Surgical resection is a major component in the standard of care for the treatment of brain cancers, where clinical studies have demonstrated that improved outcomes correlate with more complete resections, especially in conjunction with adjuvant therapies such as radiochemotherapy.^{1, 2} Histological guidance provided by a miniaturized microscope could be used to improve the accuracy of resection at selected sites where tumor margins are difficult to identify, thereby improving survival and reducing neurological damage. We have been developing dual-axis confocal (DAC) microscopes for in vivo imaging with cellular resolution.^{3, 4} Unfortunately, the $10\text{-}\mathrm{mm}$ -diam form factor of our current microscopes greatly exceeds their field of view (FOV) of less than $0.5\mathrm{mm}$ . The size of these instruments also surpasses that of conventional tools for tumor resection, which are typically $1\text{to}2\mathrm{mm}$ in diameter, rendering such a device inconvenient for guiding surgical procedures.

Here we demonstrate that the incorporation of a gradient-index (GRIN) lens at the tip of a microelectromechanical system (MEMS)-scanned DAC allows the image plane to be relayed forward by $3\mathrm{cm}$ through a $1.8\text{-}\mathrm{mm}$ -diam optic (see Fig. 1 ). This form factor is designed to enable convenient microscopy in a clinical setting for optical biopsy and image-guided resection of questionable tumor-margin locations using fluorescent contrast agents. Previously, GRIN relay lenses have been utilized for conventional single-axis confocal⁵ and nonlinear microscopes.⁶ Here we show that two low-NA beams, with a crossing angle of $\sim 45\mathrm{deg}$ , can also be relayed and scanned through such an optical element with minimal aberrations.

Studies have demonstrated the ability of a DAC to effectively reject out-of-focus scattered light for high-contrast optical sectioning in turbid media.^{7, 8, 9} The DAC utilizes low-power diode lasers along with simple low-NA optics to achieve deep tissue imaging. The long working distance afforded by the low-NA focused beams allows for postobjective beam scanning with a biaxial MEMS scanner.^{3, 4} This eliminates the need for compound lenses to mitigate the off-axis aberrations that result from scanning a beam through a focusing objective.

Our MEMS scanning device contains a total of four electrostatic actuators: a pair of actuators for each axis of the mirror to achieve tilt in opposing directions (pull-pull configuration).¹⁰ We have previously achieved raster-scanned imaging with these MEMS-scanned microscopes by actuating one axis of the mirror at its resonance frequency $(\sim 1\text{to}3\mathrm{kHz})$ and actuating the orthogonal axis with a slow sawtooth waveform at a frame rate of $4\text{to}30\mathrm{Hz}$ . The fast axis, because it is driven at resonance, can achieve large deflection angles ( $\pm 3\mathrm{deg}$ or more) with relatively low-voltage waveforms $(\sim 20\mathrm{V})$ . Furthermore, only one actuator is necessary to drive an axis at its natural resonance frequency. On the other hand, relatively large voltages $(\sim 100\text{to}120\mathrm{V})$ are applied to two actuators to achieve modest deflection angles $(\pm 1–3\mathrm{deg})$ at off-resonance frequencies. Therefore, the ability to drive both axes of the mirror at resonance, in a Lissajous scanning pattern,¹¹ enables large deflection angles to be achieved with fewer wired connections and lower voltages.

Previous implementations of Lissajous scanning have generally utilized stable scan patterns that self-repeat at a frame rate determined by the frequency ratio of the driving waveforms along each axis.^{12, 13} However, with arbitrary resonance frequencies, it is difficult to achieve a stable Lissajous scan pattern that repeats a rate of $1\text{to}10\mathrm{Hz}$ and also provides coverage over a large FOV of $500\times 500\text{pixels}$ . Here we demonstrate a general method to utilize an unstable (nonrepeating) “sliding” Lissajous pattern to fully sample $500\times 500\text{pixels}$ at a frame rate of $2\mathrm{Hz}$ . A similar strategy utilizing an unstable Lissajous scan of a MEMS mirror was demonstrated previously for two-photon microscopy.¹⁴ In that work, high frame rates of up to $10\mathrm{Hz}$ were achieved with a FOV of $256\times 256\text{pixels}$ . In our particular implementation, the scan frequencies are tuned to yield a Lissajous pattern that predictably slides at an optimized rate to ensure that each pixel is sampled. This eliminates the need for filtering or averaging to account for unsampled pixels.

