Remote focusing in a temporal focusing microscope

Michael E. Durst; Samuel Yurak; Joseph Moscatelli; Isabel Linhares; Ruben Vargas

doi:10.1364/OSAC.443116

1. Introduction

Two-photon-excited fluorescence microscopes can image through thick tissue because the fluorescence signal is confined to a single depth, which is known as optical sectioning [1,2]. In a laser-scanning two-photon microscope, a femtosecond-pulsed laser is focused to a point, and an image is formed by raster scanning the focused beam across the sample, acquiring serial data one pixel at a time. To acquire image data in parallel with a camera, temporal focusing (TF) creates wide-field two-photon excitation while retaining its optical sectioning capability [3–5].

Temporal focusing works by spreading the frequencies of an ultrashort laser pulse in space with a diffraction grating, collimating them with a lens, and then recombining them with an objective lens. Because the different frequency components only overlap near the focus, the pulse width is short only at the focal plane of the objective lens, creating a temporal focus. For points outside this geometric focus, however, different frequencies will have traveled different path lengths and will therefore be out of phase, thus broadening the pulse. This focusing in time replaces focusing in the spatial dimension, yielding wide-field two-photon excitation with optical sectioning.

One major advantage of temporal focusing is its ability to remotely tune the depth of the excitation plane using dispersion [4,6–14]. In general, ultrashort laser pulses are formed by the interference of a wide bandwidth of frequencies, and different phase shifts of these frequencies due to dispersion will lead to broadening of the pulse. In a typical system, we are most concerned with the parabolic phase shift, i.e., the group delay dispersion (GDD), because it is the lowest-order phase term which leads to pulse broadening. Temporal focusing is also sensitive to dispersion because the diffraction grating spreads the frequency components of the pulse in space, and this frequency-space mapping means that any spectral phase will become phase shifts in space and vice versa. In the presence of GDD, this quadratic phase in spectrum will result in a quadratic phase shift in space, and the corresponding quadratic wavefront created by the objective lens will shift the depth at which the individual frequency components add up in phase. That is, adjusting the amount of GDD will shift the location of the temporal focal plane, allowing for remote axial scanning via dispersion tuning.

In this paper, we demonstrate axial scanning in a temporal focusing microscope using dispersion compensation by a liquid lens (DisCoBALL) [15]. In this technique, an electrically tunable lens (ETL) is placed at the Fourier plane of a $4f$-grating pulse shaper. Because the individual frequency components of the pulse are spread out in space by the first grating of the pulse shaper, the different thicknesses of the ETL at different points in space lead to varying path lengths for each frequency. To a first approximation, the ETL shape is a parabola, which means that it generates parabolic spectral phase shifts, leading to tuning over a large GDD range which is electronically controlled and stable even at speeds over 100 Hz [16]. This GDD tuning enables remote axial scanning in a temporal focusing microscope.

Dispersion management is important for temporal focusing even when GDD is not used for axial scanning. In line-scanning temporal focusing, the beam passes through a cylindrical lens after the grating, making the different frequency beams parallel in the $x$-dimension but leaving the beam unaltered and the same size in the $y$-dimension [17–26]. (Here, the grating spatially disperses the wavelengths in the $x$-direction). After the objective lens, the separation of wavelengths in the $x$-dimension by the grating creates a temporal focus, and the $y$-dimension focuses tightly at the geometric focus. Dispersion compensation is important in line-scanning TF because if there is non-zero dispersion in the system, then these two foci will not overlap, exciting two separate planes. Similarly, temporal focusing with sculpted light requires pulse shaping to regain a transform-limited pulse width, maximum two-photon signal, and optimal axial confinement [20,27–29]. Lastly, while regular wide-field TF creates a transform-limited pulse even when shifted by dispersion, there is a limit to how far the temporal focus can shift before the frequencies no longer overlap [4,9]. Thus, minimizing the GDD is necessary to maximize the two-photon signal in a TF microscope.

Remote axial scanning with dispersion has not seen widespread adoption due to the difficulty of imaging these moving focal planes with a fixed camera. If the camera, sample, objective lens, and other detection optics are fixed in position, then only the geometric focus of the objective lens will be in focus on the camera. That is, the two-photon excited plane will deviate from the detection plane in focus on the camera. Translating the camera or any of the optics is too slow and can compensate for only a limited scan range [30]. Light-field detection uses a microlens array to gather both intensity and directional information, and while this can limit the lateral resolution, this is a strong candidate because TF illuminates a spot size which is much smaller than the field of view of the camera [31]. In fact, with the use of Fourier light-field microscopy [32], the axial resolution could possibly be enhanced through a deconvolution alogorithm. Unfortunately, splitting an already weak two-photon fluorescence signal across multiple pixels is not feasible with typical Ti:sapphire laser excitation. Another possibility is multifocus microscopy which uses a multifocus diffraction grating to image different planes on different regions of a camera [33], but it again requires larger signals to split the image into different regions of the camera. Compressive sensing is very promising because it uses a single pixel detector and has been shown to create images through extremely deep samples [34–37]. If one is not interested in forming images at all, simple 1D data could also be acquired [4,8], but our goal is to acquire volumetric 3D stacks. Lastly, one can ignore the need for re-focusing altogether by imaging point sources and interpreting the depth through either the defocus [12,38] or the astigmatism [39] of the point spread function.

In this paper, we demonstrate re-focusing with a second electrically tunable lens in front of the camera. By shifting the temporal focus excitation plane with a GDD-tuning ETL and re-focusing with a camera ETL, we create 3D image stacks with remote axial scanning with GDD tuning (with the sample in a fixed position) that are equivalent to moving the sample stage (with the GDD fixed). This is the most light-efficient approach to re-focusing the camera onto each axial plane, but more passive schemes like microlens arrays for light field and diffractive multifocus gratings for multifocus microscopy will improve the speed and accessibility when TF is excited by a regenerative amplifier or an otherwise increase in signal levels.

