2.1.

Background

AODs are often regarded as tunable diffraction gratings. By varying the acoustic frequency, the grating constant can be altered, allowing a monochromatic laser beam to be steered. For a typical AOD operating in the Bragg regime, the deflection angle of the beam is given by

Ultrafast laser pulses, however, are not monochromatic and are thus dispersed by this acoustic diffraction grating. This phenomenon can be termed spatial dispersion, or spatial chirp, to distinguish it from temporal dispersion. It is manifest as an angular broadening of the beam (Δθ _beam ) that limits the spatial resolution of the AOD, which is generally specified in terms of the AOD’s time-bandwidth product N. This quantity reflects the number of distinct resolvable spots in the far field, which directly translates into the number of resolvable spots in the microscope objective’s field of view,

2.2.

Slow-Shear TeO₂ AODs

Typical biomedical applications of an AO-MPLSM involve imaging very small cellular structures—for instance the dendritic spines found on many neurons—which are <1 μm in size. As an estimate of the required resolution, the field of view of a typical 60× water-immersion objective used for brain slice imaging is ∼300 μm. The best (diffraction-limited) lateral resolution possible, assuming some typical conditions—λ=900-nm excitation and an objective lens with NA=1.0—is ∼450 nm, i.e., λ/(2NA). An ideal AO-MPLSM would permit diffraction-limited imaging throughout practically the entire field of view. Using these numbers as a guideline, a resolution of N∼500 spots is a good estimate of the required AOD performance.

Commercial AODs made of tellurium dioxide (TeO ₂) are readily capable of providing such resolution. TeO ₂ deflectors can be designed to either employ a longitudinal or slow-shear acoustic wave mode. The former mode is faster (v _acoustic ∼4200  m/s) and can support large frequency bandwidths (Δf∼200  MHz), while the latter mode is slower (v _acoustic ∼650 m/s) but restricted to operate at lower acoustic frequencies (to satisfy the off-axis angle requirement particular to shear-mode acoustic waves to avoid a dip in the diffraction efficiency across the scan bandwidth¹⁶). For Ti:S laser wavelengths (e.g., λ₀=850  nm), a central frequency of f₀=70  MHz is indicated, which practically—considering limitations in transducing an effective phased array acoustic field—allows an acoustic frequency bandwidth of Δf=f₀/2=35 MHz. ¹⁷ Applying Eq. (3), this implies that the slow-shear mode offers 1.3× greater spatial resolution per unit of beam diameter (d), compared to the longitudinal mode.

Such a modest benefit weighed against the significantly faster (6.5×) positioning time (scales inversely with v _acoustic ) of the longitudinal mode device would seem to argue that this mode is preferable. Indeed, the recently developed system employing 1-D AO deflection for MPLSM¹² adapted a commercial (Oz; Noran) unit containing a single longitudinal mode TeO ₂ AOD. However, longitudinal mode devices such as this one are not well suited for extension to a 2-D AO scanning system, which is necessary to achieve the benefits of random-access scanning. The acousto-optic figure of merit of longitudinal TeO ₂ devices is inferior to that of slow-shear TeO ₂ devices, which causes two difficulties for the extension to 2-D AO scanning. First, the diffraction efficiency is greatly reduced (∼25 at the center position for 850 nm) and, second, these devices necessarily have a very thin rectangular aperture (∼0.5 mm), forcing the user to employ cylindrical optics. A robust cylindrical optics 2-D AO scanning system is far more complex to develop. For these reasons, a custom-made slow-shear TeO ₂ device with high diffraction efficiency (>70 at peak) and a large square aperture was used for the work here. Using such devices, a 2-D AO-MPLSM system can be constructed following a spherical optics design similar to that previously employed in our laboratory.^{5 6}

2.3.

Spatial Dispersion of Custom Slow-Shear TeO ₂ AOD

The custom-made AOD (ATD-7010CD2; IntraAction) has a large active aperture of 10×10 mm. Given the acoustic bandwidth Δf=35  MHz and the slow-shear acoustic mode velocity of 660 m/s, the angular range Δθ _scan is 45.1 mrad at an optical wavelength of 850 nm. Meanwhile, applying the sinc ² [(πd/λ)θ] form for diffraction at a rectangular aperture, an angular spread of Δθ _{beam,diffraction} =0.88λ/d=75 μrad, is found for λ=850 nm, using the full-width half maximum (FWHM) to define the beam angular width (somewhat more relaxed than customary Rayleigh criterion). Computing the time-bandwidth product N=Δθ _scan /Δθ _beam , a spatial resolution figure of N∼600 spots is obtained in the absence of dispersion.

