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In many situations in which an optic fiber carries a signal through a radiation field, an unwanted background signal is produced consisting of fluorescent and/or Cerenkov light. This presents a major problem in the measurement of the light signal, for example, in scintillation dosimetry of medical therapeutic beams. In this paper, we demonstrate a new method of measuring and removing the background signal through the use of a twisted pair of optic fibers. The twisted pair consists of a fiber carrying the scintillation signal that is twisted with a second optic fiber to form a double helix. The two twisted fibers will experience the same radiation environment provided the periodicity of the twist is correlated to the dose rate gradient. An expression for the required twist periodicity is presented. A scintillation dosimeter with a twisted pair optic fiber was tested in a megavoltage beam and found to accurately measure its beam characteristics. The twisted pair approach is not restricted to medical applications and can be used in many situations in which optical signals are carried through radiation fields.