In this work, we report simple optical design of a high speed and high spectral resolution spectrometer based on the first order calculation. The spectrometer was design and optimized for high speed detection of spectral interference signal to be used as a detection unit of our developed Frequency Domain Optical Coherence Tomography (FD-OCT). We then detailed the hardware implementation of both the spectrometer and the FD-OCT system in our laboratory at Suranaree University of Technology, Thailand, by utilizing only off-the-shelf optical components. The spectrometer is capable of capturing of the spectral interference fringes at up to the camera limit of 130,000 spectra per second, enabling cross-sectional microscopic imaging of biological sample of more than 100 frames per second (for a 1000 depth scans per frame). In addition, we reported several simple yet robust techniques for characterization of the system performance in the context of FD-OCT 3D imaging, such as an effective lateral resolution, depth scale calibration, and depth penetration limit. The development of this high speed and high resolution spectrometer is part of our ultimate goal to develop a prototype of a research-grade FD-OCT system that provides better imaging speed and resolution in comparing to available commercial OCT systems at relatively lower cost. The design of low-cost, high performance FD-OCT system would make the technology widely accessible to other researchers in the field of biomedical research and related areas in Thailand in the next few years.