To what extent would spatial dispersion worsen this spatial resolution? Applying Eq. (5) at the center of the scan angle range, we find the dispersed beam’s angular spread to be

Figure 2

Spatial dispersion by AOD. Spatial dispersion of an ultrafast laser pulse over angle Δθ _beam , limiting the number of resolvable spots across the angular range Δθ _scan . The amount of beam dispersion grows linearly with the scan angle for increasing acoustic frequencies.

Assuming Gaussian pulse shapes, a 130-fs (FWHM) pulse (the specification pulsewidth of the Mira900D laser primarily used here) implies that Δλ∼8 nm (FWHM), following the 0.441 time-bandwidth product (ΔtΔν) for the Gaussian pulse shape.¹⁸ Applying f₀=70  MHz, one finds Δθ _{beam,dispersion} =740  μrad (FWHM) at the center of the scan pattern. This is approximately ten times worse than Δθ _{beam,diffraction} . Thus, the spatial resolution is limited to only ∼60 spots, or >5 μm when filling the field of view of a typical 60× objective. Figure 3(a) compares the calculated angular distributions for the diffraction- and dispersion-limited cases.

Figure 3

Spatial dispersion by custom-made TeO ₂ AOD. (a) Computed angular beam width due to diffraction (solid) at overfilled 10×10-mm AOD aperture and dispersion (dotted) of the laser’s nominal 130-fs pulsewidth. Dispersion is predicted to worsen spatial resolution by ∼10×. (b) Measured intensity distribution of focused spots of deflected Ti:S beam, with a laser in continuous wave (CW) and modelocked (ML) modes. Spatial dispersion of femtosecond pulses (ML) leads to a 2.8× broadening of focused spot size. (c) Two-spot scan patterns demonstrating severely compromised lateral spatial resolution with ultrafast pulses (ML mode).

We verified the presence of spatial dispersion using one such custom slow-shear TeO ₂ device, overfilling its 10×10-mm aperture with an expanded and spatially filtered beam from a commercial Ti:S laser (Mira 900D; Coherent), tuned to 850 nm. The AOD was driven by a voltage-controlled oscillator (DE-702M; IntraAction). First, the acoustic frequency was tuned to a constant value near the central frequency f₀ (70 MHz), and the resulting deflected beam was focused onto a distant screen at an angular magnification of 2.5×. Figure 3(b) shows smoothed (eight-point moving average) line sections through captured video images [not shown, but similar to those in Fig. 3(c)] of the focused spot when the laser was alternately operated in mode-locked (ML), i.e., femtosecond-pulsed, and continuous wave (CW) modes. The ML mode spot had a 28-pixel-wide FWHM, compared to 10 pixels FWHM for the CW mode spot. Next, the acoustic frequency was switched rapidly between two closely spaced acoustic frequencies (Δf∼800 kHz) about the center frequency f₀ (70 MHz) to produce a two-spot scan pattern. The resulting video images of the focused scan patterns in CW and ML modes are shown in Fig. 3(c). While the spots are clearly resolvable in CW mode, they are entirely indistinguishable in ML mode.

The observed dispersion effect (2.8×) was less than that predicted, owing to aberration-limited focusing of the spots. Nevertheless, these tests reveal that spatial dispersion does indeed significantly limit the achievable resolution of an AO-MPLSM system, when uncompensated.

2.4.

Spatial Dispersion Compensation

To remedy this, we have employed a compensation scheme based on a single diffraction grating that significantly reduces this dispersion-induced spatial broadening. This compensation grating, inserted directly after the AOD, has a grating constant matched to the central acoustic frequency of the AOD and is configured to diffract efficiently in the opposite diffraction order compared to the AOD (i.e., the -1 order).

