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Abstract
Wavefront distortion in temporal focusing microscopy (TFM) results in a distorted temporal profile of the excitation pulses owing to spatio-temporal coupling. Since the pulse duration is dramatically changed in the excitation volume, it is difficult to correct the temporal profile for a thick sample. Here, we demonstrate adaptive optics (AO) correction in a thick sample. We apply structured illumination microscopy (SIM) to an AO correction in wide-field TFM to decrease the change in the pulse duration in the signal detection volume. The AO correction with SIM was very successful in a thick sample for which AO correction with TFM failed.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Temporal focusing microscopy (TFM) enables high-speed imaging owing to its optical sectioning capability with a wide field of view (FOV) in multiphoton excited fluorescence microscopy (MPFM) [1,2]. For example, two-photon video-rate imaging was demonstrated in the range of 5000–20000 µm2 [3,4]. Wide-field multi-photon excitation with optical sectioning capability can be combined with patterned illumination for photostimulation [3,5]. Additionally, TFM has the unique feature of axial scanning by controlling the group delay dispersion (GDD) [6–8]. This is possible because multiphoton excitation in TFM is confined near the focal plane by focusing an ultrashort laser pulse with spectral dispersion, which changes the pulse duration along with the propagation and generates the shortest pulse duration at the focal plane. Owing to spatio-temporal coupling, the GDD is converted to the quadratic phase factor of the focused wavefront, which results in displacement of the temporal focal plane. On the other hand, third-order and higher-order dispersion degrades the signal intensity and the axial resolution [9,10]. The GDD in the microscope system can be compensated for by a pre-chirper such as a prism pair. The higher-order dispersion can also be compensated for by a 4-f pulse shaper in which a spatial phase modulator, such as a deformable mirror (DM) or a spatial light modulator (SLM), is placed at the Fourier plane where wavelengths are spatially dispersed.
The spectral phase corrected by the pulse shaper is determined by a pulse characterization method, such as frequency-resolved optical gating (FROG) [11], spectral phase interferometry for direct electric-field reconstruction (SPIDER) [12], or multiphoton intrapulse interference phase scan (MIIPS) [13], or by optimizing the multiphoton excitation signals with the pulse shaper [14]. In FROG, second harmonic generation (SHG) spectra produced by two copied signal pulses with a delay time are typically recorded by a spectrometer. Although an iterative pulse-retrieval algorithm is employed to reconstruct the spectral phase from SHG-FROG spectrograms, 100% reliable convergence has been achieved [15]. In SPIDER, the sum frequency generation (SFG) spectrum, which is induced by two copied signal pulses and a long chirped pulse, is generally measured. The spectral phase is easily retrieved without an iterative algorithm from the group delay obtained from the SFG spectrum. In MIIPS, there is no need to prepare copied signal pulses for the measurement. SHG spectra generated from the pulses whose spectral phases are modulated with a pulse shaper are recorded. The spectral phase is easily retrieved from the group delay dispersion estimated from the SHG spectra. In an optimization method, an iterative algorithm such as simulated annealing (SA) or genetic algorithm (GA) is used to increase the multiphoton excitation signal generated in the sample [16,17]. Although the optimization method does not need a spectrometer, copied signal pulses or SHG sources, it takes a long time to determine the spectral phase compared to the pulse characterization time.
In laser scanning MPFM, wavefront distortion is induced by aberrations in the optical elements and/or the inhomogeneous refractive index distribution of samples, especially biological tissues. This can be overcome by employing adaptive optics (AO) [18,19] that provides aberration free images. In an AO system, the wavefront distortion is compensated for by a wavefront corrector, such as a DM or an SLM. The corrected wavefront is obtained by measuring the wavefront with a wavefront detector such as a Shack–Hartman wavefront sensor or by optimizing the fluorescence signals with a wavefront corrector. In MPFM, since all wavelengths propagate in a common path, chromatic aberration is small. Thus, AO is typically utilized for correcting monochromatic aberration, which is spatially variant in a wide FOV. Generally, a wavefront corrector is placed at the conjugate of the microscope pupil [18,19], called pupil AO. Pupil AO is useful for a small FOV because monochromatic aberrations can be assumed to be spatially invariant for a small FOV. However, in pupil AO, it is difficult to correct spatially variant monochromatic aberrations over a wide FOV. To correct spatially variant aberrations, it is better to place a wavefront corrector at the conjugate of the primary aberration source, called conjugate AO [20].
