The purpose of the SCRIT project is to determine size and shape of short-lived and rarely-produced nuclei by elastic electron scattering, which is the best probe for the structure studies, for the first time. In traditional electron scattering, a solid target having an order of 1023 nuclei/cm^2 is normally used, which is not possible for short-lived and rarely-produced nuclei. In this project a Self Containing Radioactive Isotope Target scheme (SCRIT) is going to be employed. This innovative ion-trap method is shown to be a way to make measurements with a very small amount of nuclei, an order of only 106 nuclei. In order to determine the absolute cross section for elastic electron scattering for structure study, the simulates measurement of the bremsstrahlung from the trapped nuclei is required. Since the bremsstrahlung cross section for a nucleus of the atomic number Z is well know, the precise measurement of the bremsstrahlung provides the luminosity. My theme in this SCRIT project was a construction of a bremsstrahlung luminosity monitor. It consists of a position monitor for measuring the spatial distribution of bremsstrahlung and a Pb-glass Cerenkov detector for energy measurement. My efforts have been mainly devoted to the construction of a position monitor system using fiber scintillators. The construction of the position monitor was divided into five parts; detector construction, support construction, trigger detector construction, software programming, software testing and detector tests. The position monitor consists of two sets of fiber scintillation detectors. Each of them uses 16 fibers, Bicron BCF-10 with a cross section of 2x2mm^2, optically coupled to a multi-anode photomultiplier, (Hamamatsu H6568-10). The position monitor can measure the XY distribution of bremsstrahlung. Strictly speaking, the fiber detector detects not bremsstrahlung directly but electrons and/or positrons by pair creation of bremsstrahlung in a materials. The data acquisition system has been programmed in NI LabVIEW. The software is an advanced X/Y-coordinate counting system, which can additionally preform functions as save data to file and 3D-plot to determine the spreading of the bremsstrahlung luminosity. The results can be saved and transferred online to a server so that is possible to access the data from anywhere. The system has been tested using beta rays from 90Sr source. The results of the test shown that the detectors can detect minimum ionizing particle, i.e. electrons and positrons. The detector and software testings shows that the system is ready to use for luminosity measurements at SCRIT experiment. This system I constructed surely provides a new and useful information for the SCRIT experiments. / SCRIT Project