Presented here in this thesis is the project work performed for the Master of Science degree in Space Engineering from Luleå University of technology, Sweden. This project work was conducted at the Arecibo Observatory in Arecibo, Puerto Rico, where I, during 6 months, designed and built a Potassium (K) -vapor Faraday filter to make daytime lidar observations of the mesopause region (80-105 km altitude) in the atmosphere a reality. The K Doppler-resonance lidar at the Arecibo Observatory is used to probe the temperature structure of the mesopause region. The climatology of this region is of vital importance in the understanding of earth’s climate system. The effects of global change are expected to be reflected strongly in the mesopause region, where tropospheric global warming will cause substantial cooling. This thesis will talk more about the background for making lidar observations of the mesopause region and the need for extending this observation to, not just nighttime, but also to daytime by making a filter that blocks broadband background skylight and only lets the ultra-narrow band signal pass. The thesis will present and explain the physical effects applied in the filter, such as anomalous dispersion and absorption at resonance frequency, the Zeeman effect and Faraday rotation. The filter characteristics will be given and the function of the filter will be explained. A computer program to determine the filter parameters (magnetic field strength, operating temperature and K-vapor cell length) is explained briefly and attached as an appendix, and the design and integration of the filter will be shown. The design and construction is based on a magnetic field strength of 1.3 kG, a temperature of 114 degrees C and a K-vapor cell length of 40 mm, which will give a full width half maximum (FWHM) of 5 pm for the filter. This is wide enough for a 99% transmission (for already polarized incident light and without reflection in the optical surfaces in the filter) of the three frequencies used in the observations.