (a) the 600 lines/mm grating with the gold-coating surface and a 600 mm focal length collimating lens and (b) 830 lines/mm grating with the gold-coating surface and a 500 mm focal length collimating lens. The illumination power densities at different excitation wavelengths were normalized using their maximum value.
4. Conclusions
Using quantitative evaluation, we presented investigated the intensity of excitation light passing through a diffraction grating and the excitation area, optical sectioning, and illumination power density of a TFMPEM imaging system with tunable wavelength excitation. The excitation wavelength of the TFMPEM system can be varied in the range 700–1000 nm by using gratings of groove density 600 and 830 lines/mm and controlling the incident angle of the excitation light on the gratings. In the diffraction analysis, the excitation light passing through the grating maintains high intensity and small variation for the 830 lines/mm gratings with the gold coating at excitation wavelengths 700–1000 nm. Moreover, a large illumination area is achieved using the 830 lines/mm grating and a short focal length of the collimating lens. However, the illumination area dramatically changes with varying wavelength. Thus, a collimating lens with a longer focal length is used to reduce the variation in the illumination area. Because of the filling effect of the spectrum of the pulse at the aperture of the back focal plane of the objective, the focal length of the collimating lens also regulates the optical sectioning of TFMPEM imaging. The spectrum band of the pulse on the back focal plane of the objective should fill the aperture of the back focal plane of the objective yet not block it. If a higher fraction of the pulse spectrum is filtered out, the illumination power density loss is larger. Consequently, considering the trade-off between the excitation area, optical sectioning, and illumination power density of TFMPEM imaging, a collimating lens with a focal length of 500 mm and the 830 lines/mm grating enable TPE fluorescence imaging using a 60× objective and result in better excitation area, optical sectioning, and illumination power density at excitation wavelengths of 700–1000 nm. Therefore, the proposed system can help in implementing TFMPEM imaging to achieve a large excitation area, high optical sectioning, and tunable wavelength excitation for imaging of multiple fluorophores at optimal absorption.
Funding
Ministry of Science and Technology, Taiwan (MOST) (MOST 105-2112-M-008-007-MY3).
Acknowledgments
We are deeply grateful to Prof. Shean-Jen Chen (College of Photonics, National Chiao Tung University) for the insightful advising.
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