Definition of DN
Question
What is the definition of DN? I notice that if I load N-BK7 from the Schott catalog, convert it into a model glass, and mark the dispersion (DN) of the glass as a variable, the initial DN is calculated as DN = 0.246045 while the VNBR = 64.16641. How do you calculate one from the other?Synopsis
Definition of DN, the material dispersion variable that is used in the optimizationSolution
Important:
Before reading this Knowledge Base item, it is recommended that you first read the Knowledge Base item titled Clarifying use of the terms "dispersion" and "V-number.
Most optical engineers are used to seeing a glass map where the refractive index (nd) is graphed versus V-number (Vd) [See hotlink above for these definitions]. This graph results in the commonly available glasses lying along a curved " glass line". During optimization, it would be difficult to limit glasses to this curved glass line. The area containing available glasses is a very ill-defined spaced when you are limited by the variables "nd" and " Vd". To view an example of this glass map, choose the OSLO menu item: "Lens>>Glass Catalogs>>Browse Glass Database>>Schott" and click on any glass name in the resulting database.
OSLO chooses a different approach to defining the variable space for glass optimization within OSLO. If you graph the Refractive Index of a glass (RN1) versus its Dispersion (RN2-RN3), the commonly available glasses that make up the "glass line" will fall along a straight line (see the graph below). Note also, that the area containing the available glasses fits in a roughly triangular shape. For a complete discussion on this topic, see the last 2 pages of Chapter 2 in the OSLO 6.x Optics Reference.
The variation of the optimization variables RN and DN are shown by double-sided arrows in the above graph.
RN is simply the refractive index of a material at wavelength #1 (RN1).
The variable DN varies the dispersion without changing the refractive index. DN is also normalized in such a way that a value of 0.0 corresponds to a point along a line connecting the glass SK16 to the glass FK5, and the value 1.0 corresponds to a point along a line connecting the glass SF11 to the glass FK5. Note that DN=1 is aligned along the glass line. Normalizing DN results in a rather complex equation:
Given: X & Y are glasses on the glass mapand Disp(X) = nF(X)-nC(X)and fm(X,Y) = (nd(Y)-nd(X))/(Disp(Y)-Disp(X))Then A = (fm(SK16,FK5)*fm(SF11,FK5))/(fm(SK16,FK5)-fm(SF11,FK5)) B = -1/fm(SK16,FK5)and DN(X) = [[(Disp(X)-Disp(FK5))/(nd(X)-nd(FK5))] + B] * A"
