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 can be correlated so that B (total P-V irregularity) and C (P-V rotationally symmetric irregularity) are simultaneously satisfied. When correlated, 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 A56terms.
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.
Currently, there are some conditions that must be met to correlate ISOB with ISOC:
  • The order of operands in the TDE must be: ISOC, then ISOB in the next row.
  • Other ISO operands applied to the surface must occur after ISOB in the TDE.
  • The ISOC Max value must be less than ISOB Max value.

Notes on usage of ISOC

  • ISOC may not be applied multiple times to the same surface and will trigger an error.
  • If used with ISOB, the preferred order in the TDE is: ISOC, ISOB, and then ISOA. If the order is violated, ISOB and ISOC will each operate independently and will not be correlated.
  • 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.

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