This scheme is depicted in Fig. 4. Without the grating, as shown in Fig. 4(a), the focused spots are broadened in a linearly varying fashion across the field of view. With the practical assumption that the acoustic bandwidth Δf≈f₀/2, the spot size varies linearly from its minimally broadened value s at f _min to 1.67s at f _max , as shown in Fig. 4(a). By employing the diffraction grating, as shown in Fig. 4(b), the scan angles are realigned with the original optical axis and, more importantly, the dispersion Δθ _{beam,dispersion} is uniformly reduced throughout the scan range by Δλf₀/v _acoustic . Thus, from Eq. (6), the separated spectral components are brought exactly back together at the central scan position, so that

Figure 4

Spatial dispersion compensation. (a) Uncompensated deflection of ultrafast laser pulse by AOD results in broadened spot sizes (s to 1.67s) in the specimen plane. (b) Single diffraction grating matched to a central acoustic wavelength eliminates spatial dispersion in the center of a scan pattern, with maximal residual dispersion of 0.33 s at the borders. Note the direction of the residual spatial dispersion is reversed for acoustic frequencies below central value (f₀) (c) Demonstration of spatial dispersion compensation using a second AOD with a counterpropagating acoustic wave tuned to a central frequency of the first AOD. The multiline Ar laser acts as broadband source (488 to 514 nm).

In summary, the extent of the predicted compensation can be quantified as, at minimum, a three-fold improvement relative to the uncompensated pattern. The improvement is five-fold at the other scan pattern border and is maximal at the center of the pattern. These values assume that the spatial dispersion effect leads to a large (>5×) broadening throughout the field of view, as in the case of 10× broadening for the custom-made TeO ₂ previously described [Fig. 3(a)]. In this specific case of employing a large-area slow-shear TeO ₂ AOD and filling the field of view of a high-NA objective lens, the compensation grating would restore the spatial resolution to ∼1 μm near the borders of the field of view, while allowing the full diffraction-limited resolution at the center.

We tested this scheme for dispersion compensation by employing the two main lines of a multiline argon laser (488 and 514 nm) to model the extremes of the broadened spectrum of an ultrafast pulse. These lines were passed through a PbMbO ₄ deflector (1205C-2; Isomet), driven by a repeating staircase of five frequencies to produce a simple five-spot scanning pattern. The compensation grating was fashioned from a second identical AOD, which was tuned to the central frequency of the first (scanning) AOD, and oriented in the opposite direction (i.e., the acoustic waves were counterpropagating). Figure 4(c) shows the 0 (uncompensated) and -1 (compensated) diffraction orders that passed through the second AOD. The compensation was highly effective, allowing the five-scan positions to be clearly distinguished where they could not be without compensation.

3.1.

Background

Temporal dispersion refers to the broadening of ultrashort pulses propagation through dispersive materials, i.e., those with a frequency-dependent index-of-refraction n(ω). On traversing a medium of length L, light of a particular frequency ω is phase shifted by an amount ϕ

By the Fourier theorem, a pulse of light is necessarily composed of several wavelengths. Within this pulse spectrum, each infinitesimally small group of wavelengths travels at a group velocity given by dω/dk. The GVD of a material reflects the variation in group velocity across the spectrum, usually such that higher frequencies travel at slower group velocities, causing the pulsewidth to broaden. Assuming an input pulsewidth of τ_in, a GVD constant D, and a propagation length L, the output pulsewidth τ _out is given by¹⁸

In an MPLSM system, the aggregate material GVD of all the optics in the path—particularly the objective lens—yields a broadened pulsewidth at the specimen focus. As the average power required to maintain a fixed multiphoton excitation (and hence emission) rate scales as τ^(n−1)/n, broadened pulses force the user to employ higher average powers.¹⁹ This accelerates the rates of photodamage and photobleaching, reducing the useful experimental time.

3.2.

Temporal Dispersion by Slow-Shear TeO₂ AOD

In a typical mirror-based scanning system, a total GVD of up to ∼5000  fs ² may be found,¹⁵ which has only a modest effect on the ∼100-fs pulses obtained from most commercial Ti:S oscillators. In comparison, an AO-MPLSM would incorporate two AODs, each of which gives rise to more than 10,000  fs ² of GVD. This is due to the large GVD constants of the AO media employed for visible and near-IR wavelengths— PbMbO ₄ and TeO ₂ —as well as their long interaction path length (2 to 4 cm), which are necessary to achieve an adequate diffraction efficiency.

