Removing the Mystique of Glass SelectionRobert E.Fischer Alastair J.Grant,OPTICS 1,Inc.,Dr.Ulrich Fotheringham,Dr.Peter Hartmann,Dr.Steffen Reichel,SCHOTT AGAbstractGlass selection tends to be both a science and an art.It is the intent of this paper to remove the"mystique"surrounding glass selection,primarily based on the chromatic properties of the glass,and to show via careful parametric analyses how we can optimally select glasses for lenses ofdifferent f/numbers,spectral bands,and performance requirements.The important roles ofrefractive index and Abbe number as well as partial dispersion will be considered.Using theSCHOTT glass map,six separate and identifiable regions along with glasses within each regionwill be discussed.The goal for this paper is to make glass selection easier to understand.Basic glass characteristicsThe most basic characteristics of optical glass that influence the glass selection process arerefractive index which refracts light and V number or Abbe number which is used in quantifyingthe variation in refraction with wavelength.Figure 1 shows a plot of the above information onwhat is called an Abbe diagram (sometimes known as a glass map).The abscissa shows Abbenumber increasing from right to left.This places lower dispersion glasses to the left of the mapand higher dispersion glasses to the right.The ordinate axis is refractive index.This maptherefore allows easy selection of glasses with large or small refractive index,or dispersionvalues.The focal length of a lens at the helium yellow d wavelength of 0.5876um can generally bethought of as the primary focal length of a lens.Variation in the foci from red (typically the redhydrogen C lines at 0.6563um is used)to the blue (typically the blue hydrogen F line at0.4861um is used)gives a definition of primary axial color.As the Abbe number increases theamount of shift between red and blue focus decreases.In theory,if the Abbe number wereexceedingly high,such as 500 or 1000,there would be virtually no primary axial color.As theAbbe number decreases,the amount of color shift in focus between red and blue increases.Inorder to create a lens whose red and blue come to a common focus we need to use at least twodifferent materials,one with a low Abbe number and one with a high Abbe number.Table 1 below lists the major terminology describing glass characteristicsParameterDefinitionMain dispersion Principal dispersionAbbe number Va number(na-1)/(nF-nc)Relative Partial Dispersion Px.yRefractivityPrimary Axial ColorAmount of defocus between the best red focusposition the best blue focus positionSecondary Axial ColorAmount of defocus between the best yellowfocus position and the best red focus position.Primary Lateral ColorThe lateral displacement (in the image plane)between the best red image and the best blueimage,commonly known as color fringing.Secondary Lateral ColorThe lateral displacement (in the image plane)between the best red image and the bestyellow image at the d wavelength.Wavelengths usually referencedg=435.834nmC=656.273mm,d=587.562nm,F=486.133nmTable 1:Glass TerminologyRefractive Index2.00Abbe-DiagramCrownFlint◆LASF1.9001.80LAF01.70BASBAFBK71.60SCHOTTlass maKF1.50FKAbbe NumberSCHOTT ML Q1.401009080706050403020Figure 1 shows a typical Abbe diagram provided by SCHOTT AG.The location BK7 and SF2,two of the morepopular and commonly used glass materials,have been noted.Some common plastic lenses have been included forreference.Primary Axial ColorPrimary axial color is defined above as the focal length change between the red and bluewavelength of 0.6563um and 0.4861um(C and F).For a very distant object point,the primaryaxial color can be expressed as follows [3]f'c-fF=f'a {nF-nc)(na-1)=f'a Abbe Number (or V number).....1If in Equation 1,the Abbe number is 2,then the change in focal length between red and bluewill be one half of the basic focal length in the yellow at 0.5876um.The effect of this can beseen in Figure 2,which shows the dispersive properties of a positive singlet element using theexaggerated Abbe value of 2.For this example,Abbe #=262.5mmfcFigure 2 This is a real ray trace showing the red and blue focus positions for a positive singlet with an artificiallyhigh dispersion,V=2.For two lenses in contact we find that the optical power for the group of 2 elements is equal tothe sum of the optical power of the individual components.It can be shown that a lens can bedesigned such that focal length in the red and blue are equal to one another,and this is achievedby using two different materials of different Abbe numbers [3].Specifically,and=Av2-Vi /V2 ..............Equations 2 show how we can determine the focal lengths of the positive powered componentand the negative powered component of a doublet,such that the red and blue focuses are at thesame position.