Endoscopy allows imaging deep inside biological tissues overcoming tissue scattering. Some endoscopes consist of one single-mode fiber equipped with a focusing lens and a scanning system at the distal end. This can give high-resolutions images at the expense of a large device footprint [1]. Multicore fibers (MCFs) are mostly used in practice due to their simplicity and small footprints. An endoscope based on MCFs has a resolution limited by the core-to-core spacing [1,2]. MCF endoscopes are usually equipped with a GRIN lens on its distal end, which gives a fixed imaging plane at some distance, an increased resolution at the expense of field of view. Because of the lens, aberrations occur at the edges of the field of view.

Recently, wavefront shaping techniques have shown a path to ultrathin and high-resolution endoscopy. It has been shown that multimode fibers (MMFs) with a few hundred micrometers in diameter can be turned into a high numerical aperture (NA) microscope objective for microscopy and optical trapping [3–6]. Lensless MCFs benefit from wavefront shaping to produce pixelation-free images, with a resolution higher than the inter-core spacing distance [7–9].

Approaches based on wavefront shaping have two main drawbacks: they usually require a calibration step, and the ability to image assumes that the fiber endoscope does not change its conformation. If the fiber bends, another calibration is needed which usually requires access to both sides of the endoscope. Recently, it has been shown that it is possible to calculate the right wavefront to focus through a MMF, even a bent one. This is possible modeling the fiber, by knowing the refractive index profile of the MMF and its spatial conformation [10]. Calibration techniques that require one-step calibration to focus light through a lensless MCF have been described in [11] and [12]. If a light beacon is available at the distal end, it can be used to dynamically recalibrate the fiber, as was shown in [13]. Depending on the core-to-core coupling, phase gradients at the input of a MCF are preserved within some extent. This effect is similar to what has been observed in thin scattering materials [14,15]. This results in an angular “memory effect” that can be used to scan a given pattern in the three dimensions (for example, a focus spot [12]). Recently, a rotational memory effect has been observed in MMFs: the rotation of an input pattern results in a rotation of the output of the MMF [16]. Recent advancements in imaging through scattering media showed that, using the angular memory effect, it is possible to obtain an image of a sample behind a scattering layer without any calibration or wavefront precompensation [17,18]. The approach demonstrated in [18] has been adapted to MCFs in [19], showing one-shot widefield imaging. The technique is based on the fact that two emitting points at the same plane in the distal end will generate two shifted speckle patterns on the proximal side. Points of an object lying within the angular memory effect of the MCF can be retrieved by recording the generated speckle pattern on the proximal side and by a post-processing step [19]. In this case, the memory effect is used on the detection side. This is possible when the light coming from the sample is coherent or has a reduced bandwidth. An increase in bandwidth reduces the contrast of the attainable image [19].

Here we show that, using the memory effect on the excitation side (the distal end), we could image a fluorescent sample with broadband emission with a resolution superior to the core-to-core spacing of the MCF and without any calibration. Our only assumption is that the fiber does not change conformation during the acquisition of a single image, but it can bend arbitrarily between acquisitions. We adapted the speckle scanning microscopy (SSM) technique described by Bertolotti et al. [17] to MCFs.

As described in [17], if a speckle pattern is translated across a fluorescent sample, the intensity of the fluorescent signal $I$, as a function of the incidence angle $\theta$, is given by

The averaged autocorrelation of the intensity map over different scans can be expressed as

Figure 1 shows the optical setup used in the experiments. A 532 nm laser beam is expanded, collimated, and sent toward a spatial light modulator (SLM, Pluto-Vis, Holoeye) using a polarizing beam splitter (PBS). The facet of the SLM is imaged onto the MCF (Fujikura, FIGH-06-300S; 6000 cores, core diameter of 2.5 μm, 30 cm long, core-to-core spacing of 3.2 μm; $\mathrm{NA}=0.34$) facet by the 4 f system composed of the lens L2 and the objective OBJ2. Linear phase gradients are assigned to the SLM to rock the incidence angle of the laser beam on the MCF. The beam that reaches the MCF covers an area of 200 μm in diameter, corresponding to illuminate approximately 3000 cores. Core-to-core coupling in a MCF illuminated with coherent light results in a speckle pattern $S$ at the output of the MCF. Thanks to the memory effect, this speckle can be spatially scanned, rocking the angle $\theta$ of the input field to the MCF using the SLM. The fluorescence from the sample is collected through the same MCF and redirected toward an avalanche photodiode (APD) using a dichroic mirror (DM). This simple setup, indicated in Fig. 1 as a SSM path, is enough to perform SSM imaging using a MCF.

