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Message ID: 91     Entry time: Mon Apr 1 18:17:01 2013
Author: Koji 
Type: Optics 
Category: General 
Subject: Mirror curvature center test 

Locations of the curvature minimum on the OMC curved mirrors have been measured.

Motivation:

When a curved mirror is misaligned, the location of the curvature center is moved.
Particularly, our OMC mirror is going to be attached on the PZT and the mounting prism with the back surface of the mirror.
This means that a curved mirror has inherent misalignment if the curvature minimum of the curved mirror is shifted from the center of the mirror.
Since we have no ability to control mirror pitch angle once it is glued on the prism, the location of the curvature minima
should be characterized so that we can oush all of the misalignment in the horizontal direction.

Measurement technique:

When a curved mirror is completely axisymmetric (in terms of the mirror shape), any rotation of the mirror does not induce change on the axis of the refected beam.
If the curvature minimum is deviated from the center of the mirror, the reflected beam suffer precession. As we want to precisely rotate the mirror, we use the gluing
fixture for the PZT assembly. In this method, the back surface of the curved mirror is pushed on the mounting prism, and the lateral position of the mirror is precisely
defined by the fixture. As you rotate the mirror in clockwise viewing from the front, the spot moves in counter clockwise on the CCD.
curved_mirror_precession1.png

 

 

Setup and procedure:

The mounting prism (#21) is placed on the gluing fixture. A curved mirror under the test is loaded in the fixture with no PZT.
i.e. the back surface is aligned by the mounting prism. The fixing pressure is applied to the curved mirror by the front plate
with spring loads. The mirror needs be pushed from the top at least once to keep its defined position in the fixture.
The incident beam is slightly slated for the detection of the reflected spot. The beam is aligned and hits the center of the mirror as much as possible.

curved_mirror_precession2.png

The position of the spot on the CCD (WinCamD) is recorded, while the mirror is rotated 90deg at once. The rotation of the mirror is defined as shown in the figure below.
The angle origin is defined by the arrow mark of the mirror and rotated in clockwise being viewed from the front face. The mirror is rotated 540deg (8points) to check
the reproducibility.

curved_mirror_precession3.png

Measurement result:

8 point for each mirror is fitted by a circle. The fitting result provides the origin and radius of the circle, and the angle correspond to mirror angle of 0deg.

Analysis:

d: distance of the curvature minimum and the mirror center (quantity to be delived)

D: distance of the prove beam spot from the center of the mirror

R: Radius of curvature of the mirror

theta_R: angle of incidence/reflection

curved_mirror_precession4.png

 

 

The interesting consequence is that precession diameter (X-X') on the CCD does not depend on the spot position on the mirror.
This ensures the precision of the measurement. In the measurement, the radius of the precession (r = (X-X')/2) is obtained.

Therefore,

d = r R / (2 L)

Mirror name, distance[mm]
C1: 0.95
C3: 1.07
C4: 1.13
C5: 0.97
C6: 0.73
C7: 1.67
C8: 2.72
C9: 1.05
C10: 0.41
C11: 0.64
C12: 0.92
C13: 0.14

Resolution:
The angle to be rotated is depicted in the following plot for each mirror.

curved_mirror_minimum_position.png

Attachment 5: curved_mirror_precession.pdf  136 kB  Uploaded Mon Apr 1 20:34:30 2013  | Hide | Hide all
curved_mirror_precession.pdf
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