2.1.

Axial Excitation Confinement

The axial image resolution of TFMPEM is based on two major parts such as the axial excitation confinement, which is related to the excitation wavelength and spectral components of the light source, the dispersion distortion of the spectral components in the optical path, the NA of the objective, and the back-focal plane filling; and, the emission collection capability, which is related to the emission wavelength of the sample and the NA of the objective. Herein, the axial excitation confinement is considered; hence, the axial excitation profile is described. First, the Rayleigh range $z_R$ is defined as¹⁵

Fig. 1

Comparison of axial excitation profiles, beam shapes at the back-focal plane, and excitation patterns at the front-focal plane among five different multiphoton excitation systems.

The axial excitation confinement will affect the axial image resolution by reducing the background signal excitation. From the illustration in Fig. 1, the improvement in the optical sectioning ability of our developed TFMPEM with DMD is concentrated to further confine the axial excitation volume via fully filling the back-focal aperture of the objective using binary CGFH. In this manner, it is possible to improve the axial excitation confinement of TF to approach those of line scanning and MUTF while retaining the fast and concise widefield excitation of the developed TFMPEM without a mechanical line scanner and a large-area echelle grating.

2.2.

Temporal Focusing Multiphoton Excitation Microscope with Digital-Micromirror-Device

Figure 2(a) shows a schematic diagram of the developed TFMPEM with computer-controlled DMD. The overall setup includes a Ti:sapphire ultrafast regenerative amplifier (Spitfire Pro, Spectra-Physics) coupled with a Ti:sapphire ultrafast oscillator (Tsunami, Spectra-Physics) as the seed beam of the amplifier, an upright optical microscope (Axio imager.A2m, Carl Zeiss, Germany), a triple-axis sample positioning stage (H101A ProScan, Prior Scientific, UK), a piezo stage (NanoScanZ 200, Prior Scientific, UK), an EMCCD camera (iXon Ultra 897, Andor, UK) with a camera adapter (T2-T2 SLR 2.5X, Carl Zeiss, Germany) to magnify the images 2.5X, a data acquisition card with a field-programmable gate array module (PCIe-7842R, National Instruments), and a DMD with 0.7-in. diagonal micromirror array with 12-deg tilt-angle micromirrors on the chip (DLP7000, Texas Instrument). The amplifier has a pulse energy of $400\mu \mathrm{J}/\text{pulse}$, a pulse width of 100 fs, and a repetition rate of 10 kHz, which is sufficient for TPEF of an $\sim 200\text{-}\times 200\text{-}{\mu \mathrm{m}}^2$ area, while a blazed grating functions as the dispersion device.⁹ However, the current excitation area is around $40\times 40{\mu \mathrm{m}}^2$ due to the restrictions by the 0.7–in. size and the 12-deg tilt angle of the DMD. The DMD replaces the blazed grating as the spectral dispersion for TF; therefore, according to the diffraction equation, the incidence angle should be close to twice the tilt angle of 12 deg to reach the maximum diffraction efficiency.¹⁹ Herein, the incident angle is adjusted to 24.4 deg as the diffraction order of 10, the central wavelength of 800 nm of the ultrafast amplifier, and the effective pitch of the micromirrors is $19.35\mu \mathrm{m}$, due to the flip axis being on the diagonal direction of each micromirror. Furthermore, a half-wave plate and a linear polarizer first adjust power and maintain the horizontal polarization of the beam from the amplifier while a mechanical shutter controls the excitation time to prevent unnecessary exposure. A set of relay lenses with focal lengths of 200 and 80 mm was inserted to lengthen the beam path and adjust the beam size to fit the back-focal aperture of the objective lens as a Fourier lens. The dispersed beam propagates through the $4f$ setup, which comprises a collimating lens and a $60\times$ objective lens with a NA 1.2 (UPlanSApo 60XW/NA 1.2, Olympus, Japan).

Fig. 2

(a) Optical setup of TFMPEM with the DMD as the grating dispersion and spatial modulation, which is similar to our previous research.¹⁹ (b) A new progress here includes binary CGFH on the excitation-conjugate plane via the DMD, the spectral dispersion for the TF effect and the diffraction for filling the back-focal aperture, and the two complementary excitation patterns on the MPE plane via rapid PWM switching.