Figure 1 illustrates the optical circuit of our microscope. This diagram includes a ray-trace simulation (Zemax, Bellevue, Washington) depicting the beam paths of the DAC as they are relayed through a nonmagnifying (1:1) GRIN triplet relay assembly consisting of a pair of $\frac{1}{4}$ -pitch, $4.25\text{-}\mathrm{mm}$ -long, high-NA (0.51) GRIN lenses on either side of a $\frac{1}{2}$ -pitch, $21.85\text{-}\mathrm{mm}$ -long, low-NA (0.19) GRIN lens. Figures 1 and 1 are design drawings of the basic components of the microscope. The parabolic reflector (AgilTek) insures that the two collimated beams intersect and focus to the same point, which defines the focal volume of the microscope. A pair of $0.1\text{-}\mathrm{deg}$ wedged alignment (Risley) prisms, shown in Fig. 1, are rotated to bring the collimated beams into parallel alignment with each other. Figure 1 is a photograph of a fully packaged microscope, including the piezoelectric actuator at the proximal end that translates the MEMS mirror in the axial direction for adjusting the focal depth.

The single-mode fiber-pigtailed collimators (GRINTECH Gmbh, Jena, Germany, focal $\text{length}=4.5\mathrm{mm}$ ) used in our microscope yield a $1∕{\mathrm{e}}^2$ beam diameter of $0.9\mathrm{mm}$ . As a result of the parabolic reflector having a $6\text{-}\mathrm{mm}$ focal length and the collimators being spaced apart by $4.7\mathrm{mm}$ , the focusing half angle of each beam $(1∕{\mathrm{e}}^2)$ and the intersection half angle between the beams, respectively, are $\alpha =0.075\mathrm{rad}$ and $\theta =22.2\mathrm{deg}$ [see Fig. 1]. If the Gaussian illumination and collection beams are truncated (apodized) to allow 99% power transmission, diffraction theory predicts a full-width at half-maximum (FWHM) spatial resolution (in micrometers) of:⁷

where $\theta =22.2\mathrm{deg}$ ; $\alpha =0.075\mathrm{rad}$ , $n=1$ (air), and $\lambda =488\mathrm{nm}$ . The experimentally measured FWHM resolution of our microscope is: $\Delta x_d=3.7\mu \mathrm{m}$ , $\Delta y_d=3.6\mu \mathrm{m}$ , and $\Delta z_d=8.0\mu \mathrm{m}$ . The degradation in resolution is due to aberrations from the GRIN collimation and relay lenses, as well as alignment imperfections and diffraction noise introduced by imperfections in the MEMS mirror (beam clipping and hinge structures within the mirror surface). The spatial resolution of the GRIN-relayed DAC is degraded by less than 10% compared to the resolution measured without the GRIN relay lens (data not shown). A ray-trace simulation was performed to roughly compare the effects of aberrations due to the GRIN relay lens on our dual-axis beams versus a single large-NA beam used for conventional confocal or multiphoton microscopy. The DAC simulation reveals minimal aberrations [Fig. 1], with various rays converging to a region well within the $3.2\text{-}\mu \mathrm{m}$ theoretical spot size ( $1∕{\mathrm{e}}^2$ diameter) of a diffraction-limited Gaussian beam with $\mathrm{NA}=0.075$ $(1∕{\mathrm{e}}^2)$ at $488\mathrm{nm}$ in air. In Fig. 1, a ray trace simulation is shown for a single on-axis Gaussian beam that fills the collection NA of the GRIN relay lens (99% power transmission $\mathrm{NA}=0.5$ ; $1∕{\mathrm{e}}^2$ $\mathrm{NA}=0.32$ ). The spread in the spot diagram extends beyond the $0.77\text{-}\mu \mathrm{m}$ theoretical spot size ( $1∕{\mathrm{e}}^2$ diameter) of a diffraction-limited Gaussian beam with $\mathrm{NA}=0.32$ $(1∕{\mathrm{e}}^2)$ at $488\mathrm{nm}$ in air. Evidently, since the DAC utilizes low-NA beam paths through the GRIN relay lens, rather than relying on the full NA of the lens, the effects of aberrations are minimized. A complete diffraction analysis, which is not presented in this work, is required to fully characterize the tradeoffs between GRIN-relayed versions of the DAC and single-axis confocal microscopes.