2. Theory

2.1 Temporal focusing excitation path

In a wide-field TF microscope (Fig. 1), a grating is imaged onto the sample using a collimating lens and an objective lens. Here, we follow the derivation from Ref. [4], except we begin our derivation at the diffraction grating and include extra factors of two in each exponential term [40]. For an input beam that is Gaussian in space and time, we can describe the electric field at the grating for a particular frequency $\omega$ as:

(1)$$A_0 (x,\omega) = A_{00} e^{-\frac{x^2}{2 s_0^2}} e^{-\frac{\left(\omega-\omega_0 \right)^2}{2 \Omega^2}} e^{i \frac{1}{2} \textrm{GDD} \left(\omega-\omega_0 \right)^2}$$

where $A_{00}$ is a constant, $2 s_0 \sqrt {\ln 2}$ is the FWHM input beam width in intensity, $2 \Omega \sqrt {\ln 2}$ is the FWHM intensity of the spectrum, $\omega _0$ is the center frequency of the pulse, and $\textrm {GDD}$ is the group delay dispersion. We have ignored the $y$-dimension because we are interested in wide-field temporal focusing in which only the $x$-dimension contributes to the signal.

Fig. 1. Excitation path in a temporal focusing microscope. Individual frequency components are spatially dispersed by a grating, collimated by a spherical lens, and recombined with an objective lens. The lenses are separated by the sum of their focal lengths. Note that the bandwidth of a typical Ti:sapphire laser is on the order of 10 nm; the colors are exaggerated for illustration purposes.

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At the Fourier plane after the collimating lens, the electric field becomes:

(2)$$A_1 (x, \omega) = A_{01} e^{-\frac{\left[ x-\alpha \left(\omega-\omega_0 \right) \right]^2}{2 s_1^2}} e^{-\frac{\left(\omega-\omega_0 \right)^2}{2 \Omega^2}} e^{i \frac{1}{2} \textrm{GDD} \left(\omega-\omega_0 \right)^2}$$

where

s_1 = \frac{f_{\textrm{col}} c}{s_0 \omega}

\alpha \approx f_{\textrm{col}} g \frac{2\pi c}{\omega_0^2}

where $g$ is the groove density of the diffraction grating, $f_{\textrm {col}}$ is the focal length of the collimating lens, $s_1$ is the beam size at the Fourier plane, and $\alpha$ is a constant describing the displacement in $x$ of each frequency component by the diffraction grating. To find $\alpha$, we have used the diffraction grating equation and set the diffraction angle for the center frequency $\omega _0$ to be zero. We use a small diffraction angle approximation and assume that $\omega \approx \omega _0$ so that $\alpha$ can be treated as a constant.

The electric field near the sample in a temporal focusing microscope can be found by Fourier transforming again to the sample plane and applying a defocus term [40]. In the end, the total two-photon excitation (TPE) signal can be found [4]:

(3)$$\textrm{TPE}(\Delta z)=\iint{I^2 \left(x,\Delta z, t\right) dx dt}\propto \left[\left(1+\textrm{GDD}\cdot\Omega^2 \frac{\Delta z}{z_M}\right)^2+\left(\frac{\Delta z - \textrm{GDD}\cdot\Omega^2 \cdot z_R}{z_R}\right)^2\right]^{-\frac{1}{2}}$$

where $\Delta z = z-f_{\textrm {obj}}$ is the displacement from the geometric focal plane of the objective lens (focal length $f_{\textrm {obj}}$) and:

z_R = \frac{f_{\textrm{obj}}^2 c}{\omega_0}\frac{1}{s_1^2 + \alpha^2 \Omega^2}

z_M = \frac{f_{\textrm{obj}}^2 c}{\omega_0}\frac{1}{s_1^2}

In this case, $z_R$ represents the Rayleigh range of the spatially-chirped beam, and $z_M$ represents the Rayleigh range of each monochromatic beam. The inverse square root in Eq. (3) is essentially a Lorentzian shape when the GDD is small $\left (\textrm {GDD}\cdot \Omega ^2 \ll 1\right )$.

For $\Delta z \ll z_M$, the second term in the square root determines the shape of the axial profile, but with a maximum value affected by the first term. For small GDD values, the location of the peak $\textrm {TPE}(\Delta z)$ signal and therefore the temporal focus is given by:

(4)$$\Delta z = \textrm{GDD} \cdot \Omega^2 \cdot z_R$$

The shift is linear with GDD.

There is a limit to how far one can shift the temporal focus. As described in detail in Ref. [4], the maximum shift $\Delta z_{\textrm {max}}=\sqrt {z_M z_R}$ occurs when the shift $\Delta z$ and the Rayleigh range of an individual wavelength beam $z_M$ are comparable in size, i.e., the individual monochromatic beams no longer overlap. For a larger maximum scan range, the incident beam size $s_0$ can be increased, yielding a correspondingly larger $z_M$. At the scan limit $\Delta z_{\textrm {max}}$, the peak TPE signal decreases by half, which can be shown by substituting Eq. (4) into Eq. (3). In addition, the illuminated spot size increases by a factor of $\sqrt {2}$ relative to the width at zero GDD [4].

