Conoscopic interference pattern

This page is about the geology/optical mineralogy term. For general information about interference, see Interference (wave propagation) or Interference patterns.

A conoscopic interference pattern or interference figure is a pattern of birefringent colours crossed by dark bands (or isogyres), which can be produced using a geological petrographic microscope for the purposes of mineral identification and investigation of mineral optical and chemical properties. The figures are produced by optical interference when diverging light rays travel through a optically non-isotropic substance - that is, one in which the substance's refractive index varies in different directions within it. The figure can be thought of as a "map" of how the birefringence of a mineral would vary with viewing angle away from perpendicular to the slide, where the central colour is the birefringence seen looking straight down, and the colours further from the centre equivalent to viewing the mineral at ever increasing angles from perpendicular. The dark bands correspond to positions where optical extinction (apparent isotropy) would be seen. In other words, the interference figure presents all possible birefringence colours for the mineral at once.

Viewing the interference figure is a foolproof way to determine if a mineral is optically uniaxial or biaxial. If the figure is aligned correctly, use of a sensitive tint plate in conjunction with the microscope allows the user to determine mineral optic sign and optic angle.

Creation of a figure

In optical mineralogy, a petrographic microscope and cross-polarised light are often used to view the interference pattern. The thin section containing the mineral to be investigated is placed on the microscope stage, above one linear polariser, but with a second (the analyser) between the objective lens and the eyepiece. The microscope's condenser is brought up close underneath the specimen to produce a wide divergence of polarised rays through a small point, and light intensity increased as much as possible (e.g., turning up the bulb and opening the diaphragm). A high power objective lens is typically used. This both maximises the solid angle subtended by the lens, and hence the angular variation of the light intercepted, and also increases the likelihood that only a single crystal will be viewed at any given time.

To view the figure, the light rays leaving the microscope must emerge in parallel. This is typically achieved either by pulling out the eyepiece altogether (if possible), or by placing a Bertrand lens (Emile Bertrand, 1878) between the objective lens and the eyepiece.

Other techniques may also be used to observe the interference pattern.

Any crystal section can in principle produce an interference pattern. However, in practice, only a few different crystallographic orientations are both 1. convenient to identify to allow a figure to be produced, and 2. able to produce reliable information about crystal properties. Typically, the most useful and easily obtainable orientation is one looking down the optic axis of a crystal section, which yields a figure referred to as an optic axis figure (see below). Such crystal orientations are findable in thin section by looking for slices through minerals which are not isotropic but that nevertheless appear uniformly black or very dark grey under normal cross-polarised light at all stage angles (i.e., are "extinct"). If you are far from looking down an optic axis, a flash figure may be seen - a higher order birefringence colour, interrupted four times as the stage is rotated through 360 degrees by "flashes" of black which sweep across the field of view.

Characteristic figures of uniaxial and biaxial minerals

Sketches of uniaxial interference figures, viewed along the optic axis of each mineral. The colours approximate birefringence colours which might be seen if this were a mineral with second order maximum birefringence.The dark "maltese cross" pattern is characteristic of uniaxial minerals, and will not vary as the microscope stage is turned. Also shown are schematics of the shape of a cross section through the mineral's optical indicatrix (recording its refractive index in 3D) that would be seen at each position. The elongated direction could be distinguished by adding a sensitive tint plate to the microscope, letting the user discriminate between "uniaxial positive" (left) and "uniaxial negative" (right) minerals.

An interference figure produced looking straight down or close to the optic axis of a uniaxial mineral will show a characteristic 'Maltese' cross shape to its isogyres. If you are looking perfectly down the optic axis, the pattern will remain completely unchanging as the stage is rotated. However, if the viewing angle is slightly away from the optic axis, the centre of the cross will revolve/orbit around the central point as the stage is rotated. However, the form of the cross will stay constant as it moves.

Interference figures for a biaxial mineral, viewed along one of its two optic axes. The curved shape of the dark arc (the "isogyre") is characteristic of biaxial minerals - though the degree of curvature will change as the microscope stage is rotated, and at some orientations the pattern will resemble the "maltese cross" pattern of a uniaxial mineral. The left hand image illustrates the figure alone; the grey patch at the centre indicates the low first order (grey) birefringence colours seen here (the order of the colours seen would in reality increase away from the center, but these colours are not shown). The two right hand figures show the effect of adding a sensitive tint plate to the setup, replacing the grey at the centre with second order blue and first yellow birefringence colours. The polarity of the yellow and blue reveals whether the mineral being viewed is optically "biaxial positive" (top) or "biaxial negative" (bottom), which can be a key property in identifying the mineral (or investigating its composition).

The optic axis figure of a biaxial mineral is more complex. It will typically show a saddle-shaped figure (with one isogyre thicker than the other, typically) that will often morph into two curved isogyres (called brushes) with rotation of the stage. The difference in these curved isogyres is known as the optic angle, or"2V". In minerals that have far-off-center optic axes, only one part of the above sequence may be seen. On either side of the saddle the interferences rings surround two eye like shapes called melanotopes. The closest bands are circles, but further out they become pear shaped with the narrow part pointing to the saddle. The larger bands surrounding the saddle and both melanotopes are figure 8 shaped. By combining interference pattern microscopy with use of a sensitive tint plate, the optic sign and optic angle can be determined together. This information can help both with mineral identification, and with interpreting the chemical composition of some minerals (for example, feldspars).

A Michel-Levy Chart is often used in conjunction with the interference pattern to determine useful information that aids in the identification of minerals.

References

• W.D. Nesse (1991). Introduction of Optical Mineralogy (2nd ed.).

• Albert Johannsen (1914). Manual of Petrographic Methods.