We measured the GVD of one of the custom-made slow-shear TeO ₂ AODs previously discussed, using a commercial autocorrelator that employs a two-photon absorption GaAsP photodiode (Mini-Microscope Autocorrelator; APE Berlin). In Fig. 5(a), a pair of interferometric autocorrelograms are taken using a commercial Ti:S laser (Mira 900D; Coherent) at λ=840 nm with and without the (undriven) AOD positioned before the autocorrelator. The characteristic rising of the “pedestal” associated with significant temporal chirp (i.e., dispersion) is evident in the lower (AOD+) figure. Because it is difficult to extract quantitative information about pulsewidths from such interferometric traces, we employed the instrument’s filter function to eliminate the fringes and the pedestal characteristic, revealing intensity autocorrelograms such as those shown in Fig. 5(b), also taken at λ=840 nm. The FWHM of these traces, obtained by a parametric fitting of an assumed Gaussian shape, was used as a robust measure of the pulsewidth. We obtained such values with and without the AOD at 20-nm intervals from 760 to 880 nm. Assuming a Gaussian laser pulse shape, the actual pulsewidths (stated as the FWHM) can be calculated as 0.71 times the measured autocorrelation FWHM pulsewidths.¹⁸ From the original and dispersed pulsewidths and the AOD’s known path length (L=2.79 cm), the GVD parameter D was calculated at each wavelength using Eq. (12). The measured values, shown as the data points in Fig. 5(c), follow a decreasing trend toward greater wavelengths. The Gaussian pulsewidths measured at each wavelength and the calculated values of D are given in Table 1. The intracavity prism pair of the laser was adjusted to produce the minimal pulsewidth for each wavelength, and pulses substantially shorter than the manufacturer’s specification of 130 fs were obtained at most wavelengths.

Figure 5

Temporal dispersion of custom TeO ₂ AOD. (a) Measured interferometric autocorrelograms of laser pulsewidth without (AOD-) and with (AOD+) deflector, λ=840 nm. Effect of temporal dispersion is evident in the rising of a pedestal in the AOD+ case. (b) Measured intensity autocorrelogram without (AOD-) and with (AOD+) deflector present. Laser pulses are presumed Gaussian-shaped with a FWHM of 0.71×. (c) Dispersion (GVD) parameter computed from data such as in (b) at various laser wavelengths shown. The predicted GVD parameter is based on Sellmeir coefficients for the ordinary (solid) and extraordinary (dotted) indices of refraction of TeO ₂.

Table 1

We compared these values to a theoretical curve determined by employing published Sellmeir equations²⁰ for both the ordinary (n₀) and extraordinary (n_e) indices of refraction of TeO ₂,

The amount of dispersion, both measured and theoretical, was significant. Each AOD has a path length of 2.8 cm, so it is apparent that a pair of AODs would by themselves give rise to ∼30,000  fs ². Under such conditions, an input pulsewidth of 100 fs (similar to those we measured in the 820 to 860 nm tuning range) would be broadened by ∼8×, which would necessitate a nearly three-fold increase in average power to maintain the same fluorescence yield.

3.3 GVD Compensation: Prechirper Principle

To avoid a marked increase in the requisite incident power, it is desirable to add an adjustable amount of negative GVD in the optical path to compensate for the temporal broadening caused by material dispersion. This is typically achieved by employing either diffraction gratings²¹ or dispersive prisms.²² Such devices for adding negative GVD are often referred to as prechirpers. Both gratings and prisms are spatially dispersive elements—they deflect different wavelengths of light by varying angles—by virtue of diffraction and refraction, respectively. Using either mechanism, prechirpers force longer wavelengths to travel through a longer optical path length, thereby reversing the temporal broadening incurred by the positive material GVD.

The canonical layout of such prechirpers is shown in Fig. 6, in which four of each dispersive element are employed. In both cases, the first element disperses the light as a function of wavelength, such that longer wavelengths traverse a longer distance through glass (prisms 2 and 3) in the prism case, or a longer distance through air in the grating case. The lengths of the converging and diverging regions labeled in the schemes must be identical to cancel out the spatial chirp introduced by the first dispersive element. However, the combined value of this length L can be adjusted to vary the amount of negative GVD—the greater the length, the greater the separation of wavelengths.

