TIRR: Tolerance on Surface Irregularity

For a more detailed treatment of irregularity, search the help files for the discussion on the TEXI and TEZI operands which follows.

TIRR is used to analyze irregularity of a Standard surface. The Int1 value indicates the number of the surface, and this surface must be a Standard surface type. Analysis of irregularity on surface types other than Standard 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.

Modeling irregularity is somewhat more problematic than other types of tolerances. This is primarily because irregularity by nature is random, and not deterministic such as a change in radius. Therefore, some assumptions about the nature of the irregularity need to be made in order to perform the analysis. The assumption OpticStudio makes when using TIRR is that the irregularity is half spherical aberration, and half astigmatism. This is less restrictive model than assuming 100% astigmatism, because astigmatism cannot be compensated by focus, and is therefore a more serious defect in the lens.

The min and max values are the irregularity in units of fringes measured at the maximum radial aperture of the surface where the maximum radial aperture is defined by the clear semi-diameter or semi-diameter of the surface. The TWAV operand is used to define the test wavelength.

OpticStudio assumes fringes are measured in a double pass Newton's rings type test. For example, a TIRR of "W" fringes would yield a change in sag of the surface of

where λt is the test wavelength (defined by the TWAV operand), ρ is the normalized radial coordinate, and ρ'y is the normalized and rotated radial coordinate as defined in "Irregular". The change in wavefront optical path is related to the change in sag and the index of refraction of the two media the surface separates:

The analysis of TIRR uses the Irregular surface type.

When computing the Monte Carlo analysis, the angle of the astigmatism is chosen randomly between 0 and 360 degrees. This allows simulation of randomly oriented astigmatic error, which is less severe and more realistic than placing all the astigmatism along the y axis of each element.

Search the help files for the discussion "Tolerancing with the Irregular surface type" for more information.

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