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.
When the polarizer and analyser are parallel or crossed, the pattern is the same as with inactive plates, with the exception that the brushes do not extend to the centre of the field; but as the analyser is rotated a small cross begins to appear at the centre of the field, while the rings change their form and become nearly squares with rounded corners, when the planes of polarization and analysation are at 45°.
Poynting, is before analysation to impress unequal rotations upon the plane of polarization of the two parts of the field, either by means of an active medium, or by oblique transmission through glass plates.
If then a stream of polarized white light traverse the biquartz, it is possible by an analyser to cut off the mean yellow light from each half of the field, and the whole will then have the sensitive tint; but a small change in the plane of analysation will give the one half a red and the other half a blue tone.
In order to correct this, the light after analysation is passed through another plate of quartz and then the sensitive tint may be more or less restored by cutting off some colour, the same for the whole field, by a Nicol's prism placed in the eyepiece of the telescope.