2.2 Dispersion tuning

We implement dispersion tuning using an electrically tunable lens (ETL) [15]. An ETL is a liquid lens whose focal length can be adjusted electronically with a voice coil actuator. Here, we use an ETL (the GDD ETL) in a $4f$ pulse shaper to create tunable GDD (Fig. 2). From Ref. [15], the GDD created by the pulse shaper is given by:

(5)$$\textrm{GDD}={-}\frac{\omega_0}{c} \left(\frac{D}{\Omega_{\textrm{aperture}}}\right)^2 \frac{1}{f_{\textrm{ETL}}^{\textrm{GDD}}}$$

where $\omega _0$ is the center frequency of the pulse, $D$ is the diameter of the ETL aperture, $f_{\textrm {ETL}}^{\textrm {GDD}}$ is the focal length of the ETL in the pulse shaper, and $\Omega _{\textrm {aperture}}$ is the frequency bandwidth across the aperture of the ETL. Note that $\Omega _{\textrm {aperture}}$ depends on the range of grating diffraction angles and corresponding frequencies which pass through the ETL, and this geometric effect also depends on the focal length of the lens in the pulse shaper $f$, and the width of the GDD ETL aperture $D$. With this result and Eq. (4), we can now relate the focal length of the GDD-tuning ETL to the displaced depth within the sample:

(6)$$\Delta z = \textrm{GDD} \cdot \Omega^2 \cdot z_R ={-}\frac{\omega_0}{c} \left(\frac{D}{\Omega_{\textrm{aperture}}}\right)^2 \frac{1}{f_{\textrm{ETL}}^{\textrm{GDD}}} \Omega^2 \cdot z_R$$

Observe that the axial shift depends linearly on the focal power (inverse focal length) of the GDD-tuning ETL.

Fig. 2. $4f$ Pulse shaper for dispersion tuning with an ETL. Two transmission gratings map the individual frequency components into different lateral positions, and the path length difference of the ETL generates spectral phase shifts. The spectral phase is approximately parabolic, corresponding to GDD.

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2.3 Detection path

We use a second electrically tunable lens (camera ETL) to keep the axially scanned excitation plane in focus on the camera. While the ETL can be placed almost anywhere in the detection path to focus on each depth, the ETL must be placed at a Fourier plane to avoid changes in magnification at different focal powers [41–43]. In principle, the ETL can be placed at the Fourier plane immediately behind the objective lens, but this is typically inaccessible due to the thickness of the housing surrounding both the objective lens and the ETL itself. Plus, this position would be common to both the excitation and detection paths [44], and our goal is to re-focus only the detection path. Instead, we use a pair of lenses to relay the Fourier plane to a physically accessible conjugate plane (Fig. 3). There are a couple ways to relay the Fourier plane of the objective lens to the ETL: (1) relay the objective Fourier plane to the ETL using a relay lens pair and then put the tube lens after it, or (2) leave the original microscope alone and place the relay system at the end. We employ the latter so that we can build a standard TF microscope as an intermediate step in the alignment process.

Fig. 3. Detection path in a temporal focusing microscope. The fluorescence emitted from the sample forms an intermediate image after the objective lens and tube lens. The camera ETL is placed between a pair of relay lenses in order to re-focus to a different object plane while forming an image on the camera.

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Using ray tracing matrices, we calculate the effect of the ETL and relay lenses on the imaging system [43]. We assume that the lenses are each separated by the sum of their focal lengths, and with the camera lens placed one focal length away from the last relay lens, an object at the focal plane of the objective will be in focus on the camera. We then allow the object to be placed a distance $\Delta z$ farther from the objective lens. To find the ETL focal length required to keep the image in focus on the fixed camera position, we apply the following series of ray tracing matrices:

(7)$$\begin{aligned} &T_{f_{\textrm{relay}}}M_{f_{\textrm{relay}}}T_{f_{\textrm{relay}}}M_{\textrm{ETL}}^{\textrm{camera}} T_{f_{\textrm{relay}}}M_{f_{\textrm{relay}}}T_{f_{\textrm{relay}}}T_{f_{\textrm{tube}}}M_{f_{\textrm{tube}}}T_{f_{\textrm{tube}}}T_{f_{\textrm{obj}}}M_{f_{\textrm{obj}}}T_{f_{\textrm{obj}}}T_{\Delta z} \\ &=\begin{pmatrix} \frac{f_{\textrm{tube}}}{f_{\textrm{obj}}} & \frac{f_{\textrm{obj}}\, f_{\textrm{relay}}^2}{f_{\textrm{tube}} \,f_{\textrm{ETL}}^{\textrm{camera}}}+\frac{f_{\textrm{tube}}}{f_{\textrm{obj}}}\Delta z\\ 0 & -\frac{f_{\textrm{obj}}}{f_{\textrm{tube}}} \end{pmatrix} \end{aligned}$$

where $T_{\textrm {distance}}$ is a free-space propagation matrix for a distance corresponding to the subscript, and $M_{\textrm {lens}}$ is a thin lens matrix corresponding to a focal length in the subscript.

For a ray tracing ABCD matrix, the image is formed where $B=0$:

(8)$$\begin{aligned} B=0&=\frac{f_{\textrm{obj}} \,f_{\textrm{relay}}^2}{f_{\textrm{tube}} f_{\textrm{ETL}}^{\textrm{camera}}}+\frac{f_{\textrm{tube}}}\,{f_{\textrm{obj}}}\Delta z \\ \Delta z&={-}\left(\frac{f_{\textrm{obj}}\, f_{\textrm{relay}}}{f_{\textrm{tube}}}\right)^2\frac{1}{f_{\textrm{ETL}}^{\textrm{camera}}} \end{aligned}$$

The axial shift of the object plane is proportional to the focal power (inverse focal length) of the camera ETL required to keep the plane in focus on the camera.

Observe that the lateral magnification (matrix element $A$) is constant with respect to the focal power of the ETL:

(9)$$M=A=\frac{f_{\textrm{tube}}}{f_{\textrm{obj}}}$$

Because the magnification is independent of the focal length of the camera ETL, the magnification will remain constant when re-focusing.

