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

2. Technique Focus with highest power objective
Be certain observation is conoscopic light
Flip in conoscope on some microscopes
Most of them have to raise light sources as high as possible
Insert Betrand lens or remove ocular
Interference figure forms on top of objective lens
Betrand lens required to refocus the image

3. Slightly more modern version
Bertrand lens
conoscope

4. One type of Uniaxial Interference Figure
Isogyres
Isochromes
Melatope
Fig. 7-35

5. Figure consist of isogyres and isochromes
Isochromes: patterns of interference colors
Isogyres: dark bands (extinction)
Nature of interference figure and patterns as stage rotated determines optical property
Types of figures controlled by cut of the grain

6. Uniaxial Interference Figure
Three types:
Optic axis figure
Off-center optic axis figure
Flash Figure
Note – these correspond with the principle cuts of the indicatrix

7. Optic Axis Figure Forms when optic axis perpendicular to stage
Grain exhibits low interference color (extinct)

8. Figure Black cross of isogyres Circular isochromes
Melatope - location of optic axis
Isochromes are increasingly higher order colors outward

9. Isochromes (and isogyres) result from ray paths of conoscopic light:
Light traveling along optic axis (melatope) has no retardation
Light near melatope has low retardation (d and d little higher
Light far from melatope have higher retardation (d and d increase more)
Thicker and high birefringent minerals have more isochromes
E.g. calcite (large d) vs quartz (small d)

10. Thin section
Indicatrix
Longer path length, greater d, higher interference colors
Perpendicular to light ray is section of indicatrix, larger d
Fig. 7-36

11. Origin of Isochromes and Isogyres
w rays vibrate tangent to isochromes
e rays vibrate perpendicular to isochromes
Isogyres are where vibration directions are N-S and E-W, extinct

12. Thin section Indicatrix Fig. 7-37
Note: each ray path has its own section of indicatrix;
Each has unique ne’, so has increasing d outward
Thin section
Indicatrix
Fig. 7-37

13. Off-center OA figure
Figure forms when OA is not perpendicular to stage
Correct grain will have intermediate interference colors
Use of figure similar to centered OA figure

14. Off-center OA figure
If OA < ~30º to stage, melatope in field of view
Isogyres swing around center of cross hairs
If melatope is out of field of view, difficult but possible to determine optic sign

15. Off-center OA, melatope in field of view
Optic Axis inside field of view
Fig. 7-38

16. Off-center OA figure, melatope outside field of view
Thin section
Indicatrix
Optic Axis outside field of view
Fig. 7-38

17. Optic Normal (Flash Figure)
Formed when OA is parallel to stage
Grains have highest interference colors
Broad diffuse isogyres, split and leave field of view
Not much use
Determines orientation of OA – e.g. pleochroism

18. Fig.7-39

19. Determining Optic Sign
Orientation of vibration directions known in each quadrant
Insertion of accessory plate will cause subtraction and addition
Determines sign

20. e>w - e<w + e’ always points toward melatope,
Orientation of vibration directions from fig. 3-37
Addition
Subtraction
e>w -
e<w +
Fig. 7-40

21. Biaxial Interference Figures
5 major figures
2 useful ones:
Acute bisectrix (Bxa) figure
Optic axis figure
3 worthless ones:
Obtuse Bisectrix (Bxo) figure
Optic Normal figure (Flash figure)
Off-center figure

22. Acute bisectrix figure
Bxa axis (X or Z depending on sign) oriented perpendicular to stage
Biaxial Indicatrix
Fig. 7-27
Optically positive
Optically negative

23. Acute bisectrix figure
Grains have intermediate to low interference colors (depends on 2V)
Isogyres form cross that splits and leaves field of view as stage is rotated
Two melatopes (i.e. two OA)
Isochromes are oval or figure 8 around the melatope

24. Acute bisectrix figure
Optic Plane
Optic Plane
Grain 45º from extinction
Grain at extinction
Fig. 7-41

25. Optic Axis Figure Formed when OA is vertical
These grains have zero or small retardation
If 2V > 30º, only one melatope (OA) in field of view
If 2V very small, looks like an off-center Bxa figure

26. 2V < 30º
2V > 30º
Fig. 7-44

27. Determining Optic Sign
Done with Bxa or OA figure
Example of Bxa figure:
Two light rays vibrate along Bxa axis (either Z or X, the other must be Y)
Y vibration is nb, this one is perpendicular to the optic plane
Other depends if mineral is + or –
If +, then vibration is X = na
If -, then vibration is Z = ng
Use accessory plate to determine if vibration is fast or slow

28. Two vibration directions depend on which axis is Bxa
Addition
Subtraction
Fast on slow?
Slow on slow?
Shows if Bxa is Z or X
Remember:
Think about slice of indicatrix to give you vibration directions
Two vibration directions depend on which axis is Bxa
Fig. 7-48
Light from bottom

29. Determining optic sign with Biaxial OA figure
Subtraction
Addition
Slow over fast - subtraction
Slow over slow - addition
Fig. 7-49

30. Determining 2V – several techniques
Bxa figure:
Spacing between melatopes relates to 2V
Depends on numerical aperture (NA) of objectives
Can guess within about 10º

31. Numerical aperture
15º
30º
45º
60º
Fig. 7-51

32. Optic axis figure Curvature of the isogyre depends on 2V
If 2V = 90º, the isogyre is a straight line
If 2V = 0º, the isogyre forms a cross – it is uniaxial

33. Fig. 7-52