IIPTIIIA V
`MIIA
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`The International Journal of Applied and Theoretical Optics
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`Page 1 of 14
`
`GIA EXHIBIT 1004
`
`

`
`OPTICA ACTA
`
`The International Journal of Applied and Theoretical Optics
`
`English Editor and Honorary Secretary
`1... R. BAKER, Sira Institute Ltd, South Hill, Chislehurst, Kent BR’? SE1-I, U.K.
`
`Rédactear Frangais
`F. ABBLES, Laboratoire d’0ptique des Solides. Université Pierre et Marie Curie,
`4 place Jussieu. 75230—Paris Cedex 05, France
`
`Detttscher Herausgcber
`J. HERTEL, Optisches lnstitut der Technischen Universitiit, 1000 Berlin 12,
`Strasse des 17 Juni 135. Federal Republic of Germany
`American Editor
`BRIAN J. THOMPSON, Dean. College of Engineering and Applied Science.
`The University of Rochester, Rochester, New York l462?. U.S.A.
`
`Japanese Editor
`K. MURATA, Department of Applied Physics, Faculty of Engineering,
`Hokkaido University, Sapporo, Japan
`
`Editorial Advisers
`R. W. DITCHBURN. F.R.S., U.K., E.
`INGLESTAM, Sweden, A. MARECHAL. France.
`G. TORALDO or FRANCIA, Italy
`
`Advisory Board
`Chairman: H. H. HOPKINS, F.R.S.. U.K.
`
`Representing the International Commission for Optics
`K. M. BAIRD, President (1975-1978)
`J.-CH. VIENOT. Secretary General (1975-4978)
`
`Members: F. Aussnunoo, Austria (1981). K. BIEDERMANN, Sweden (1980). J. M.
`BURCH, U.K. (1981), P. D. CARMAN, Canada (1979). M. DE, India (1979). H.
`J.‘
`FRANKENA. The Netherlands (1979). P. Hssrmmn. Australia (1979), A HERMANSEN.
`Denmark (1978), G. KOPPELMANN, Germany (1978), A. KUJAWSKI. Poland (1981),
`A. LOHMANN, Germany (1978). G. M. Marrsnnv. U.S.S.R. (1978). LAURA RDNC.'Hl- .'
`Annozzo, Italy (1979), J. SANTAMARIA. Spain (1981),
`I. Sanmvi, Czechoslovakia l
`(1980). I. TSUJIUCHI. Japan (1973), A. VANDBR LUGT, U..S'.A. (1979).
`Permission is hereby given for the reproduction of authors’ abstracts contained }
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`@) 1978 Taylor 3: Francis Ltd.
`ISSN 0530-3909.
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`Page 2 of 14
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`

`
`1vBn&'—nqIpxtnD(my'q:—f|i2I1usn:a]
`
`OPTICA ACTA, 1978, VOL. 25, NO. 8, 681-692
`
`A statistical assessment of brilliance and fire for the
`round brilliant cut diamond
`
`'
`
`I. S. DODSON
`Blackett Laboratory, Imperial College, London, England
`
`(Received 27 April 1978)
`
`Abstract. The 58-facet round brilliant cut diamond is considered as a random
`scatterer of incident light. The diamond, of an axisymmetric design, is con-
`sidered to be spinning and surrounded by a hypothetical sphere. The optical
`properties brilliance, sparkliness and fire are represented by statistical properties
`of the intensity distribution on the sphere. Using a computer model of the system.
`the effects on the three optical properties of changing the length of the pavilion
`halves and the table spread were investigated. The results confirmed that the
`traditional ‘ ideal ' cuts are satisfactory, showing the trade-off between sparkliness
`and fire that results with these ideal cuts. A new style is proposed with a
`deeper pavilion angle (53°), and this is shown to be superior to the traditional
`styles using the statistical measures.