As mentioned previously, an unstable Lissajous scan pattern is achieved by driving our MEMS mirror at resonance along both axes, enabling large-FOV imaging with relatively low-voltage waveforms. The resulting scan pattern is described by the following parametric equations as a function of time:

where ${\varphi }_x$ and ${\varphi }_y$ are phase shift constants (in radians), $a$ and $b$ are the slow and fast frequencies, respectively, in cycles/sec (Hz), and the FOV of the scan extends from 0 to $2A$ in the $x$ direction and 0 to $2B$ in the $y$ direction (in this case, $A=B=250$ ). The resonant frequencies of the two axes of our MEMS mirror are $985\pm 10\mathrm{Hz}$ and $2220\pm 10\mathrm{Hz}$ (FWHM bandwidth $\sim 20\mathrm{Hz}$ ).

Figure 2 depicts the trajectory of a Lissajous scan pattern between $t=0$ and $4\mathrm{ms}$ (assuming ${\varphi }_x={\varphi }_y=0$ ). If the frequency ratio of the fast- and slow-axis waveforms is exactly $9∕4$ , then a stable Lissajous pattern results, repeating once for every four cycles of the slow axis or every nine cycles of the fast axis ( $4∕a$ or $9∕b\sec$ ). If the ratio between the frequencies is slightly different than $9∕4$ , an unstable Lissajous pattern is generated that appears to slide in time in the horizontal direction [Fig. 2]. The sliding speed, determined by the frequency ratio, is optimally chosen such that the Lissajous pattern shifts by a distance of less than $1\text{pixel}$ for every nearly repeated cycle ( $4∕a$ or $9∕b\sec$ ), ensuring that no pixels are missed over time. Figures 2 and 2 illustrate how an entire image is sampled over time by the sliding Lissajous pattern. Taking the derivative of Eq. 3 with respect to time reveals that the maximum velocity of the fast-axis scan is given by $2\pi \cdot b\cdot B\cong 3.5{\left(10\right)}^6\text{pixels}∕\sec$ . Thus, a data acquisition rate of $4\mathrm{MHz}$ is chosen to obviate dead (unsampled) pixels along the trajectory of the Lissajous scan.

Sinusoidal waveforms are generated with National Instruments (Austin, Texas) boards programmed in LabVIEW and sent through a voltage amplifier (Agiloptics, Albuquerque, New Mexico) to drive our biaxial MEMS mirror. A National Instruments digitizer board is used to record signals from a PMT detector at a rate of $4\mathrm{MHz}$ . All processes are synchronized for phase-locked operation, and the phase shifts ${\varphi }_x$ and ${\varphi }_y$ are determined via calibration. In our implementation, $a=986.0\mathrm{Hz}$ and $b=2219.0\mathrm{Hz}$ . For each detector value sampled at time $t$ , Eqs. 2, 3 are used to calculate the exact coordinates $x$ and $y$ of the Lissajous scan. These coordinates are rounded to the nearest integer to locate the most appropriate pixel for data entry within the $500\times 500\text{pixel}$ bitmap image (programmed in LabVIEW). Image degradation due to rounding errors is minimal due to the fact that we oversample the image. The spatial dimension of our target FOV is approximately $500\times 500\mu \mathrm{m}$ . Therefore, with a pixel density of $500\times 500$ , and a lateral resolution of $\sim 4\mu \mathrm{m}$ , our sampling $(1\text{pixel}∕\mu \mathrm{m})$ exceeds the Nyquist criterion by a factor of 2. Two million points are collected per image, resulting in a frame rate of $2\mathrm{Hz}$ . Redundantly sampled pixels contain an average of the sampled values at that pixel location.

