The dark halo substructures predicted by current cold dark matter simulations may in principle be detectable through strong-lensing image splitting of quasars on small angular scales ( 0.01 arcseconds or below ) .
Here , we estimate the overall probabilities for lensing by substructures in a host halo closely aligned to the line of sight to a background quasar .
Under the assumption that the quasar can be approximated as a point source , the optical depth for strong gravitational lensing by subhalos typically turns out to be very small ( \tau < 0.01 ) , contrary to previous claims .
We therefore conclude that it is currently not feasible to use this strategy to put the simulation predictions for the dark matter subhalo population to the test .
However , if one assumes the source to be spatially extended , as is the case for a quasar observed at radio wavelengths , there is a reasonable probability for witnessing substructure lensing effects even at rather large projected distances from the host galaxy , provided that the angular resolution is sufficient .
While multiply-imaged , radio-loud quasars would be the best targets for unambiguously detecting dark matter subhalos , even singly-imaged radio quasars might be useful for setting upper limits on the abundance and central surface mass density of subhalos .