Adaptive Multiphoton Endomicroscope Incorporating a Polarization-Maintaining Multicore Optical Fibre

We present a laser scanning multiphoton endomicroscope with no distal optics or mechanical components that incorporates a polarization-maintaining (PM) multicore optical fibre to deliver, focus, and scan ultrashort pulsed radiation for two-photon excited fluorescence imaging. We show theoretically that the use of a PM multicore fibre in our experimental configuration enhances the fluorescence excitation intensity achieved in the focal spot compared to a non-PM optical fibre with the same geometry and confirm this by computer simulations based on numerical wavefront propagation. In our experimental system, a spatial light modulator (SLM) is utilised to program the phase of the light input to each of the cores of the endoscope fibre such that the radiation emerging from the distal end of the fibre interferes to provide the focused scanning excitation beam. We demonstrate that the SLM can enable dynamic phase correction of path-length variations across the multicore optical fibre whilst the fibre is perturbed with an update rate of 100 Hz.


I. INTRODUCTION
ultiphoton microscopy [1] provides inherently optically sectioned images, enabling biochemical structure and activity to be studied in biological tissue [2]- [4], and is increasingly applied in vivo. To explore its potential for preclinical and clinical imaging, several groups are developing miniaturized instruments for multiphoton endomicroscopic imaging [5]- [14]. Most commonly these approaches are based on miniaturization of distal scanning and optical components integrated with a fibre-optic delivery system that can be implemented using double-clad large mode area photonic crystal fibre [15] or hollow-core photonic crystal fibre for minimal dispersion [16] with the double-cladding providing a high epi-detection efficiency through the inner cladding. To reduce the minimum size of endoscopes beyond the limits imposed by the size of the distal components, it is interesting to consider approaches that require no distal scanner. One such approach is proximal scanning of the excitation beam focused at the proximal end of a multicore optical fibre to sequentially couple into the individual cores. Thus transverse scanning is realised at the distal end with no need for mechanical components [17], although distal optics are required for focusing light into the sample and these must be translated to adjust the position of the focal plane. This approach is in clinical use [5] and has been adapted for rapid fluorescence lifetime imaging, including for FRET experiments [6]. We have previously presented [18] a further approach to laser scanning endomicroscopy that enables 3-D imaging without any distal mechanics or optics, utilising a multicore optical fibre in which multiple cores are simultaneously illuminated. At the distal end of the multicore fibre, the phase of the radiation emerging from each of the multiple fibre cores is controlled so as to interfere to produce a focused scanning beam in a manner analogous to phased-array radar. This is realised using a spatial light modulator (SLM) at the proximal end of the multicore optical fibre to precompensate for aberrations arising from differences in the pathlengths of the fibre cores and to control the phase profile of the light at its output. This approach could ultimately permit the production of thinner endomicroscopes and also facilitate coherent imaging and adaptive aberration correction. For multiphoton endoscopy, this approach enables the transmission of the excitation radiation with significantly lower peak intensity per core compared to propagating ultrashort pulses in a single mode optical fibre (or a single fibre core), thereby reducing nonlinear optical effects that can lead to pulse broadening and/or distortion. In subsequent work it has been implemented with a double-clad multicore optical fibre to realise a lensless multiphoton endoscope [19].
This proximal phase-correction approach is similar in concept to the adaptive optics techniques used for the control of beam propagation through inhomogeneous media that have been studied in the context of atmospheric propagation [20] and more recently used in optical microscopy [21]- [23]. Several groups have extended this to transmit images through a single multimode optical fibre, utilising the higher order modes to convey the image information [24]- [26]. While this approach M is compact and does not require specialised multicore optical fibres, the modal dispersion makes it challenging to transmit the ultrashort pulses required for multiphoton excitation, although we note progress is being made in this area by restricting the modes utilised to a small subset with similar optical path lengths [27]. In our previous work [18], we utilised a single interferogram recorded at the distal end of the fibre bundle to determine the phase required at the input of all of the fibre cores in order to correct for path length variations between them. While this offered the relative advantage of simplicity over the methods used in other work [19], [27], [28] that required separate distal interferometric measurements to determine the required phase for the input of each fibre core (or mode), our implementation of the algorithm required many seconds to calculate the required phase distribution and to apply it to the SLM, which is not practical for endoscopy. In this paper, we report progress towards the development of an ultracompact laser scanning multiphoton endomicroscope with no distal optics or mechanical components and demonstrate real-time dynamic correction of the required input phases at the proximal end of the multicore optical fibre with an update rate of 100 Hz. We further demonstrate the use of a novel polarization-maintaining multicore optical fibre [29] that increases the efficiency and contrast of the system without the need for a distal polarization filter.

