10 11 Multicore fiber bundles are widely used in endoscopy due 12 to their miniature size and their direct imaging capabilities. 13 They have recently been used, in combination with spatial 14 light modulators, in various realizations of endoscopy with 15 little or no optics at the distal end. These schemes require 16 characterization of the relative phase offsets between the 17 different cores, typically done using off-axis holography, 18 thus requiring both an interferometric setup and, typically, 19 access to the distal tip. Here we explore the possibility of 20 employing phase retrieval to extract the necessary phase in-21 formation. We show that in the noise-free case, disordered 22 fiber bundles are superior for phase retrieval over their peri-23 odic counterparts, and demonstrate experimentally accurate 24 phase information for up to 10 simultaneously illuminated 25 cores. Thus, the phase retrieval is presented as a viable al-26 ternative for real-time monitoring of phase distortions in 27 multicore fiber bundles. Endoscopy is a powerful tool used to image hollow organs with-32 out the need for surgery [1]. Miniaturization of the endoscope 33 probe will allow for a wider range of accessible organs to be 34 examined and, thus, is crucially important for applications. 35 Some miniature endoscopes are based on a single-mode optical 36 fiber which is mechanically scanned [2,3] or spectrally spread at 37 the distal end [4,5]. The use of a single-mode fiber circumvents 38 distortions due to propagation within the fiber. Yet, for minia-39 turization purposes, it is generally desirable to minimize the 40 number of elements at the distal end of the endoscope [6]. 41 Indeed, various techniques have been suggested for endoscopic 42 imaging where all the active elements are in the proximal end of 43 the fiber. Recent implementations are typically based on multi-44 mode optical fibers [7-9], GRIN fibers, or bundles of single-45 mode fibers [10-13]. In all these, light propagation through the 46 device, reflected in relative phase accumulated by the various 47 modes propagating through the optical system (which is also 48 dependent on bending and temperature) has to be taken into 49 account. Confocal scanning endoscopy, circumventing the 50 need to account for the accumulated phase, was performed ei-51 ther by using multi-core fiber (MCF) bundles or by using 52 GRIN fibers while scanning a confocal pinhole (or an input 53 single-mode fiber) at the proximal end [14]. The use of speckle 54 correlations and the "memory effect" in multicore fiber bundles 55 have also been recently suggested as a means to perform either 56 scanning endoscopy [15] or wide-field imaging [16] without 57 the need to compensate for the differences in the phase intro-58 duced by the different cores. Active phase compensation is, 59 however, by far the most direct and efficient approach to ad-60 vanced endoscopy applications. 61 Indeed, following the dramatic advances in spatial light 62 modulation technology, active compensation of the phase dis-63 tortion due to propagation either in a multimode fiber [7-9] or 64 in a multicore fiber bundle [10-13] has been pursued in recent 65 years. This requires accurate characterization of the phase dis-66 tortion induced by propagation in the endoscope. In multi-67 mode fibers, the measurement of the fiber transmission 68 matrix is sufficient to perform widefield imaging [9,17]. In 69 multicore bundles, this reduces to the problem of characteriz-70 ing the phase delay within each core, which can then be com-71 pensated for via the use of a spatial light modulator (SLM) [18]. 72 Alternatively, using an SLM, it is possible to perform confocal 73 scanning by adding a combination of a linear and a parabolic 74 phase profile on top of the phase distortion correction [11]. 75 The latter approach is especially useful for multiphoton imag-76 ing [12]. In most of the above cases, off-axis holography or self-77 referenced interferometry, was used to characterize the phase 78 distortion. This requires a stable interferometric setup and usu-79 ally requires access to the distal end of the fiber, and is difficult 80 to implement for correction of time-dependent distortions. For 81 multicore bundles, it is also possible to separately characterize 82 the phase shift between individual pairs of cores [11] (which 83 can, in principle, even be done in backscattering mode, taking 84 advantage of the light reflected from the distal fiber end). This 85 is, however, a painstakingly slow process. Therefore, a rapid 86 characterization method for the time-varying phase distortion 1 Letter Vol. 42, No. 4 / /Optics Letters 1 0146-9592/17/040001-01 Journal