`
`1. Historical survey
`Diamond has been valued as a talisman since ancient times, but only since the
`17th century, and the styles associated with Cardinal Mazarin and Peruzzi, has
`cutting to produce a pleasing optical effect become popular. A stage in the
`development of the point cut into what now is called the round brilliant cut
`diamond, by trial-and-error methods aided by serendipity, was the ‘ old mine
`cut ’ style (see figure 1), popular at the turn of this century. This style, with its
`high crown, steep pavilion and recognizable arrangement of facets, exhibits the
`three prized effects in a gemstone—brilliance, a measure of the light
`that,
`entering the crown of the stone, is scattered out of the crown facets, sparkliness,
`the amount by which this light sparkles, and fire, the chromatic variation of the
`sparkles. These visual effects are still quantified by reference to :experienced
`judgement, there being no engine available to measure all three parameters.
`
`Figure 1. The old mine cut style (after Tolkowsky [1]).
`
`With the fashion for mathematical determinaism in Victorian science, which
`carried over into the 20th century, it was inevitable that a mathematical descrip-
`tion of the optical effects in a polished diamond should be sought.
`It was in
`1919, when the technical optics section at Imperial College was ‘ one and just
`
`Page 3 of 14
`
`

`
`682
`
`j’. S. Dodson
`
`begun ’, that Tolkowsky published a book, Diamond Design [1], while a member
`of the City and Guilds College (now the engineering school of Imperial College).
`This theoretical monograph was the first attempt to list the causes of the optical
`effects in gem diamond and set some simple criteria for their measurement.
`Taking as his starting point a simple triangular cross-section, he used geo-
`metric and optical arguments to justify the necessity for, number of and arrange-
`ment of the facets on the centrosymmetrie round brilliant cut diamond that was the
`old mine cut, and hence to confirm this as the ideal style for cutting a gem
`diamond by defining a criterion for maximum brilliance. This stated that the
`optical goodness of a stone is the product of the angular dispersion for a red and
`blue ray and the transmitted intensity for a green ray at the same angle of
`incidence. However, in the derivation of the functional form of this product,
`[1, p. 72] he appears to have confused Lambert’s law with Fresnel’s equations,
`and hence fortuitously deduces the ideal pavilion angle to be 402;”.
`If the
`brilliance criterion is calculated using the exact formulae, but otherwise following
`the analysis of Tolkowsky, an ideal pavilion angle of about 39;” is found.
`It is to be noted that Tolkowsky’s ideal proportions (see figure 2) are accepted
`by the Gemmological Association of America as the best of the ‘ideal’ proportions
`proposed up to the present time.
`
`I
`
`Ibo. o
`
`J5-o
`
`I
`
`I
`
`.I
`
`l
`
`Figure 2. The ‘ ideal ’ proportions proposed by Tolkowsky [1].
`
`In 1926, Johnsen [2] used similar geometric methods to obtain another
`idea] set of proportions. These had a pavilion angle of about 39°, similar to the
`more exact analysis of Tolkowsky.
`In the same year, Rijsch [3] published a set
`of ideal proportions and also developed a technique for producing, ‘for a gem
`diamond, a reflection spot picture, the light analogue of the X-ray back-scattered
`Lauegram. These spot diagrams can be used to aid identification and to assess
`the optical goodness of the gem.
`One prevalent argument at the time was that these optically ‘ ideal ' cuts were
`less economic than the mine cut since more material was removed, resulting in a
`lower yield from the rough. Because extra material had to be removed, and a
`higher accuracy and standard of workmanship were demanded, the stones took
`longer to manufacture and so the new styles were slow to be adopted. The final
`value of a stone depends on the ‘ four-Cs '———cut, colour, clarity (the freedom from
`
`Page 4 of 14
`
`

`
`Brilliance and fire of the round brilliant cut diamond
`
`683
`
`both internal imperfections and artefactual blemishes) and carat weight (1 carat=
`200 mg). By appraising many stones, Eppler [4] produced in the 19303 a set of
`practical cuts which helped to combat the resistance to the new styles of cutting.
`In a paper which appeared in 1968, Eulitz [5] adopted a geometrical approach
`similar to that of Tolkowsky and Iohnsen. Elbe [6, 7] has also produced some
`designs for a new type of round brilliant, as well as a diamond grading engine
`based on the method of Roach. Most recently, Stern [8] has developed a
`computer programme that uses finite ray-tracing methods, and has confirmed
`that the traditional ideal cuts are satisfactory. He fails, however, to discuss any
`quantitative measures of optical goodness, proposing only a loose criterion for
`optical quality that is a restatement of a well-known preference;
`this will be
`given in the next section.
