Grid Gradient

This surface is a flat circular surface with an index of refraction defined for a grid of coordinates in three dimensions. The index data is user defined and is stored in any ASCII file with a .GGD extension. Select the file name from the "GGD File" control of the Type tab of the Surface Properties dialog (see "Surface Type"). The index data file must reside in the <glass> folder (see "Folders"). OpticStudio will interpolate between the points defined in the GGD file using a tri-cubic spline. When the selected surface type is Grid Gradient, the index is calculated based on the specified grid data file, and not the material cell in the Lens Data Editor.

GGD maximum file size

The maximum size of the GGD file is based on the following formula:

 
limit = 6400*nx*(1 + ny + ny*nz)
 

In 32-bit we require that limit is less than 1 billion (1E9), while in 64-bit we require that limit is less than 4 billion (4E9).

GGD File Format

The file is split into two parts: the first line is the header and the second is the index and dispersion data. The header contains information about the contents of the file and the dispersion formula that OpticStudio will use. The main part will contain either index data, dispersion coefficients or both. The syntax is shown below.

 
DISPERSION_FORMULA_IDENTIFIER NX NY NZ DX DY DZ
X Y Z n0 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10
.
.
.
 

In the header, the dispersion formula is a string that corresponds to one of the dispersion formulas described under "The glass dispersion formulas". The dispersion formula identifiers are the formula names with the spaces removed (e.g. the Sellmeier 3 formula would be Sellmeier3). Only those formulas listed in the aforementioned section are currently supported. The NX, NY and NZ values are the number of x, y and z points in the file, respectively. These values must be greater than 5. The DX, DY and DZ are the spacing between the points in x, y and z, respectively.

In the main body of the file the first three values are the x y and z coordinates. These should be evenly spaced points that increase monotonically over their range. That is, z should increase from zero to its maximum extent before repeating for the next set of x and y coordinates. The first index value is n0, which is an index offset that can be set to zero if it is not required. The constant index offset is applied to the index, after it has been calculated from the dispersion data given. The remaining values are dispersion coefficients that can be used to define an index distribution through the selected dispersion formula. For example, if you wished to define a Schott dispersion formula you would use the first six coefficients C1 through C6 and define the rest as zero. You would also have to make sure that Schott is the dispersion formula identifier defined in the file header. If you wish to define an index using the offset only, select a dispersion formula without a unity term, for example the Schott or Sellmeier 3 formulas, then set all the dispersion coefficients to zero. In this case, the index calculated via the dispersion relation is made to return 0, so that index of refraction is defined strictly by the constant index offset term.

The maximum step size is the only parameter for this surface type. See "Discussion on maximum step size for GRIN surfaces" for details.

Restrictions on Surfaces Following Grid Gradient

Surfaces other than the following are not allowed to be placed directly after a Grid Gradient surface.

  • Even Asphere
  • Extended Polynomial
  • Extended Asphere
  • Extended Odd Asphere
  • Gradient 1-12
  • GRADIUM
  • Grid Gradient
  • Grid Sag
  • Irregular
  • Odd Asphere
  • Standard
  • Tilted
  • Toroidal
  • Q-Type Asphere
  • User Defined
  • Zernike Fringe Sag
  • Zernike Standard Sag

PARAMETER DEFINITIONS FOR GRID GRADIENT SURFACES

Parameter # Definition
1 Δt

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