Fancy-Color Diamonds: Better Color Appearance by Optimizing Cut

Oral Prezentation at IV Gemological Symposium, San Diego, Ca, USA 27-30 Aug 2006

Sergey Sivovolenko, OctoNus Software, Moscow, Russia 
Yuri Shelementiev, Diamond Design, Moscow, Russia

  1. Content
  2. Color optimization method
  3. Diamond absorption spectra
  4. Two representations of colors
  5. A good fancy colored diamond should be bright and saturated
  6. Color potential of a colored diamond plate
  7. DiamCalc ray tracing options and photorealistic images
  8. One spectrum – different cuts and different lightings
  9. Process flow
  10. Exploring rough diamond potential
  11. Rough allocation example
  12. Different allocation plans
  13. Automatic color optimization
  14. Optimization by color
  15. Optimization by contrast
  16. Optimization results
  17. Computer-aided color optimization
  18. Expert considerations
  19. The final stage: expert decision
  20. Verification of the technology: CZ material
  21. Real photos of CZ stones and photorealistic images based on Helium scanned 3d models
  22. Verification on fancy shapes CZ
  23. Summary
  24. More information about diamond cut study technologies
  25. Terms of colorimetry science (Hunt, 2004)
  26. Acknowledges
  27. References

2. Color optimization method

Colored rough diamond challenges:
  • How to get better saturation?
  • How to get better brightness?
  • How to get better color distribution?
  • How to get better yield?
  • How to get it all?

We present a method for selecting rough diamonds,
and determining the optimal shape and proportions

The color optimization technology what is discussed here is closely related to fancy colored diamond cutting. The goal in fancy colored cutting is yield & at the same time color: its brightness, saturation and distribution. Despite centuries of experience there is no rule book or technology for rough selection or best cutting practice. Advances in colorless diamond cut grading are often inappropriate for fancy colored diamonds. In this presentation we discuss which rough diamond can be cut for fancy color and the steps to find the best shape and proportions.

3. Diamond absorption spectra

There is a method to record an absorption spectrum is the visible wavelength range and calculate the absorption coefficient for each wavelength. These data can be used to numerically describe the plate's color in any color system. The best way to get quantitative spectral data is to record spectrum through two parallel windows polished on the rough piece. There are various absorption spectra for different diamonds and we can see examples here.


4. Two representations of colors

The range of all colors of one hue can be represented by different ways.
Two diagrams: Saturation vs. Brightness (top) and Chroma vs. Brighness (bottom) represent the same colors of yellow hue (Munsell 7.5Y). Circles show positions of Munsell color chips and dashed lines outline modern fancy grades of yellow diamonds.

If a hue is fixed, for example, yellow, all colors of this hue described in terms of Saturation and Brightness of through Chroma and Brightness. Two diagrams here have the same horizontal coordinate: brightness but different vertical one on the left - saturation , on the right - chroma. The described technology supports both of these types of coordinates. There is an open question: which representation is the better to describe human abilities to differentiate color and describe this difference. On these pictures the positions of Munsell yellow chips used for color grading on the both diagrams are indicated as blank circles. First we recognize the position of Munsell chips on this diagram (different color system cross reference tables were used). After this we have used color grades for each Munsell chip according to the GIA paper published in Gems&Gemology in 1994.



5. A good fancy colored diamond should be bright and saturated

Munsell color coordinates are converted to xyz in: G. Wyszecki, W. S. Stiles. 2000. Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd Edition. We have converted xyz to Luv color coordinates according to standard formulae.

A good colored diamond should have both high brightness and saturation. On the Brightness/Saturation diagram of the fixed yellow hue one can see yellow colors of different brightness and saturation. These colors are tending to be near the upper right corner.

The Munsell color chips positions are placed as described before.

While grading diamond fancy color a grader determines the masterstone or color chip closest to the graded diamond. For color calculations it is necessary to draw borderlines between different color grades. First we draw these borderlines in the middle between Munsell color positions.

