INTRODUCTION

Compensators consist of thin-sections of minerals (e.g., quartz, calcite, gypsum/selenite, mica, etc.), or polymer film equivalents, whose thickness and optical orientation are carefully controlled so as to provide known values of retardation and known direction of high and low refractive indices.  When introduced into the light path of a polarizing microscope, these known retardation values and refractive index directions are superimposed on an unknown anisotropic specimen and, by noting the resultant effects (addition or subtraction of retardation, etc.), the microscopist obtains valuable identifying characteristics about the sample.

Compensators, such as the first-order red (530 nm; 550 nm; also known as the “gypsum plate,” or “selenite plate,” or “sensitive violet”), the quarter-wave plate (λ/4; ~137 nm), and the quartz wedge (3-7 orders; 1-4λ), are standard accessories used with polarizing microscopes for determining an anisotropic specimen’s optic sign (sign of double refraction), sign of elongation (location of high and low refractive indices in an elongated specimen), and characteristic birefringence.  Birefringence determination requires that one obtain the sample thickness and retardation color (B = r/t 1000).  For the majority of samples encountered by industrial microscopists, an estimate of the thickness obtained through use of a calibrated eyepiece micrometer, and an estimate of the retardation color obtained by reference to a Michel-Lévy Interference Color Chart (1), are usually sufficient, along with a couple of other characteristics, for rapid sample identification.  For the purposes of this article, it will be assumed that the reader is generally familiar with these procedures.

Problems in obtaining the birefringence, and, therefore, the identification, arise especially when the retardation colors of the sample are very low (shades of gray in the lower part of the first order) or very high (100-200+ orders).  These very low or very high retardation colors may be due to the sample being either very thick or very thin, or having very low or very high characteristic birefringence, or both.

click image to enlarge (521K) Figure 1

Look at Figure 1, for example; this is a 30 µm thick rock thin-section as viewed between crossed polarizers using a 4X objective for a visual magnification of 40X.  The individual mineral grains that make up this rock section are all lying at different orientations, and showing many shades of white and gray.  When I view this figure filling up my monitor screen, I can go from grain to grain and name off colors: snow white, off- white, bone, ivory, cream, steel gray, bluish gray, greenish gray, light gray, medium gray, dark gray, charcoal, blue-green gray, olive gray, slate gray, gun metal, mushroom, etc.  What I need, however, are not these often-creative verbal descriptions, but a value in nanometers, that the color I am looking at corresponds to; this is why I prefer a Michel-Lévy Interference Color Chart with colors printed as accurately as possible, but with the names of the colors as well.  Only with an accurate determination of interference color can I obtain the characteristic birefringence that I need to identify the mineral (and, of course, the sample need not be a mineral; it could be anything).  A little later, you will see from experiments I made with experienced microscopists that their estimates of retardation are not very accurate.  The accurate measurement of very low or very high values of retardation is the realm of the specialized compensators.  For very low values of retardation, there are the Brace and Brace-Köhler compensators which measure in the range 0-1/10λ, 0-1/20λ, and 0-1/30λ; many bio-medical specimens fall in this category.  The Berek compensators are made for measuring larger ranges of retardation: 0-3λ, 0-20λ.  The Ehringhaus compensators are used for measuring very large values of retardation: 170-200+λ; these are useful for highly birefringent samples, which also may be thick.

The Berek compensator is particularly well-suited for measuring retardations from zero up to many orders.  It is based on an experimental compensator by W. Nikitin [Drehbarer Compensator fϋr Mikroskope.  Zeitschr. f. Kryst., XLVII (1910), 378-379], in which a crystal plate (quartz in the early version made by Fuess) cut perpendicular to the c-axis is introduced above the objective.  In its starting position – pointer set at “0” – the crystal surface is normal to the instrument axis, and the field of view will be dark between crossed polarizers, because the uniaxial indicatrix in this position exhibits a circular index ellipse (retardation 0).  The crystal plate can be tilted about the direction of vibration of the ordinary ray, so that the circular section changes into an index ellipse in which the ratio of major to minor axis increases with the tilt angle; the effective thickness is thereby increased.  As with Sénarmont compensation, the anisotropic specimen is oriented in a subtractive position so that at some tilt angle extinction occurs, provided the compensator’s range is sufficient for the sample.  Berek made mechanical refinements to this compensator so that the tilt angle could be read to 1/10 of a degree (1/20 degree in the current version); and he further developed the equations and tables to convert tilt angles into retardation values.  The resolution of the readout of a current Leica/Leitz 5-order Berek compensator with magnesium fluoride crystal plate is equal to 0.2nm at a retardation of 3nm; 0.5nm at a retardation of 25nm; and 2nm at a retardation of 556nm.  Many microscopists find the Berek compensator more useful than the Sénarmont, provided they can justify the additional expense.  The Sénarmont does have higher resolution, but it is only realized by averaging over several measurements. Over the last 170 years or so, there have been about a hundred different kinds of compensators described and made, but only the simple fixed ones and a couple of Bereks and Brace-Köhlers have been available new in the last two or three decades.  You can read about many of these specialized compensators (Babinet, Bravais, Soleil, Biot, Savart, Klein, Traube, Sommerfeldt, Wright, Nikitin, Evans, Von Fedorow, Von Chrustschoff, etc.) in Johannsen’s Manual of Petrographic Methods (2).

7/5/2003 (revised 2/18/2004)

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