## Signal and image frequency axes in the observatory frame

The RF tuning frequency, , can be choosen in either band. This band is called the signal band. The other band is then called the image band. The associated RF frequencies are written and . We obtain

(15)
and
(16)
The sign of the product is arbitrary. Indeed, it only defines how the brightnesses are ordered in memory, i.e., whether the frequency increases or decreases when increases. It thus is simpler to assume that this product is always positive. This implies that the signal frequency increases and the image frequency decreases when increases. In other words, we adopt the convention that the signal brightnesses are ordered by increasing frequency when increases, i.e., the product is always positive.

As the absolute value of is 1, we will greatly simplify the equations by replacing with with the convention that in Eqs and . We can then rewrite them as

(17)
and
(18)
with
(19)