This paper presents the design, construction and testing of grounded Frequency Selective Surfaces (FSSs) used to eliminate speckle, produced by coherent mm-wave sources. The reflection amplitude and phase of two dimensional periodic arrays of slot FSS printed on a grounded Roger 4003C substrate are investigated. It is shown that the reflection phase variation as a function of slot length is controlled by the difference in the central resonance frequencies of different FSS arrays. Simulations and measurements results at W-band demonstrate that this parameter can be used to deduce the gradient and to improve the linearity of the reflection phase. The FSSs were simulated by Finite Integral Technique, fabricated with photolithography-etching technique and measured with MVNA.