The cosmological lens equation in a universe with non zero cosmological   constant
  We derive and solve exactly the Dyer-Roeder equation in a Friedman-Robertson-Walker cosmological model with non zero cosmological constant. To take into account non homogeneous distribution of matter we use the phenomenological clumpiness parameter. We propose also a general form of an approximate solution which is simple enough to be useful in practical applications and sufficiently accurate in the interesting range of redshifts. 
M. Demianski (Institute for Theoretical Physics, University of   Warsaw), R. de Ritis (INFN and Dipartimento di Scienze Fisi...