The binary CGFH pattern at the top-right of Fig. 2(b) can be implemented via the DMD placed at the excitation-conjugate plane; meanwhile, the Fourier transform of the CGFH is converted via the Fourier lens onto the back-focal plane. Therefore, the beam shape of each spectral component at the back-focal plane could be implemented using binary CGFH via the DMD. Accordingly, the DMD not only implements spectral dispersion for different spectral components as with a blazed grating but also produces diffraction light at each spectral component perpendicular to the spectral dispersion via a designed CGFH. The TFMPEM setup enables each spectral component to be independently diffracted via the DMD with a designed CGFH, after which the Fourier transform of the CGFH can be projected onto the Fourier plane (i.e., ack-focal plane) through the Fourier lens, as shown at the mid-right of Fig. 2(b). Finally, the objective performs the beam-shape Fourier transform of each spectral component, and then recombines them at the front-focal plane. As such, only in the front-focal plane do the different spectral components overlap in phase and produce a short, high-peak power pulse with the conjugated CGFH pattern, as shown at the bottom-right of Fig. 2(b). Although this allows MPE to simultaneously occur over the entire projection area, the patterned illumination of CGFH cannot offer a uniform excitation plane for matching the image quality requirement. The bottom-right of Fig. 2(b) also presents the concept of using the rapid DMD’s PWM switching to produce a pseudouniform excitation pattern by combining two complementary binary CGFH patterns.

2.3.

Binary Computer-Generated Fourier Hologram

As shown in Fig. 2, the CGFH is governed by the Fresnel diffraction with a Fourier lens (i.e., raunhofer diffraction with the Fourier transform relation between the hologram and the reconstructed image) to perform the Fourier transform. An original intensity CGFH can be acquired by first executing the inverse Fourier transform of the designed beam shape, which is a line perpendicular to the spectral dispersion, and then simply weighting the intensity information of the inverse Fourier transform by the intensity distribution of the laser source beam. The phase information is neglected. The DMD can only produce instant binary intensity, so the original intensity CGFH must be converted to a binary CGFH. Herein, the binary Gerchburg–Saxton (GS) algorithm²¹ is chosen to calculate the binary CGFH, the advantages of which are good diffraction efficiency, simple and fast evaluation of a binary CGFH with fast Fourier transform iteration to optimize the hologram, and high convergence speed.^21,23 Currently, the back focal aperture of the $60\times$ objective lens is about 9 mm in diameter; therefore, the DMD should diffract the regenerative amplifier’s output with a 10-mm beam size to completely fill the objective lens’ aperture at the Fourier plane according to an excitation wavelength of around 800 nm, a DMD pixel size of around $13.6\mu \mathrm{m}$, and the 250-mm focal length of the Fourier lens.

2.4.

Theoretical Analysis of Temporal Focusing-Based Multiphoton Excitation Microscopy

To explicate our experimental results, theoretical analysis based on Fourier optics is adopted to evaluate the axial confinement of our TFMPEM system. As we know that an ultrashort pulse is generated by superposition of light with different wavelengths in phase. Hence, an ultrashort pulse passes through a grating in the TFMPEM can be decomposition of plane waves of different wavelengths in a different diffractive angle ${\theta }_{\omega }$ that can calculate from the grating equation. After passing through the collimated lens, decomposed plane wave of different wavelengths is focused on the back aperture plane of an objective in different focal points. Then, electric field distribution with a different wavelength $A_F$ is filter by the back aperture (circular aperture) of an objective. After that, the Fourier transform in a space domain based on the theory of Fourier optics is adopted to calculate the electric field distribution of different wavelengths in the TF plane (imaging plane) $A_{TF}$

3.1.

Axial Confinement Enhancement via Binary Digital-Micromirror-Device Holography

A PMMA thin film doped with rhodamine-6G (R6G) dye ($<200\text{-}\mathrm{nm}$ thick) and prepared via spin coating¹⁸ was first placed on the front-focal plane of the objective lens for TPEF imaging. Figures 3(a) and 3(b) show images of the beam shape near the back-focal aperture of the objective lens and the TPEF images at the front-focal plane, respectively. The images from left to right are: TF spectral dispersion only (without the CGFH diffraction), TF spectral dispersion with $0.58\text{-}{\mu \mathrm{m}}^{-1}$ spatial-frequency sinusoidal structured diffraction, TF spectral dispersion with CGFH diffraction at the optimized expansion (almost filling the aperture), and TF spectral dispersion with CGFH diffraction at an expansion exceeding the aperture (twofold expansion greater than the aperture). Figure 3(c) shows the normalized intensities of the red-dashed lines in Fig. 3(a). From the results, it can be seen that utilizing the binary CGFH can precisely and efficiently control the diffraction light at each spectral component on the back-focal plane and optimize it according to the back-focal aperture size to exploit the full NA of the excitation light. The $\pm 1\mathrm{st}$ order diffraction intensity at the optimized CGFH diffraction condition (named Holo-1) has more condensed diffraction light than those at the non-optimized conditions (termed Holo-2), and therefore produces superior axial confinement. The TF spectral-dispersion result with the $0.58{\mu \mathrm{m}}^{-1}$ sinusoidal structured diffraction (denoted as Sinusoidal) shows that the energy can be specifically diffracted to partially fill the aperture; hence, the axial excitation confinement can be improved.