On the other hand, in wide-field TFM, since wavelengths are spatially dispersed and propagate in different paths, the difference in the optical path length affects the spectral phase and distorts the temporal profile as chromatic aberration. If the FOV is small, chromatic aberration as well as monochromatic aberrations can be assumed to be spatially invariant in a small FOV. Correcting chromatic aberration in a small FOV by a pulse shaper can be almost completely compensated for. However, in wide-field TFM, the optimization technique to correct the temporal profile can only be used when the sample is much thinner than the axial excitation volume [21]. This is because the signal intensity is integrated along the axial direction in the excitation volume where the pulse duration is a function of the axial position. The pulse duration change in the excitation volume makes signal evaluation in the optimization algorithm difficult. If strong fluorescence at the edge of the axial excitation volume and weak fluorescence at the center of the axial excitation volume are observed simultaneously, the effect of the optimization algorithm is to increase the fluorescence intensity at the edge of the axial excitation volume. The optimization creates a mismatch between the focal planes of the excitation system and the detection system, which results in degradation of the image quality. This limitation can be relaxed by using line-scanning TFM [22,23]. Since in line-scanning TFM, both temporal focusing and line focusing reduce the axial excitation volume [24], the pulse duration change is negligibly small in the axial excitation volume. In contrast, the imaging speed is limited by the mechanical scanning of the line-shaped beam to create a two-dimensional image.
Here, we present an AO technique of wide-field TFM combined with structured illumination microscopy (SIM) [25–27] which allows enhancement of the axial resolution of TFM [28–31]. By applying SIM to AO of wide-field TFM, the axial detection volume becomes small enough to neglect the pulse duration change. Thus, the SIM based detection scheme, which acts as spatial lock-in detection, enables us to perform an AO correction in wide-field TFM with a thick sample. We demonstrate that the AO correction in wide-field TFM combined with SIM allows correction of system and/or sample chromatic aberrations. To obtain the corrected spectral phase without a spectrometer, copied signal pulses and SHG sources in a sample, two-photon excited fluorescence (TPEF) signals generated by pulses whose local spectral phase is modulated with a pulse shaper are measured with homodyne detection. Since homodyne detection works as temporal lock-in detection, the spectral phase at the modulated local frequency can be easily acquired from the homodyne signals.
2. Methods
2.1 Optimal phase estimation
In this section, we describe the analytical theory of optimal phase estimation in the AO technique. By assuming that chromatic aberration is spatially invariant in a small FOV, we consider only the temporal profile. When the local spectral phase of the laser pulse is modulated, the electric field in the spectral domain $\tilde{E}(\omega )$ can be written as
Then, the electric field of the second harmonic (SH) $E_m^{(2 )}(t )$ is calculated as
Measuring the SH intensity with homodyne detection, which acts as temporal lock-in detection, the homodyne signal H is obtained as
For a phase difference of ${\phi _m} - {\phi _0} = 0$, the SH intensity in Eq. (5) is maximized. Therefore, the optimal phase is ${\phi _0}$. By iterating this process for all frequencies involved in the pulse, the Fourier transform limited (FTL) pulse is obtained. Because the intensity of TPEF is proportional to the SH intensity, this technique can be used for a fluorescent sample. Therefore, the corrected spectral phase is obtained without a spectrometer, SHG sources, and copied signal pulses.
