With reversed sign?

Should " with reversed sign" be "as reversed sign"? Because the reversed sign leads the moths/insects home".

Context:

here's one possibility, which will serve to make the point.
Artificial light is a recent arrival on the night scene. Until
recently, the only night lights on view were the moon and the stars.
They are at optical infinity, so rays coming from them are parallel.
This fits them for use as compasses. Insects are known to use
celestial objects such as the sun and the moon to steer accurately in
a straight line, and they can use the same compass, with reversed
sign, for returning home after a foray. The insect nervous system is
adept at setting up a temporary rule of thumb of this kind: 'Steer a
course such that the light rays hit your eye at an angle of 30
degrees.' Since insects have compound eyes (with straight tubes or
light guides radiating out from the centre of the eye like the spines
of a hedgehog), this might amount in practice to something as
simple as keeping the light in one particular tube or ommatidium.