`
`2. Factors affecting optical goodness
`The non-expert normally observes a diamond set into jewellery with the
`pavilion obscured by the setting in diffuse illumination, with the unaided eye,
`and at a distance of about 50 cm (a relaxed arm’s length). The observer moves
`both his head and the stone, and the overall brightness, rate of sparkle and
`chromatic variations in the sparkles are translated into degrees of optical at-
`tractiveness.
`It would appear that, when he judges optical attractiveness, the
`observer has in mind certain general principles and some specific likes and dis-
`likes.
`In particular the illumination over
`the stone should be reasonably
`uniform, and there are two styles which offend this rule in the round brilliant
`out. One is a stone with a deep pavilion (pavilion anglec:4-5°), which gives the
`impression of a dark table, which is not surprising since the table—pavi1ion
`combination is like a corner—cube retro-reflector with the observe1’s head forming
`a dark central obstruction. The other is a stone with a shallow pavilion angle (of
`37° or less) where the girdle, which often has a brutted or frosted appearance, is
`visible through the table as a white ring.
`In general terms, the greater the number
`and the smaller the average size of the sparkles, the more evenly will they be
`distributed.
`If this situation were to be modelled in every detail by a computer
`programme, it has been estimated that three hour’s computing time would be
`required to perform the ray tracing alone, before any analysis of the data would
`be possible. A refinement of the Rtisch’s method [3] was therefore adopted,
`
`3. The diamond grading model
`A diamond is sourrounded by a hypothetical sphere centred on the table ;
`rays in several azimuthal and meridional orientations, a form of pseudo-diffuse
`illumination, are then traced through the diamond, noting their Fresnel com-
`ponents at each partial transmission or total internal reflection, for it is necessary
`to know both the intensity and direction of the rays. The final positions on the
`sphere of rays scattered out of the prism are then calculated, and since the
`intensities of the spots at those points are known, a map of intensity ‘can be built
`up for a given sphere radius and a particular refractive index. By tracing at
`different refractive indices, the various colours can be modelled.
`In using this
`technique, one piece of information is lost :
`the position on the stone from which
`the light came. Thus it is not possible to directly take account of the visible
`girdle or dark table effects in this approximation. The resultant spot pattern for
`
`Page 5 of 14
`
`

`
`684
`
`a good diamond is a random scatter of points in the whole of the forward
`hemisphere, and some property of this randomness is required as the measure of
`optical goodness.
`The overall brightness is relatively easy to define :
`..
`Intns't
`ctte d°tfwdd'ct'n
`Forward br,11,ance=
`Total illumination
`
`But how are sparkliness and chromatic Variation to be measured ? Two
`authors have given the analysis of spot patterns some consideration. Elbe [7]
`used a photometer to measure the intensity distribution of a diamond, the stone
`being rotated while a radial scan of the intensity distribution was made.
`resultant distribution, the total number of sparkles was taken as the measure of
`optical goodness. Stern [8] modelled the ‘ gemprint ’ of Bar-Isaacs, which
`uses the same technique as Riisch and Elbe except that a laser light source, in
`which a lens brings the far-field diffraction pattern to a convenient image plane, is
`used. Stern's criterion was that the far—field diffraction pattern should show an
`even distribution of spots, which is, in fact, a special case of the well-established
`criterion that an even distribution of sparkles is preferred. No chromatic effects
`could be measured because of the laser illumination. Elbe’s criterion, based on a
`count of sparkles, also only partly fulfils the requirements of a visual grading
`measure for diamond ; again no criterion for chromatic variation was given.
`However, Elbe’s simplification of the two-dimensional intensity distribution to a
`one—dimensional intensity scan, coupled with a technology that enables scans for
`several wavelengths to be made, yields a technique and data base that are suitable
`for further analysis.
`The analysis of random signals has led to ideas of correlation analysis. The
`thesis of this paper is that the intensity scan produced by a gem diamond can
`be considered and analysed as a random signal.
