Kiwamu and Koji

Summary

We have visited GariLynn's lab to make a calibration of the metrology interferometer. 

The newly calibrated value is

RoC(SRMU01) = 153.3+/- 1.6 [m]

This is to be compared with the specification of 142m +/- 5m

Although the calibration deviation from the previous value was found to be 1.3%, it is far from explaining the curvature difference between the spec (142m) and the measured value.

Motivation

The previous measurements of the SRM curvatures showed larger RoCs by ~10% compared with the spec.

It can be caused by the mis-calibration of the pixel size of the CCD in the metrology interferometer.
In order to confirm the calibration value, an object with known dimension should be measured by the instrument.

Method

We've got a flat blank optic from "Advanced Thin Film" together with a metalic ring.
The ring has been attached on the blank optic with 3 fragments of a double sided tape.
The RoC of SRMU1 was also measured in order to obtain "the radius of curvature of the day".

The calibration process is as follows:

1. Measure the diameters of the ring by a caliper in advance to its attachment to the blank.
2. Determine the inner and outer diameter of the ring in the obtained image.
   Note that the obtained image is pre-calibrated by the default value given by the measurement program
     (i.e. 0.270194mm/pixel for horizontal)
3. Check the ratio of the diameters with the measured value by the caliper. Correct a systematic effect.
4. Compare the image measurement and the caliper measurement.

Results

1. The outer and inner diameters of 2.000" and 1.660" (measured by a caliper, error 0.005"). The ratio is 0.830+/-0.003.
2. The center and radius for the inner circle were estimated to be (79.7924, 91.6372) and 21.4025 [mm].
   The center and radius for the outer circle were estimated to be (79.6532, 91.6816) and 25.6925 [mm].
   The error would be ~0.01mm considering they sweep 500 pixels by the circle and the pixel size is 0.27mm. i.e. 0.27/Sqrt(500) ~ 0.01mm
3. Ratio of the inner and outer diameter is 0.8330 +/- 0.0005.
   The systematic error of x is given by solving (21.4025+x)/(25.6925-x)=0.83 ==> x = -0.042 +/- 0.043 [mm]. This is just a 0.2% correction.
   By correcting the above effect, we get (Rin, Rout) = (21.36 +/- 0.046, 25.74 +/- 0.047).
4. By comparing the result with the caliper measurement, we get calibration factor of 1.013 +/- 0.005.
   This means we measured "1mm" as "1.013mm". The scale was too small.
   We have got the calibration of 0.2737+/-0.0014 [mm/pixel].

Discussion

Because of the calibration error, we measured too long RoC. The same day, we measured the curvature of SRMU01 as 155.26 m.
The newly calibrated value is

RoC(SRMU01) = 153.3+/- 1.6 [m]

This is the value to be compared with the specification of 142m +/- 5m