2.4 Relationship between excitation and detection

To keep this plane in focus on the camera, the camera ETL focal power must be set to focus on the excitation plane, which is determined by the GDD ETL. Setting Eqs. (6) and (8) equal, we find:

(10)$$\begin{aligned} \Delta z &={-}\frac{\omega_0}{c} \left(\frac{D}{\Omega_{\textrm{aperture}}}\right)^2 \frac{1}{f_{\textrm{ETL}}^{\textrm{GDD}}} \Omega^2 \cdot z_R ={-}\left(\frac{f_{\textrm{obj}}\, f_{\textrm{relay}}}{f_{\textrm{tube}}}\right)^2\frac{1}{f_{\textrm{ETL}}^{\textrm{camera}}} \\ \frac{1}{f_{\textrm{ETL}}^{\textrm{camera}}} &=\frac{\omega_0}{c} \left(\frac{D}{\Omega_{\textrm{aperture}}}\right)^2 \Omega^2 \cdot z_R \left(\frac{f_{\textrm{tube}}}{f_{\textrm{obj}} \,f_{\textrm{relay}}}\right)^2 \frac{1}{f_{\textrm{ETL}}^{\textrm{GDD}}} \end{aligned}$$

We expect a linear relationship between the focal power of the GDD-tuning ETL and the camera re-focusing ETL.

3. Experimental setup

Our apparatus shown in Fig. 4 can be divided into three main components: the pulse shaper, the temporal focusing excitation path, and the detection path. Our Ti:sapphire laser (Spectra Physics Mai Tai) is an 800 nm pulsed excitation source which has a repetition rate of 80 MHz and a minimum full-width-at-half-maximum (FWHM) pulse width of 140 fs. The output beam passes through an isolator (ConOptics), and a half waveplate and polarizing beamsplitter cube control the laser power.

Fig. 4. Experimental apparatus. The GDD ETL in the pulse shaper generates tunable dispersion. The output of the pulse shaper is coupled into an optical fiber. The fiber output is expanded vertically by a cylindrical lens telescope, and then the beam enters the TF microscope consisting of a diffraction grating and two lenses. In the detection path, a flip mirror can switch between 1D detection with a PMT and 2D detection with a camera.

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3.1 Pulse shaper

We tune the dispersion using an ETL in a $4f$ pulse shaper, using two 1400 l/mm transmission diffraction gratings (LightSmyth T-1400-800-24x14.9-94), two 20 cm focal length plano-convex lenses, and a $-10$ to $+10$ diopter ETL (Optotune EL-16-40-TC-VIS-20D-1-C, aperture diameter 16 mm) driven by a lens controller (Gardasoft TR-CL180). The incident angle is chosen to be as close to Littrow as possible ($34^\circ$) to maximize the diffraction efficiency, and the spacing between each element is equal to the focal length of the fixed lenses (20 cm).

The output of the pulse shaper is focused into an endlessly single-mode, large-mode-area photonic crystal fiber (NKT Photonics LMA-20, length 90 cm) using a 4 cm focal length achromatic doublet lens. The purpose of the optical fiber is to isolate the pulse shaper from the temporal focusing microscope, ensuring that the output beam is a fixed shape regardless of ETL focal power. However, for low ETL focal powers such that the focal length of the ETL is always much larger than the fixed lens focal lengths in the pulse shaper, spatial chirp is less of a concern, and this optical fiber could be omitted. In this paper, we seek to maximize the GDD range, and this single mode fiber guarantees that the beam entering the temporal focusing microscope maintains a constant size and divergence, and therefore the pulse shaper introduces only dispersion to the beam.

To align the pulse shaper, we place the ETL on a translation stage and center it by monitoring the power output from the fiber, obtaining <4% power fluctuations for a 100 Hz sine curve fluctuating between $-2$ and $+2$ diopters (Fig. 5). From Eq. (5), the corresponding GDD range is $+2.08\times 10^5 ~\textrm {fs}^2$ to $-2.08\times 10^5 ~\textrm {fs}^2$. Fiber coupling efficiency decreases for larger diopter ranges, resulting in changes in bandwidth which would affect the quality of the temporal focus. In addition, we split the fiber output and focus it onto a two-photon absorbing photodiode (GaAsP photodiode, Hamamatsu G1115) to confirm that the pulse width changes and that dispersion is indeed applied despite the steady power output. Lastly, we offset the last grating to pre-compensate for the length of the optical fiber so that zero diopters for our GDD ETL corresponds to zero dispersion for our system. While we chose this approach to create symmetry in our data, we instead could use the GDD ETL to compensate for this dispersion.

Fig. 5. Stability of pulse shaper. The focal power of the GDD ETL (solid red curve) oscillates between $-2$ and $+2$ diopters. The power output of the fiber (blue dash-dot curve) shows less than 4% power fluctuations. Simultaneously, the two-photon absorption curve (blue dashed curve) shows a peak signal when the dispersion is a minimum.

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3.2 Excitation path

The temporal focusing microscope consists of a 1200 l/mm diffraction grating (Newport 33009FL01-360R), a 50-cm focal length plano-convex collimating lens, and an objective lens (Olympus UPlanFL 40x/0.75). The beam is coupled out of the fiber using an Olympus 4x/0.10 objective lens, and the focal length of this coupling lens determines the size of the beam and therefore the illuminated spot size at the sample. The beam is incident on the diffraction grating at an angle of $73.7^\circ$ so that the center wavelength is diffracted at an angle of $0^\circ$ from the normal. The diffracted beam is collimated by the collimating lens and re-focused onto the sample with the objective lens.

