that is accurately reproducible and which corrects for smile to within two microns or less uniform bending of the cylinder lens is achieved by letting the cylinder lens 20 sag under its own weight when a cylinder lens 20 is laid across the posts 26 of cylinder lens holder 25 shown schematically in fig5 the free ends 22 sag causing a bend in the cylinder lens 20 the bend shown is exaggerated for purposes of illustration for small bends the deflection of a cylinder is given by the following formula coordinates associated with sag in the cylinder lens are shown in fig5 and 7 equ1 where z a height of the bend above the x axis calculations for the bend as a function of l and d were performed by using the above equation for a 150 micron diameter cylinder lens with a density of 2 2 grams per cubic centimeter and a young 39 s modulus of 10 000 000 psi fig8 shows a graph of the cylinder lens bend for a value of d 1 cm and value of l from 3 to 8 cm bend values from the center of the cylinder lens to the end of the cylinder lens of 1 micron to 12 microns across the 1 0 cm length of the cylinder lens are easily achieved fig9 shows a graph of the cylinder lens bend for a value of d 2 cm and value of l from 2 to 7 cm by.