Then we found that sometimes these borderlines have a little logic and we have changed borderlines positions in a way that better describes the logic of color difference. It is just an idea how the current color grading system can be improved in future.

For different diamond spectra shown before, here there are coordinates of the diamond plates of various thickness having same spectra are plotted on the diagram. Here a question comes: at that thickness the given material will receive a fancy grade?

The middle blue line shows that this material can be fancy colored in very thin plates. The red curve shows bigger range between max and min thickness.

From the one hand, maximum and minimum thickness corresponds with the particular color grade. From the other hand, its corresponds with light path in a cut diamond.


6. Color potential of a colored diamond plate

Chroma value C combines Brightness and Saturation.
Fancy-color grades depend on the path length of light through the cut stone.

Here one can see a potential for different spectra to achieve a particular grade, for example Fancy Vivid or Fancy Intense. Chroma on this diagram is a combination of brightness and saturation. The potential means that if a cutter can cut a diamond with a light path between maximum and minimum plate thickness the diamond will be graded accordingly.


7. DiamCalc ray tracing options and photorealistic images

The average ray path length is different for different shapes
DiamCalc photorealistic images: shapes made of the same material

Here there is some information about modeling abilities of Diamcalc software by OctoNus.

1. A user can work with parametrical cut or open a scanned 3D model - more realictic facet positions and symmetry deviations. 
2. The single ray tracing mode can reveal light path coming to diamond from any point. One can see the difference between light path in the assher cut (left picture: light goes out after 2 internal reflections) and in oval cut (right picture: 7 internal reflections). 
3. One can see a photorealistic image of a cut stone with given absorbtion spectrum. In a contrary to usual belief that the deeper stone will have more saturated color appearance it is shown that the flatter oval cut is more saturated because the average light path is longer. Important: photoreal images should be compared at the same illuminating and viewing conditions.


8. One spectrum – different cuts and different lightings

If illumination conditions are changed one can see that that the stone's appearance is also changed. This table represents 10 shapes in 8 different illuminations. Compare round cut and princess. On the related poster this issue is discussed in more details.


9. Process flow

The process flow is suggested for colored diamond cutters. It is a modification of already existing cutting process flow. Initial data are collected with a rough diamond scanner and a spectrophotometer.

  • A few shapes can be selected for further planning on the base of their maximum and minimum light path corresponding with the size of rough stone.
  • A planner comes up with several allocation plans.
  • Color optimization process consists from two parts: computer optimization by color metrics in the case when we can develop mathematical definition and expert evaluation and study of optimization results for better appearance in various lighting and viewing conditions.
  • After good proportions are founded and fixed, we need to allocate these cuts one more time. At this stage the yield can be changed.
  • And if we still have more that one prospective solution, a cutter should decide which one is more preferable.


10. Exploring rough diamond potential


A yellow colored model of the 11,28 ct rough diamond.

Yellow color of the model is due to application of this type of absorption spectrum taken from another diamond.


Here a 3D model of yellow rough diamond and an absorption spectrum are shown. These are initial data.


11. Rough allocation example

Weight, Yield 4.02 ct 44.42 %
Diameter min, max 9.056 mm 11.886 mm
Girdle ratio 1.312      
Pavilion angle 43.00 °    
Crown angle 36.00 °    
Total depth 67.25 % 6.091 mm
Pavilion depth bezel 46.63 % 4.223 mm
Crown height bezel 16.35 % 1.480 mm
Girdle bezel 4.28 % 0.388 mm
Pavilion depth valley 47.56 % 4.307 mm
Crown height valley 17.20 % 1.557 mm
Girdle valley 2.50 % 0.226 mm
Table 55.00 % 4.981 mm
Lower facets 82.00 %    

This is an example of allocation plan for this rough stone including allocation picture and dimensions/proportions table with cutting instructions. It can be more that one allocation plan.