Example images acquired with our GRIN-relayed DAC are shown in Figs. 3, 3, 3, 3, 3, 3 . Figure 3 is a reflectance image of a United States Air Force (USAF) bar target (group 7), in which the width of the smallest set of lines is $2.2\mu \mathrm{m}$ per line. Due to the field curvature of the microscope, only the center of the FOV is in focus for this flat reflective target. In practice, field curvature is not a major concern, since our device is designed to image at least ten microns beneath the surface of a thick tissue, rather than imaging a flat surface. Figure 3 is a depth projection $(\mathrm{FOV}=400\times 400\mu \mathrm{m})$ of $10\text{-}\mu \mathrm{m}$ -diam fluorescent beads embedded in Matrigel. The color map encodes depths from $0\text{to}250\mu \mathrm{m}$ . Figure 3 is an in vivo image at a depth of $50\mu \mathrm{m}$ $(\mathrm{FOV}=325\times 325\mu \mathrm{m})$ of vasculature within the cerebrum of a mouse after a portion of the skull has been surgically removed (five-frame average). To highlight the vasculature in this image, fluorescein-dextran $(\mathrm{MW}=\mathrm{70,000})$ was injected into the retro-orbital capillary plexus at a dose of $\sim 1\mathrm{mg}$ ( $40\text{-}\mathrm{mg}∕\mathrm{kg}$ body weight) in a $200\text{-}\mu \mathrm{L}$ volume. Figure 3 is of the same tissue as Fig. 3, except that it was acquired at a depth of $100\mu \mathrm{m}$ (five-frame average). Figure 3 is an ex vivo image at a depth of $25\mu \mathrm{m}$ $(\mathrm{FOV}=350\times 350\mu \mathrm{m})$ of cerebellum from a transgenic mouse ( $10\text{days}$ of age) that expresses green fluorescent protein (GFP) under the Math1 promoter.¹⁵ After weaning, expression of this promoter is repressed in the cerebellum, except in medulloblastomas, a cerebellar brain tumor that spontaneously develops in this gene knock-out mouse ( $Pt{c}^{+∕-}p{53}^{-∕-}$ Math1-GFP). In Fig. 3, in vivo imaging of the tumor is performed after surgical removal of a portion of the skull. This image ( $\mathrm{FOV}=350\times 350\mu \mathrm{m}$ ; $\text{depth}=30\mu \mathrm{m}$ ) reveals the GFP-expressing tumor in contrast to the dark normal brain tissue, and indicates that this instrument would have utility in detecting tumor margins when used in conjunction with appropriate exogenously applied fluorescent molecular probes. Figures 3 and 3 are single frames that have been filtered with a smoothing algorithm that replaces each pixel with an average of its adjacent pixels. Spatial resolution is minimally affected, since the image is oversampled.

We have presented the design and demonstration of a miniature DAC outfitted with a $1.8\text{-}\mathrm{mm}$ -diam GRIN relay lens for convenient macroscopic positioning of the device at surgical sites. Our previous designs implemented raster-scanned MEMS mirrors, which were limited in their FOV because of the modest scan range attained by the nonresonant slow axis of the MEMS device. In addition, the raster-scanned MEMS mirrors required higher operating voltages that may not be preferred in clinical applications. Here we have described the use of resonant scanning along both axes of the MEMS mirror to achieve a large FOV with low actuation voltages and reduced numbers of actuators. We have developed the calibrated and synchronized instrumentation to decode the nonrepeating Lissajous pattern that results, and have demonstrated in vivo imaging of normal brain and tumor in living mice. Our goal is to use the GRIN-relayed DAC technology, along with exogenous fluorescent contrast agents, for spatially precise and molecularly specific resection of brain tumors