A. Double-clad polarization-maintaining multicore fibre
We used a novel double-clad polarization-maintaining (PM) multicore fibre with 98 cores and low cross-talk [29] that was designed to achieve single mode operation at a wavelength of 800 nm with the cores arranged in a rectangular structure with center-to-center distances of 14 µm and 16 µm in the horizontal (x) and vertical (y) directions (relative to the image shown in the inset of Fig. 1(a)). Each core was manufactured from a gradient index germanium doped silica preform (Draka-Prysmian) with a pure silica jacket. The numerical aperture (NA) of the preform was 0.3 and the final core diameter in the fibre was 2 µm. To preserve the polarization of input light, stress-applying rods manufactured from boron doped silica (Draka-Prysmian) were inserted into the fibreidentifiable as the dark features in the inset of Fig. 1(a). The overall diameter of the 98 cores and inner cladding was 230 µm. To improve the signal collection efficiency in the PM fibre necessary for proximal detection, the inner cladding was jacketed with a fluorine doped low refractive index outer cladding material (Heraeus), providing multimode guiding for fluorescence collection with a NA = 0.2. Thus the outer diameter of the whole double clad PM multicore fibre was 260 µm. The experimental set-up for the adaptive multiphoton endomicroscope is illustrated in Fig. 1(a). Excitation pulses of 100 fs duration were provided by a Ti:Sapphire mode-locked femtosecond laser (Tsunami 3941-M3BB, Spectra-Physics) at 800 nm centre wavelength and 80 MHz repetition rate with 10.9 nm spectral bandwidth and a corresponding coherence length of 52 µm. For the low average power (~1 mW) in each optical fibre core used here, there was no measureable increase in spectral bandwidth after propagation through the PM multicore fibre. Thus we expect negligible pulse broadening due to self-phase modulation and can calculate that the pulses will be broadened by the group velocity dispersion (GVD), which is dominated by the material dispersion at 800 nm, to result in an output pulse duration of 370 fs after propagation through the 30 cm long PM multicore fibre. We measured the optical path length variation between cores of the PM multicore fibre and found that the standard deviation was 31.9 µm, which is less than the coherence length.

