Optic Sign Determination

The optic sign is a property of anisotropic gem materials that describes the relationship
between the principal refractive indices:

• Uniaxial positive (U+): the extraordinary ray RI (ε) is greater than the ordinary ray
  RI (ω): ε > ω.
• Uniaxial negative (U−): ε < ω.
• Biaxial positive (B+): the intermediate RI (β) is closer to α (the minimum) than to
  γ (the maximum): β − α < γ − β.
• Biaxial negative (B−): β is closer to γ: γ − β < β − α.

The optic sign can be determined by two methods:

1. Refractometer rotation (uniaxial stones only) – observing which shadow edge moves as
   the stone is rotated.
2. Conoscopic interference figure with an accessory plate (lambda plate or quartz wedge),
   reading the colour change in the isochromatic rings.

The interference-figure method uses Newton's colour series (the interference colour
sequence seen between crossed polars as retardation increases): yellow → orange → red →
violet → blue → green → yellow (2nd order) …). The lambda plate (530 nm full-wave
retardation plate, "first-order red plate") shifts the retardation by a fixed amount:
addition raises colours toward the next order (blue, 2nd-order tints); subtraction lowers
them (yellow, back toward 1st-order grey).

Source: Sturman, B.D., J. Gemmology, 2007. DOI: 10.15506/jog.2007.30.7.443. [VERIFIED];
Read, P., Gemmology 3rd ed. DOI: 10.4324/9780080507224 [VERIFIED]

For uniaxial stones with measurable birefringence, the refractometer can be used directly:

1. Place the stone table-down on the refractometer hemisphere with contact liquid.
2. Observe the shadow edge (or edges). A uniaxial stone shows two shadow edges –
   the fixed edge (ω, ordinary ray) and the moving edge (ε, extraordinary ray).
3. Rotate the stone slowly through 360°. The ε edge moves; the ω edge stays fixed.
4. If the moving edge (ε) is above the fixed edge (ω) at maximum separation:
   • ε > ω → Uniaxial positive.
5. If the moving edge (ε) is below the fixed edge at maximum separation:
   • ε < ω → Uniaxial negative.

Note: when the stone is oriented with the optic axis perpendicular to the hemisphere
(c-axis pointing up into the contact liquid), both readings coincide as a single shadow
edge at the ω position. Rotate the stone off this orientation to see both edges.

The conoscope (convergent polarised light through the polariscope, using a high-powered
condensing lens or the stone itself as a condenser) produces an interference figure for
a stone oriented with its optic axis vertical.

Uniaxial optic axis figure:

• Shows a Maltese cross (isogyre) pattern with concentric isochromatic colour rings.
• The centre of the cross marks the optic axis.

Inserting the lambda plate (530 nm first-order red plate):

The lambda plate has a defined "slow" direction (the direction of high refractive index,
i.e. the slow vibration direction). When inserted, it adds retardation where the crystal's
slow direction aligns with the plate's slow direction, and subtracts retardation where they
are opposed.

• In the two quadrants where the crystal's slow ray is parallel to the plate's slow ray:
  retardations add → colours rise in Newton's series (toward blue, 2nd order).
• In the other two quadrants: retardations subtract → colours fall (toward yellow).

Reading the sign (principle – without committing to a specific diagram convention):

The orientation rule for the plate-in-figure is described in standard optical mineralogy
texts (Read 3rd ed.; Sturman 2007). The key relationship is: in the quadrants where the
crystal's slow ray aligns with the plate slow direction, rising colours indicate the slow
direction of the crystal in that quadrant – from which the sign follows. Consult your
course's specific diagram orientation, as the convention depends on the physical direction
the plate is inserted relative to the polariser/analyser orientation.

Practical rule (curriculum-level): the lambda plate colour shift directly reveals
whether ε or ω is the slow direction:

• If the quadrant showing rising colour corresponds to the ε direction → ε > ω → positive.
• If the quadrant showing rising colour corresponds to the ω direction → ε < ω → negative.

A quartz wedge works analogously, showing a series of colour changes as it is inserted,
rather than a single shift.

For biaxial stones, the acute bisectrix (Bxa) interference figure is used. The stone must
be oriented with the acute bisectrix perpendicular to the polariscope stage – typically
requiring the stone to be oriented by trial and error (or by knowledge of the optic
orientation of the species).

Biaxial Bxa figure:

• Shows two isogyres (hyperbolic curves) that sweep across the field as the stage is rotated.
• The two isogyres curve toward each other; the separation of the two optic axes (2V) is
  estimated from the curvature of the isogyres and their angular separation.

Inserting the lambda plate:

• Observe the colour of the isochromatic rings in the concave region between the two
  isogyres (facing toward the acute bisectrix).
• Rising colour (blue) in the concave region between the isogyres → biaxial positive.
• Falling colour (yellow) in the concave region → biaxial negative.

This method follows from the same addition/subtraction principle as the uniaxial case,
applied to the orientation of the optic plane.

Source: Sturman 2007, DOI: 10.15506/jog.2007.30.7.443 [VERIFIED]

Several situations complicate optic sign determination in practice:

• Wrong orientation: if the stone is not oriented with the optic axis (uniaxial) or
  acute bisectrix (biaxial) sufficiently close to vertical, an off-centre figure results,
  making colour interpretation unreliable.
• High birefringence: very high birefringence (e.g. zircon 0.059, calcite 0.172) compresses
  the isochromatic rings to tiny concentric circles near the melatope; the lambda plate effect
  is harder to read. Thinner sections (or smaller stones) help.
• Low birefringence: very low birefringence (e.g. apatite 0.002–0.006) produces very few
  or no isochromatic rings – the figure shows only the isogyre cross against a near-uniform
  background. The lambda plate still produces a colour shift in the quadrants; read the shift
  in the area immediately around the melatope.
• Dauphiné twinning in quartz: sector-by-sector anomalous extinction can mimic biaxial
  behaviour. Check birefringence (quartz 0.009 is consistent) and look for the sector pattern.
• Anomalous double refraction (ADR): cubic (isotropic) stones that have been strained
  may show anomalous birefringence under the polariscope. They do not have a true optic sign.
  Spinels commonly show ADR (mottled or patchy extinction) rather than a true interference
  figure.

• Sturman, B.D. "Determination of the optic axial angle in biaxial gemstones and its use
  in gemmology." Journal of Gemmology, 30(7), 2007, pp. 443–452.
  DOI: 10.15506/jog.2007.30.7.443. [VERIFIED]
• Read, P. Gemmology, 3rd ed. Routledge, 2012. DOI: 10.4324/9780080507224. [VERIFIED]
• Gem-A Diploma syllabus §3.2: "Optic sign determination from interference figures";
  §4.1: "Optic sign from refractometer rotation."