Fig. 3

(a) Beam shape images close to the back-focal aperture (from left to right) by TF spectral dispersion only (TF); TF spectral dispersion with sinusoidal structured diffraction (Sinusoidal); TF spectral dispersion with optimized CGFH diffraction (Holo-1); and, TF spectral dispersion with CGFH diffraction (Holo-2) at the twofold expansion over the aperture. The spectral dispersion direction here is horizontal. (b) TPEF images at the four different TF excitation conditions in (a). (c) Normalized intensity profiles of red-dashed lines cut from (a).

The prepared fluorescent PMMA thin film was examined to verify and demonstrate the axial confinement improvement via the four different TF excitation conditions (TF, Sinusoidal, Holo-1, and Holo-2) as shown in the simulation of Fig. 4. From the simulation comparison of Fig. 4, Holo-1 and Holo-2 can fill-in more of the back focal aperture; therefore, the ACE of Holo-1 and Holo-2 are superior to that of TF. The film was axially scanned with a range of $20\mu \mathrm{m}$ and a step size of $0.5\mu \mathrm{m}$ by controlling the piezomotorized stage. Figure 4 shows the axial MPE fluorescent intensity profiles of the PMMA thin film under the aforementioned four conditions. In the experimental results of Fig. 4, the excitation energy and the exposure time of each curve are the same and normalized with the maximum intensity of each curve, and then fitted with a spatially-chirped beam fitting equation to determine the full width at half maximum (FWHM).²⁵ The axial excitation depths fitted with spatially-chirped beam fitting equation ²⁶ are around 2.94 and $2.37\mu \mathrm{m}$ (FWHM) for the TF and Holo-1 conditions, respectively. Theoretical analysis of axial MPE fluorescence intensity profiles for TF (blue line) and Holo-1 (red line). The simulated axial resolutions of TF and Holo-1 are around 2.93 and $2.35\mu \mathrm{m}$, respectively. In comparison, the axial excitation depth with the Holo-1 condition was improved to nearly $2.37\mu \mathrm{m}$ [about $(2.94-2.37)/2.37\times 100\%=24\%$]. Moreover, it can be seen from the results of Fig. 4 that not only does the FWHM of the optimized CGFH decrease by fully filling the back aperture of the objective lens, but the excitation intensity is also reduced in both sides of spatially chirped beam fitting profile. Accordingly, to further improve axial excitation confinement in the TFMPEM, two modifications can be considered. One is to use similar sinusoidal frequency combinations to design the periodic illumination pattern; however, this approach requires providing a uniform excitation pattern despite the rapid PWM switching. The other remains adopting CGFH diffraction; but to increase diffraction efficiency, the binary intensity DMD can be replaced with a gray-level phase generator, such as a spatial light modulator.^25–27 Nevertheless, a blazed grating or a DMD is still required for spectral dispersion in the DMD-based TFMPEM setup.

Fig. 4

Axial MPE fluorescence intensity profiles of the thin film under TF (blue circle) and Holo-1 (red circle). Theoretical analysis of axial MPE fluorescence intensity profiles for TF (blue line), Holo-1 (red line), and Holo-2 (green line).

Repeat the above process of calculation of Sec. 2.4 that overall time-average fluorescence signal in the defocus plane can be obtained. According to these theoretical analyses, an axial resolution of the TFMPEM with different pattern on DMD can be evaluation. The theoretical analysis is shown in Fig. 4. It is clear to see that the axial resolution is an enhancement by the binary DMD holography. In our simulated results, axial resolution that is also fitted with spatially chirped beam fitting equation is around 2.93 and $2.35\mu \mathrm{m}$ for the TF and Holo-1 conditions, respectively. Axial resolution in our simulated results is similar to our experimental results and demonstrates that the TFMPEM with binary DMD holography can improve image quality through enhancing axial excitation confinement and rejecting out-of-focus excitation.

