Fiber Bragg grating characterization using factorial design.

The design of the experiment is a scientific approach that provides the maximum amount of information with the minimum number of experiments. It is applicable in scientific and industrial research. We represent a three-variable two-level factorial design to assess fiber Bragg grating properties under simultaneous temperature, humidity, and strain stimuli. Three uniform gratings were inscribed in a single-mode standard optical fiber using the interferometric technique. Two gratings were recoated, one with acrylate and another with a layer of polyimide, while the third grating remained bare. With only eight measuring points, the sensitivities of temperature, strain, and humidity were computed. Moreover, with this technique, the cross-sensitivities between temperature and strain, temperature and humidity, humidity and strain, and between all three factors could also be quantified. We have proven that the results of this design are comparable with those of the classic method. For all gratings, the temperature and strain sensitivities were obtained in the order of 10 pm/°C and 1.1 pm/με, respectively. The humidity sensitivity of the polyimide recoated grating was estimated to be in the order of 4.47 pm/%RH at room temperature.