Refractive index determinationtechnique with

Introduction

The general term "focal masking" is applied to thosetechniques of microscope illumination in which selectedwavelengths of the image-forming light rays are removedor modified by insertion of a pair of conjugate masks, onein the focal plane of the objective and the other in thefocal plane of the substage condensing system. Includedhere are such well known techniques as dark-field micros-copy and phase-contrast microscopy. The chief formdealt with in this paper, called central focal masking, hasbeen used with success for two decades in laboratories ofthe U.S. Geological Survey for routine mineral identifica-tion by the immersion method.

The central focal masking technique as applied toimmersion methods is one variant of the "focal screen-ing" techniques of Cherkasov (1955a, 1955b, 1957, 1969;see also Wilcox, 1962; Feklichev,1963; Hartshorne andStuart, 1970, p.311 ff). The same technique is termed"dispersion staining" by Brown and McCrone (1963; alsoBrown et al., 1963; McCrone et al., 1978). All thesetechniques have the advantage over conventional Beckeline techniques in that no manipulation of focus is re-quired. Rather, the difference between refractive index of

Rnv E. Wrlcox

U.S. Geological SurveyDenver, Colorado 80225

Abstract

The central focal masking ("dispersion staining") technique is convenient and effectivefor determining the refractive index of a microfragment by the immersion method and fordistinguishing between minerals in an immersion mount. For most microscopes the onlymodification needed is the installation of a small opaque dot at or near the focal point of themedium power objective. White light illumination, stopped down to the angular aperture ofthe opaque dot, produces a dark field on which the image of the fragment is outlined indiagnostic dispersion color.

Precision of refractive index determination by this technique, about :0.ff)l underroutine controlled conditions, is similar to that of the conventional Becke line techniqueusing monochromatic yellow illumination. However, it has the advantages that (l) near thematch the direction and approximate amount of mismatch may be inferred from thedispersion color of the image alone without the need for manipulation of the focus, (2) at thematch the microfragment is clearly visible, and (3) results are obtainable even in thepresence of an appreciable amount of inclusions or specific absorption (body color) in thefragment.

Besides providing a useful means for refractive index determination, focal maskingpermits rapid distinction among constituents in a mixture and an estimation of theirproportions. As a teaching aid the focal masking technique provides a convincingdemonstration of the manner of image formation and resolution in the microscope.

American Mineralogist, lolume 68, pages 1226-1236, 1983

using the central focal maskingdispersion colors

fragment and liquid is shown at once for all grains in thefield of view by the dispersion colors of their images. Thetechnique is useful further in revealing variations ofrefractive index within grains, the extent of which may betranslated into terms of zoning of chemical composition.

In the immersion method by focal masking, advantageis taken of the fact that the wavelength dispersions ofrefractive index of the common organic immersion liquidsare appreciably greater than those of most inorganicsolids of similar index. A typical example is illustratedgraphically on Figure I for a glass that, at a giventemperature, matches an immersion liquid for the orange-yellow light of the standard Fraunhofer DJine wavelength(589.3 nm) at refractive index 1.534. It is seen that forshorter wavelengths (the greens, blues, and violets of thespectrum) the refractive index of the liquid is higher, andfor longer wavelengths (the oranges and reds) it is lowerthan that of the glass. It may be noted also on Figure Ithat the higher liquid (no : 1.538) matches this glass atwavelength near 650 nm, whereas the lower liquid (no =1.530) matches near 520 nm, and that the match for liquidno = 1.522 falls far outside the visible spectrum.

Figure 2 represents the essential behavior of axiallyparallel rays of white light passing through a fragment

0003-004)u83/ | | t2-1226$02.00 1226

WAVELENGTH lnm)

Fig. 1. Dispersion curves (refractive index vs. wavelength) fora typical glass and immersion liquids at a given temperature.

immersed in such a "matching" liquid. Because upperand lower surfaces in the central part ofthe fragment arelargely at right angles to the incident light, rays of allwavelengths pass without deviation. Near the edge of thefragment, however, the solid/liquid interface is steeplyinclined, with the result that the rays of shorter wave-length (the blue and green colors, for which the index ofliquid is higher than that ofthe glass) are refracted towardthe normal to the interface. In contrast, those of longerwavelength (orange and red) are refracted away from thenormal. (Note that here the sequence of colors of theresulting spectrum is the reverse of that in the commonlyillustrated prism dispersion of white light at a solidlairinterface, in which case the dispersion of the solid is thegreater.) The yellow rays of wavelength near the D-line,pass through without significant deviation, because therefractive indices of solid and liquid are essentiallymatched for those wavelengths. Those light rays that donot pass through the fragment are not refracted of courseand continue on to the objective without change indirection.