B. Experimental setup
The laser beam was split into two arms of a Mach-Zehnder interferometer via a polarizing beam splitter (PBS), one part to be delivered to the sample via the multicore fibre and the other providing a reference beam enabling optical path length variations between cores to be measured from interference fringes recorded by the camera (C). The relative intensity between the two beams was controlled by rotating the half-wave plate (HWP1). In the sample arm, the beam incident on the SLM (HSPDM512, Boulder Nonlinear Systems) was expanded through a magnifying telescope (L1 and L2) and its polarization was rotated to be vertical by HWP2 in order for it to be aligned with the axis of the SLM. We used a phase-only reflection SLM, which has 512 × 512 pixels and a pixel pitch of 15 µm. As part of the alignment process, the SLM was initially imaged onto the proximal end of the multicore fibre with a de-magnification factor of M = 30 by two 4-f imaging systems (L3, L4 and L5, OL3). To minimize the intensity of light propagating through the cladding and to transmit the light through the cores of the multicore fibre efficiently, a microlens array of focal length f = 36 mm was generated on the SLM, as shown in Fig. 1(b). Subsequently the proximal end of the multicore fibre was translated 40 µm from the focal plane of the proximal objective lens (OL3), i.e. by the focal length of the microlenses divided by the axial magnification ( ). With the microlens spacing equal to the fibre core spacing this arrangement results in a light injection numerical aperture of approximately 0.19. Thus the SLM could be used to control the phase of the light coupled into each fibre core. To further minimise the amount of excitation light travelling in the cladding of the multicore fibre, binary amplitude modulation was implemented by applying a large phase-ramp to those areas of the SLM where an amplitude of zero was required. Such light diffracted from these regions was blocked by an iris diaphragm (ID) placed between L3 and L4. The distal end face of the multicore fibre was imaged onto a scientific complementary metal oxide semiconductor camera (Zyla 10-tap sCMOS, Andor) through a 4-f imaging system (OL4 and L8) with 16.7 magnification.
In principle, the phase modulation scheme above should be able to provide phase-only modulation without affecting the coupling efficiency into the multicore fibre. In practice, however, the power transmitted through each core with the phase correction applied relative to the power transmitted with no phase correction applied was 1.03 ± 0.19 (mean ± standard deviation over all cores), which could be attributed to the wrapping of the microlens phase profile due to the limited phase-stroke of the SLM and/or to a misalignment of the polarization state of the beam incident on the SLM relative to the vertical axis of the SLM.
For the initial calibration, the sample shown in Fig. 1(a) was not present. In the reference arm of the interferometer, a single mode fibre (780HP, Thorlabs) of the same length (30 cm) as the PM multicore fibre was used to approximately match the dispersion in the two arms. The sample and reference beams were recombined to generate interference fringes on the camera using a non-polarizing beamsplitter (BS). A polarizer (P) placed in front of the camera was used during alignment of HWP3 to ensure that light in the sample arm was correctly coupled into one axis of the PM multicore fibre. HWP4 was used to rotate the orientation of the reference beam polarization state to match that from the distal end of the fibre so as to maximize the contrast of interference fringes obtained. The relative time delay between the sample and the reference beams was adjusted to maximize the contrast of the interference fringes using the mechanical delay stage (DS). Fig. 1(c) shows an image of the interferogram. The reference arm beam was aligned so as to produce a fringe pattern with a period of 14 µm at the location of each fibre core, as shown in Fig. 1(d). Thus we could measure an interferogram associated with phase distribution at the distal end of the multicore fibre. The system was controlled through a custom-written software package written in C++.
In order to determine the affine transformation between the SLM pixels and the camera pixels, we displayed 5 well-separated microlenses on the SLM. In the first alignment step, their positions were adjusted manually so that the light was coupled through 5 separate cores of the fibre. A software algorithm was then applied to optimize the position of each of the 5 microlenses individually to maximize the coupling through each core. The positions of these 5 conjugate positions were used to calculate the affine transformation from SLM to camera coordinates [30]. We were then able to calculate the corresponding SLM coordinates for each fibre core image on the camera.
To correct the phase distortion introduced by the variation in pathlength of individual cores and achieve 3-D scanning of a focused beam at the distal end of the multicore fibre, we conducted the following procedures: 1) The phase of the optical field exiting each core of the multicore fibre was calculated from the interferogram acquired on the camera using a Fourier-transform method [31]. 2) For each core on the interferogram, the corresponding SLM microlens was identified using the affine transformation from SLM to camera coordinates 3) The phase of each microlens at the SLM is adjusted to eliminate the phase variation between cores that was measured in step 1. 4) Subsequently the SLM is programmed to impose appropriate phase curvature on the light emerging from the fibre cores in order to form a focused beam spot and to realize 3-D scanning at the distal end of the multicore fibre as described in reference [18].
To demonstrate two-photon excited fluorescence (TPEF) imaging, a sample was inserted at the focal plane of the wavefronts emerging from at the distal end of the multicore fibre. TPEF from the sample was transmitted by the multimode inner cladding of the multicore fibre for proximal detection by PMT1 (PMH-100-0, Becker & Hickl GmbH) after the dichroic beamsplitter DS1 (Di01-R594-25x36, Semrock).