`In particular, the two questions,
`how sparkly and how fiery a diamond is, are asked in terms of probability theory
`in the following way : how different in intensity is each point in the distribution
`of light from each other point, and how different is the distribution in red light
`from those in green and blue E‘ The answers are obtained by autocorrelating the
`intensity distribution and cross-correlating say, the red and blue intensity scans.
`In our case, we require an even distribution of sparkles and a measure of their
`average size, which is given by the half-width of the autocorrelation.
`In one dimension the autocorrelation of a constant is another constant, but
`that of a far-field speckle pattern from many diffusing elements has the well-
`known gaussian form. For a diamond, these would correspond respectively to
`no sparltliness, the worst case, and to an even distribution of sparkles.
`A suitable measure for sparkliness would therefore be how far the auto-
`correlation deviates from a constant ;
`the higher the deviation, the better, in a
`sparkling sense, for the diamond. Such a possible measure is the variance of a
`
`distribution,
`
`<x2>—[r1=.
`
`which enables a sparlcliness criterion to be defined as the variance of the auto-
`correlation of the total radial intensity scan, where, as done by Elbe, the diamond
`is rotated, and for a particular azimuth with respect to the table normal all the
`
`Page 6 of 14
`
`

`
`Brilliance and fire of the round brilliant cut diamond
`
`685
`
`intensity spots are sampled, whatever meridional angle they subtend. Concern-
`ing the fire, the intensity distribution is calculated for wavelengths in the red,
`green and blue regions of the spectrum. An argument similar to that used for
`sparkliness is proposed, the variance of the cross-correlation of the red and blue
`fields being taken as a measure of fire. However, if the red and blue fields are
`equal, and equal to the green field, this cross-correlation would yield the same
`result as would the autocorrelation. That is, if
`
`then
`
`R+G+B
`
`3
`
`“”
`
`(=D)=R=G=B,
`
`_[D(u) 4: D(u+ A) du= _[R(u) It B(u+A) du,
`which implies white sparkles. Hence the proposal for a measure of fire is that it
`is the quotient of the variance of the cross-correlation for the red and blue
`intensity scans and the variance of the autocorrelation of the total intensity
`distribution.
`We now have a measure for brilliance, sparkliness and fire. Some might
`prefer a more simple, single figure for the optical goodness of a gem diamond,
`instead of a triplet. One method of assigning a single figure to each point in the
`intensity distribution is to assign colour~coordinates to the elemental areas, i.e.
`R
`B
`
`R+G+R R+G+E
`
`and then form a colour-difference coordinate for each point (R — B)/(R + G + B).
`The variation of this factor, which we can call the differential chroma, could then
`be used as a simple measure of fire.
`Similarly for sparkliness, we could take the
`variation of the intensity distribution.
`;However, sith the forward brilliance
`three factors are again required to fully describe the round brilliant cut diamond,
`and so it would be naive to expect a single quantity to describe the optical good-
`ness of such a complex effect.
`
`4. The computer programme
`A computer programme was written to incorporate the details of the model
`and calculate the statistical measures outlined above.
`It can be split into three
`major units: the calculation of the shape of the prism, the ray-tracing through the
`
`§TART
` convert spot-d iogrnm
`cnrculote shape N
`W10 in‘ieF'5lW
`of
`Fish‘!
`distribution
`
`truce ruys onto
`surface of prism
`
`tr-ace rays
`
`.thr‘ough prisrn
`
`trace rays onto
`spherical
`image Dione
`
`colcufotei
`brilliance
`
`sporkliness
`
`Itje
`
`Outut dam
`
`Figure 3. The basic structure of the computer programme.
`
`Page 7 of 14
`
`

`
`636
`
`_7. S. Dodson
`
`a schematic
`
`prism and the statistical analysis of the resultant spot pattern;
`diagram of these main elements is given in figure 3.
`The calculation involved in finding the direction cosines of the normals for
`the planes that define the prism can be greatly reduced by exploiting the eight-
`fold rotational and mirror symmetry of the round brilliant cut (see figure 4), this
`resulting solid (see figure 5) having only eight bounding planes. Then by
`requiring that the table when, viewed perpendicularly, should form with the
`stars two interlocking squares, it is possible to describe the prism in terms of six
`factors. These are the total spread, the table spread, the crown height, the
`pavilion depth, the total depth and the pavilion half—factor (PHF), the fraction by
`which the pavilion halves extend towards the collet from the girdle (see figure 6).