2.2 Experimental setup
Figure 1 shows a schematic of the AO system for wide-field TFM. As an excitation light source, we used a custom-built Yb-fiber laser system that consists of an Yb-doped mode-locked fiber oscillator and four-stage chirped-pulse fiber amplifiers, modified from Ref. [32]. A fiber stretcher was located between the oscillator and the 1st amplifier. The GDD and third-order dispersion (TOD) were compensated for by a diffraction grating compressor placed after the 4th amplifier. Higher-order dispersion was compensated for by a 4-f pulse shaper with a 128-pixeled SLM, placed between the 1st and 2nd amplifiers to prevent damage to the liquid crystal (LC) and reduce the spatial distortion caused by the 4-f pulse shaper [33]. In the pulse shaper, the LC-SLM was placed at the Fourier plane where wavelengths are spatially dispersed. The laser system generated 100-fs, 1.3-µJ pulses at a center wavelength of 1055 nm. The repetition rate was reduced from 40 MHz of the oscillator to 3.3 MHz by an acousto-optic modulator. After the grating compressor, a combination of a half-wave plate and a Glan laser polarizer controlled the illumination pulse energy. The laser pulse was introduced to a digital micromirror device (DMD: DLP4500NIR, Texas Instruments) at an incidence angle of 23.1°. The image on the DMD was projected into the sample using a combination of a water-immersion objective lens (UPLSAPO60XW, Olympus, numerical aperture of 1.2) and an imaging lens with a focal length of 375 mm. The latter lens was assembled from two achromatic doublets (AC508-750-C, Thorlabs) placed symmetrically around a small air gap, known as the Plössl eyepiece [34]. The DMD was used both as an amplitude grating for SIM [35] and as a phase grating for TFM [31,36]. Wavelengths are spatially dispersed at the pupil of the objective lens for TFM. The generated fluorescence signals were separated from the excitation pulses by a dichroic mirror (FF875-Di01, Semrock) and then relayed to a water-cooled complementary metal-oxide semiconductor (CMOS) camera (ORCA-Fusion C14440-20UP, Hamamatsu Photonics) with an imaging system consisting of an objective lens and an achromatic doublet lens with a focal length of 200 mm. The residual excitation pulses were removed by a short-pass filter (FF01-890/SP-25, Semrock). The SIM image was reconstructed from the four fluorescence images, which were obtained under structured illumination with a phase step of π/2. Since the FOV diameter was 30 µm, we assumed that chromatic aberration is spatially invariant for a small FOV. In the AO process, the spectral phase at the local frequency was modulated by the LC-SLM in the 4-f pulse shaper from 0 to 2π by a step of 2π/3 (n=3 in Eq. (7)). Then, the optimal phase was estimated by the theory described in Section 2.1.
Fig. 1. Schematic of the AO system of wide-field TFM. LC-SLM: liquid crystal spatial light modulator, AOM: acousto-optic modulator, HWP: half-wave plate, GLP: Glan laser polarizer, DMD: digital micromirror device, DM: dichroic mirror, SF: short-pass filter.
3. Experimental results
First, the dispersion compensation with the optimal phase estimation was experimentally validated by replacing the DMD and the CMOS camera with a flat mirror and a photo-multiplier tube (PMT: R4220, Hamamatsu Photonics), respectively. Before the higher-order dispersion compensation, the GDD and TOD were compensated for by adjusting the distance and angle of the grating compressor to increase the TPEF intensity from a rhodamine B solution dispersed in an agarose gel. The higher-order dispersion was then compensated for by the 4-f pulse shaper with the optimal phase estimation.
Figure 2(a) shows an entire signal transition during dispersion compensation with the optimal phase estimation. Figure 2(b) illustrates an enlarged view of the area indicated by the pink square in Fig. 2(a). Three TPEF signals were detected by modulating the phase of the local frequency at one pixel of the LC-SLM with a step of 2π/3 in one iteration cycle. As described in Sec. 2.1, the optimal phase was estimated from the three TPEF signals. After the obtained optimal phase was applied to the modulated local frequency, the TPEF signal increased. The iteration cycle number indicates the pixel number, and all pixels of the LC-SLM consisting of 128 pixels were sequentially adjusted to the optimal phase through 128 iteration cycles. We call the 128 iteration cycles one-round-trip compensation. After one-round-trip compensation, the pixel number was returned to the first pixel. The optimal phase was determined by repeated round-trip compensation. The dotted line in Fig. 2(a) illustrates the end of each compensation round-trip. The optimization process was stopped when the TPEF signal at the end of the round trip compensation is smaller than that of the previous round trip. In this experiment, the TPEF signal was maximized with two-round-trip compensation and the optimization process was stopped after a three-round-trip compensation. As a result, the TPEF signal was 3.78-times higher than the initial value, and the optimized phase was obtained as shown in Fig. 2(c). With the optimized phase, we measured the second-order interferometric autocorrelation (IAC) trace. Figures 2(d) and (e) show the recorded IAC traces before and after dispersion compensation. Each trace is normalized to the peak signal value of 8. In Fig. 2(d), the upper and lower envelopes of the IAC trace are for the FTL pulse, which was calculated from the laser spectrum. Before dispersion compensation, dispersion still remains because the peak to background ratio of the IAC trace is 4.8. In contrast, since the IAC trace of the experimental result is in good agreement with that of the calculated result, we concluded that the dispersion was compensated for completely.
