ISOC: Tolerance on P-V RSI (rotationally symmetric irregularity)

Operand purpose

The ISOC operand adds peak-to-valley RSI (rotationally symmetric irregularity) to the target surface. As specified in ISO-10110-5 Surface Form Tolerances, this operand corresponds to C in the drawing note 3/A(B/C).

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=αi=0, Zernike Polynomials 11, 22, 37, 56, 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 ISOC operand are: Surf, Units, Statistics, 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 P-V RSI value from a Gaussian distribution.

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

Min: Always set to -Max

Max: Specifies the maximum P-V RSI to be added to the surface.

Sensitivity analysis

During sensitivity analysis, the effect on the Criterion is evaluated for two cases of P-V RSI: -Max and +Max.

MonteCarlo analysis

For Monte Carlo analysis, a random value for P-V RSI between 0 and Max is selected from a Guassian distribution with a mean of Max/2, a standard deviation of σ = Max/8, and truncated below 0 and above Max.

Correlation of ISOC and ISOB

If ISOC is also applied to the target surface, then ISOB and ISOC will be correlated so that B (total P-V irregularity) and C (P-V rotationally symmetric irregularity) are simultaneously satisfied. The Zernike Standard Sag surface for the ISOB operand will have rotationally symmetric terms set to zero: A11 = A22 = A37 = 0. The Zernike Standard Sag surface for the ISOC operand will carry the A11, A22, A37, and A56 terms.
The coefficient values are selected so that the P-V of the ISOC surface is satisfied, and the sum of the ISOB and ISOC surfaces gives the total P-V irregularity specified in the ISOB operand Max value.
The ISOC Max value must be less than ISOB Max value.
Note that we have removed the piston term from the RSI so that a ray falling at the aperture vertex will remain unchanged and not acquire any phase.
If ISOC is applied multiple times to the surface, each occurrence will over-write the previous values in the relevant LDE row in the Monte Carlo file. Only the last occurrence of the operand will be present in the Monte Carlo file.

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