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Throughout all this paper we are going to analyze one application of the optical beam deflection method (OBDM), the procedure for its development, as well as its ideal implementation to reach measurements of displacements that could be the most accurate and of the smaller scale possible, this condition is essential for the magnitude of the results to evaluate. We also give an application of the OBDM such as a fine particle densimeter principally in solids. This present work will analyze the laser beam deflection technique, the procedure to apply, as well as its ideal implementation in order to obtain measures of displacements that can sense to the most exact and the smaller possible scale, obtaining results from microns, micrometers and even, until nanometers. Our objectives that are considered in this investigation are two: the first one is to build a device based on this technique, make accurate measures on a very low scale, which could be reliable and in the order of scale of microns until nanometers. The second objective that we are searching is to obtain an alternative method for verify the values of density that some substances that are hard to get like titanium oxide.

Most of the investigations that exist about the interferometer of Sagnac in our days, are made through fiber optic, which has the great advantage of having a big area size in very little space wound in a nucleus. The first interferometers of Sagnac, were used for very big angular speeds measures, it didn't have the advances to carry out detections of small signs, because the measurements systems like photo-detectors, amplifiers, filters, etc. didn't have the capacity of the systems that now exist. That is one reason that our experiments are based on the electronic advances, to make detections of phase changes of until less than 0.1 nm with area of 0.025 m 2 . Besides we proposed changes in the original interferometer diagram, adding some elements that can help s to achieve a bigger sensibility, accuracy and reduction of noise. Another of the advantages of use an interferometer of Sagnac, is work directly with the beams that travel through it, because we can observe the behavior from the optic road to external physical effects, like angu lar velocity or speed and little movements. Finally the acquisition devises and the software were used for calculate the angular frequency of the sensor directly from the experiment and know the parameters of the movement. Keywords : Fiber optic gyroscope, Sagnac’s interferomete r, optic interference, electronic stage.