3.2.

Complementary Patterned Illumination via Pulse Width Modulation

From the results in Fig. 3, it is illustrated that via the optimized binary CGFH, each spectral component of the ultrafast laser beam can be expanded to a vertical line-like shape on the back focal plane; meanwhile, the different spectral components are dispersed to a horizontal line shape via the DMD spectral dispersion. The average excited power on the sample was controlled to below 20 mW with an exposure time of 100 ms. Accordingly, the different spectral components can be horizontally dispersed and vertically diffracted to fully fill the back-focal aperture. However, in the multiphoton excitation plane, the excitation pattern is binary-interference shaped due to the initial phase of our chosen light source being in random phase distribution; therefore, uniform excitation is not possible. To overcome this problem, the PWM is taken into consideration with respect to the characteristics of the DMD.²⁸ Because the light intensity control of the DMD is operated with fast-flips of each micromirror, the time of each mirror is governed/controlled by the 8-bit coding with gray-levels of 0 to 255. Due to the display of the DMD projector being based on persistence of vision, the different gray-levels represent the different remaining action times of each micromirror. For 8-bit coding, the gray-levels of 127 and 128 have similar remaining action times. Therefore, to demonstrate the concept of binary CGFH for TFMPEM, two complementary excitation patterns, both of which contain the effect of the Fourier hologram, with respective gray-levels of 127 and 128 via the PWM are sequentially switched to produce a pseudouniform excitation, as shown at the bottom-right of Fig. 2. Figures 5(a) and 5(b), respectively, show the original and complementary CGFH excitation patterns via rapid PWM switching, the pattern intensities of which are nearly the inverse of each other. Figure 5(c) is the merged excitation pattern and features near-uniform excitation. Furthermore, Fig. 5(d) presents the cross-section profiles of the red-dashed lines from Figs. 5(a)–5(c). As seen in Fig. 5(d), the numerous peaks and valleys of Holo-1 and Holo-1-c are nearly complementary. Comparatively, the PWM-1 curve reveals a smoother Gaussian distribution.

Fig. 5

(a) & (b) TPEF images by TF with the original and complementary CGFH excitation patterns via rapid PWM switching, respectively. The intensity of each pattern is nearly the inverse of the other. (c) Merged image showing near-uniform excitation. (d) Cross-section profiles of the red-dashed lines from (a) to (c).

3.3.

Bioimaging for COS-7 Cell

To demonstrate the axial confinement improvement in practical application, the COS-7 cell line was stained with secondary antibody Alexa Fluor 488 fluorescein, after which the cytoskeleton’s $\alpha$-tubulin was imaged by TF alone [Fig. 6(a)] and TF with the two complementary CGFH excitation and mergence approach [Fig. 6(b)]. Furthermore, to avoid photobleaching, the average excited power on the sample was controlled to below 20 mW with an exposure time of 200 ms. The filtered images, after the iterative deconvolution process, are respectively shown in Figs. 6(c) and 6(d). In comparing Figs. 6(a) and 6(b), it can be seen that a sharper image via the TF with the complementary CGFH approach can be obtained through enhancing axial excitation confinement. This TF method with DMD-based CGFH diffraction targets axial excitation confinement improvement; consequently, a portion of the background noise in TFMPEM is rejected. Therefore, the image contrasts of Figs. 6(b) and 6(d), respectively, compared with those of Figs. 6(a) and 6(c) are superior. From the TPEF images of Figs. 6(b) and 6(d), and with the support of rapid PWM switching, a near-uniform TPEF image can be achieved even with the binary CGFH pattern excitation. Figure 6(e) shows the section profiles of the red-dashed lines in Figs. 6(c) and 6(d). Due to the ACE becoming narrower, some details in Fig. 6(b) can be slightly clarified via this approach. The overall improvement, however, is minor due to the low power efficiency.

Fig. 6

TPEF images of $\alpha$-tubulin of the COS-7 cell line stained with Alexa Fluor 488 by (a) TF only, and (b) TF with the two complementary CGFH excitation. (c) and (d) Filtered images of (a) and (b) after iterative deconvolution process. (e) Intensity profiles along the intersecting red dashed lines in Figs. 6(c) and 6(d). Scale bar: 5 μm.