ISOD: Tolerance on total RMS irregularity

Operand purpose

The ISOD operand adds RMS irregularity to the target surface. As specified in ISO-10110-5 Surface Form Tolerances, this operand corresponds to D in the drawing note 3/A(B/C) RMS<D.

Operand behaviour

During tolerancing, this operand adds sag to the target surface using a Zernike Standard Sag surface, which is added as a Composite Add-on surface. The added sag follows the Zernike Standard Sag equation, with c = k = α i = 0, Zernike polynomials 5-37, and to remove piston:

Apertures

If the target surface has a circular off-axis aperture, the Zernike Standard Sag surface will be positioned at the vertex of the off-axis surface by adjusting the tilt and decenter in the Composite property. The Clear Semi-diameter of the new surface is set to the aperture semi-diameter of the target surface, or to the Clear Semi-diameter if no aperture is present on the target surface. Apertures other than circular are not supported at this time.

Inputs

Inputs for the ISOD operand are: Surf, Statistics, Units, Nominal, Min and Max.

Surf: The row number in the Lens Data Editor of the target surface.

Units: Choice of units of the Max value. 0 = units of nanometers and is currently the only option.

Statistics: 0 = Always use the Max value for P-V RSI during Monte Carlo analysis. 1 = Choose the RMS irregularity value from a Gaussian distribution.

Nominal: The Nomincal value is always 0 for this operand, indicating no added irregularity.

Min: Specifies the lowest added irregularity term and is always set to -Max.

Max: Specifies the maximum RMS irregularity to be added to the surface.

Sensitivity analysis

During sensitity analysis, the effect on the Criterion is evaluated for two cases of RMS irregularity: -Max and +Max.

MonteCarlo analysis

For Monte Carlo analysis, a random value for RMS irregularity between 0 and Max is selected from a Gaussian distribution with a mean of Max/2, a standard deviation of σ = Max/8, and truncated below 0 and above Max.

Notes on usage of ISOC

  • ISOD may not be applied multiple times to the same surface and will trigger an error.
  • ISOD should not be used with other operands that adjust surface irregularity, such as TEZI, TEXI, or TIRR.
  • ISOD should not be used with ISOB. Two irregularity surfaces would be added to the target surface if both operands are present.
  • ISOD cannot be correlated with ISOC.
  • Piston is removed for the ISOD surface, which could give a larger RMS surface irregularity than expected if the piston term were chosen to minimize the RMS.
  • ISOD is approximately equal to RMSi, as defined in ISO-10110. However, power and tilt are not removed from the surface perturbation that is added to the target surface. Some random combinations of Zernike terms may have enough residual tilt or power to affect the result, making the system seem more sensitive to this error than it would be otherwise.

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