`
`Figure 4-. The round brilliant cut for clia-
`mood, showing the facet names.
`
`the
`Figure 5. The generating solid for
`round brilliant cut.
`The plane
`labelled a is the false plane.
`
`l--total spread ———-I
`stable spread-I
`
`c:-own height
`1'
`l
`povil ion
`deth
`
`-1
`
`Figure 6. The proportions for the round brilliant cut diamond.
`
`The ray-tracing section has three subdivisions. The first traces the input
`rays to the surface of the prism, the second traces the rays, using vector ray
`tracing equations, through the prism, and the third traces rays scattered out of the
`prism onto the hypothetical sphere. The false planes of symmetry (see figure 5)
`have special optical properties;
`the Fresnel equations are not applied, as the
`planes are only a mathematical device, and all rays are simply reflected, whatever
`their angle of incidence.
`Finally, the statistical package calculates the measures for brilliance, sparkli-
`ness and fire, both the autocorrelation and cross-correlation being approximated
`by a serial product, i.c. for a function
`the serial form is
`ac.-I-[I at (i-l-1]]
`
`T(z')=
`
`I
`
`x.+(¢x:'
`
`, mu) :1»-
`
`Page 8 of 14
`
`

`
`Brilliance and fire of the round brz'i'h'ant cut diamond
`
`For two functions, say T(r') and S(£), the serial product is
`
`P(j) =
`
`T(z') x S(r'+j).
`
`This package also contains routines for producing graphical output on the
`systems in use at the Imperial College Computer Centre.
`-4
`
`5. The effect of the pavilion halfv-factor
`Of the many approximate calculations that have been made of brilliance and
`fire, only one has used a three-dimensional model, and of the two-dimensional
`models many have considered only the classic diamond cross—section A—A in
`(figure 7).
`It has been argued that the table, kites and pavilion mains are the
`principle facets, and that the stars and halves play only a secondary role in optical
`effectiveness. Historically, the fashion was to polish the table to about 40 per
`cent of the diameter of the stone and to have short pavilion halves, and for such
`cuts the argument about principal and secondary facets was probably valid.
`Recently, however, especially in Europe, the fashion has been to polish the table
`to up to 65 per cent of the total spread and the pavilion halves to up to 80 per
`cent of the distance from girdle to collet.
`In this case, the pavilion halves have an
`area greater than the pavilion mains, and the two-dimensional argument breaks
`down.
`Some authors have tried to overcome this problem by considering a
`non-complex two-dimensional cross-section (such as B—B in figure 7). This
`can only, at best, be considered a first approximation as the normals to the facets
`for these cross-sections do not
`lie in the same plane. Hence the three-
`dimensional character of the prism must be considered. The programme was
`used to investigate the effect of changing the PHF for a round brilliant cut
`diamond with a crown height of 15 per cent and a table spread of 50 per cent, a
`style not dissimilar to that of Tolkowsky [1].
`In addition, the pavilion angle is
`
`Figure 7. The round brilliant cut diamond showing the classic cross-section (a—-a), and a
`more complex cross-section (b—b).
`
`Page 9 of 14
`
`

`
`683
`
`j‘. S. Dodson
`
`restricted to between 37 and 45°, the range into which all so-called ‘good’
`brilliants fall. The results are presented in figures 8 to 13.
`
`brilliance
`
`
`
`var-lanceofIntensitydistribution
`
`pavilion angle
`
`Figure 8. The effect on brilliance of a
`change in PI-IF : PHI-‘=0-2, full
`line; PHF = 0-5, dashed line; PI-IF:
`0-8, dash-dotted line.
`
`Figure 9. The effect on the variance of
`the intensity distribution of a change
`in PHF (values as in figure 8).
`
`pcwl lion angie
`
`
`
`differentialchroma
`
`DWEFFOH GnQ!e
`
`Figure 11. The effect on the sparkliness
`of a change in PHF (values as in
`figure 8).
