TEZI: Tolerance on Surface Irregularity Using the Standard Zernike Model
See also the discussion for TEXI. TEZI is a superior alternative to TEXI.
TEZI is used to analyze random irregular deviations of small amplitude on a surface that is either a Standard, Even Aspheric, or Toroidal surface. Analysis of irregularity on surface types other than these is performed through addition of a Composite Add-on surface on top of the surface being toleranced. For details, see Tolerancing irregularity with Composite surfaces. The Int1 value indicates the number of the surface, Int2 defines the maximum Standard Zernike term (must be between 3 and 231), and Int3 defines the minimum Standard Zernike term (must be between 2 and the maximum term).
TEZI uses the Zernike Standard Sag surface (search the help files for "Zernike Standard Sag") to model the irregularity on Standard and Even Aspheric surfaces, while Toroidal surfaces use the Zernike terms already supported by the Toroidal surface. When using TEZI, the max tolerance value is the exact RMS error of the surface in lens units. The min tolerance value is automatically set to the negative of the max value; this is done to yield both positive and negative coefficients for the Zernike terms. The resulting RMS is of course always a positive number whose magnitude is equal to the max tolerance value.
Analysis:
For the sensitivity analysis, if the surface is a Standard, Even Aspheric, or Toroidal surface, the surface is converted to a Zernike Standard Sag or Toroidal surface and all the coefficients of the Zernike polynomial for terms greater than #1 (the "piston" term) are set to a value so that the square root of the sum of the squares of the coefficients yields the specified RMS value. All coefficients are set to the same value. For all other surface types, the sensitivity analysis will be performed through addition of a Zernike Standard Sag Composite Add-on surface on top of the surface being toleranced. For details, see section: Tolerancing irregularity with Composite surfaces.
For the Monte Carlo analysis, the surface is dealt with as for the sensitivity analysis, but each polynomial term is assigned a coefficient randomly chosen between -1.0 and 1.0, and the resulting coefficients are then normalized to yield the exact RMS tolerance. The random value is chosen using the statistical model selected for the operand; search the help files for the STAT command for a discussion.
The number of terms is given by Int2 - Int3 + 1. Generally speaking, if lower order terms are used, the irregularity will be of low frequency, with fewer "bumps" across the surface. If higher order terms are used, there will be higher frequency irregularity, with more "bumps" across the surface. Note the TIRR irregularity operand models the lowest frequency form of irregularity, with just a quadratic and quartic deviation across the surface. TEZI can model much more irregular surfaces.
Because the Zernike Standard Sag surface sag expression contains portions of both the Standard and Even Aspheric surfaces, either of these surface types may be modeled by the Zernike Standard Sag surface created with the TEZI operand. If the surface is Toroidal, the Toroidal surface is retained since the Zernike terms are already supported with this surface type, however, the nominal value of all the Zernike terms must be zero if the nominal surface is Toroidal. The normalization radius for the Zernike terms is set to the clear semi-diameter or semi-diameter of the surface.
TEZI always ignores Zernike term 1, the piston term, and sets this value to zero.
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