Fig. 1. Principle of the DECOUPLE system. (a) DECOUPLE accurately corrects dispersion and aberrations caused by MMF and tissue scattering, ensuring a high signal-to-noise ratio and resolution for deep-tissue imaging. (b) Measure the TM of the MMF using the Hadamard orthogonal basis vectors and convert the spatial domain TM to the spatial-frequency domain TM using the Fourier transform. (c) Guided by the spatial-frequency domain TM, independently control the light-field distribution in the output spatial-frequency domain of the MMF to scan the sample with subpupils. Determine the positional deviations of each pupil and calibrate them to ensure alignment. (d) Guided by the spatial-frequency domain TM, keep the phase of one subpupil unchanged while varying the phase of another pupil. Scan the sample and determine whether the focal point reaches optimal phase-contrast interference by analyzing the returned light intensity. (e) Adding all pupils’ positions and relative phases to the spatial-frequency domain of the TM cancels out aberrations and achieves a diffraction-limited focus.

Fig. 2. Simulation of DECOUPLE. Simulated aberrations and mode dispersion caused by MMF dispersion and tissue are compensated by the DECOUPLE method. (a) DECOUPLE’s image enhancement simulation results are shown, where the first column displays the ground truth. The second and third columns introduce mode dispersion and aberrations, respectively. The second column shows the images after DECOUPLE has corrected the mode dispersion, whereas the third column displays the images after DECOUPLE has corrected the aberrations. The first row of image panels simulates images of fluorescent microspheres, the second of a resolution test target, and the third line a set of colored letters. All scale bars are 10μm. (b) Simulated aberration wavefront by Zernike polynomial, and the measured aberration wavefront using DECOUPLE by 16 independent subpupil measurements. The second row shows the wavefront after aberration compensation. (c) Enlarged region corresponding to the region indicated by dotted boxes in the second row of panel (a) and calculated PSNR. (d) Enlarged area corresponding to dotted box in panel (a), third row, and calculated PSNR.

Fig. 3. Experimental setup for a dual-color MMF endoscopy system. The setup allows for the precise control and manipulation of light within the MMF, enabling the acquisition of its TM and fluorescence point-scanning imaging in two colors. Dispersion, deformation, and aberration are continuously tracked and compensated for. The transmission measurement module is used to obtain the complex amplitude of the output field of the MMF. During imaging, this module is removed. CMOS, complementary metal-oxide-semiconductor transistor; M, mirror; DMD, digital micromirror device; MMF, multimode fiber; DM, dichroic mirror; L, lens; HWP, half-wave plate; QWP, quarter-wave plate; FC, fiber coupler; OBJ, objective; PBS, polarizing beam splitter; PMT, photomultiplier tube; S, single-mode fiber; F, fiber-optic collimator; LP, polarizer; BS, beam splitter; OF, optical filter; FOBC, fiber-optic broadband coupler.

Fig. 4. Correction of aberrations caused by refractive index mismatch and multilayer cell scattering. (a) The schematic diagram illustrates the imaging process of samples in different environments, namely, air, glue, and onion epidermis. The calibration measurements for the TM are performed in an air environment. Once the calibration is completed, imaging through aberrating test samples takes place, including glue and a weakly scattering medium. (b) Images of a 1-μm fluorescent bead situated in glue, imaged using an MMF with or without the aberration correcting step 2 of DECOUPLE performed. Signal profiles are shown along the dashed lines indicated on the image panels. (c) Lateral images of a 1-μm fluorescent bead viewed in thick onion epidermis using an MMF with and without aberration correcting step 2 of DECOUPLE. Signal profiles in the lateral images are shown along the dashed lines. The scale bar is 8μm.

Fig. 5. Correction of aberrations on samples with complex samples. Here, DECOUPLE step 1 represents the removal of fiber dispersion only, whereas DECOUPLE step 2 represents the removal of both fiber dispersion and aberrations caused by the sample. (a) These imaging results were obtained under varying bending conditions with/without the DECOUPLE technique. The scale bar is 27μm. The right images show the fiber in different bent states. (b) Samples including lung slice and roundworm slice were both covered by a 120-μm onion epidermis. (c) Utilization of 10% fat emulsions above a resolution target as a weakly scattering sample. (d) Images of lung slice and roundworm slice acquired with and without DECOUPLE, respectively. The images in the third row depict the resolution target captured under 80-μm thick layers of fat emulsions. The scale bar corresponds to 15 μm in the top two rows and 24μm in the bottom row. (e) The intensity profile along the dashed lines is shown in panel (d). The resolution increases with the application of DECOUPLE. (f) Power spectrum comparison of the images in panel (d). The power of spatial-frequency distribution broadens after the application of DECOUPLE.

Fig. 6. Volumetric imaging of two color microbeads randomly distributed in a volumetric sample covered by a layer of onion epidermis. (a) Dual-color imaging of fluorescent microbeads covered by onion epidermis at a depth ranging from 110 to 180μm. (b) The top row shows results obtained without DECOUPLE, whereas the bottom row illustrates results by DECOUPLE method. The scale bar is 10μm.