Interference figuresInterference figures

Very important tool to determine Very important tool to determine optical characteristics. They will tell optical characteristics. They will tell you:you: Uniaxial vs biaxialUniaxial vs biaxial Optic signOptic sign 2V angle – for biaxial2V angle – for biaxial Used for estimating chemistry of mineralUsed for estimating chemistry of mineral

TechniqueTechnique Focus with highest power objectiveFocus with highest power objective Be certain observation is Be certain observation is conoscopic lightconoscopic light

Flip in conoscope on some microscopesFlip in conoscope on some microscopes Most of them have to raise light sources as high Most of them have to raise light sources as high

as possibleas possible Insert Betrand lens or remove ocularInsert Betrand lens or remove ocular

Interference figure forms on top of objective lensInterference figure forms on top of objective lens Betrand lens required to refocus the imageBetrand lens required to refocus the image

Slightly more modern Slightly more modern versionversion

conoscope

Bertrand lens

Fig. 7-Fig. 7-3535

Isogyres

Melatope

Isochromes

One type of Uniaxial One type of Uniaxial Interference FigureInterference Figure

Figure consist of isogyres and Figure consist of isogyres and isochromesisochromes IsochromesIsochromes: patterns of interference colors: patterns of interference colors IsogyresIsogyres: dark bands (extinction): dark bands (extinction)

Nature of interference figure and Nature of interference figure and patterns as stage rotated determines patterns as stage rotated determines optical propertyoptical property

Types of figures controlled by cut of Types of figures controlled by cut of the grainthe grain

Uniaxial Interference FigureUniaxial Interference Figure

Three types:Three types: Optic axis figureOptic axis figure Off-center optic axis figureOff-center optic axis figure Flash FigureFlash Figure

Note – these correspond with the Note – these correspond with the principle cuts of the indicatrixprinciple cuts of the indicatrix

Optic Axis FigureOptic Axis Figure

Forms when optic axis perpendicular Forms when optic axis perpendicular to stageto stage Grain exhibits low interference color Grain exhibits low interference color

(extinct)(extinct)

FigureFigure Black cross of isogyresBlack cross of isogyres Circular isochromesCircular isochromes Melatope - location of optic axisMelatope - location of optic axis Isochromes are increasingly higher Isochromes are increasingly higher

order colors outwardorder colors outward

Isochromes (and isogyres) result from ray Isochromes (and isogyres) result from ray paths of conoscopic light:paths of conoscopic light: Light traveling along optic axis (melatope) has Light traveling along optic axis (melatope) has

no retardationno retardation Light near melatope has low retardation (d and Light near melatope has low retardation (d and

little higherlittle higher Light far from melatope have higher retardation Light far from melatope have higher retardation

(d and (d and increase more) increase more) Thicker and high birefringent minerals have Thicker and high birefringent minerals have

more isochromesmore isochromes E.g. calcite (large E.g. calcite (large ) vs quartz (small ) vs quartz (small ))

Fig. 7-36Fig. 7-36

Thin sectionThin section

IndicatrixIndicatrix

(1)(1)Longer path Longer path length, greater length, greater dd, , higher higher interference interference colorscolors

(2)(2)Perpendicular to Perpendicular to light ray is light ray is section of section of indicatrix, larger indicatrix, larger

Origin of Isochromes and Origin of Isochromes and IsogyresIsogyres

rays vibrate tangent to isochromesrays vibrate tangent to isochromes rays vibrate perpendicular to rays vibrate perpendicular to

isochromesisochromes Isogyres are where vibration Isogyres are where vibration

directions are N-S and E-W, extinctdirections are N-S and E-W, extinct

Fig. 7-37Fig. 7-37

Thin section

Indicatrix

Note: each ray path has its own section of indicatrix;Each has unique n’, so has increasing outward

Off-center OA figureOff-center OA figure

Figure forms when OA is not Figure forms when OA is not perpendicular to stageperpendicular to stage

Correct grain will have intermediate Correct grain will have intermediate interference colorsinterference colors

Use of figure similar to centered OA Use of figure similar to centered OA figurefigure

Off-center OA figureOff-center OA figure

If OA < ~30º to stage, melatope in If OA < ~30º to stage, melatope in field of viewfield of view

Isogyres swing around center of Isogyres swing around center of cross hairscross hairs

If melatope is out of field of view, If melatope is out of field of view, difficult but possible to determine difficult but possible to determine optic signoptic sign

Fig. 7-38Fig. 7-38

Off-center OA, melatope in field of Off-center OA, melatope in field of viewview

Optic Axis inside field of view

Fig. 7-38Fig. 7-38

Off-center OA figure, melatope outside field of viewOff-center OA figure, melatope outside field of view

Thin section

Indicatrix

Optic Axis outside field of view

Optic Normal (Flash Figure)Optic Normal (Flash Figure)

