### 7.4 Astigmatic beams: the tangential and sagittal plane

If the interferometer is confined to a plane (here the x-z plane), it is convenient to use projections of the
three-dimensional description into two planes [46]: the tangential plane, defined as the x-z plane and the
sagittal plane as given by y and z.
The beam parameters can then be split into two respective parameters: , for the sagittal
plane and and for the tangential plane so that the Hermite–Gauss modes can be written as

Beams with different beam waist parameters for the sagittal and tangential plane are astigmatic.
Remember that these Hermite–Gauss modes form a base system. This means one can use the separation
into sagittal and tangential planes even if the actual optical system does not show this special type of
symmetry. This separation is very useful in simplifying the mathematics. In the following, the term beam
parameter generally refers to a simple case where and but all the results can also
be applied directly to a pair of parameters.