6

Schemes of canonical prechirpers. Either reflection gratings (a) or prisms (b) can be used as dispersive elements. In both schemes, beams are dispersed by the first element and then propagate over L/2 to separate wavelengths. Longer wavelengths are delayed by traveling longer paths. Wavelengths are recombined by a third element, followed by another L/2 propagation. Changing the total converging/diverging distance L adjusts the amount of negative GVD.

Since optical gratings can be made much more dispersive than prisms, the total path length of a grating-based prechirper is typically much shorter than a prism-based one for a given amount of GVD compensation. However, prisms offer two important advantages. First, they are more transmissive, approaching 99 when used at Brewster’s angle incidence, whereas grating efficiencies rarely exceed 80 (which leads to only 0.8⁴, or ∼40, transmission on four reflections, compared to >90 with prisms). Second, when used in a minimum-deviation configuration, each of the prisms in Fig. 6(a) can be translated without affecting the optical path between the prisms. Since the path length through the prisms is a source of positive GVD, the total GVD can be continuously tuned by the addition and removal of glass. This degree of freedom adds a fine GVD control to the prechirper. For these important reasons, prism prechirpers are the method of choice where possible.

Based on the analysis of Fork, Martinez, and Gordon,²² the negative GVD imparted by a prism prechirper is given by

Table 2

At all wavelengths, the total interprism path length L required is ∼3 to 4 m. This does not include the extra length that would be required to compensate for the positive GVD imparted by other optical glass including the objective lens and the SF10 prisms themselves. The large physical footprint implied by large interprism spacings can be cumbersome, particularly in a biomedical laboratory setting, where space is often more critical than in a physics laboratory. Therefore, it is desirable to devise geometries that significantly reduce the prechirper’s physical size.

3.4.

Space-Saving Geometry: Stacked-Prism Prechirper

As shown in Fig. 7(a), a plane of mirror symmetry exists between the second and third prisms in the canonical four-prism design. This is generally exploited by placing a roof mirror assembly at that plane, which reflects the beam along the same path as the incident beam, but at a different optical height. This results in the situation shown in Fig. 7(b), where the number of prisms and the physical interprism path length are both reduced by a factor of 2 by directing the beam a second time between prisms 1 and 2.

Figure 7

Space-saving prism prechirper schemes. (a) Canonical four prism sequence. (b) Common scheme with 50 reduced physical path length using a roof mirror at the plane of mirror symmetry in (a), requiring only two prisms. (c) Novel scheme with another 50 reduction of physical path length by insertion of another roof mirror at the folding plane in (b), and vertically stacking the prisms.

Because of the exceptional length L (3 to 4 m) required to compensate for a pair of TeO ₂ AODs, we endeavored to reduce the physical path length even further. To achieve this, we devised the stacked prism prechirper geometry in which an additional roof mirror assembly was placed at the midpoint between the two prisms in Fig. 7(b), to create the situation shown in Fig. 7(c). The second prism is now located above the first prism (stacked) and rotated to deflect the beam into a separate short arm that contains the collimated region. The beam now traverses the distance between the two prisms four times, and thus the physical path length (of the longest dimension) is reduced by an additional factor of 2.

The stacked-prism design is shown in more detail in Fig. 8. The structure forms a Y shape [Fig. 8(a)], with the input/output section forming the tail, and the long and short arms of the Y corresponding to the converging/diverging regions (B,D) and the collimated region (C) of the canonical four-prism prechirper depicted in Fig. 8(b). The beam travels at four separate heights through the long arm, which are enumerated in relation to the canonical four-prism design in Fig. 8(b). The height steps are made by the customary roof mirror assembly (region C) located at the end of the short arm and the additional roof mirror, termed the periscope assembly, located at the end of the long arm.

Figure 8

Stacked-prism pair prechirper design. (a) Mechanical layout of Y-shaped stacked-prism prechirper. Conceptual locations of prisms, roof mirror, and periscope mirror assemblies are indicated, according to a canonical four prism prechirper shown in (b). Heights of beam propagation in each segment are indicated by circled numbers. Labeled regions A through E are referred to in text. (c) Photographs of stacked prism prechirper. Note that two alignment tools, each with holes at the four optical heights (a, b), are inserted in the long arm. Long and short arms can be rotated relative to prism assembly during alignment. (d) Prism assembly. Prisms on translation stages are mounted onto tilt/rotation stages. (e) Roof mirror assembly. (f) Periscope assembly. The beam passes at all four optical heights. This assembly translates on the long arm to adjust the amount of negative GVD.