All light rays that were undeviated in the immersionmount are gathered by the objective and made to passthrough the focal point, whereas the deviated rays pass tothe side of the focal point. In central focal masking, anopaque dot at the focal point (Fig. 3), blocks the undeviat-ed rays to produce a dark field. (Specific directions formodification of the microscope are given in Appendix l.)Superposed on this dark field is a sharp image formed bythe rays that are deviated by the edges and surfaceirregularities of the fragment and passed to the side of theopaque mask at the focal point. Because the rays ofcolor(wavelength) ofthe match are blocked by the opaque dot,the image of the fragment is seen in the combined color ofthe remaining parts of the spectrum-essentially thecomplement of the wavelength band of the match. Thus,

l2n

Fig. 2. Spectrum formed by a beam of white light at an inclinedsolid/liquid interface. Refractive indices of solid and liquid matchin the region of the yellow wavelengths. (Dashed line is normal tothe interface.)

for the refractive indices that match for the orange-yellowwavelengths near the D-line, as in Figure 3, the resultingimage is a diagnostic deep violet color.

Other masking configurations in the conjugate focalplanes, useful in certain situations, are described in

IMAGE PLANE

DOT MASK ATFOCAL POINT

OBJECTIVE

WHITE LIGHT

Fig. 3. Diagramatic representation of the formation of thecolored image of an immersed fragment using central focalmasking. Refractive indices of fragment and liquid match in theregion of the yellow wavelengths, rays of which are blocked bythe dot mask at the focal point of the objective lens.

WILCOX : REFRACTIVE IN DEX DETERMINATION

Xu

zU

Fo

Eu

Y(J

5dt

\ j\ i \

o

r

\ |t \

- : 9\

r22E W I LC OX : REFRACTIV E I N DEX DETERMI NATI ON

1

Approx-imate

matching

(nm)

660

625

600

589

575

w

505

480

465

2 3 4

CENTRAL MASKING(dark field)

at focus

raising focus

movrng In moving out

brightgreenish

blue

brightgreenish

blue

sky blue sky blue

bluefaintdarkreo

greenishblue

deep

violet

weakreo

strongblue

purple red blue

reddishpurpre

orange-red

bluish-violet

orange-reo

orangeweakblue

violet

orange VellowweaKviolet

brightgold

brightgold

5

APERTURALMASKING

(bright field)

red

orangish-red

orange

orangish-vellow

yellow

green

bluishgreen

blue

violet

Fig. 4. Dispersion colors observed in focal masking, modifiedspectral composition of the illumination.

Appendix 2. These include apertural, unilateral, annular,and strip focal masking, the latter two especially wellsuited for refractive index determination of verv finegrained fragments requiring high magnifi cation.

Determination of refractive index

Isotropic substqnces

Fragments of an isotropic substance mounted in animmersion liquid and illuminated as described above willbe seen outlined on a dark field. If refractive indices offragments and liquid are far apart, the fragments appeardark with bright outlines. In such case the direction ofmismatch is revealed by the conventional Becke line test.Based on this test, successive immersion liquids arechosen until one is found in which the fragment outlinestake on a pellucid color, indicating the approach to amatch in index. With the fragments in focus, and remem-bering that a match is being sought for the index at thewavelength of the DJine (Fig. l), the following may beinferred: If the edges and surface irregularities of thefragments appear light-blue or blue-green, the refractiveindex of the fragments is slightly lower than the liquid; ifpurple, red, or orange, refractive index of the fragments

6 7 8 I

UNILATERAL MASKING

Gray field Dark field

One edgeOpposite

edoe One edgeOpposite

eoge

verydarkreo

palegleenish

azuredark

greenishazure

dark redgreenish

blue darkbrightazure

redlight

greenishblue

dark redgreenish

blue

orangish-red 9reen red bluish

green

reddish-orange

bluish-green

orangish-reo blue

orange blueorange-

reodarkblue

canaryyellow

darkblue

orangedarkblue-violet

yellowdarkblue-violet

vellowdarkviolet

brightyellow

darkviolet

brightyellow dark

1 0

Indexnp of

Sol id is :

Lowerthanl iquid

same asl iquid

Higherthan

l iquid

from Cherkasov (1957). Colors may vary somewhat depending on

is slightly higher; if deep violet, refractive index of thefragments is very close to a match with the liquid. Thecolors observed at focus in representative situations aredescribed in Figure 4, column 2 and serve as a generalguide. Because of the possible different connotations ofthese descriptors to different people, however, and be-cause of different spectral compositions of light sourcesofdifferent microscopes, each person should standardizehis or her own color judgment and microscope system,especially in the immediate vicinity of the match ofindices. For this a procedure is outlined in the section"Calibration of color perception" (Appendix 3).

As a further check on the degree of match, columns 3and 4 ofFigure 4 list the colors ofthe separate Becke linesthat are produced by slightly raising the focus. At theindex match for the D-line, for instance, a blue line movesoutward and a somewhat weaker red line moves inwardas the focus is raised.

Thus far it has been assumed that the observationshave been made with the immersion mount at or nearconstant temperature. At the match, if the temperature isnot that at which the liquid was calibrated, one must ofcourse make a correction, using the stated thermal coeffi-cient of the liquid. With the microscope equipped for

WILCOX : REFRACTIVE INDEX DETERMINATION 1229

Fig. 5. Interpolation on;luii'ulillu|nl'ret to refractive index pof anhydrite, bracketed by two immersion liquids of knowndispersive strength.

measured temperature variation, one may change thetemperature to achieve the final match of index, thenmake the appropriate correction to the nominal index ofthe liquid.