A. Phase correction and control
We measured the phase of the optical field of the radiation emerging from every core of the PM multicore fibre before and after phase correction, as shown in Figs. 2(a) and (b). The phases before correction (Figs. 2(a) and (c)) are randomly distributed due to the phase distortions caused by the PM multicore fibre, whereas the corrected phase map and angular histogram after phase correction (Figs. 2(b) and (d)) show a narrower distribution. The circular variances measured from the angular histograms before and after phase correction correspond to 0.849 and 0.011, respectively.
For practical endoscopy, it is essential to compensate for aberrations arising from variations in pathlength across the cores of the multicore optical fibre dynamically. To ensure stable phase control, a key step is to demonstrate real time phase stabilisation, which we implemented here by imaging the distal interferograms of the end face of the fibre at a frame rate of 417 Hz using a sCMOS camera (Zyla 10-tap sCMOS, Andor). The phase at each core was determined using the algorithm previously described [16] and a proportional-integral-derivative (PID) controller was implemented for each core to estimate the phase compensation to apply to the microlens array on the SLM. The interferogram processing, PID filter and microlens array calculation was implemented on a GPU (Nvidia GeForce GTX960). The phase compensation calculation required 1.5 ms in total to execute for the 512 512 pixel camera image and dynamic phase correction of every core of the fibre was realised with an update rate of 100 Hz determined by the switching rate of the SLM liquid crystals.     3 demonstrates the performance of the dynamic phase correction algorithm. A phase correction procedure utilising a single distal interferometric measurement was performed at the start of the experiment. Initially the sample was static with the dynamic phase correction switched off and the phase in every core was measured at 417 Hz. The mean value of the circular variance of the phase was 0.015 over the time period t = 0-5.7 s when the PM multicore fibre was stationary (i.e. with no perturbation applied). At t = 5.7 s, a 4 Hz sinusoidal voltage was applied to a loudspeaker cone to introduce ~10 degrees of bend to the PM multicore fibre at its midpoint along its length with a repetition rate of 4 Hz. This motion caused the mean value of the circular variance of the phase to increase to 0.221 for the time period t = 5.7-11.5 s. At t = 11.5 s we switched on the dynamic phase correction and the mean value of the circular variance of the phase reduced to 0.046, illustrating the ability of the system to compensate for the applied motion in real time. Fig. 4 illustrates how the phase control enables the focused spot to be scanned in three dimensions by varying the phase map applied to the SLM in order to adjust the tilt and curvature of the wavefronts emerging from the distal end of the multicore fibre. In Figs 4(g-j) we illustrate the focal spot formed as we vary the focal length from 300 to 500 μm. As the focal length is increased the effective numerical aperture of the focused spot is decreased and so the full width at half maximum (FWHM) of the focused spot increases accordingly.

B. Two-photon excited fluorescence imaging
To verify the applicability of adaptive multiphoton endomicroscope for TPEF imaging, we acquired TPEF images of a single fluorescence bead with both proximal and distal detection, as shown in Fig. 5. The measurements were performed with an applied focal length of 450 µm. The fluorescence signal is lower for proximal detection due to the lower fluorescence collection NA provided by the inner-cladding of the multicore fibre (NA = 0.2) compared to the NA of the distal objective (OL4, NA = 0.4). The background signal in the TPEF images was attributed to two-photon excited autofluorescence generated from the multicore fibre itself. Using a higher input power to the fibre increases not only the peak power at the central focused spot but also the background autofluorescence by the same factor. This background autofluorescence could be decreased in the future by increasing the number of cores in the multicore fibre to reduce the excitation power in any single core: for example, increasing the number of cores by a factor of 10 should reduce the background signal by a factor of 100.

C. Generation of multiple foci and limitation of the field of view
A consequence of the light emerging from the periodic arrangement of fibre cores is that the coherent interference results in a periodic array of foci, as illustrated in Fig. 6, which shows the intensity distributions measured 400 µm away from the distal end of the multicore fibre with the phase of the cores programmed to generate a focal length of 400 µm. Before phase correction, the intensity distribution at the focal plane is a speckle pattern caused by random interference of light emitted by each core at the distal end of the multicore fibre ( Fig. 6(a)). After the phase correction and application of the appropriate curved phase profile, multiple focused beam spots were observed, as can be seen in Fig. 6(b). Because the different foci are not independently controllable, the maximum size of object that can be imaged is limited by the separation distances between the central and the adjacent focused spots. For the applied focal length, these are 19 µm and 22 µm for the indicated axes a and b. Fig. 6(c) shows the central focused beam spot whose FWHM is 2.7 µm, which determines the lateral resolution when imaging with this system. The average power within the central spot was 374 µW.
For future work, both the peak power in the central focus and the separation between foci could be increased by designing a multicore fibre with smaller center-to-center separation of cores, such that fewer foci fall within the intensity envelope of the radiation emitted by the cores. Alternatively a single illumination focus could be achieved if the multicore fibre could be designed with a random spatial distribution of fibre cores.

