This work presents a procedure for measuring displacements of tens micrometer, in one and two dimensions, based on the correlation between two speckle patterns. For this purpose, two objective speckle patterns arerecorded by a digital camera -one before and one after the object has been moved- and placed in the input plane of nonlinear joint transform correlator. Nonlinear transformation of the joint power spectrum allows a sharper correlation peak and a high signal to noise ratio. The autocorrelation peak coordinates of the first pattern are set as a reference for measuring shifts of the successive cross-correlation peak. One criterion for reliable measure is proposed. Results related with different distances sample-sensor and illuminating wavelengths at 632.8 nm and 543.5 nm are presented.