The work aims to test the stability of the removal function during ion beam polishing on the surface of fused silica components. By controlling the ion beam to scan along the Faraday cup, the ion beam density information was detected. Based on the sputtering theory, a mathematical model of the removal function was established. Experimental research was carried out on the ion beam density and the removal function information, and the relationship between them was obtained by comparing and analyzing the experimental results, and a method for calculating the removal function information was obtained based on the Faraday scan results. Using this method, the characteristic quantity of removal function in ion beam etching process was obtained, the fluctuation of the characteristic quantity of the removal function over time was analyzed to judge the stability of the removal function, and the ion beam polishing experiment was carried out on the surface of the fused silica element. The ion source was operated for a long time under the energy of 1 keV ion beam, and the removal function during the experiment was calculated by the above method. Through calculation, the peak removal rate (Pmax), volume removal rate (V) and full width at half maximum (FWHM) of the removal function during the ion beam polishing process were all less than 3% in 8 hours. Combining the ion beam polishing experiment, the Φ100 mm fused silica optical element was polished, the PV value of the polished back shape dropped from 0.78λ to 0.16λ, and the RMS value dropped from 72.39 nm to 16.64 nm. The removal function is monitored for a long time by Faraday scanning, and the characteristic parameters of the removal function have good stability in the long time experiment. The surface parameters of fused quartz element are processed by ion beam, and the parameters meet the requirements of optical ultra-precision machining.