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# TRAD, TCUR, TFRN tolerance operands conversion to ISO10110-5(Surface Form Tolerance)

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TRAD, TCUR, and TFRN tolerancing operands can be converted to ISO 10110- 5 3|A format. The basic surface form is expressed as (3/A(-|-) lambda 633 nm), where the quantity A is the maximum power deviation PV expressed in fringes.

To convert these operands to ISO 10110 format, we should understand what each of these tolerancing operands is computing. TRAD is the tolerance on the surface radius of curvature in lens units (Data = 0) or ROC percentage (Data = 1). TCUR is the tolerance on the surface curvature in inverse lens units (curvature = 1/ROC). TFRN is tolerance on the surface radius of curvature in fringes. TFRN is expressed in fringes from a double pass system with respect to the wavelength specified in TWAV.

These operands use a Gaussian distribution for the Monte Carlo tolerance analysis.

1. Calculating the radius of curvature and edge sag

The first step to convert TRAD and TCUR to ISO 10110 format is to calculate the minimum and maximum radius of curvature and delta edge sag. The minimum and maximum ROC tolerance values can be obtained with the following equations:

The edge sag can be determined from the sphere sag equation:

where k is the conic value and is equal to 0 in this application, and r is the surface radial height.

The delta edge sag equation:

Under the defined wavelength, the surface power in fringes can be calculated as

1. Converting TRAD to fringe power

Suppose that Nominal ROC = 100 mm, surface semi-diameter r is 10mm, and the TRAD tolerance value is 0.015mm. By utilizing the provided code snippets, we can swiftly calculate the Power fringe is 0.55 fringes at 550nm.

1. Converting TCUR to fringe power

Suppose that Nominal ROC= 17.484123 mm, surface semi-diameter r is 4.178mm, and the TCUR tolerance value is 0.00002mm. By utilizing the provided code snippets, we can swiftly calculate the Power fringe @840nm is 0.87 fringe.
To execute the function for performing the calculation, the Matlab command you would input is as follows: PowerFringeConversionTCUR(17.484123,0.00002,4.178,0,0.00084)

1. TFRN

The advantage of using TFRN is that the value is already in ISO 10110 format. For example, if the TFRN has a tolerance value of 3 fringes, 3 is the A value in the ISO 10110 format. Currently, the tolerance operand TFRN conforms with ISO10110 5 3A format, as it is in fringes.

1. Discussion:

The above edge sag to power fringe conversion equation is only accurate for spherical surfaces. The above method will be less accurate for surfaces with asphericity since the surface can deviate from the best-fit sphere shape.

Matlab functions PowerFringeConversionTCUR &PowerFringeConversionTRAD are shared for the fringe calculation.