`
`spurkliness
`
`pavmon angle
`
`Figure 10. The effect on the differential
`chroma of :1 change in PHF (values
`as in figure 8).
`
`Page 10 of 14
`
`

`
`Bn'1!z'ance and fire of the round brflliant cut diamond
`
`varianceofcross-cor-r-elation
`
`poviiion angle
`
`pavilion angle
`
`Figure 12. The effect on the variance of
`the cross-correlation of a change in
`PHF (values as in figure 8).
`
`Figure 13. The effect on fire of a change
`in PHF (values as in figure 8).
`
`6. Discussion of the effect of the pavilion half-factor
`The forward brilliance is fairly constant over the range of pavilion angles, and
`equal for all the PHFs), thus confirming that forward brilliance alone is no guide
`to the optical goodness of a diamond.
`-
`Considering first the variance of the intensity distribution, all PHFs have a
`peak value for a 40° pavilion with PHF 0-8 and 0-2, peaking again at 4-3 and 45° ;
`the results for the differential chroma are still more confused. The accepted
`ideal pavilion angle being 41°, PHF 0-8 and 0-5 peak at 39° in accord with
`Tolkowsky exact and Johnsen while the differential chroma increases again for
`pavilion angle 4-5° independent of PHF.
`.
`Considering the measure for sparkliness, both PHF 0-2 and 0-5 peak at
`pavilion 41° and PHF 0-8 peaks at 40° with 0-5 max > 0-8 max > 0-2 max. Again
`the Sparkliness increases for all PHFs at pavilion 4-5° ; however, these values are
`less than those at the preferred pavilion angle. The measure of fire gives a less
`confused result than the differential chroma : all PHFS peak at a 41° pavilion
`with the PHF 0-8 15 per cent greater than PHF 0-5.
`As the normal practice is to keep_ the pavilion angle between 39° and 42°,
`and as it is possible to gain a higher yield from a piece of rough diamond with a
`lower pavilion angle, the shallow pavilion style is often encountered. For a
`pavilion 39°, PHF 0-S still shows more sparkliness than either PHF 0-2 and 0-8.
`However, the fire factor of PHF 0-8 is 45 per cent higher than PHF 0-5. Thus
`the effect of the economics of production may have resulted in a stone with lower
`sparkliness and higher fire, which is acceptable to the current fashion.
`
`7. The effect of varying the table spread
`Let us now consider the other current fashion, that of polishing the table to
`up to 65 per cent of the total spread, bearing in mind that the ‘ideal’ table
`diameter is 50~55 per cent of total diameter, and that the earlier preference with
`the old mine style was for 4-0 per cent table spreads. Recall also that Elbe has
`
`cm.
`
`3 C
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`690
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`y
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`3. s. Dodson
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`produced a_ design for a brilliant that has a pavilion angle outside the range
`39-423, and that several other authors have also produced designs with un-
`orthodox proportions and facet arrangements. The programme was used to
`investigate pavilion angles of from 37 to 55°, virtually the angle of the octahedral
`face, a typical ‘ habit ’ for rough diamond, the PHF being held at 0-5. The
`results are presented in figures 14-19.
`
`briiiiance
`
`3'97
`
`:7?‘
`i.E3'_1
`pavilion ongie
`
`51'
`
`Figure 14. The effect on brilliance of a
`change in table spread. Table spread,
`in percent: A, 40;
`[Z], 50; O, 60;
`x , 70.
`
`(D
`
`
`
`varianceofintensitydistribution
`
`°°V“'°" angle
`
`Figure 15. The effect on the variance of
`intensity of a change in table spread
`(symbols as in figure 14-).
`
`
`
`differentialchroma
`
`sparkliness
`
`pavilion angle
`
`pavilion angle
`
`Figure 16. The effect on the differentia—
`tion chroma of a change in table
`spread (symbols as in figure 14-).
`
`Figure 17. The effect on the sparkliness
`of a change in table spread (symbols
`as in figure 14).
