A conoscopic interference pattern or interference figure is a pattern of
birefringent
Birefringence is the optics, optical property of a material having a refractive index that depends on the Polarization (waves), polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or ...
colours crossed by dark bands (or ''isogyres''), which can be produced using a
geological
Geology () is a branch of natural science concerned with Earth and other astronomical objects, the features or rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Eart ...
petrographic microscope
A petrographic microscope is a type of optical microscope used in petrology and optical mineralogy to identify rocks and minerals in thin sections. The microscope is used in optical mineralogy and petrography, a branch of petrology which ...
for the purposes of
mineral
In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. ( ...
identification and investigation of
mineral optical and chemical properties. The figures are produced by
optical interference
In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
when diverging light rays travel through an optically non-isotropic substance - that is, one in which the substance's
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
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
Slide or Slides may refer to:
Places
* Slide, California, former name of Fortuna, California
Arts, entertainment, and media Music Albums
* ''Slide'' (Lisa Germano album), 1998
* ''Slide'' (George Clanton album), 2018
*''Slide'', by Patrick Glees ...
, 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
In geology and mineralogy, a mineral or mineral species is, broadly speaking, a solid chemical compound with a fairly well-defined chemical composition and a specific crystal structure that occurs naturally in pure form.John P. Rafferty, ed. ( ...
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
Optical mineralogy is the study of minerals and rocks by measuring their optical properties. Most commonly, rock and mineral samples are prepared as thin sections or grain mounts for study in the laboratory with a petrographic microscope. Optic ...
, a
petrographic microscope
A petrographic microscope is a type of optical microscope used in petrology and optical mineralogy to identify rocks and minerals in thin sections. The microscope is used in optical mineralogy and petrography, a branch of petrology which ...
and cross-
polarised light
Polarization (also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the ...
are often used to view the interference pattern. The
thin section
In optical mineralogy and petrography, a thin section (or petrographic thin section) is a thin slice of a rock or mineral sample, prepared in a laboratory, for use with a polarizing petrographic microscope, electron microscope and electron mic ...
containing the mineral to be investigated is placed on the microscope
stage
Stage or stages may refer to:
Acting
* Stage (theatre), a space for the performance of theatrical productions
* Theatre, a branch of the performing arts, often referred to as "the stage"
* ''The Stage'', a weekly British theatre newspaper
* Sta ...
, above one
linear polariser, but with a second (the "analyser") between the
objective lens
In optical engineering, the objective is the optical element that gathers light from the object being observed and Focus (optics), focuses the ray (optics), light rays to produce a real image. Objectives can be a single Lens (optics), lens or mirr ...
and the
eyepiece
An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is named because it is usually the lens that is closest to the eye when someone looks through the device. The ...
. 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 more or less in parallel. This is typically achieved either by pulling out the eyepiece altogether (if possible), or by placing a
Bertrand lens A phase telescope or Bertrand lens is an optical device used in aligning the various optical components of a light microscope. In particular it allows observation of the back focal plane of the objective lens and its conjugated focal planes. The pha ...
(Emile Bertrand, 1878) between the objective lens and the eyepiece.
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
An optical axis is a line along which there is some degree of rotational symmetry in an optics, optical system such as a camera lens, microscope or telescopic sight.
The optical axis is an imaginary line that defines the path along which light ...
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
Extinction is the termination of a kind of organism or of a group of kinds (taxon), usually a species. The moment of extinction is generally considered to be the death of the last individual of the species, although the capacity to breed and ...
"). 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
![Uniaxial interference figures](https://upload.wikimedia.org/wikipedia/commons/5/5a/Uniaxial_interference_figures.jpg)
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. The form of the cross will stay constant as it moves.
The optic axis figure of a biaxial mineral is more complex. One or two curved isogyres (sometimes called "brushes") will be visible, one of which will have its point of maximum curvature perfectly centred. (The figure shows an example with a single isogyre visible.) If two isogyres are visible, they will be positioned back-to-back. Rotating the stage will cause the isogyres to move and change shape strikingly - moving from a position where the isogyres curve smoothly and are widely separated at their closest point, then gradually becoming more tightly curved/squarer at their midpoints as they approach each other (a second isogyre appearing from out of the field of view if it was absent before), then merging to form a maltese cross pattern very much like that of a uniaxial mineral. Continuing to rotate the stage will cause the isogyres to separate again - but into the opposite quadrants to where they were previously - then meet again, then separate again into their original quadrants, and so on. The isogyres will touch each other four times in one 360 degree revolution, with each time corresponding to one of the
extinction position
Extinction is a term used in optical mineralogy and petrology, which describes when cross-polarized light dims, as viewed through a thin section of a mineral in a petrographic microscope. Isotropic minerals, opaque (metallic) minerals, and amo ...
s seen in normal cross polarised light.
The maximum separation between isogyres occurs when the slide is rotated exactly 45 degrees from one of the orientations where the isogyres come together. The point where the isogyres is most tightly curved represents the position of each of the two optic axes present for a biaxial mineral, and thus the maximum separation between the two curves is diagnostic of the angle between the two optic axes for the mineral. This angle is called the optic angle and often notated as "2V". In some cases, knowing the optic angle can be a useful diagnostic tool to discriminate between two minerals which otherwise look very similar. In other cases, 2V varies with chemical composition in a known way for a given mineral, and its measured value can be used to estimate ratios between elements in the
crystal structure
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystal, crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric pat ...
- for example, Fe/Mg in
olivine
The mineral olivine () is a magnesium iron silicate with the chemical formula . It is a type of nesosilicate or orthosilicate. The primary component of the Earth's upper mantle, it is a common mineral in Earth's subsurface, but weathers quickl ...
s. However, in these cases it becomes important to also be sure of the ''optic sign'' of the mineral (essentially, this tells you how the optic angle is orientated with respect to the whole
optical indicatrix In crystal optics, the index ellipsoid (also known as the ''optical indicatrix'' or sometimes as the ''dielectric ellipsoid'') is a geometric construction which concisely represents the refractive indices and associated polariz ...
describing the refractive indices of the mineral in 3D). The optic sign and optic angle can be determined together by combining interference pattern microscopy with use of a
sensitive tint plate.
On either side of the "saddle" formed by the isogyres, birefringent rings of colour run concentrically around 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.
A
Michel-Levy Chart
Polarized light microscopy can mean any of a number of optical microscopy techniques involving polarized light. Simple techniques include illumination of the sample with polarized light. Directly transmitted light can, optionally, be blocked with ...
is often used in conjunction with the interference pattern to determine useful information that aids in the identification of minerals.
See also
*
Wave interference
In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
References
*
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{{DEFAULTSORT:Conoscopic Interference Pattern
Optical mineralogy
Interference