Anis otropic s ub s t anc e s

The procedure outlined in most textbooks for determin-ing the principal refractive indices, € and t.l of uniaxialsubstances and a, B, and Tofbiaxial substances, involvesthe use of random multiple grain mounts in a successionof liquids of different refractive indices (see Stoiber andMorse, 1972; Bloss, 196l). By observation of interferencefigures, it is possible in many mounts to find a fragmentclose to the correct orientation for a particular principalindex, which then may be compared to the liquid by focalmasking and the liquid for the next random grain mountchosen accordingly. The method, however, is time con-suming and requires experience, patience, and persever-ance as well as careful cross checking to obtain reliablevalues of principal refractive indices. Further, it may begreatly complicated and even misleading when the frag-mented sample contains two or more anisotropic mineralsof similar or overlapping optical properties, or when thefragmented sample comes from a chemically-zoned crys-tal belonging to an isomorphous mineral series.

For maximum definitive information gained with mini-mum time and effort, the spindle stage offers by far themost efective method for determination of the opticalproperties of an anisotropic material, because all princi-pal refractive indices as well as other diagnostic proper-ties may be obtained on a single fragment (Wilcox, 1959;Hartshorne and Stuart, 1970; Bloss and Light, 1973;Bloss, l98l). This at once eliminates the uncertainties andcomplexities of random grain mounts of a powderedsample composed of more than one substance or of arange of compositions. (A number of fragments, ofcourse, should be so examined to ascertain the range ofproperties or the presence of more than one substance.)Orientation of the fragment for each principal index iscarried out conoscopically by interference figures, where-

upon the illumination is converted to central focal mask-ing for determination of that principal refractive indexfollowing the procedure described above for isotropicfragments. Lacking favorable conditions for conoscopicorientation, the values of a, B, and 7of a biaxial fragmentcan be determined as maxima and minima of indexencountered along the two series of extinction positions(Wilcox 1959, p. 1282; Bloss, l98l), changing liquids asnecessary and using the criteria of dispersion colors.

Interpolation and extrapolation

In determining the refractive index of an unknown solidby mounting its fragments successively in liquids of aregularly graduated set of immersion liquids, one arrivesfinally either at the liquid that matches the solid, or at twoadjacent liquids that bracket the index ofthe solid. In thelatter case if the spacing of liquids in the set is small, forexample 0.002, one may interpolate the index of the soliddirectly with sufficient precision for routine work. If thespacing is appreciable, one may use a Hartmann net(Stoiber and Morse, 1974, p.74), on which the dispersioncurves of the liquids are drawn as straight lines inaccordance with the dispersion data for the liquids. Thisis illustrated by Figure 5 for the case of two adjacentliquids ofnp indices 1.570 and 1.580, having dispersion np- ns of 0.0190 and 0.0200, respectively. Judging fromdispersion colors (as listed in Fig. 4, column 2), the &index of the anhydrite fragment matches the 1.570 liquidat a wavelength about 500 nm, and the 1.580 liquid atabout 650 nm. The line between these respective points ofintersection with the liquid curves represents the disper-sion curve ofthe solid, and it intersects the wavelength ofthe DJine, (589.3 nm) at np = 1.577 .

Should the dispersion of the solid as well as that of theliquid be known already, as in dealing with a member of aknown solid solution series (plagioclase, olivine, certainglasses, etc.), an extrapolation to the refractive index ofthe solid for the standard D-line could be made from theresults of only one immersion mount, in which the solidhas been observed in a diagnostic clear dispersion color.Thus in the Hartmann net of Figure 6, a liquid nn : 1.540

WAVELENGTH (nml

Fig. 6. Extrapolation on the Hartmann net to refractive indexo of a plagioclase of known dispersive strength.

TPFi

I

i4

3z

Fo

E

1230 WI LC OX : REFRACTIV E I N DEX DETB.M I NATION

WAVE-LENGTH

al malchlnm I

J

, oo

, o

iUo=ul

F(J

ELUEzUozuJEuJtttJ-o

700

l ine650

600- l ine

0 O O t 0 O 2 0 u 3

D IFFERENCE lN D ISPERSION (n r - n6 )11q - ( n6 - nc l so l

Fig. 7. Observed dispersion colors for various combinations of refractive index difference and dispersion difference between liquidand immersed fragment (adopted from Schmidt and Heidermanns, 1958.) Colors may vary somewhat depending on spectralcomposition of the illumination.

and dispersion np - ns = 0.0164 matches the c-index of aplagioclase ofdispersion rr - hc : 0.0083 at wavelengthabout 520 nm, as inferred from the reddish-orange disper-sion color under central focal masking (Fig. 4, column 2).The solid's dispersion curve through this match pointintersects the D-line at 1.543, which may be taken then asthe a-index of the plagioclase.

Figure 7 relates index difference, dispersion difference,and observed color. For the previous example the disper-sion difference between solid and liquid, (np - nc)riq -(nF - nc)sot = 0.0081, may be projected vertically from0.fi)81 on the abscissa to intersect the inclined line for thematch at 520 nm, thence horizontally to read the indexdifference as (-) 0.003 on the ordinate scale.