We characterize the system with a thin film of Rhodamine B. The emitted fluorescence is collected in the epi-direction through the same objective and re-directed by a dichroic mirror (Semrock FDi03-R635-25x36) through a series of filters (Semrock FF501-550/200-25, Thorlabs KG3 color glass, and Semrock FF01-590/104-25) to further remove the laser light. A removable right-angle mirror (Thorlabs DFM1-P01) directs the fluorescence to a photomultiplier tube (PMT, Hamamatsu H10492-003). The output pulses are converted to TTL pulses by a comparator (Pulse Instruments PRL-350TTL) which are then counted by a counter board (National Instruments PCI-6602) and a computer running LabVIEW.

To characterize the excitation profile, a thin film of Rhodamine B is swept axially through the temporal focus with a translation stage driven by a stepper motor (Thorlabs ZFS13B). As shown in Fig. 6(a), as the film passes through the temporal focus, the two-photon excited signal traces out a Lorentzian shape [4]. Next, we vary the GDD to a new fixed value, scan the sample, and identify the new peak position. In Fig. 6(a), the different axial scans are plotted together, with increasing GDD shifting the curve from right to left in the graph. In Fig. 6(b), the peak of each curve has been plotted versus GDD, revealing a linear relationship in agreement with Eq. (4).

Fig. 6. Thin film axial scans. (a) A thin film of dye is swept through the temporal focus for different GDD values, with increasing GDD moving shifting the temporal focus right to left. (b) The peak positions of each axial scan are plotted versus GDD ETL focal power, with a linear fit shown in solid blue.

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In a TF microscope, the illuminated area is narrower in one dimension due to the diffraction grating; the cross-section of the beam changes upon diffraction to be wider by a factor of $1/\cos \left ( \theta _{\textrm {incident}} \right )$. We compensate for this using a cylindrical lens pair to expand the beam vertically in the $y$-dimension. The illuminated area is initially 32 $\mu$m by 9 $\mu$m, which agrees with theory for our incident angle. After a cylindrical lens beam expander (30 cm and 10 cm focal lengths) placed before the grating, the illuminated area is 32 $\mu$m by 27 $\mu$m.

3.3 Detection path

For 2D detection with a camera, the right-angle mirror is removed to bypass the PMT. After being separated by the dichroic mirror and passing through the optical filters, the fluorescence propagates through the tube lens (180 mm focal length achromatic doublet lens), a relay lens (100 mm focal length achromatic doublet lens), the camera ETL (Optotune EL-16-40-TC-VIS-5D-C, $-2$ to $+3$ diopters, 16 mm diameter aperture), and a second relay lens (100 mm focal length achromatic doublet lens). The image is formed on an sCMOS camera (Hamamatsu Orca Flash 4.0 v2) controlled by LabVIEW.

To align the detection path, we begin by assembling a standard microscope without the relay lens system. First, the tube lens is placed a focal length away from the camera sensor such that a distant object is in focus on the sensor. Then, the camera and lens are moved together into the emission path until the distance between the tube lens and the back aperture of the objective lens is about one tube lens focal length (180 mm). At this point, a sample at the focus of the objective lens will be in focus on the camera. We use a 1951 USAF Target (Thorlabs R3L3S1P) as a high-contrast sample, and adjust the position of the sample until it is in focus on the camera. The sample is locked in place for the rest of the alignment process.

For the relay system, we remove the camera and attach a relay lens a focal length away (100 mm) until a distant object is in focus on the sensor. Then, we add the other relay lens after the tube lens with a separation equal to the sum of their focal lengths (280 mm). Next, we add the camera and relay lens, with a distance equal to the sum of the relay lens focal lengths (200 mm) after the first relay lens. We now have a complete microscope system, and the image of the USAF target on the camera should be the same magnification as before. Lastly, we insert the ETL halfway between the relay lenses. At a camera ETL focal power of zero, the image on the camera should be unaffected. The axial position of the camera ETL must be fine-tuned to eliminate magnification fluctuations as the focal power is changed. We accomplish this by sliding the ETL while iterating through many sample positions and corresponding camera ETL focal powers until the image no longer changes magnification.

To map the camera ETL focal powers to the corresponding object plane positions, we place the thin film Rhodamine B sample at the exact same stage positions used in the axial stage scan process (Fig. 7(a)). By bringing scratches in the film into focus on the camera using the camera ETL, we obtain a calibration curve for going back and forth between sample position and camera ETL focal power. As shown in Fig. 7(a), there is a linear relationship between depth and focal power, in agreement with theory (Eq. (8)).

Fig. 7. Camera re-focusing calibration. (a) A thin film of dye is brought into focus on the camera using the camera ETL at different stage positions. (b) Combining the stage position curves for the GDD ETL and the camera ETL, the calibration curve for camera ETL to GDD ETL is obtained.

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Putting it all together, we can take our GDD ETL to sample position curve (Fig. 6(b)) and our camera ETL to sample position curve (Fig. 7(a)) to generate a map of GDD ETL focal power to camera ETL focal powers (Fig. 7(b)). As shown in Fig. 7(b), the linear relationship between camera ETL focal power and GDD ETL focal power agrees with the theory in Eq. (10). The calibration is now complete. To acquire images, a LabVIEW program synchronizes GDD ETL and camera ETL values to acquire the desired number of images in a particular focal power range.

4. Results

We have acquired images of simple stained lens tissue fibers and pollen grains. In Fig. 8, we show a 3D stack taken of Rhodamine-stained lens tissue fibers. In the top row of Fig. 8, the sample position is held fixed while the GDD ETL and camera ETL are scanned together. In the bottom row, the GDD is held constant and the sample is shifted axially by the motorized translation stage. For the same laser and camera settings and equivalent step sizes calculated from the thin-film calibration, we observe that the GDD-scanning stack and the stage-scanning stack are equivalent, revealing different fibers crossing at different depths. With an average laser power of 100 mW, the dwell time for each image is 1 s. From observations with our thin film sample, the illuminated area is 32 $\mu$m by 27 $\mu$m.