Fig. 2. (a) Signal transition during dispersion compensation using optimal phase estimation. The black dotted lines at 128 and 256 iteration cycles show the end of each compensation round-trip. (b) Enlarged view of the area indicated by the pink square in (a). (c) Obtained phase mask and laser spectrum. (d) IAC trace before dispersion compensation. (e) IAC trace after dispersion compensation and calculated FTL envelopes.
Next, in order to qualitatively confirm the pulse duration change of the temporally focused pulse in the axial detection volume, we measured the axial responses of TFM and SIM. We used a mono-layer of fluorescent beads with diameters of 200 nm (F8809, Molecular Probes) as a thin sample. The pulse duration was measured at each axial position by IAC. As shown in Fig. 3(a), the pulse duration is nearly constant in the axial detection volume for SIM, whereas the pulse duration significantly changes in that for TFM. Thus, we expect that SIM would allow us to perform AO correction in wide-field TFM.
Fig. 3. (a) TPEF axial responses of SIM and TFM, compared to the pulse duration change of the temporally focused pulse near the focal plane. (b) TPEF axial responses of a mono-layer of fluorescent beads before (green) and after (blue) dispersion compensation, after AO correction with SIM (red), and after AO correction with TFM (black). (c) Signal transition during AO correction with SIM before dispersion compensation. The black dotted lines at 128, 256, and 384 iteration cycles show the end of each compensation round-trip.
By employing a rhodamine B solution dispersed in an agarose gel, AO correction in wide-field TFM was experimentally validated for a thick sample. Since agarose gel has a refractive index close to that of water and a homogeneous structure, aberrations of the sample are small. Accordingly, AO mainly corrects the dispersion and chromatic aberration due to the optical elements and/or misalignment of the illumination system. The focal plane was set at a depth of 200 µm from the surface of the sample. First, to confirm whether or not AO correction works in a thick sample, AO correction was started after dispersion compensation. The signals by AO correction with SIM and TFM were maximized with two-round-trip compensation and the optimization process was stopped after three round-trips. After AO correction with SIM and TFM, the signal was improved by a factor of 1.64 and 1.27, respectively. Although both signals increased, it is inconclusive whether the optimal phase for correcting chromatic aberration was obtained. To investigate the effect of AO correction for chromatic aberration, axial responses of TFM after AO correction with SIM and TFM were measured. The axial signal distribution of a mono-layer sheet of fluorescent beads with diameters of 200 nm was acquired by scanning the objective lens, which was mounted on a piezoelectric transducer stage, in the axial direction with a step of 80 nm. The incident pulse energy was 4.7 nJ and the exposure time was 10 ms. As shown in Fig. 3(b), after dispersion compensation, the peak TFM signal was improved by a factor of 2.6, compared to that before dispersion compensation. The full width at half maximum (FWHM) before and after dispersion compensation with SIM were 37.6 µm and 3.5 µm, respectively. The response after AO correction with SIM has the same FWHM as that after dispersion compensation. Nevertheless, the axial response after AO correction with SIM has a higher peak compared with that after dispersion compensation by a factor of 1.2. This is because the chromatic aberration induced by the aberration of optical elements and/or misalignment in the TFM configuration has been compensated for. In contrast, the axial response after AO correction with TFM was degraded compared to that after dispersion compensation even though the AO correction was started after the dispersion compensation. This shows that the increase of the signal after AO correction with TFM was caused by the expansion of the axial excitation volume, not by the correction of the chromatic aberration. This is because the pulse duration change in the excitation volume makes signal evaluation difficult. On the other hand, AO correction with SIM worked well since SIM decreases the change in the pulse duration in the signal detection volume. Therefore, SIM enables us to achieve AO correction of wide-field TFM for a thick sample, for which correcting the temporal profile by AO correction with TFM is difficult. Next, AO correction with SIM was started before dispersion compensation. Figure 3(c) shows the signal transitions during AO correction with SIM before dispersion compensation. The SIM signal was maximized with three-round-trip compensation and the optimization process was stopped after four round-trips. The SIM signal after AO correction with SIM was improved by a factor of 2.8 even though the initial temporal profile was significantly distorted with dispersion.