Substituting in the expression

Index difference : op111q; - rtp(sol)- 0 . 0 0 3 : 1 . 5 4 0 - n D ( s o l l

then

np156n = 1.543

It is obvious that accuracy will be poorer the greaterthe distance of extrapolation to the D-line and the lesscertain the estimate of the wavelength of match.

Precision and limitations of the technique

For refractive index determination by the central focalmasking technique with calibrated immersion liquids atintervals of 0.fi)2, a precision of about -'-0.001 can beobtained when careful attention is paid to corrections fortemperatures above or below the temperature at whichthe immersion liquid was calibrated. This is similar to theprecision attainable on favorable material by the conven-tional Becke line ("central illumination") method usingmonochromatic sodium light. The precision with central

;':$s4

WI LCOX : REFRACTIV E IN DEX DETERM I N ATIO N

focal masking stands up well for less-than-ideal naturalsubstances. whereas that of the conventional Becke linemethod deteriorates in several common situations: forinstance, when abundant foreign inclusions are present inthe substance under investigation, edges of the fragmentdo not approach wedge- or lens-shape, or the mineral hasappreciable color or absorption. As compared to themethod of "Becke line colors" of Emmons and Gates(1948), the central focal masking method has somewhatgreater precision, probably because the diagnostic colorsare not diluted by the white light of the field and thereforeare more definite and easily recognized. (If the immersionliquid is itself highly colored, however, account must alsobe taken ofthis color added to that ofthe dispersion colorat the wedge edge of the fragment.)

A factor affecting precision in central focal masking is

l23l

the amount of difference in dispersion between the solidand the near-matching liquid. The greater this difference,the greater is the range of mismatch over which thedispersion colors are seen. Precision will therefore fall offsomewhat for greater differences in dispersion, as may beinferred by examination of Figure 7. It might appear that,conversely, the precision should be better for very lowdifferences in dispersion between solid and liquid, but apractical limit is soon reached because the angular aper-ture of the spectrum produced becomes so small thatmost of it is blocked by the opaque dot. In this circum-stance, the index of the liquid must be very close to thatof the solid before any dispersion color is seen, and thecolor itself is muddy because now only the colors atopposite ends of the spectrum come through.

Thus, taking the expression [(nn - nc)riq - (ne - nc),or]

uCI

;oanEIIJcLo

REFRACTIVE INDEX

Fig. 8. Plot ofdispersion vs. refractive index for selected organic immersion liquids and inorganic solids. Values for solids takenfrom Winchell (1929, table V) and Winchell and Winchell (1964, p. 137.)

O mdium chromate tetrahydrate

OCINNAMALDEHYDE(unstable)

o looo-NAPHTHALENE

O metaorbernhe -p

o o 'CHLOFO-NAPHTHALENE

ostrontianite .p

O rinneite -p

O datolite -P

dolomite -o,

oo . . .

o o lvne.p

calcite . o

a apatite - (,

muscovite-po

O tourmaline - o

O anthophyllire.F

O tremolite-p

a fluorite I calche.€

1232 WILCOX : REFRACTIVE INDEX DETERMIN ATION

as a measure ofdispersion difference, values about 0.010to 0.020 appear to be well suited for routine work withmost minerals. Examination of Figure 8 shows, however,that for the commonly available immersion sets (Cargille"Certified"; Butler, 1933) dispersion differences aresmaller than desired for work with many low-indexminerals and higher than desired for many high-indexminerals. To improve the situation in the low-index rangea special set of liquids was formulated (Wilcox, 1964)from mixtures of ethyl cinnamate (no = 1.558, flp - n6 =0.028) and glyceryl triacetate (no = 1.429, rr - nc :0.007). This series can be extended to higher refractiveindex by mixture with a-iodonaphthalene (no : 1.700, nr- nc : 0.037). A few inorganic solids (for instance,certain chromates, vanadates, and HgS) and probablyquite a number of organic solids have dispersions greaterthan that of the matching organic immersion liquid. Insuch rarely encountered cases the movements of thecolored Becke lines (Fig. 4, columns 3 and 4) are re-versed, as are the combined colors above and below thematch for the D-line. Nevertheless. at the match thedispersion color is the same deep violet.

Additional applications

Some other applications of focal masking techniques,mainly utilizing the difference in dispersion colors fordifferent degrees of index mismatch, are worth mentionhere. To estimate the proportions of quartz, microline,and oligoclase in a granite, for example, a sample of thepulverized rock may be mounted in a liquid of indexabout 1,542 and dispersion 0.017. The quartz grains (np1.544 to 1.553, depending on their orientation) showdispersion colors in various shades of purple, red, andorange and can be counted in comparison to the oligo-clase grains (no 1.534 to 1.545), which shows colbrs frompurple to strong blue, and the microcline (np 1.519 to1.525), which shows cold bright blue color. (Conceivably,the chore of counting the frequency distribution of themineral constituents might be taken over by an automatedmicroscope scanner fitted with appropriate color filters.)A related important problem in industrial hygiene is thedetermination of the amount of quartz particles in theaspirable fraction of dust, such as in a quarry or mineoperation (Crossmon, 1966). In control ofa beneficiationprocess, the product may be mounted in an immersionliquid that gives a distinctive coloration to the unwantedconstituent, from which the degree of remaining contami-nation may be estimated.

