This latter process is termed analysation, and an instrument is called a polarizer or an analyser according as it is used for the first or the second of these purposes.
When, however, the planes of polarization and analysation are parallel or crossed, the two pairs of principal lines of like polarization coincide, and the intensity is at all points in the former case not greater than, and in the latter case not less than, it was before the introduction of the plate.
With a crossed polarizer and analyser the rings are interrupted by a dark hyperbolic brush that cuts the plane of the optic axes at right angles, if this plane be at 45° to the planes of polarization and analysation - the so-called diagonal position - and that becomes a rectangular cross with its arms parallel and perpendicular to the plane of the optic axes when this plane coincides with the plane of primitive or final polarization - the normal position.
These attain their maximum visibility when the plane of analysation is at 45° to these planes, and vanish when the plane of polarization is parallel to either of the principal planes.
According to Fresnel's explanation the light in each of the interfering streams consists of two trains of waves that are circularly polarized in opposite direction and have a relative retardation of phase, introduced by the passage through the quartz: the central fringes are then due to the similarly polarized waves; the lateral systems are produced by the oppositely polarized streams, these on analysation being capable of interfering.