The prechirper was aligned through the use of two custom alignment tools that were inserted at two separated points in the long arm. Mirrors were adjusted so that the beam propagated through two separated pinholes at each of the four optical heights. Once aligned, the amount of negative GVD imparted by the stacked-prism prechirper could be adjusted by translating the periscope assembly along the long arm to vary the total interprism spacing L, with little to no beam realignment. The prisms in the central assembly were each located on translation stages, which allowed glass to be added and removed at each level (primarily the lower one is used, as the beam is not spatially dispersed there) as an effective fine-tuning knob for the GVD compensation.

Referring back to Table 1, the additional two-fold reduction in physical path length provided by the stacked-prism prechirper design presented here allows the length of the long arm to be kept <1 m, for the entire Ti:S tuning range, for the compensation of two of the custom TeO ₂ AODs described. Such a length can be accommodated by most optical tables, with sufficient room to spare for other equipment.

3.5.

GVD Compensation Demonstration

We tested the stacked-prism prechirper using a Ti:S laser (Kapteyn-Murnane Laboratories Kit) tuned to ∼780 nm. An interferometric autocorrelator based on a GaAsP photodiode that exhibits multiphoton conductivity (FR-103PD; Femtochrome Research) was employed. The interference fringes were filtered out, producing an intensity autocorrelogram (with background).

Figure 9 shows four autocorrelation traces illustrating the effect of GVD compensation. The traces were measured in the absence or presence (AOD-/AOD+) of a single PbMoO ₄ AOD (1205C-2; Isomet). The distance L _phys of the periscope assembly from the central prism assembly along the long arm was set to be either short (COMP-: L _phys =25  cm) to self-compensate for the prechirper’s prisms (fully inserted), or longer (COMP+: L _phys ∼60 cm) to compensate for the additional GVD from the deflector.

Figure 9

GVD compensation with stacked-prism pair prechirper. Intensity autocorrelograms of Ti:S laser pulses acquired with a GaAsP photodiode-based autocorrelator. Lengths L _phys reflect the distance from the periscope assembly to the prism assembly on the long arm. COMP-/AOD-: L _phys =25 cm; AOD removed. The prechirper is self-compensated, producing net zero-GVD, revealing ∼240-fs autocorrelation trace of laser pulsewidth. COMP-/AOD+: L _phys =25  cm; single AOD was added. Autocorrelation trace broadened to ∼800 fs (FWHM). COMP+/AOD-: L _phys =62  cm; AOD removed. Prechirper provided large uncompensated negative GVD, yielding equally broadened autocorrelation trace. COMP+/AOD+: L _phys =55  cm; AOD inserted. Negative and positive GVD balance, restoring original pulsewidth.

The AOD-/COMP- case represents the original laser pulsewidth, as verified in a separate measurement with the prechirper entirely removed. The FWHM observed was ∼240 fs, reflecting a Gaussian pulsewidth of ∼170 fs. This pulsewidth was somewhat long for this cavity and likely reflected a nonoptimal GVD of the intracavity prechirper. Alternatively, temporal filtering of the photodiode signal employed to improve the signal-to-noise ratio may have contributed to this broadening. Insertion of the AOD increased the measured pulsewidth to ∼800 fs (AOD+/COMP-), or ∼570 fs for the underlying Gaussian. This broadening corresponds to a total GVD of ∼12,000  fs ², which is similar in magnitude to that provided by a single TeO ₂ device. The AOD-/COMP+ case showed that the same broadened pulse could be observed with a long interprism path length in the absence of the AOD, demonstrating that both positive and negative GVD of the same quantity yield the same temporal broadening. Finally, the AOD+/COMP+ case revealed that positive and negative GVD can be combined to restore the original pulse width.

These results demonstrate that the stacked-prism prechirper provides the large amounts of negative GVD required to fully compensate the GVD of this commercial AOD, with a relatively short physical path length of only 30 cm. Its GVD was comparable in magnitude to that of the custom TeO ₂ devices suited for an AO-MPLSM system. Thus, GVD compensation of two TeO ₂ AODs with a prism pair separated by <1 m is readily feasible with the stacked-prism design.