Optimizing the internal phase reference to shape the output of a multimode optical fiber

Pre-shaping light to achieve desired amplitude distributions at the tip of a multimode fiber (MMF) has emerged as a powerful method allowing a wide range of imaging techniques to be implemented at the distal facet. Such techniques rely on measuring the transmission matrix of the optically turbid waveguide which scrambles the coherent input light into an effectively random speckle pattern. Typically, this is done by measuring the interferogram between the output speckle and a reference beam. In recent years, an optical setup where the reference beam passes through the MMF has become an attractive configuration because of the high interferometric stability of the common optical path. However, the merits and drawbacks of an internal reference beam remain controversial. The measurement of the transmission matrix is known to depend on the choice of internal reference and has been reported to result in "blind spots" due to phase singularities of the reference beam. Here, we describe how the focussing efficiency of the calibration can be increased by several percent by optimising the choice of internal reference beam.