 

Fig. 1. Experimental optical setup. The output of a diode pumped solid-state laser ($\lambda =532\mathrm{nm}$) is expanded by the telescope OBJ1-L1 and is sent to the spatial light modulator (SLM) by the polarizing beam splitter (PBS). Tilted beams are created on the SLM plane, which is imaged on the MCF facet. Rocking the incidence angle on the MCF produces shifting speckle patterns in the sample plane $S$. For each angle of incidence, the fluorescence emitted by the sample is collected back through the MCF, reflected by a dichroic mirror (DM) and integrated by an avalanche photodiode (APD). HWP= half-wave plate; BS1= BS2 = 90:10 R:T beam splitter. BS1= BS2 = 50:50 R:T beam splitter. $\mathrm{OBJ}1=10\times$, $\mathrm{NA}=0.25$, Newport; $\mathrm{OBJ}2=40\times$, $\mathrm{NA}=0.65$, Newport; $\mathrm{OBJ}3=20\times$, $\mathrm{NA}=0.4$, Newport. Focal length lenses: $L1=150\mathrm{mm}$, $L2=L3=200\mathrm{mm}$, $L4=100\mathrm{mm}$.

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As described before, the technique allows imaging a fluorescence sample after averaging $N$ scans by using $N$ independent speckle patterns. In [17], this was obtained starting each scan at a different incidence angle, such that the difference in starting angles is larger than the angular size of the object (or larger than the angular memory effect range). Here we created independent speckles assigning to each core of the MCF a random input phase. In this way, we are sure about the independence of consecutive scans, and we do not need to introduce an angular difference in starting incidence angles that may exceed the NA of the MCF. To address the MCF’s cores in a predictable way, we introduced a separate alignment path to know exactly the correspondence between the SLM and MCF facet. This is possible by performing a digital phase conjugation of a focus spot as in [12], where the SLM is placed at the imaging plane of the MCF facet, and a perfect alignment SLM-fiber is required [4]. The CMOS camera is also placed at the imaging plane of the MCF facet and is aligned pixel by pixel with the SLM, so that the MCF can be mapped with one pixel precision on the SLM. Once the mapping is obtained, the alignment path can be permanently removed, and there is no need for access to the sample side.

We first measured the angular memory effect of the used MCF. Figure 2(a) shows an experimental correlation map of the speckle pattern projected by the MCF as a function of the incidence angle ($\theta -{\theta }_0$), where ${\theta }_0$ is the initial incidence angle. The speckle patterns were imaged on a CCD camera. The correlation map was formed taking the maximum of the two-dimensional cross-correlation between the speckle pattern at each angle and a reference speckle acquired for $\theta ={\theta }_0$. The resolution of SSM is given by the average speckle grain size which, in turn, depends on the NA of the MCF and the working distance (i.e., the distance between the MCF facet and the object), [17]. Figure 2(c) shows the experimental mean size of the speckle grain as a function of the working distance obtained with the MCF. The speckle grain size has been calculated as the full width at half-maximum (FWHM) of the autocorrelation of the speckle pattern at each working distance, in a $50\times 50\mathrm{\mu m}$ area in front of the MCF. As shown in the curve in Fig. 2(c), without any calibration, creating a speckle pattern and rocking the angle of the incidence beam on a MCF, it is possible to obtain sufficient information to form a fluorescence image of an object with a resolution higher than the core-to-core spacing (3.2 μm, in our case), for a large range of working distances. The technique has an infinite depth of field. A planar object can be imaged at any working distance with a resolution decreasing with the distance from the fiber facet. This means that the technique does not have axial discrimination, as discussed in [18].

 

Fig. 2. SSM through MCFs characterization. (a) Speckle pattern generated at the sample plane $S$ for normal incidence on the MCF is recorded on a CCD camera. Once the incidence angle is varied, the shifted version of the speckle is recorded, and the cross-correlation with the first pattern is calculated. The intensity map represents the calculated degree of correlation as a function of the incidence angle. (b) Line profile along the yellow dashed line in (a). We consider the FWHM of this curve as memory effect range, which gives the maximum field of view. Imaging 300 μm far from the fiber facet gives a field of view of 35 μm. (c) Measured mean speckle grain size as a function of distance from the fiber facet, an indicator of the resolution of the SSM technique. It has been calculated measuring the FWHM of the autocorrelation of the speckle pattern in a $50\times 50\mathrm{\mu m}$ area in front of the MCF. The lines in (b) and (c) are drawn only for clarity.