Fig. 8. Lens tissue fibers. On the top row, the stack is formed using dispersion tuning while holding the lens tissue fibers sample position fixed. The GDD ETL and camera ETL values are labeled with units of diopters. On the bottom row, the GDD is held fixed and the stage is moved. The stage position is listed in microns. Each image corresponds to 82 $\mu$m by 82 $\mu$m in object space.

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In Fig. 9, a stack of pollen grain images reveal fine features. The top row of Fig. 9 is a dispersion-tuning stack with the sample position held fixed. The bottom row is a traditional stage scan while the GDD ETL and camera ETL are held constant near zero diopters. We again observe similar stacks obtained from the two methods using the same laser and camera settings.

Fig. 9. Pollen grains. On the top row, the stack is formed using dispersion tuning while holding the pollen grain sample position fixed. The GDD ETL and camera ETL values are labeled with units of diopters. On the bottom row, the GDD is held fixed and the stage is moved. The stage position is labled in microns. Each image corresponds to 41 $\mu$m by 41 $\mu$m in object space.

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5. Discussion

In this paper, we shift the excitation plane with GDD tuning and re-focus this plane onto the camera with an electrically tunable lens. While axial scanning with GDD tuning has been published before [4,6–14], acquiring rapidly re-focused images from these planes has not been previously reported, to our knowledge. The advantage of this technique is that it is equivalent to a traditional stage-scanning stack, and it can be done without any moving parts in the excitation path.

While this two ETL approach solves the problem of re-focusing the excitation plane shifted by GDD-tuning, it requires a complex system and the calibration of the two ETLs. A single ETL common to both the excitation and detection paths would significantly simplify the apparatus. In Ref. [44], it has been demonstrated that placing the ETL at the back focal plane of the objective lens allows for high-speed axial scanning in a temporal focusing microscope with a single ETL. In this paper, however, we seek to acquire images using remote axial scanning of the excitation plane with GDD tuning, a significant advantage of temporal focusing which warrants further investigation.

While it would be simpler to use a single ETL shared by both the excitation and detection paths [44], temporal focusing microscopes still require careful dispersion management. As described earlier, line-scanning temporal focusing microscopes require dispersion tuning to keep the temporal focus and the geometric focus overlapped. In addition, simple adjustments like changing the objective lens or switching to a different immersion medium require different amounts of dispersion compensation to keep the excitation plane in focus on a fixed camera. Plus, the possibility of remote axial scanning with fiber delivery could enable a TF fiber probe [8,45].

The ability to independently tune the focus on the detection side is important for many imaging techniques, including temporal focusing and light-sheet microscopy [42]. For TF, independent re-focusing of the excitation plane is not only needed to keep the dispersion-based axially scanned excitation plane in focus, but because the shifting of the temporal focus is refractive-index dependent [4], it is also needed to compensate for the heterogeneity of the sample. In fact, we see this effect in Fig. 8 and Fig. 9, in which the corresponding GDD ETL values and stage positions were calculated from the thin-film calibration in air (Fig. 6). Due to phase shifts introduced by the heterogeneity of the refractive index of the sample, the planes illuminated by the GDD-scan and stage-scan methods are slightly offset. This approach could still be advantageous, though, as the independent re-focusing could allow for a fast determination of in-focus and out-of-focus light for enhanced axial resolution. Ultimately, light-field and multifocus microscopy could be simpler approaches for re-focusing because they do not require synchronization of the detection and excitation paths.

Another advantage of temporal focusing is that the axial resolution and spot size can be scaled independently, but the maximum axial scan range is dependent on both. Dispersion tuning shifts the temporal focus axially by an amount proportional to the GDD and $z_R$ (Eq. (4)), and the FWHM axial resolution is $2\sqrt {3}\cdot z_R$ at zero GDD [4]. At larger GDD values, however, the axial FWHM widens (Eq. (3)), and the two-photon excitation signal decreases. In this paper, for a 40x objective lens and the chosen grating groove density and collimating lens focal length, the FWHM at zero GDD is 4 $\mu$m, and we are able to shift the temporal focus by 40 $\mu$m, or 10 distinct planes relative to the minimum axial FWHM at zero GDD. Switching to a 20x objective would double the objective lens focal length and increase $z_R$ by 4x, meaning that the scan range would be even larger but with wider axial resolution. Increasing the spot size could accommodate a larger scan range at the expense of a reduced signal from spreading the laser power over a larger area [4]. Although temporal focusing excitation is a photon-hungry approach, high-energy pulsed fiber lasers and amplified laser sources could enable much faster data acquisition, with the ultimate goal of acquiring volume images at video rates.

6. Conclusion

We have demonstrated axial scanning in a TF microscope using dispersion tuning with an ETL. With each excitation plane kept in focus on a camera with a second ETL, we produce 3D stacks that are equivalent to stage-scanning stacks without moving the sample or the objective lens. Ultimately, with a higher pulse energy source, this technique will be able to acquire high-speed volume images with no moving parts near the sample.

Funding

National Institute of Biomedical Imaging and Bioengineering (R15EB025585).

Acknowledgments

M. E. Durst thanks C. Laurence and A. Turcios for preliminary investigations and E. McMahon for custom-machined parts. Research reported in this publication was supported by the National Institute of Biomedical Imaging and Bioengineering of the National Institutes of Health under award number R15EB025585. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Disclosures

The authors declare no conflicts of interest.

Data availability

No data beyond the included figures were generated or analyzed in the presented research.

