By use of evaporation conditions adjusted for the deposition of hafnium dioxide (HfO2), a series of films ranging in thickness from 50 to 10000 nm was prepared by using an electron beam gun inside an evacuated coating chamber of pressure 1×10-5 mbar. The films were obtained on optical glass substrate by using oxygen with a backfill pressure of 2.4×10-4 mbar during the deposition processes. The optical constants of the films were computed in the spectral wavelength region (350-2000 nm) from the transmission, reflection and thickness measurements. A computer program was created to determine two optical parameters n and k of the films, and this was achieved by entering the practical results into the computer program, which solved a series of equations for each wavelength. The effects created by changing various evaporation conditions (thickness, substrate temperature and evaporation rate) were studied in the spectral wavelength range, and the optimum values of the various conditions were obtained while achieving the best optical performance. According to the investigations of the HfO2 material, two applications of the anti-reflection (AR) multi-layer coatings were achieved in two different spectral wavelength ranges. The first application was measured in the visible and near infra-red (VIS/NIR) range from 500 nm to 850 nm deposited on the glass substrate. The second application was measured in the infrared (IR) range from 7500 nm to 11500 nm deposited on germanium substrate. Computer modelling for designing the optical multi-layer system has been presented. The theoretical formulation and experimental results with the same specification were achieved. The correlation between the theoretical and the experimental results reveals a close agreement that offers a convenient method for predicting and controlling the multi-layer coating. By continuous measurement of the optical and mechanical (durability) performances of the coating process, high-quality films were produced in the manufacture of various optical devices.