After validation of the AO correction, we examined its effect for patterned illumination. Agarose gel containing a rhodamine B solution was illuminated by a temporally focused pulse with a stripe-pattern beam profile formed by the DMD. The pulse energy was 16 nJ and the exposure time was 100 ms. The focal plane was set at a depth of 200 µm, as for the validation of the AO correction. Figure 4 shows TPEF images obtained by stripe-pattern illumination before and after AO correction with SIM. As shown in Figs. 4(a) and 4(b), the image contrast of the stripe pattern was enhanced after AO correction. Figure 4(c) compares the line profiles along the lateral yellow dotted line in Fig. 4(a). In the line profile after AO, the signal intensity at the valleys decreases, while that at the peaks is maintained. The contrast ratios were evaluated from the peaks to the valleys at the five locations labeled 1–1′, 2–2′, 3–3′, 4–4′, and 5–5′, and were enhanced by factors of 2.8, 1.9, 1.6, 2.3, and 2.2, respectively.
Fig. 4. TPEF images of agarose gel containing a rhodamine B solution illuminated by stripe-patterned temporal focusing pulses: (a) before AO correction, (b) after AO correction. (c) Line profiles of (a) and (b) along the lateral yellow dotted line in (a). The labeled numbers indicate the peak-to-valley locations for calculating the contrast.
We considered the mechanism for the contrast enhancement. As shown in Fig. 3(c), the AO correction with SIM improves the SIM signal, indicating that the TPEF signal generated at the focal plane increased despite the narrowing of the axial detection volume by the SIM technique. The increase of the TPEF signal at the focal plane is due to the enhanced constructive interference at the focal plane. Since the AO correction with SIM enhances not only constructive interference at the focal plane and but also destructive interference at the out-of-focus regions, the excitation intensity at the focal plane was enhanced, while that at the out-of-focus regions was suppressed. Therefore, as shown in Fig. 3(b), the signal fluorescence generated at the focal plane increased whereas the background fluorescence at the out-of-focus regions decreased. Since the TPEF intensity is integrated along the axial direction in the excitation volume, the improvement of the TFM signal after the AO correction with SIM is not as high as that of the SIM signal. This is also why it is difficult to evaluate the signal of the optimization algorithm in AO for TFM with a thick sample. However, because the signal fluorescence at the focal plane could be distinguished from the background fluorescence at the out-of-focus regions by using the SIM technique, the optimization algorithm was successful and worked well. As a result, the contrast of the TFM image after the AO correction with SIM could be enhanced as shown in Fig. 4(c).
In order to confirm the improvement of the imaging performance with optical system correction, we performed TPEF imaging of a biological sample. Figure 5 shows the results of TPEF imaging of sliced-mouse-brain tissue stained with rhodamine phalloidin. The sample was fixed with 4% paraformaldehyde. The imaging position was set at a depth of 10 µm from the surface of the sample. The images were captured with an illumination energy of 31 nJ and an exposure time of 100 ms. Figures 5(a) and 5(b) show the obtained images after dispersion compensation and AO correction for optical system aberration, respectively. The images visualize sub-cellular structures of the labeled actin. The image with AO correction has a higher signal compared with that with dispersion compensation. Figure 5(c) shows a comparison of the line profiles along the longitudinal yellow dotted line in Fig. 5(a). We can see the signal enhancement in the fine structures indicated by the arrows in Figs. 5(b) and 5(c).
Fig. 5. (a, b) TPEF images of mouse-brain tissue visualized by rhodamine phalloidin for actin staining: (a) before AO, (b) after AO correction. (c) Line profiles of (a) and (b) along the longitudinal yellow dotted line in (a).