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To test the SSM imaging through MCF and its resolution, we first imaged portions of a 1951 USAF resolution target (Edmund Optics) in a transmission geometry. The sample was placed 500 μm away from the MCF facet and imaged on the CCD through the 4 f system OBJ3-L4. For each plane wave, the image on the CCD is the equivalent of the product between the shifting speckle pattern and the resolution target. An image consisting of many features of the resolution chart was acquired for each plane wave. We isolated from the image the pattern of the group 7 element 6 (stripes 2.19 μm wide) and the digit 7 of the group 7 to show that the technique has a resolution superior to the core-to-core spacing and the ability to image complex patterns, respectively. For each angle, we integrated all the light transmitted through the pattern to obtain one point of the intensity matrix $I(\theta )$. To form an image, we averaged the autocorrelation of intensity maps obtained using 20 speckle realizations. Figure 3 shows the experimental results. Each row represents a separate imaging experiment. The columns, form left to right, show the average autocorrelation map of 20 scans, the calculated Fourier transform of the object $O$, the transmission widefield image of the sample, and the reconstructed object via SSM. The image reconstruction was obtained using 2000 iterations of the hybrid input-output algorithm [21], followed by 50 iterations of error reduction algorithm [21], as described in [17].

 

Fig. 3. SSM imaging through a MCF of a 1951 USAF target. The four columns are the autocorrelation of the intensity map $I(\theta )$, the Fourier transform of the object obtained from the autocorrelation map, the transmission widefield image of the sample, and the sample imaged by SSM. The scale bars are 10 μm. The SSM image of the Group 7 Element 6 of the USAF target was 2D interpolated to double the number of pixels.

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We now demonstrate the ability of fluorescent imaging using SSM in MCFs in reflection geometry, with no access to the distal end. We prepared a sample depositing 1 μm diameter fluorescent beads on a 150 μm thick microscope glass slide, and we placed it 300 μm away from the MCF facet where, according to Fig. 2(c), a resolution superior to 1.5 μm should be attainable. For this experiment, we averaged the autocorrelation of intensity maps over 10 different speckle patterns. In Fig. 4(a), three of these intensity maps are shown. Also in this case, the image reconstruction was obtained using 2000 iterations of the hybrid input-output algorithm, followed by 50 iterations of error reduction algorithm. Figures 4(b) and 4(c) show the comparison between the widefield fluorescent image of two beads 3 μm apart from each other and the image obtained with the SSM technique through MCF. Since the distance between the two beads is comparable to the core-to-core spacing (3.2 μm), the fact that the two beads are completely resolved indicates that the resolution is finer than inter-core distance, as predicted in Fig. 2(c), measuring the speckle size, and in Fig. 3.

 

Fig. 4. SSM imaging through a MCF of 1 μm fluorescent beads deposited on a glass slide. (a) Example of intensity patterns $I(\theta )$ recorded by the APD. For the experiments, 10 different intensity maps were acquired to calculate the average autocorrelation. (b) Fluorescence widefield image of the sample. (c) Sample imaged and recovered by SSM. The distance between the two beads is approximately 3 μm. The scale bars are 5 μm.

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Figure 5 shows additional experiments of SSM using a MCF. As in Fig. 3, the columns, form left to right, show the average autocorrelation map of 10 scans, the calculated Fourier transform of the object $O$, the fluorescence widefield image of the sample, and the reconstructed object via SSM. Similar images were obtained after bending the fiber, unless the bending introduces too high coupling between cores [12]. Bending can also be used to change the speckle pattern between two scans, as shown in [19].

 

Fig. 5. SSM imaging through a MCF of 1 μm fluorescent beads deposited on a glass slide. The four columns are the autocorrelation of the intensity map $I(\theta )$, the calculated Fourier transform of the object, the fluorescence widefield image of the sample, and the sample imaged by SSM. The scale bars are 5 μm.

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In conclusion, we have demonstrated pixelation-free images through MCFs of fluorescent samples with no calibration step. Bending does not affect the image quality as long as it does not happen during one single scan. In the experiments we described, an image consisting of $50\times 50$ pixels is scanned in 125 s at the SLM full speed. (The maximum refresh rate is approximately 20 Hz.) This speed can be drastically increased using instead digital micromirror devices, with refresh rates up to 20 kHz. Higher speed can be obtained by scanning the incidence angle with galvo-mirrors: we tested that with commercially available galvo-mirrors we can acquire five $100\times 100$ pixel intensity maps per second (not shown here).

The obtained field of view is relatively small. This can be increased, for example, with a higher core-to-core spacing (which does not affect the resolution of SSM). Another way to increase the field of view would be to use a CCD camera to collect the fluorescence signal, instead of the APD. The main limiting factor for the field of view is the memory effect range. If there are two objects in the imaging plane and their distance is larger than the angular memory effect, the technique will fail. Using a CCD camera and imaging the distal facet of the MCF, we would be able to collect the fluorescence of the two objects independently, thanks to the widefield imaging capability of the MCF. At this point, two independent reconstructions can be run, and the two SSM images can be combined in a larger image. This can enlarge the field of view considerably, as shown in [22], where SSM using scattering media was integrated with a widefield microscope.