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`Brflfiance and fire of the round brz'H1'ant cut diamond
`
`0'1
`
`varianceofcross-correlation
`
`pwmon angle
`
`pavilion angle
`
`Figure 18. The effect on the variance of
`the cross-correlation of a change in
`table spread (symbols as in figure
`14-).
`
`Figure 19. The effect on the fire of a
`change in table spread (symbols as
`in figure 14).
`
`8. Discussion of the effect of changing the table spread
`The brilliance falls off with increasing table spread, exhibiting progressively
`two sets of peaks centred on pavilion angles of 4-1-43° and 51-53“. Again, the
`simpler measures of sparkliness and fire are confused, both having many peak
`values in the pavilion angle range 3'}'—55°.
`The results for the two statistical measures of brilliance and fire are again less
`confused. The double peak seen for the brilliance appears again for the sparkli-
`ness. The 4-0, 50 and 60 per cent table designs peak at pavilion angle 41°, the 70
`per cent design at pavilion 4-5 °, the second set of peak values occurring at pavilion
`51° for the 60 and 70 per cent tables and 53° for the 40 and 50 per cent tables.
`In terms of fire, the 40 and 50 per cent tables still peak at a 41° pavilion angle.
`While the 60 and 70 per cent tables are falling at 41° pavilion, being lower by
`50 per cent over the preferred pavilion range 39-42”, the position is reversed, these
`table spreads having, at 39°, a value higher by 55 per cent than the 50 and 4-0 per
`cent table spreads.
`We can invoke the previous argument that 39° pavilions are as acceptable as
`41° pavilions, and that the lower sparkliness can be compensated by an increased
`chromatic effect without detriment to the stone's optical goodness ;
`the modern
`practice of large tables and long pavilion halves can then be accounted for in
`some measure by economic expediency influencing a caprice (more fire,
`less
`sparkle) of fashion, another popular belief being that a stone with a larger table
`looks bigger for the same diameter.
`The statistical measures for sparkliness and fire confirm the traditional ideal
`proportions are correct ;
`they also help to reconcile the differences between the
`sets of ideal proportions by showing the increase in sparkliness and loss in fire
`for the PHF 0-5 4-1° pavilion against the PHF 0-8 39° pavilion. This helps to
`establish a scale of optical goodness but no definite conclusions can yet be drawn
`
`3C2
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`692
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`Br£2l:'a:rzce and fire of the round br:'!z'z'ant cut diamond
`
`It is,
`as to how much greater sparkliness is valued above fire, or vice versa.
`however, tentatively suggested that brilliance and sparkliness are the two most
`important factors.
`
`9. A proposed new cut
`The multiple peaks in the sparkliness and fire factors lead to the conclusion
`that the traditional design for the round brilliant cut diamond is not the only
`solution.
`It is proposed that a design with a table spread of between 40 and 50
`per cent, crown height of 15 per cent of the total spread, a pavilion angle of 53°
`and pavilion half—factor of 06 would look as attractive, if not more so, than a
`stone of similar diameter in the traditional preferred proportions.
`
`ACKNOWLEDGMENTS
`
`I would like to thank Professor W. T. Welford for his encouragement during
`the course of the project and useful discussions concerning this paper.
`I am also
`indebted to the Diamond Trading Company (Pty) Ltd. for supporting the pro-
`_ ject, and their Executive Committee for permission to publish this paper.
`
`REFERENCES
`
`[1] TOLKOWSKY, M., 1919, Diamond Design (London : E. 85 F. N. Sport).
`[2] JOHNSEN, A., 1926, Silver. preuss. Akad. W£ss., 19, 322.
`[3] Riiscn, S., 1926, Deutxche Goldsehmiedeztg, Nos. 5, 7, 9.
`[4] EPPLER, W. F., 1934, E'a'eZste:'ne mid Schmucksteine (Leipzig).
`[5] EULITZ, W., 1968, Gems Gemol, 12, 263.
`[6] ELBE, M., 1971, Z. dt. Gemmol. Gen, 20, 57.
`[7] ELBE, M., 1972, 2'. dz. Gamma}. Ges., 21, 189 -, 22, 1.
`[8] STERN, N., 1975', M.Sc. Thesis, Weizmann Institute, Rehovot, Israel.
`
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