Fig. 2: Data acquisition and image reconstruction.

a Bright-field image of the fibre bundle taken at the IP by illuminating the incoherent source from the OP. The fibre cores where the illumination beam was focused are indicated as red dots. b Raw images captured by the camera for the scanning of \(\left({u}_{{{{{{\rm{i}}}}}}},{v}_{{{{{{\rm{i}}}}}}}\right)\). For better visibility, the images shown here were taken without the reference beam, while the interference images were recorded for the endoscopic imaging (see the Supplementary section 2 for raw interference images). The colour bar indicates normalized intensity excluding the back-reflection noise. c Complex field maps \({E}_{{{{{{\rm{camera}}}}}}}\left({u}_{{{{{{\rm{r}}}}}}},{v}_{{{{{{\rm{r}}}}}}};{u}_{{{{{{\rm{i}}}}}}},{v}_{{{{{{\rm{i}}}}}}}\right)\) obtained from the raw interference images in b. Circular colour map: real and imaginary values of \({E}_{{{{{{\rm{camera}}}}}}}\). d and e Fibre core-dependent phase retardations \({\phi }_{{{{{{\rm{i}}}}}}}\left({u}_{{{{{{\rm{i}}}}}}},{v}_{{{{{{\rm{i}}}}}}}\right)\) and \({\phi }_{{{{{{\rm{r}}}}}}}\left({u}_{{{{{{\rm{r}}}}}}},{v}_{{{{{{\rm{r}}}}}}}\right)\), respectively, identified via the algorithm. The colour bar signifies the phase in radians. Scale bar, 0.1k. f and g The same as d and e, respectively, but for a low-contrast resolution target. h Conventional endoscopic image of a USAF target taken by the incoherent illumination from the IP. The fibre bundle was in contact with the target surface. i Coherent addition of inverse Fourier transformed images of the complex field maps in c before correcting for the fibre core-dependent phase retardations. j The same as i but after the correction. The colour bar signifies normalized amplitude. k–m The same as h–j, respectively, but for a low-contrast resolution target. The 350-μm-diameter fibre bundle was used, and the fibre-to-sample distance d was 500 μm for i, j, l, and m. Scale bars in a to c: 50 μm. Scale bars in j and m: 30 μm.