Sweet Line in Round Diamonds

The proportion combinations that keep a round bright across lighting conditions.

The Sweet Line is the set of crown and pavilion angle combinations that give a round diamond optics close to the Tolkowsky reference.

This article uses these terms:

  • Ca is the crown angle, and Pa is the pavilion angle.
  • Tolkowsky is the reference round diamond with Ca 34.5° and Pa 40.8°.
  • LGF length is the length of the lower girdle facets.
  • GIA EX is the Excellent cut grade of GIA.

Ca and Pa variation

A change of the pavilion angle alone changes the ray path in a round diamond. See Ray Path in Round Diamond. This article shows what happens when Pa and Ca change at the same time.

We vary Ca and Pa together and keep the other round parameters fixed. We chose these two parameters because Ca and Pa have the largest effect on the optics of a diamond.

The diagrams show ASET images and Office videos. A violet square marks the Tolkowsky proportions. The borders of the GIA EX area are gray.

Parameters:

  • Ca and Pa vary
  • Table 57%
  • Star 50%
  • LGF length 80%

Ca-Pa chart of ASET images, with the Tolkowsky proportions in a violet square and the GIA EX area in gray

Pa variation with fixed Ca

When the pavilion angle decreases or increases and the other parameters stay fixed, the ray path in the diamond changes a lot. So the optical characteristics of the diamond change too.

For example, we change the pavilion angle from 40.8° (Tolkowsky) to 41.4° and keep the other parameters fixed.

The diamond with Pa 41.4 is very different from the Tolkowsky round, both in the ASET image and in Office lighting. Note the partial leakage under the table.

ASET images of the Tolkowsky round and of a round with Pa 41.4, with partial leakage under the table

Pa variation compensated with Ca

A smaller crown angle can compensate a deeper pavilion.

In this case, we reduce Ca from 34.5° to 31.5° to compensate the deep pavilion.

The proportions Ca 31.5, Pa 41.4 are optically close to the Tolkowsky round, but have different Ca and Pa values.

ASET images of the Tolkowsky round and of a round with Ca 31.5, Pa 41.4, which look alike

Sweet Line

The Sweet Line is the set of Ca-Pa combinations that give a round diamond optics similar to the reference (Tolkowsky).

Sweet Line on the Ca-Pa chart: ASET images along the line look like the Tolkowsky round

Anti Sweet Line

The line in the opposite direction to the Sweet Line is the Anti Sweet (Bitter) Line. A move along it changes the optics of the diamond a lot.

Anti Sweet Line on the Ca-Pa chart: ASET images along the line change strongly

Vertical variation

This section shows what happens with a vertical move away from the reference on the Ca-Pa chart.

At Pa 40.2, we get the Head Obscuration area. In this area, the arrows of the diamond stay dark while a person looks at it. In such diamonds, blue in the ASET image lowers brilliance, because it creates Dead Zones (Dead Arrows) that are always black.

At Pa 41.4, the diamond has partial leakage under the table, as shown above. The partial leakage area creates both white and black zones while a person looks at the diamond.

The Ca-Pa chart has 3 main areas:

  • the area of good proportions, optically close to the reference (Sweet Line area);
  • the area of Dead Zones caused by Head Obscuration (above the Sweet Line);
  • the area of partial table leakage (below the Sweet Line).

Ca-Pa chart with the Sweet Line area, the Head Obscuration area above it and the table leakage area below it

In practice

A manufacturer can cut diamonds with proportions on the Sweet Line to increase yield and still keep the optical performance.