along the length of the optical element of the pem will follow the form of a sine function 0 to u03c0 with the maximum at the center of the optical element considering for example a fused silica 50 khz pem fig3 illustrates that there are only minor differences between the experimental and theoretical data plotted in that figure with a maximum difference of only 0 004 this very small difference between the experimental and theoretical data illustrates how closely the pem operates to the simplified model of a resonating bar along the width of the optical element length gt width gt thickness the pem would ideally have unity retardation efficiency however the measured pem retardation efficiency along the width of the optical element of the same pem of fig3 is shown in fig4 the retardation efficiency drops about 5 from the center to the edges of the optical element of the pem the peak retardation for a typical symmetrical type pem hinds instruments pem 90 model ii fs42 as diagrammed in fig2 optical material fused silica frequency 42 khz is plotted in fig5 fig5 displays retardation in the units of nanometers u201c nm u201d and the upper limit of the retardation is rounded up to an integer the values of the normalized retardation efficiency are dimensionless and they have a range of 0 to 1 as seen the peak retardation distribution is highly symmetrical with near circular symmetry in the central darkest portion of the optical element examining the middle row of the.