For a rough estimate of average and range of refractiveindex of an isotropic substance, such as volcanic glass,one may make multi-grain mounts in a series of liquids atclosely-spaced index intervals. With focal masking illumi-nation, one then takes as the average (really the mode)the index of the liquid in which about half the grains areabove and half below the liquid index. If a chart ofcomposition vs. refractive index is available, this value

can be used further to infer the average chemical compo-sition.

This approach can be extended to estimate the "aver-

age" composition of a sample of an anisotropic mineral ofIow birefringence in an isomorphous series. An examplewould be a powdered concentrate of rock-forming plagio-

clase. Here again one makes a series of immersionmounts and chooses as an "average" the index of theliquid in which, under focal masking illumination, aboutas many grains of plagioclase are of greater as are oflesser index. Entering this value on a chart of anorthite-content vs. principal refractive indices, a rough "aver-

age" anorthite content may be read offfrom the intersec-tion with an imaginary line of "average" refractive indexalong the trend of the a, p, and 7 lines. This rests on theassumptions that the distribution of compositions is uni-modal and preferential orientation due to cleavages donot appreciable affect the results.

Acknowledgments

Many valuable suggestions have come from colleagues in theU.S. Geological Survey during the years that focal masking hasbeen used for routine mineral analyses and taught in refreshercourses. I am especially indebted to Ivan Mittin for translationsof the Russian literature. Special thanks are due Dr. Horst Pillerof Carl Zeiss, Oberkochen, West'Germany, Glen A. Izett and G.Donald Eberlein of the U.S. Geological Survey, and Drs. Virgin-ia Steen-Mclntyre, Elwood R. Brooks, and F. Donald Bloss forhelpful and constructive reviews of the manuscript.

References

Bloss, F. D. (1961) An Introduction to the Methods of OpticalCrystallography. Holt, Rinehart, and Winston, New York.

Bloss, F. D. (l9El) The Spindle Stage: principles and practice.Cambridge University Press, New York.

Bloss, F. D., and Light, J. F. (1973) The detent spindle stage.American Journal of Science, 273-A.536-538.

Brown, K. M., and McCrone, W. C. (1963) Dispersion staining.Part I . The Microscope, 13, 3l l -321.

Brown, K. M., McCrone, W. C., Kuhn, R., and Forl ini , L.(1963) Dispersion staining. Part II. The Microscope, 14,39-54.

Butler, R. D. (1933) Immersion liquids of intermediate refrac-tion. American Mineralogist, 14, 386-401.

Cherkasov, Yu. A. (1955a) [A dispersion method of measuringrefractive indexl (in Russian). Sbornik Nauchno-Tekhniches-kii Informatsiya (Moscow), Minsterstvo Geologii i OkhranyNedr. No. 1.140-142.

Cherkasov, Yu. A. (1955b) [A new variant of the immersionmethodl (in Russian): Issledovanie mineral'nogo syr'ia, Vse-souiznyi Nauchissled-ovatelskii Institut Mineralnogo Syr'ia.Moscow. 52-57.

Cherkasov, Yu. A. (1957) [Application of "focal screening" tomeasurement of indices of refraction by the immersion meth-odl (in Russian). In Sovremennie metody mineralogicheskogoissledovaniia gornikh porod, rud, i mineralov, Gosudarst-venno Nauch-Tekh Izdatel'stvo Litgratur po Geologii i Okh-ranym, Moscow, 184-207. (English translation, 1960. Interna-tional Geology Review, 2, 218-235.)

WILCOX : REFRACTIVE INDEX DETERMINATION 1233

Cherkasov, Yu. A. (1969) [TransmittedJight microscopy (in thevisible spectrum)l (in Russian). In Roshkova, E. V.; Sovre-mennye Metody Mineralogicheskogo Issledovianiia Izda-tel'stvo "NeoRe", Moscow, 19-69 (esp. p. 37 and 47-58).

Correns, C. W., and Piller, Horst (1974) Mikroskopie der fein-komigen transparenten Minerale. In Freund, H., Handbuchder Mikroskopie in der Technik, Bd. 4, Teil l. Umshau,FranKurt am Main, 377-431.

Crossmon, G. C. (1948) Microscopical distinction of corundumarnong its natural and artificial associates. Analytical Chemis-try,20,976-977.

Crossmon, G. C. (1966) Some macro and microscopic applica-tions of dispersion staining as applied to industrial hygiene andin air pofution. Microchemical Journal, 10,273-285.

Dodge, N. B. (1948) The darkfield color immersion method.American Mineralogist, 33, 541-549.

Emmons, R. C., and Gates, R. M. (1948) The use of Beckelinecolors in refractive index determination. American Mineral-ogist,33, 612-618.

Feklichev, V. G. (1963) [The practical application of "focalmasking" to determination of refractive indices with theimmersion methodl (in Russian). Akademiia Nauk SSSR,Institut Mineralogii, geokhimii, i Kristallokhimii Redkikh Ele-mentov, Trudy, 18, 53-59.

