Methods of measuring the refractive index profile of a transparent cylindrical object, such as a fiber preform, are disclosed. The methods include transmitting light rays through the cylindrical object in a direction transverse to the central axis at different heights and measuring the deflection angles to define a measured deflection function ψm. The methods include numerically fitting a target deflection function ψt to the measured deflection function ψm within a first object region that does not include the object's outer edge. The fit is conducted by varying the yet unknown parameters of the refractive index profile that define the target deflection function to obtain an estimated refractive index profile η*i(r) over a second object region equal to or greater in size than the first object region. For cylindrical objects having at least one refractive index continuity, the method is applied to the different regions defined by the at least one discontinuity. An example method uses the estimated refractive index profile of a fiber preform to adjust at least one parameter of a preform fabrication process.