  We introduce an algebraic formula producing infinitely many exact solutions
of the constant astigmatism equation $ z_{yy} + ({1}/{z})_{xx} + 2 = 0 $ from a
given seed. A construction of corresponding surfaces of constant astigmatism is
then a matter of routine. As a special case, we consider multisoliton solutions
of the constant astigmatism equation defined as counterparts of famous
multisoliton solutions of the sine-Gordon equation. A few particular examples
are surveyed as well.