D. Advantage of PM multicore fibre
The PM multicore fibre offers a significant increase in the intensity achieved in the focal spot compared with a non-PM fibre. This is because there is no depolarization of the light coupled into each core and therefore all of the light exiting each core the fibre can be programmed to have the correct phase to interfere to form the focal spot. In both cases, the field at the focal plane is the coherent superposition of the contributions from each fibre core. For the PM fibre, after phase correction, all components have the same magnitude, polarization and phase so the amplitude at focus A PM after correction of the phase is the sum of the magnitudes a from each of N cores (1) In the case of the non-PM fibre, the polarization state emitted from each core is randomized, i.e. with a uniform probability density over the surface of the Poincaré sphere described by a normalized Stokes vector [1, Q, U, V] [32]. A single phase correction can only compensate for one of two independent polarization states: here we use horizontal linear but the choice is arbitrary. In this situation, by projecting the surface of Poincaré sphere onto the Q axis that describes the horizontal-vertical linear states, it can be shown that Q has a uniform probability density of ( ) 1 2 p Q over the range  (5) In this simulation, the field at the end face of the fibre was given by the sum of the fields produced by each core. To calculate the field at the focal plane, the two polarization states (H and V) were independently and numerically propagated to the focal plane using the angular spectrum method to give y x C jH , ' and y x C jV , ' . The intensity at the focal plane was calculated as In Fig. 7, the results of one run of the simulation of the field in the focal plane from a PM multicore fibre are compared with those of a non-PM multicore fibre with the same geometry. Figs. 7(a) and (e) show the intensity distribution of the horizontal (H) polarization state simulated at the distal end of both the PM and non-PM simulated multicore fibres. The separation distance between adjacent cores was set at 21.5 µm and the focal length simulated was 400 µm. Figs. 7(d) and (h) show central line profiles through the intensity and two-photon intensity distributions simulated in the focal plane for both multicore fibres.
In the case of the non-PM multicore fibre, there is a variation in the simulated intensity distribution between successive runs of the MATLAB code due to the background speckle pattern formed by the perpendicular (V) component of the field for which the phase is random. By running the simulation 30 times, we found that the PM multicore fibre is expected to provide a 5.13±0.18-fold (mean±standard error in mean) increase in fluorescence signal compared to the non-PM multicore fibre, which is in agreement with the theoretical value calculated above. (h) shows the corresponding normalized line profiles taken across the center of (f) and (g). For clarity, (c) intensity and (g) two-photon intensity images for the non-PM multicore fibre were displayed with 2 and 4 gains, respectively compared to (b) and (f). Scale bars 50 µm.

IV. CONCLUSIONS
We have reported an adaptive multiphoton fluorescence endomicroscope implemented with a double-clad PM multicore fibre for the first time that is demonstrated to generate and scan a focused beam at the distal end with no distal optics or mechanical components. We note that our calculations indicate that the PM multicore fibre provides significantly higher excitation power for multiphoton endoscopic imaging compared to non-PM fibres. In addition, we have demonstrated dynamic correction of the proximal phase distribution at up to 100 Hz update rate, which is a key step towards practical adaptive endoscopes. Currently our imaging rate is determined by the switching rate of the SLM liquid crystals (approximately 100 Hz) that is used to control the phase tilt on the light emerging from the fibre cores. This imaging rate could be increased by incorporating a galvanometric scanner at the proximal end of the multicore fibre [19], [34] and/or using a liquid crystal SLM with a faster update rate [35]. Thus, we envisage that our adaptive multiphoton endomicroscopy can be developed to provide imaging speeds sufficient for practical preclinical and clinical applications. We note that our experimental and numerical results indicate that the maximum size of object that can be imaged by this adaptive endoscope is limited by the scale of the lattice of foci that are (inevitably) generated by the interference of coherent radiation resulting from the periodic core structure of the multicore optical fibre. In the future the maximum size of object that can be imaged can be increased by designing a multicore fibre with smaller center-to-center separation of cores or by designing a fibre with a less periodic distribution of cores.