References

1. W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248(4951), 73–76 (1990). [CrossRef]

2. W. R. Zipfel, R. M. Williams, and W. W. Webb, “Nonlinear magic: multiphoton microscopy in the biosciences,” Nat. Biotechnol. 21(11), 1369–1377 (2003). [CrossRef]

3. D. Oron, E. Tal, and Y. Silberberg, “Scanningless depth-resolved microscopy,” Opt. Express 13(5), 1468–1476 (2005). [CrossRef]

4. M. E. Durst, G. Zhu, and C. Xu, “Simultaneous spatial and temporal focusing for axial scanning,” Opt. Express 14(25), 12243–12254 (2006). [CrossRef]

5. E. Papagiakoumou, E. Ronzitti, and V. Emiliani, “Scanless two-photon excitation with temporal focusing,” Nat. Methods 17(6), 571–581 (2020). [CrossRef]

6. H. Suchowski, D. Oron, and Y. Silberberg, “Generation of a dark nonlinear focus by spatio-temporal coherent control,” Opt. Commun. 264(2), 482–487 (2006). [CrossRef]

7. M. A. Coughlan, M. Plewicki, and R. J. Levis, “Parametric spatio-temporal control of focusing laser pulses,” Opt. Express 17(18), 15808–15820 (2009). [CrossRef]

8. A. Straub, M. E. Durst, and C. Xu, “High speed multiphoton axial scanning through an optical fiber in a remotely scanned temporal focusing setup,” Biomed. Opt. Express 2(1), 80–88 (2011). [CrossRef]

9. B. Leshem, O. Hernandez, E. Papagiakoumou, V. Emiliani, and D. Oron, “When can temporally focused excitation be axially shifted by dispersion?” Opt. Express 22(6), 7087–7098 (2014). [CrossRef]

10. F. He, B. Zeng, W. Chu, J. Ni, K. Sugioka, Y. Cheng, and C. G. Durfee, “Characterization and control of peak intensity distribution at the focus of a spatiotemporally focused femtosecond laser beam,” Opt. Express 22(8), 9734–9748 (2014). [CrossRef]

11. O. Hernandez, E. Papagiakoumou, D. Tanese, K. Fidelin, C. Wyart, and V. Emiliani, “Three-dimensional spatiotemporal focusing of holographic patterns,” Nat. Commun. 7(1), 11928 (2016). [CrossRef]

12. Y. Ding, A. C. Aguilar, and C. Li, “Axial scanning with pulse shaping in temporal focusing two-photon microscopy for fast three-dimensional imaging,” Opt. Express 25(26), 33379–33388 (2017). [CrossRef]

13. G. Li, F. Lu, H. Liu, B. Cui, W. Fan, B. Zhu, M. Shui, and Y. Gu, “Analysis of spectral chirps and intensities evolution of a spatiotemporally focused femtosecond laser beam,” Results Phys. 7, 2898–2906 (2017). [CrossRef]

14. N. C. Pégard, A. R. Mardinly, I. A. Oldenburg, S. Sridharan, L. Waller, and H. Adesnik, “Three-dimensional scanless holographic optogenetics with temporal focusing (3D-SHOT),” Nat. Commun. 8(1), 1228 (2017). [CrossRef]

15. M. E. Durst, A. Turcios, C. Laurence, and E. Moskovitz, “Dispersion compensation by a liquid lens (DisCoBALL),” Appl. Opt. 58(2), 428–435 (2019). [CrossRef]

16. M. E. Durst and A. Turcios, “Temporal focusing with remote axial scanning via dispersion with an electrically tunable lens,” in Biophotonics Congress: Optics in the Life Sciences Congress 2019, (Optical Society of America, 2019), p. NW1C.5.

17. E. Tal, D. Oron, and Y. Silberberg, “Improved depth resolution in video-rate line-scanning multiphoton microscopy using temporal focusing,” Opt. Lett. 30(13), 1686–1688 (2005). [CrossRef]

18. H. Dana, N. Kruger, A. Ellman, and S. Shoham, “Line temporal focusing characteristics in transparent and scattering media,” Opt. Express 21(5), 5677–5687 (2013). [CrossRef]

19. P. Rupprecht, R. Prevedel, F. Groessl, W. E. Haubensak, and A. Vaziri, “Optimizing and extending light-sculpting microscopy for fast functional imaging in neuroscience,” Biomed. Opt. Express 6(2), 353–368 (2015). [CrossRef]

20. Z. Li, J. Hou, J. Suo, C. Qiao, L. Kong, and Q. Dai, “Contrast and resolution enhanced optical sectioning in scattering tissue using line-scanning two-photon structured illumination microscopy,” Opt. Express 25(25), 32010–32020 (2017). [CrossRef]

21. J. K. Park, C. J. Rowlands, and P. T. So, “Enhanced axial resolution of wide-field two-photon excitation microscopy by line scanning using a digital micromirror device,” Micromachines 8(3), 85 (2017). [CrossRef]

22. M. Žurauskas, O. Barnstedt, M. Frade-Rodriguez, S. Waddell, and M. J. Booth, “Rapid adaptive remote focusing microscope for sensing of volumetric neural activity,” Biomed. Opt. Express 8(10), 4369–4379 (2017). [CrossRef]

23. Y. Xue, K. P. Berry, J. R. Boivin, D. Wadduwage, E. Nedivi, and P. T. So, “Scattering reduction by structured light illumination in line-scanning temporal focusing microscopy,” Biomed. Opt. Express 9(11), 5654 (2018). [CrossRef]

24. K. Lou, B. Wang, A.-Y. Jee, S. Granick, and F. Amblard, “Deep line-temporal focusing with high axial resolution and a large field-of-view using intracavity control and incoherent pulse shaping,” Opt. Lett. 43(20), 4919–4922 (2018). [CrossRef]

25. Y. Zhang, X. Li, H. Xie, L. Kong, and Q. Dai, “Hybrid spatio-spectral coherent adaptive compensation for line-scanning temporal focusing microscopy,” J. Phys. D: Appl. Phys. 52(2), 024001 (2019). [CrossRef]

