1. Measuring Birefringence of Anisotropic Crystals
By Ben Grober

2. Outline Goals Background Method Results Discussion Crystals
Birefringence
Samples
Method
Senarmont Method
Results
Discussion

3. Goals Accurately measure phase retardation of anisotropic crystal
Calculate birefringence of anisotropic crystal
Identify minerals based on measurements

4. Crystals Minerals are naturally occurring crystalline solids
There are two types of crystals: Isotropic and Anisotropic
Isotropic Crystals
Single refractive index
Totally extinct under cross polarized light
Anisotropic Crystals
Two or three refractive indices
Has birefringence colors under cross polarized light

5. Anisotropic Crystals Have two or three refractive indices
The difference in refractive indices creates birefringence
Light is split into two eigenwaves
Two waves interfere with each other
This birefringence can be seen as colors under crossed polarized light

6. Types of Anisotropic Crystals
There are two types of anisotropic crystals: uniaxial and biaxial
Uniaxial Crystals
Two refractive indices
One optic axis
Biaxial Crystals
Three refractive indices
Two optic axis

7. Optic Axis

8. Birefringence ∆𝑛=( 𝑛 𝑒 − 𝑛 𝑜 )
Birefringence is the result of a crystal having two or more refractive indices
Birefringence is a natural property of anisotropic crystals
All anisotropic minerals have a range of birefringence values
Useful for identifying minerals and other applications
∆𝑛=( 𝑛 𝑒 − 𝑛 𝑜 )

9. Birefringence Colors
The product of birefringence can be seen under cross polarized light as colors
The color depends on many factors including:
Birefringence
Sample thickness
Crystal orientation
Birefringence never changes, even if color does

10. Birefringence Color Chart

11. Samples Using plagioclase and hornblende crystals
Both are anisotropic and biaxial
They have very different birefringence values

12. Samples
Plagioclase
Hornblende

13. Method Senarmont method
Pass light from a light source through light diffuser
Light then passes through interference filter
Light passes through polarizer and then our sample
From sample, light passes through Fresnel Rhomb
Observe light after passing through analyzer

14. Method Analyzer Sample Interference filter Fresnel rhomb Polarizer
White light source
Light diffuser
Interference filter
Polarizer
Sample
Fresnel rhomb
Analyzer

15. (or Senarmont compensator)
Method
Optical element
Symbol
Jones matrix
Output
polarization
Polarizer
(horizontal )
Sample
(slow axis at 45º)
Fresnel rhomb
(or Senarmont compensator)
(s =horizontal)
Analyzer
(oriented at 90º+d/2) x y x y
apply to x y g x y
x(s)
y(p) x y
d/2 x y
d/2 x y

16. Method
Orient crystal with slow axis at 45 degrees to polarizer
Use interference filter (676nm, 630nm, 532nm, 450nm)
Rotate analyzer until crystal is fully extinct
Note angle on analyzer
Repeat 4 times for each wavelength
𝛿 2 = 𝜋 𝜆 Δ𝑛𝑑

17. Method

18. Results Plagioclase at 94o Hornblende at 327o Wavelength (nm)
d/2 (degrees)
676
44.0, 43.5, 43.5, 43.0
336.5, 336.0, 332.5, 334.5
630
48.0, 46.5, 46.5, 46.0
357.5, 356.0, 357.5, 354.0
532
56.0, 57.5, 58.0, 56.5
428.0, 427.0, 424.0, 432.0
450
68.0, 66.0, 67.5, 65.0
514.0, 515.5, 512.5, 510.0

19. Results
∆𝑛= 𝑆𝑙𝑜𝑝𝑒 (180 𝑜 )𝑑

20. Results Measured Accepted Plagioclase 0.006 0.007-0.013 Hornblende
0.045

21. Discussion Measured values were very close to accepted values
Plagioclase error most likely due to optic axis
Hornblende error most likely due to sample thickness

22. Summary Birefringence is a natural property of minerals
Birefringence is important for identifying minerals and has a variety of other uses
Found phase retardation of crystal to within 2nm of accuracy
Found birefringence of crystal fairly accurately
Error due to crystal thickness and orientation