Hartshorne, N. H., and Stuart, A. (1970) Crystals and thePolarizing Microscope, Fourth Edition. Arnold, London.

McCrone, W. C., McCrone, L. B., and Delly, J. G. (1978)Polarized Light Microscopy. Ann Arbor Science Publishers,Inc., Michigan.

Saylor, C. P. (1966) Accurate microscopical determination ofoptical properties on one small crystal. In V. E. Cosslett andR. Barer, Eds., Advances in Optical and Electron Microsco-p y , l , 4 2 J 6 .

Schmidling, David (1981) Dispersion staining techniques [at]high numerical aperture. The Microscope,29, l2l-125.

Schmidt, K. G., and Heidermanns, Greis (1958) Zur Technik derStaubmikroskopie mit Phasenkontrast und Grenzdunkelfeld.Staub. 18.236-246.

Schroeder van der Kolk, J. L. C. (1906) Tabellen zur mikrosko-pischen Bestimmung der Mineralien nach ihrem Brechungsin-dex. Wiesbaden.

Stoiber, R. E., and Morse, S. A. (1972) Microscopic Identifica-tion of Crystals. Ronald Press, New York.

Wilcox, R. E. (1959) Use of the spindle stage for determinationof principal indices of refraction of crystal fragments. Ameri-can Mineralogist, 44, 1272-1293.

Wilcox, R. E. (1962) Cherkasov's "focal screening" for determi-nation of refractive index by the immersion method. Interna-tional Microscopy Symposium 1960, Proceedings, McCroneAssociates, Chicago, p. 160-165.

Wilcox, R. E. (1964) Immersion liquids of relatively strongdispersion in the low refractive index range (1.46 to 1.52).American Mineralogist, 49, 683-688.

Winchell, A. N. (1929) Elements of optical mineralogy, Part III,Determinative tables. Wiley, New York.

Winchell, A. N., and Winchell, H. (1964) The MicroscopicalCharacters of Artificial Inorganic Solid Substances. AcademicPress, New York.

Appendix I

Modification of the microscope

A conventional petrographic microscope may be converted tocentral focal masking by (l) installing an opaque stop of smalldiameter at the focal point ofthe medium power objective and (2)restricting the aperture of the substage iris diaphragm to passonly axially parallel or nearly parallel rays.

The opaque stop may consist of a 2 to 3 mm diameter dot ofopaque ink-e.g., India ink or "Lab-ink"----centered on a thinglass disc, such as a cover glass, ofproper size to fit in the barrelofthe objective. This glass disc, which should be unstrained andshould have plane-parallel surfaces, is then cemented at or nearthe level of the focal point of the objective. (The presence of thedot does not noticeably handicap the use of this objective forordinary observational work.) For the medium power objectivesof Zeiss and Leitz,'the focal point is within the barrel of theobjective, requiring disassembly to reach the correct placementby experiment. For the medium power objective of Unitron(l0x, 0.25 N.A. for MPS model petrographic microscope) disas-sembly is not necessary; a l5-mm diameter dot-bearing cover-glass may be cemented on the apertural collar at the rear of theobjective barrel. This inexpensive objective may be used on theLeitz Dialux Pol microscopes directly and on other polarizingmicroscopes with an adapter and centering collar. McCroneAssociates (2820 S. Michigan Ave., Chicago, Ill. 60616) providea "Dispersion Staining Objective" with appropriately built-inmasks.

The required narrow pencil of nearly parallel light rays may beproduced in the substage by closing down the iris of the substageapertural diaphragm until its image, as viewed with the Bertrandlens, is just slightly smaller in diameter than that of the opaquedot in the objective (Fig. Ala). With the immersion mount inplace on the stage of the microscope, the substage centeringscrews are adjusted to shift the image of the iris so that it lieswholly behind that of the opaque dot of the objective (Fig. Alb).Then with the Bertrand lens withdrawn, the images of thefragments in the immersion mount are displayed on the darkfield.

If, as is sometimes the case, the coverglass of the immersionmount does not lie strictly perpendicular to the microscope axis.rotation of the microscope stage to a new setting may result inpartial illumination of the field, whereupon insertion of theBertrand lens reveals that the image of the substage opening hasshifted from behind the opaque dot. This may be corrected in thenew setting by readjusting the centering screws of the substageto once more shift the image of the substage iris opening behindthe opaque dot. (It is of course necessary to recenter thesubstage prior to resumption of work with conventional illumina-tion.)

A more convenient arrangement for repeated repositioning ofthe substage opening employs a separate apertural stop, fash-ioned by hand from thin metal stock for insertion into thesubstage near the level of the iris diaphragm. A protrudinghandle on this stop permits it to be shifted laterally as theoccasion requires. Starting with metal foil, a small hole ispunched with a needle and enlarged in successive trials until thesize of its image is correct for the opaque dot. If desired, a more

Manuscript received, September 9, 1982;accepted for publication, April 4, 1983.

rAny use of trade names is for descriptive purposes only anddoes not imply endorsement by the U.S. Geological Survey.

