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Message ID: 3685     Entry time: Sun Oct 10 18:09:02 2010
Author: Koji 
Type: Summary 
Category: COC 
Subject: Phase map interferometer calibration for the data on Oct 8th, 2010  

Summary:

Calibration of the phase map interferometer was calculated for the data on Oct 8th, 2010.
The calibration value is 0.1905 mm/pixel.

This is slightly smaller than the assumed value in the machine that is 0.192mm/pixel.
This means that the measured radii of curvature must be scaled down with this ratio.
(i.e. RoC(new) = RoC(old) / 0.1922 * 0.19052)


Motivation:

Our tagets of the phasemap measurement are:

1. Measure the figure errors of the mirrors
2. Measure the curvature of the mirrors

The depth of the mirror figure is calibrated by the wavelength of the laser (1064nm).
However, the lateral scale of the image is not calibrated.
Although Zygo provides the initial calibration as 0.192 mm/pixel, we should measure the calibration by ourselves.

Method:

We found an aperture mask with a grid of holes with 2mm diameter and 3mm spacing (center-to-center).
Take the picture of this aperture and calibrate the pixel size. The aperture is made of stainless and makes not interference
with the reference beam. Thus we put a dummy mirror behind the aperture. (UPPER LEFT plot)

As the holes are aligned as a grid, the FFT of the aperture image shows peaks at the corresponding pitches. (UPPER MIDDLE plot)
As the aperture was slightly rotated, the grids of the peaks are also slanted.

We can obtain the spacing of the peak grids. How can we can that values precisely? I decided to make an artificial mask image.
The artificial mask (LOWER LEFT plot) has the similar FFT pattern (LOWER MIDDLE plot). The inner product of the two
FFT results (i.e. Sum[abs(fft1) x abs(fft2)]), quite a large value is obtained if the grid pitch and the aperture angle agrees between those images.
Note that the phase information was discarded. The estimated grid spacing of the artificial mask can be mathematically obtained.

Result:

The grid pitch and the angle were manually set as initial values. Then the parameters to give the local maximum was obtained by fminsearch of Matlab.
UPPER RIGHT and LOWER RIGHT plots show the scan of the evaluation function by changing the angle and the pitch. They behave quite normal.

The obtained values are

Grid pitch: 15.74 pixel
Angle: 1.935 deg

As the grid pitch is 3mm, the calibration is

3 mm / 15.74 pixel = 0.1905 mm/pixel

Discussion:

A spherical surface can be expressed as the following formula:

z = R - R Sqrt(1-r2/R2)      (note: this can be expanded as r2/(2 R)+O(r3) )

Here R is the RoC and r is the distance from the center. This means that the calibration of r quadratically changes the curvature.
We have measured the RoC of the spare SRM. We can compare the RoCs measured by this new metrology IFO and the old one,
as well as the one by Coastline optics. 

 

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calibration.pdf
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