Finally, we performed a full AO correction for the aberration including chromatic aberration given by a sample. The sample was prepared by mixing solutions of fluorescent beads with diameters of 200 nm (F8809, Molecular Probes) and 2 µm (F8825, Molecular Probes), distributed in an agarose gel on a dish. The surface on the side of the objective lens was covered by a coverslip coated with nail polish. The nail polish was scratched at random to induce additional aberration. The focal plane was set at a depth of 150 µm from the surface of the sample. The AO correction was started with the system in the condition with the dispersion compensated. Before and after AO correction, we captured TPEF images with a pulse energy of 78 nJ with an exposure time of 100 ms. Figures 6(a–c) show TPEF images acquired using TFM under three conditions: (a) only dispersion compensation, (b) dispersion and optical system correction, and (c) full correction including sample aberration. TPEF images obtained using SIM after dispersion compensation and AO full correction including sample aberration are shown in Figs. 6(d) and 6(e), respectively. In Fig. 6(a), we can see 200-nm diameter beads distributed at the center part and the out-of-focus fluorescence of a 2-µm diameter bead at the lower right side. Even though the 2-µm bead is axially separated from the focal plane by 11 µm, its intensity is comparable to that of the in-focus 200-nm beads. This is because the fluorescence intensity of an in-focus 2-µm bead is much higher than that of a 200-nm bead, and the wavefront is distorted due to the random scratching of the nail polish. As shown in Fig. 3(b), the large out-of-focus background fluorescence in the excitation volume where the pulse duration varies along the axial direction, leads to failure of AO correction. In Fig. 6(d), the in-focus fluorescence of the 200-nm beads is observed, while the out-of-focus fluorescence including that from the 2-µm beads is dramatically suppressed by SIM. Because of the suppression of the out-of-focus fluorescence, full AO correction worked well. Figure 6(f) shows the phase difference between the corrected phases with full AO correction and optical system correction. We found that the optimal phase was changed by additional aberrations. Figures 6(g) and (h) show line profiles along the longitudinal yellow dotted lines in Fig. 6(a). The TFM signals with full AO correction are higher than that with optical system correction because sample aberration was corrected. After full AO correction, the TFM signals at the three peaks labeled 1, 2, and 3 are improved by factors of 1.06, 1.11, and 1.26, respectively compared to those after dispersion compensation. Compared to the SIM signal after dispersion compensation, the SIM signal at the three peaks after full AO correction are enhanced by factors of 1.62, 1.49, and 1.69, respectively, which is higher than the enhancement factor of 1.2 by optical system correction in Fig. 3(b). These results indicate that sample aberration was corrected with full AO correction. The diameter of the out-of-focus fluorescence from the 2-µm beads is maintained. Thus, we found that the focal plane was not shifted even if the out-of-focus fluorescence was strong.
Fig. 6. (a–e) TPEF images of mixed fluorescent beads with diameters of 200 nm and 2 µm obtained using (a–c) TFM and (d, e) SIM: (a, d) only dispersion compensation, (b) AO correction for aberration of mainly optical system, (c, e) AO correction for full aberration. (f) Phase difference between the obtained phase mask after full AO correction and optical system correction. (g) Line profiles of (a–c) and (h) those of (d, e) along the longitudinal yellow dotted line in (a). The labeled numbers in (g) and (h) indicate the locations for calculating the signal enhancement factors.
4. Conclusion
We have demonstrated AO correction of wide-field TFM combined with spatio-temporal lock-in detection, based on SIM and homodyne optimal phase estimation. The present AO technique worked successfully for a thick sample and strong out-of-focus background fluorescence, using agarose gels containing a rhodamine B solution, mixed fluorescent beads, and sliced-mouse-brain tissue. The AO correction compensated for chromatic aberration due to both the optical system and the sample, resulting in enhancement of the TPEF image contrast.
The FOV of our demonstration was 30 µm in diameter and hence we assumed that chromatic aberration is spatially invariant in the FOV. For an FOV larger than 100 µm, monochromatic aberrations that vary spatially over a wide FOV must also be corrected. The combination of pulse shaping technique and conjugate-AO [20] would correct not only chromatic aberration but also spatially variant monochromatic aberrations.
Funding
Nakatani Foundation for Advancement of Measuring Technologies in Biomedical Engineering; Japan Society for the Promotion of Science (JP18H04750 “Resonance Bio”); Core Research for Evolutional Science and Technology (JPMJCR1851, JPMJCR1921).
Acknowledgments
This work was supported by the RIKEN Junior Research Associate Program.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Original images as captured by the cameras are available upon request. Processed images are available upon request.
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