I once kept Praying Mantids in a vivarium for a year,including a very large,brown female from Ghana,purchased @ the annual coleopterist market @ Kempton Park Race Course.
Once I put it on a window ledge for close up photography.
I put a small green nymph Mantid,that was almost dead of a viral infection,three inches away from it.
For a long time nothing happened,& then the giant suddenly scampered away towards the sunlight @ the window glass,in terror! Then it very slowly crept back sideways,@ rightangles to the nymph,looking sideways with it's huge,globular eyes & raised arms,very menacing; when infront it grabbed the nymph's arms with it's front front,spiked clasping arms,& bit it's jaws out,then ate the head ,then ate it's front clasping arms,then the thorax - abdomen partly eaten,held in one arm like a hamburger,& then tossed away.
It seems their vision detects movement,so they could ambush one another;or adult Mantids might runaway from each other; but they can recognise a motionless insect & know what species it is.
I photographed it until the film ran out,just after it pounced.
Although we can see distance,focus & three dimensions perfectly well with one eye (we've only kept two eyes to retain some sideways vision),perhaps the Mantid does need two (compound) eyes for it to have binocular vision?