12. Different allocation plans


Plan 1 Plan 2 Plan 3 Plan 4 Plan 5

Oval 4,02 ct

Emerald 1,16 ct

Round 3,00 ct

Round 2,12 ct

Emerald 4,80 ct

Emerald 1,14 ct

Radiant 4,60 ct

Emerald 1,14 ct

Princess 4,24 ct

Emerald 1,44 ct


Here are 5 different allocation plans are shown as DiamCalc photorealictic images of stones with the particular weight. It is easy to delete Plan 2 now: round cuts are less saturated. Other shapes are subject for further optimization by color.

13. Automatic color optimization

Numerical metrics for:

  • dark zones
  • average color brightness
  • saturation
  • chroma
  • color distribution

These enable to compare different shapes and proportions by color.


While we have several metrics for color description we can fix some cut parameters now and change other. Computer can calculate metrics for many proportion combinations and find maximum and minimum. Here it is shown for oval cut.

14. Optimization by color

C*uv= L*Suv

L – Brightness 
C*uv Chroma 
S - saturation

Calculation result for the Chroma metric of oval cut. Crown and pavilion angles were changed. Point 1. after allocation and before color optimization. Point 2. after color optimization. Chroma metric is higher.


15. Optimization by contrast

RC = L x Sd/La

RC - Relative contrast
L – Brightness
Sd - dispersion of Saturation
La – average Brightness

Another important metric is contrast: the lower contrast the better color appearance. This diagram shows the relative contrast function in the same coordinates for the sane stone in the same lighting. Point 2 again better than point 1. This solution will be also better for yield.


16. Optimization results

Chroma value is changing with lighting conditions and can not be easily transformed into a certain color grade.

Color grade borderlines are also changed with hue.

C – Chroma, RC – relative contrast

  Office light, black background Dialite light Dialite light
Tilted 15° up
Before color optimization:

4,02 ct
Cr = 36° P = 43°

Office light: C = 20.24, RC = 0.64 
Dialite light: C = 32.51, RC = 0.21

After color optimization:

5,21 ct
C = 48° P = 47.5°

Office light: C = 28.90, RC = 0.54
Dialite light: C = 31.94, RC = 0.18

Then an expert works with optimization results for each shape. It different lighting conditions one can compare stones before and after optimization:

  • by photorealistic images
  • by color metrics


17. Computer-aided color optimization

Any diamond can be considered as a mosaic of small differently colored areas with certain color coordinates.

A color grade for each proportion set can be determined from a histogram containing information about the total area of each color weighted by its brightness.

The color statistic panel of Diamcalc shows information about color for this stone and for these lighting conditions. One can see a histogram of colors of all virtual diamond facets at the brightness/saturation diagram that was discussed before.

Here we can determine color metrics such as brightness, saturation, chroma, distribution, relative contrast, and also the percentage of facets that corresponds with the particular color grade.


18. Expert considerations

For best computer predicted proportions, color appearance is checked visually with diamond photorealistic color images in different lighting conditions.

Top Row: Plan 1
Oval 5.11 ct
 Download Oval demo small size (DiamCalc DMV Video) 22,8 Mb
 Download Oval demo large size (DiamCalc DMV Video) 71,5 Mb
Bottom Row: Plan 4
Radiant 5.04 ct
 Download Radiant demo small size (DiamCalc DMV Video) 22,8 Mb
 Download Radiant demo large size (DiamCalc DMV Video) 71,5 Mb
Office (Black background) Dialite (Black background) Dialite (15° tilted up)
27.84 0.52
31.85 0.18
34.05 0.18
24.66 0.59
34.25 0.21
35.16 0.18

After the optimized proportions are fixed for each shape, these shapes are optimized to fit in the piece of rough. Some stones became smaller, other - bigger. In this example after this stage only two shapes remain: oval and radiant. One can compare both by DC photorealistic images and by color metrics.


