nass-short-stroke-metrology/short-stroke-metrology.org

NASS - Short Stroke Metrology

• Introduction
• Measurement Principle
• X-Y-Z measurement
• Tilt measurement
• Conclusion

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This report is also available as a pdf.

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Introduction   ignore

The goal of this document is to analyze the feasibility of a short stroke metrology system for the NASS using fixed interferemoter and the same reflector as for the long stroke metrology system.

It is structured as follow:

• Section sec:meas_principle: the meaurement principle is described.
• Section sec:translation_interferometers: the requirements for the interferometers measuring translations are described
• Section sec:rotation_interferometers: the same is done for the rotations

Measurement Principle

<<sec:meas_principle>>

Here are the defined wanted displacement of the reflector that should be inside the measurement stroke of the metrology system. The defined translations and rotations are defined with respect to the frame shown in Figure fig:short_stroke_metrology_concept.

d_x = 0;     % Wanted translation of the reflector in the x direction [m]
d_y = 1e-3;  % Wanted translation of the reflector in the y direction [m]
d_z = 1e-3;  % Wanted translation of the reflector in the z direction [m]
R_x = 10e-3; % Wanted rotation of the reflector along the x axis [rad]
R_y = 0;     % Wanted rotation of the reflector along the y axis [rad]

Here are the approximate dimensions shown in Figure fig:short_stroke_metrology_concept:

• $d_0 \approx 10\,[mm]$
• $L \approx 150\,[mm]$
• $R \approx 250\,[mm]$

d0 = 10e-3; % [m]
L = 150e-3; % [m]
R = 250e-3; % [m]

X-Y-Z measurement

<<sec:translation_interferometers>>

The geometry for the interferometers measuring translations is shown in Figure fig:translation_interferometers:

• $R = 250\,[mm]$
• $d_0 > 10\,[mm]$
• $d_x = \pm 1\,[mm]$
• $d_y = \pm 1\,[mm]$

Interferometers that are measuring translation

The angle of the reflected beam is approximately equal to:

\begin{equation} \theta \approx 2 \frac{d_y}{R} \end{equation}

And we obtain:

\[ \theta \approx 8.0\,[mrad] \]

Specification	Value
Axial Acceptance	$\pm 1\,[mm]$
Angular Acceptance	$\pm 8\,[mrad]$
Distance to target	$10\,[mm]$

Tilt measurement

<<sec:rotation_interferometers>>

The tilt $\theta$ of the flat mirror is directly equal to the tilt of the reflector. However, the $z$ displacement on the flat part is equal to:

\begin{equation} z \approx d_z + L \theta_y \end{equation}

And we obtain:

\[ z \approx 2.5\,[mm] \]

The geometry for the interferometers measuring rotations is shown in Figure fig:rotation_interferometers:

• $d_0 > 10\,[mm]$
• $\theta = \pm 10\,[mrad]$
• $z = \pm 2.5\, [mm]$

Interferometers that are measuring tilt

Specification	Value
Axial Acceptance	$\pm 2.5\,[mm]$
Angular Acceptance	$\pm 10\,[mrad]$
Distance to target	$10\,[mm]$

Conclusion