1234 WILCOX : REFRACTIVE INDEX DETERMINATION

(b)(a)

Fig. Al. Bertrand lens image of opaque dot and constrictedsubstage aperture (a) when out of line, and (b) after alignment bylateral adjustment of the substage aperture.

substantial stop may then be constructed by drilling a hole of thissize in heavier stock. (The design of the Leitz Dialux Polmicroscope permits yet another position for the constructedstop-it may be laid directly on the illuminator window in thebase of the microscope, apparently a conjugate focal plane of thelens system, where it is easily accessible for lateral shifting asneeded to compensate for ray deflection.)

Appendix 2

Alternative modes of focal masking

While not as easily adpated as central focal masking for use onmost petrographic microscopes, alternative configurations,known as apertural focal masking, unilateral focal masking,annular focal masking, and strip focal masking, may also beuseful in certain situations and may be helpful in demonstratingthe manner of image formation in the microscope.

Apertural focal mas king

The term apertural masking is preferred here as being moredescriptive than "annular masking", used for this configuration

APERTURALMASK

Fig. 42. Representation of the formation of the dispersioncolor image tsing apertural focal masking when refractiveindices of fragment and liquid match in the region of the yellowwavelensths.

by Cherkasov (1957; see also Brown and McCrone, 1963). Theterm annular masking is here reserved for the true ring-shapedconfiguration (see below).

In apertural masking (Cherkasov, 1957; Wilcox, 1962; Hart-shorne and Stuart, 1970) a constricted apertural stop is substitut-ed for the opaque dot of central masking at the focal point of theobjeiiive, as represented diagramatically in Figure 42. Theapertural mask may consist of a thin metal disk in the center ofwhich a hole of appropriate size has been drilled or punched.Alternatively, a universal stage objective, such as Leitz No.UM-3, may be modified to enable drastically constricting the irisdiaphragm. The apertural mask is also available as part of the"Dispersion Staining Objective" of McCrone Associates.

The apertural mask passes the rays of wavelength for whichindices of solid and liquid match, but blocks those for nonmatch-ing wavelengths, thus it is just the converse of central focalmasking. The image is displayed on a dimly lit field in the color(wavelength) for which the indices match. A match near thewavelength of the Dline, 589.3 nm, is indicated when the imageof the edges of the fragment is deep orangish-yellow, as listed inFigure 4, column 5; on the other hand, if the image is green orblue, the index ofthe fragment is greater than that ofthe liquid; iforange or red, it is less than that of the liquid. Liquids may bechanged to obtain or to bracket the diagnostic deep orangish-yellow color of the D-line. If the borders of the fragment are darkand without apparent color, the mismatch is large, and thedirection of mismatch may be determined by converting toordinary illumination for the Becke line test.

Apertural focal masking has the advantage of simplicity, inthat it displays the image directly in the color of the wavelengthof refractive index match. Yet a sharp focus of the image cannotbe obtained due to the very small angular aperture. This iscritical for small fragments, because their diagnostic dispersioncolors are lost in the background ofthe light field. As a teachingaid, however, apertural masking provides a convincing demon-stration of dispersion phenomena and also "empty magnifica-tion", that is, the loss of resolving power when the angularaperture of the lens system is drastically reduced.

U nilateral focal mas king

In unilateral focal masking (Cherkasov, 1957;Wilcox' 1962) acircular mask of about a third of the full aperture is placed in the

objective, and the much smaller apertural mask in the substage is

shifted laterally until, with the Bertrand lens in place, its imagemay be seen to be partly hidden behind the edge of the objectivemask. The bundle of parallel light rays is then at an angle to themicrosope axis, as illustrated in Figure ,{3.

This arrangement is analogous to the well known method of

oblique illumination (method of Schroeder van der Kolk' 1906)'and the colors appearing on opposite edges of the fragment areinterpreted in the same manner. If fragment and liquid diferwidely in refractive index, the fragment is seen to have high reliefwithout color. If solid and liquid are at or near a match, paired

colors appear on opposite sides of the fragment and are to be

used as listed in Figure 4, columns 6 and 7. Upon shifting thesubstage aperture a bit farther of center so that it is completelybehind the objective mask, the orthoscopic field becomes dark'and the paired colors change to those as listed in columns 8 and

9. Whereas the image definition is as sharp as in central focalmasking, the color effects are complex and somewhat moredifficult to standardize in terms of index match.

U

-3

3JJ

::.[r;Y1,1'.1fl1",

WHITE LIGHT

_ IMAGE PLANE

UNILATERALMASK

WHITE LIGHT

Fig. A'3. Representation of the formation of the dispersioncolor image using unilateral focal masking when refractiveindices of fragment and liquid match in the region of the yellowwavelengths.

Annular focal masking

Where particles are so small that a high magnification objec-tive is required, the pinhole light source ofcental focal masking,described above, may not provide sufficient intensity from theusual microscope illuminator to produce readable dispersioncolors. A solution suggested by H. Piller (written comm.,December 1963; see also Correns and Piller, 1974, p. 407;Schmidling, l98l) employs the same arrangement as in phasecontrast microscopy, except that in the objective an opaque ringtakes the place of the phase ring. A complementary annularopening in the substage admits much more light and providesbrilliant dispersion colors, even with high-N.A. oil immersionobjectives.