19. The final stage: expert decision

  • Plan 1: 5.78 ct (Oval 5.11 ct + Emerald 0.74 ct)
  • SI1 clarity
  • Office: LxS= 27.84, Contr. = 0.52
  • Dialite: LxS= 31.85Contr. = 0.18
  • Predicted grade: Fancy Intens
  • Plan 4: 5.90 ct (Radiant 5.03 ct + Emerald 0.87 ct)
  • SI1 clarity
  • Office: LxS=24.66, Contr. = 0.59
  • Dialite: LxS= 31.85Contr. = 0.18
  • Predicted grade: Fancy Intense

On the final stage a cutter has a prognosis for both shapes, including the weight of future diamonds, clarity grade, photorealistic images and allocation plans. At this stage he (or she) can choose one plan or discuss with a prospective buyer which plan is better.


20. Verification of the technology: CZ material

CZ plate photo:
RGB = 191; 193; 153
Background RGB: 203; 205; 202
  DiamCalc CZ plate model: 
RGB = 192; 190; 145
Background RGB: 202; 202; 202

This technology was verified on the colored CZ material, which is, in fact, not only diamond stimulant, but a good material to model and study diamonds.

In the DiamCalc in order to go from diamond to CZ a user should change refractive index, dispersion and absorption spectrum.

Here are a photo of a CZ colored plate and the same plate and light modeled. See the proximity of RGB values for the plate color and for the background color.


21. Real photos of CZ stones and photorealistic images based on Helium scanned 3d models

Photos taken with ring fluorescent light source
Images modeled in DiamCalc from Helium scans Open in DiamCalc Open in DiamCalc Open in DiamCalc Open in DiamCalc Open in DiamCalc

After a cut CZ stone with proportions close to Tolkowsky was scanned we compare real photos with DC photorealistic images. We have used a symmetrical ring fluorescent lighting as a light source for taking photos and the same illumination conditions were modeled in DiamCalc. These images taken with different distances from light source to diamond. You can see how photographs close to modeled images.


22. Verification on fancy shapes CZ

Photos taken with ring fluorescent light source
Images modeled in DiamCalc from Helium scans

The same veification work was made for various fancy shapes.


23. Summary

  • Using software the cutter can refine a plan for a trade off between yield and color
  • Often a slight decrease in weight, and better color appearance can result in more value
  • Combined color optimization software and expert’s judgment leads to:
    • better color brightness and saturation
    • avoids negative optical phenomena

In summary, we would like to stress that all modern computer tools can not replace expert judgments and the best results can be obtained with a proper combination of software modeling / optimization and human expertise.

These results in the direction that was discussed here should be in better color appearance, less negative optical effects and more value.


24. More information about diamond cut study technologies


25. Terms of colorimetry science (Hunt, 2004)

  • Brightness L - the extent to which an area appears to exhibit light.
  • Colorfulness M - the extent to which the hue is apparent.
  • Saturation Suv - relative colorfulness judged in proportions to the brightness of the object itself.
  • Chroma C*uv - the colorfulness of an area judged in proportion to the brightness of a similarly illuminated area that appears to be white (or highly transmitting).
  • Lightness J - the brightness of an area judged relative to the brightness of a similarly illuminated area that appears to be white (or highly transmitting, in the case of transparent objects).


26. Acknowledges

Aleksander Medvedev, Vladimir Onishchuk, Sergey Savrasov, Artem Resnynskiy and Evgenia Kuznetsova - for DiamCalc software modifications that made this work possible and for help during preparation of this paper.

Maxim Viktorov for spectra recording.

Roman Serov for discussions and optimization work.

Ksenia Gorbenko and Petr Pisarev for preparation of illustrations.

Garry Holloway for useful suggestions and text edition.

Our wives and children for their patience.


27. References

1. Hunt R.W.G. (2004). The reproduction of color. John Wiley&Sons, 6th edition, 702 pp.

2. King J.M., Moses T.M., Shigley J.E., Liu Y. (1994)

3. Color grading of colored diamonds in the GIA Gem Trade Laboratory. Gems & Gemology, Vol. 30, No. 4, pp. 220-242.

4. Wyszecki G., Stiles W. S. (2000) Color Science: Concepts and Methods, Quantitative Data and Formulae. Wiley-Interscience; 2nd edition. 968 pp.