26. R. Shi, Y. Zhang, T. Zhou, and L. Kong, “Hilo based line scanning temporal focusing microscopy for high-speed, deep tissue imaging,” Membranes 11(8), 634 (2021). [CrossRef]

27. E. Papagiakoumou, V. De Sars, V. Emiliani, and D. Oron, “Temporal focusing with spatially modulated excitation,” Opt. Express 17(7), 5391–5401 (2009). [CrossRef]

28. K. Isobe, K. Toda, Q. Song, F. Kannari, H. Kawano, A. Miyawaki, and K. Midorikawa, “Temporal focusing microscopy combined with three-dimensional structured illumination,” Jpn. J. Appl. Phys. 56(5), 052501 (2017). [CrossRef]

29. T. Ishikawa, K. Isobe, K. Inazawa, K. Namiki, A. Miyawaki, F. Kannari, and K. Midorikawa, “Adaptive optics with spatio-temporal lock-in detection for temporal focusing microscopy,” Opt. Express 29(18), 29021–29033 (2021). [CrossRef]

30. E. J. Botcherby, R. Juskaitis, M. J. Booth, and T. Wilson, “Aberration-free optical refocusing in high numerical aperture microscopy,” Opt. Lett. 32(14), 2007 (2007). [CrossRef]

31. F.-C. Hsu, Y. Da Sie, F.-J. Lai, and S.-J. Chen, “Volumetric bioimaging based on light field microscopy with temporal focusing illumination,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing XXV, vol. 10499 (International Society for Optics and Photonics, 2018), p. 104991Q.

32. C. Guo, W. Liu, X. Hua, H. Li, and S. Jia, “Fourier light-field microscopy,” Opt. Express 27(18), 25573–25594 (2019). [CrossRef]

33. S. Abrahamsson, R. Ilic, J. Wisniewski, B. Mehl, L. Yu, L. Chen, M. Davanco, L. Oudjedi, J.-B. Fiche, B. Hajj, X. Jin, J. Pulupa, C. Cho, M. Mir, M. El Beheiry, X. Darzacq, M. Nollmann, M. Dahan, C. Wu, T. Lionnet, J. A. Liddle, and C. I. Bargmann, “Multifocus microscopy with precise color multi-phase diffractive optics applied in functional neuronal imaging,” Biomed. Opt. Express 7(3), 855–869 (2016). [CrossRef]

34. M. Alemohammad, J. Shin, D. N. Tran, J. R. Stroud, S. P. Chin, T. D. Tran, and M. A. Foster, “Widefield compressive multiphoton microscopy,” Opt. Lett. 43(12), 2989–2992 (2018). [CrossRef]

35. A. Escobet-Montalbán, R. Spesyvtsev, M. Chen, W. A. Saber, M. Andrews, C. S. Herrington, M. Mazilu, and K. Dholakia, “Wide-field multiphoton imaging through scattering media without correction,” Sci. Adv. 4(10), eaau1338 (2018). [CrossRef]

36. J. Liang, L. Zhu, and L. V. Wang, “Single-shot real-time femtosecond imaging of temporal focusing,” Light: Sci. Appl. 7(1), 42 (2018). [CrossRef]

37. C. Zheng, J. K. Park, M. Yildirim, J. R. Boivin, Y. Xue, M. Sur, P. T. So, and D. N. Wadduwage, “De-scattering with excitation patterning enables rapid wide-field imaging through scattering media,” Sci. Adv. 7(28), eaay5496 (2021). [CrossRef]

38. Y. Ding and C. Li, “Dual-color multiple-particle tracking at 50-nm localization and over 100-µm range in 3D with temporal focusing two-photon microscopy,” Biomed. Opt. Express 7(10), 4187–4197 (2016). [CrossRef]

39. C.-H. Lien, C.-Y. Lin, S.-J. Chen, and F.-C. Chien, “Dynamic particle tracking via temporal focusing multiphoton microscopy with astigmatism imaging,” Opt. Express 22(22), 27290–27299 (2014). [CrossRef]

40. C.-H. Lien, C.-Y. Lin, C.-Y. Chang, and F.-C. Chien, “Simulation design of wide-field temporal-focusing multiphoton excitation with a tunable excitation wavelength,” OSA Continuum 2(4), 1174–1187 (2019). [CrossRef]

41. B. F. Grewe, F. F. Voigt, M. van’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens,” Biomed. Opt. Express 2(7), 2035–2046 (2011). [CrossRef]

42. F. O. Fahrbach, F. F. Voigt, B. Schmid, F. Helmchen, and J. Huisken, “Rapid 3D light-sheet microscopy with a tunable lens,” Opt. Express 21(18), 21010–21026 (2013). [CrossRef]

43. M. Martínez-Corral and B. Javidi, “Fundamentals of 3D imaging and displays: a tutorial on integral imaging, light-field, and plenoptic systems,” Adv. Opt. Photonics 10(3), 512–566 (2018). [CrossRef]

44. J. Jiang, D. Zhang, S. Walker, C. Gu, Y. Ke, W. H. Yung, and S.-C. Chen, “Fast 3-D temporal focusing microscopy using an electrically tunable lens,” Opt. Express 23(19), 24362–24368 (2015). [CrossRef]

45. H. Choi and P. T. So, “Improving femtosecond laser pulse delivery through a hollow core photonic crystal fiber for temporally focused two-photon endomicroscopy,” Sci. Rep. 4(1), 6626 (2015). [CrossRef]

Remote focusing in a temporal focusing microscope

Abstract

1. Introduction

2. Theory

2.1 Temporal focusing excitation path

2.2 Dispersion tuning

2.3 Detection path

2.4 Relationship between excitation and detection

3. Experimental setup

3.1 Pulse shaper

3.2 Excitation path

3.3 Detection path

4. Results

5. Discussion

6. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Equations (14)

OSA Continuum