We report on the first realization of direct absorption measurements in thin rods and optical fibers using the laser-induced deflection (LID) technique. Typically, along the fiber processing chain, more or less technology steps are able to introduce additional losses to the starting material. After the final processing, the fibers are commonly characterized regarding losses using the so-called cut-back technique in combination with spectrometers. However, this serves only for a total loss determination. For optimization of the fiber processing, it would be of great interest not only to distinguish between different loss mechanisms, but also have a better understanding of possible causes. For measuring the absorption losses along the fiber processing, a particular concept for the LID technique is introduced and requirements, calibration procedure, as well as first results are presented. It allows us to measure thin rods, e.g., during preform manufacturing, as well as optical fibers. In addition, the results show the prospects also to apply the new concept to topics like characterizing unwanted absorption after fiber splicing or Bragg grating inscription.