Formed when OA is parallel to stageFormed when OA is parallel to stage Grains have highest interference Grains have highest interference

colorscolors Broad diffuse isogyres, split and Broad diffuse isogyres, split and

leave field of viewleave field of view Not much useNot much use

Determines orientation of OA – e.g. Determines orientation of OA – e.g. pleochroismpleochroism

Fig.7-39Fig.7-39

Determining Optic SignDetermining Optic Sign

Orientation of vibration directions Orientation of vibration directions known in each quadrantknown in each quadrant

Insertion of accessory plate will Insertion of accessory plate will cause subtraction and additioncause subtraction and addition Determines signDetermines sign

Fig. 7-Fig. 7-4040

’ always points toward melatope,Orientation of vibration directions from fig. 3-37

Addition Subtraction

+ -

Biaxial Interference FiguresBiaxial Interference Figures

5 major figures5 major figures 2 useful 2 useful ones:ones:

Acute bisectrix (Bxa) figureAcute bisectrix (Bxa) figure Optic axis figureOptic axis figure

3 worthless 3 worthless ones:ones: Obtuse Bisectrix (Bxo) figureObtuse Bisectrix (Bxo) figure Optic Normal figure (Flash figure)Optic Normal figure (Flash figure) Off-center figureOff-center figure

Acute bisectrix figureAcute bisectrix figure Bxa axis (X or Z depending on sign) Bxa axis (X or Z depending on sign)

oriented perpendicular to stageoriented perpendicular to stage

Biaxial Indicatrix

Optically negativeOptically positive Fig. 7-27Fig. 7-27

Acute bisectrix figureAcute bisectrix figure

Grains have intermediate to low Grains have intermediate to low interference colors (depends on 2V)interference colors (depends on 2V)

Isogyres form cross that splits and Isogyres form cross that splits and leaves field of view as stage is leaves field of view as stage is rotatedrotated

Two melatopes (i.e. two OA)Two melatopes (i.e. two OA) Isochromes are oval or figure 8 Isochromes are oval or figure 8

around the melatopearound the melatope

Fig. 7-Fig. 7-4141

Grain at extinction Grain 45º from extinction

Acute bisectrix figureAcute bisectrix figure

Optic Plane

Optic P

lane

Optic Axis FigureOptic Axis Figure

Formed when OA is verticalFormed when OA is vertical These grains have zero or small These grains have zero or small

retardationretardation If 2V > 30º, only one melatope (OA) If 2V > 30º, only one melatope (OA)

in field of viewin field of view If 2V very small, looks like an off-If 2V very small, looks like an off-

center Bxa figurecenter Bxa figure

Fig. 7-44Fig. 7-44

2V < 30º2V < 30º 2V > 30º2V > 30º

Determining Optic SignDetermining Optic Sign

Done with Bxa or OA figureDone with Bxa or OA figure Example of Bxa figure:Example of Bxa figure:

Two light rays vibrate along Bxa axis (either Z or Two light rays vibrate along Bxa axis (either Z or X, the other X, the other must be Ymust be Y))

Y vibration is nY vibration is n, this one is , this one is perpendicular to the perpendicular to the optic planeoptic plane

Other depends if mineral is + or –Other depends if mineral is + or – If +, then vibration is X = nIf +, then vibration is X = n

If -, then vibration is Z = nIf -, then vibration is Z = n Use accessory plate to determine if vibration is Use accessory plate to determine if vibration is

fast or slowfast or slow

Fig. 7-48Fig. 7-48

Light from bottomLight from bottom

Two vibration Two vibration directions depend directions depend on which axis is on which axis is

BxaBxa

Fast on Fast on slow?slow?Slow on Slow on slow?slow?

Shows if Bxa Shows if Bxa is Z or Xis Z or X

Subtraction

Addition

RememberRemember::Think Think about slice about slice of of indicatrix indicatrix to give to give you you vibration vibration directionsdirections

Fig. 7-49Fig. 7-49

Determining optic sign with Biaxial OA figure

Slow over fast - subtraction

Slow over slow - addition

Subtraction

Addition

Determining 2V – several Determining 2V – several techniquestechniques

Bxa figure:Bxa figure: Spacing between melatopes relates to Spacing between melatopes relates to

2V2V Depends on numerical aperture (NA) of Depends on numerical aperture (NA) of

objectivesobjectives Can guess within about 10ºCan guess within about 10º

Fig. 7-51

Numerical Numerical apertureaperture

15º

60º45º

30º

Optic axis figureOptic axis figure

Curvature of the isogyre depends on Curvature of the isogyre depends on 2V2V

If 2V = 90º, the isogyre is a straight If 2V = 90º, the isogyre is a straight lineline

If 2V = 0º, the isogyre forms a cross If 2V = 0º, the isogyre forms a cross – it is uniaxial– it is uniaxial

Fig. 7-52