The question arises whether an illuminating system of suchhigh angular aperture permits accurate determination of a princi-pal refractive index of an anisotropic fragment, which necessari-ly must be oriented so that its corresponding privileged vibrationdirection is (l) parallel with the plane of the polarizer and (2)perpendicular to the microscope axis. It is seen from Figure A4that the vibration directions of the strongly convergent light raysfrom sectors A and C of the annular opening in the substage willbe inclined to the privileged direction of the oriented crystal. Itwould therefore be expected that the observed dispersion colorwill have been modified to some extent by the addition ofcomponents representing non-principal refractive indices, andthus that one might be led to infer an incorrect refractive index.Similar color contamination is to be expected in the phasecontrast technique, as pointed out by Saylor (1966), and in thedark-field technique of Dodge (1948) and Crossmon (1948), inwhich the maximum angular aperture of the substage is used.

An actual test shows, however, that the enor of the inferredprincipal index for routine work may only be significant forcrystals of extreme birefringence. Using an opaque ring objec-tive (modified Zeiss Ph 2,40x,0.75 N.A.) and complementaryannular opening in the substage, a fragment of aragonite (y - a :0.155) was oriented with its acute bisectrix sensibly parallel tothe microscope axis and with a perpendicular to the microscope

1235

Substage condenser

Substage

annular mask

Vibration directionof oolarizer

Fig. ,{4. Substage condensing system for annular focalmasking: (a) vertical section in vibration plane of polarizer, (b)bottom view of substage annular opening.

axis in the plane of the polarizer. From the "match" dispersioncolor a was inferred to be 1.534, but using an opaque dotobjective the inferred correct index was 1.530, a difference of0.004. Further tests indicated that the error is much smaller forcrystals of only "strong" birefringence and is undetectable incrystals of moderate or low birefringence.

Strip focal masking

That the source of the color contamination in the above test ofthe annular mask is indeed in sectors A and C of Figure A.4 isdemonstrated by inserting masks in the substage to lie over thesesectors, whereupon the dispersion colors became normal and thetrue index can be inferred. One should therefore be able to avoidthe contamination entirely by use of a straight illuminating slitacross the center in the substage (Fig. A5a) and a complementarystrip mask in the objective, as suggested by Saylor (1966, p.67)for the analogous problem in phase contrast methods. Narrowflared strips (Fig. A5b) conceivably would provide still greaterilluminating intensity without introducing noticeable color con-tamination.

(a ) (b )

Fig. A5. Alternative forms of substage opening for srrrp focalmasking: (a) simple strip opening, (b) flared opening forincreased illumination.

WI LC OX : REFRACTIV E I N DEX DETERMI N ATIO N

Polarized light

1236 WILCOX : REFRACTIV E INDEX DETERMINATION

Appendix 3

Calibration of color perception

The success of the method requires correct interpretation ofthe color effects observed when fragment and liquid are at ornear a match in refractive index. Rather than depending onFigure 4, each observer should "calibrate" his or her own colorperception for a particular microscope under known conditionsof match and mismatch. For this the following procedure issuggested:

(l) Adjust the microscope for conventional illumination withlight of the D-line wavelength. This may be obtained from thewell-known NaCl fragment on a Bunsen burner, a sodium vaporlamp, or more conveniently, a graduated interference filter, orappropriate monochromatic interference filter, such as Schott-Jena, Type "IL" or "PL".

(2) Mount fragments of a homogeneous isotropic substance(for instance, crushed fragments of coverglass or object slide) insuccessive immersion liquids until a percise match is obtained asjudged by the Beckeline test, or more sensitively by inclinedillumination.

(3) Without otherwise changing the mount or the temperature,convert to central focal masking illumination, and at focusobserve and fix mentally the shade ofdispersion color seen at theedges and surface irregularities of the fragment (the "deepviolet" of Fig. 4, column 2). Also observe the colors of the

oppositely moving Becke lines as the focus is raised slightly (Fig.4. columns 3 and 4).

(4) In mounts 0.001 or 0.002 above and below that of the indexmatch, observe and fix mentally the dispersion colors at focusand with slightly raised focus.

In carrying out the above procedure, it will be noted that thesteeper the margin of a fragment the greater is the intensity of thecolor. With an index match at the D-line, the steep edge mayappear brighter and more bluish than the "deep violet" of theless steep edges. This is because a larger proportion of the visiblespectrum is enabled to pass the dot mask, even though it iscentered about the same wavelength of true match. In practiceany possible confusion of the wavelength of match may beresolved by also observing the fragments in liquids of index justabove and just below that of the match. In the liquid of lowerindex, the color of the fragment edge takes on a definitelypurplish or reddish hue, whereas in the liquid ofhigher index, theimage is definitely blue or greenish blue. The refractive index ofthe fragment for the D-line may therefore be taken with confi-dence to lie between those of the two liquids.

With very thick fragments, it is not possible to bring the entireheight of a steep edge into focus at the same time, and the twocolored Becke lines persist at all levels of focus. Here it may bepossible to obtain the combination of the two Becke lines atminor irregularities of the surface of the fragment. Otherwise onemay use the colors of the deliberately separated Becke lines, aslisted in Figure 4, column 3 and 4.