%
%
% International Cosmic Ray Conference 2007
% July 2nd - 11th, Merida, Mexico
%
% John Toner et al
% Bias Alignment of the Veritas Telescopes
%
%

%Class Requeried
\documentclass[dvips]{article}
%The ICRC Style
\usepackage{icrctc07}

%The paper title
\title{Bias Alignment of the VERITAS Telescopes}

%Short title to print in the headers to the final publication (Not showed in this print).
\shorttitle{Bias Alignment}

%All paper authors
\authors{J. A. Toner$^{1,2}$, V. A. Acciari$^{2,3}$,
A. Cesarini$^{1,2}$ G. H. Gillanders$^{1}$, D. Hanna$^{4}$,
G. E. Kenny$^{1}$, J. Kildea$^{2}$, A. McCann$^{4}$,
M. McCutcheon$^{4}$, M. J. Lang$^{1}$, P. T. Reynolds$^{5}$,
M. Schroedter$^{6}$, A. W. Smith$^{2,7}$, J. E. Ward$^{8}$,
T. C. Weekes$^{2}$, B. Zitzer$^{9}$}

%Short title to print in the headers to the final puplication (Not 
%showed in this print).
\shortauthors{J. A. Toner et al}

%All the affiliations.
\afiliations{$^1$Dept. of Experimental Physics, National University of
Ireland, Galway, Ireland\\ 
$^2$FLWO, Harvard-Smithsonian Center for Astrophysics, Amado, AZ
85645, USA\\
$^3$Dept. of Physical and Life Sciences, Galway-Mayo Institute of
Technology, Galway, Ireland\\
$^4$Physics Dept., McGill University, Montreal, Quebec, H3A 2T8,
Canada\\ 
$^5$Dept. of Applied Physics and Instrumentation, Cork Institute of
Technology, Bishopstown, Cork, Ireland\\ 
$^6$Dept. of Physics and Astronomy, Iowa State University, Ames, IA
50011, USA\\ 
$^7$School of Physics and Astronomy, University of Leeds, Leeds, LS2
9JT, England\\
$^8$School of Physics, University College Dublin, Belfield, Dublin 4,
Ireland\\ 
$^9$Dept. of Physics, Purdue University, West Lafayette, IN 47907,
USA}

\email{john.toner@nuigalway.ie}

%The abstract.
\abstract{The mirror facets on the VERITAS telescopes, which are of
Davies-Cotton design, are aligned in the horizontal stow position
using a laser projector at their radius of curvature. The instrument
used will be described. The optical support structure is subject to
some gravitational slumping with elevation which can be counteracted
by bias alignment (deliberate misalignment at 0$^\circ$ elevation). In
practice this allows the optimum point spread function (PSF) to be
attained over an elevation range from 50$^\circ$ to 85$^\circ$.}



%%%%%%%%%%%%%%%%%%%% Begin Body %%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\maketitle

% INTRODUCTION

\section{Introduction}
VERITAS (Very Energetic Radiation Imaging Telescope Array System) is
an array of four identical imaging atmospheric Cherenkov telescopes
(IACTs), currently located at the base of Mt. Hopkins in southern
Arizona (altitude=1268m). The telescopes are of Davies-Cotton design
\cite{ref1}, with 12m aperture and a focal distance of 12m.

Each telescope's reflector is made up of 345 identical, individually
mounted aluminized and anodized mirror facets of area
$0.322\:\mathrm{m}^2$ \cite{ref4}, giving a total reflective area of
$\sim$$110\:\mathrm{m}^{2}$ per telescope. The facets are hexagonal in
shape to permit close packing. They are sections of a sphere with a
24m radius of curvature. The optics are modeled on those of the
Whipple 10m telescope \cite{ref3}. The mirror facets are mounted on
3-point adjustable brackets to allow manual alignment from the front
of the facet.

When imaging extensive air showers, the width of the image is the most
important criterion, both in regard to gamma-hadron separation and the
angular resolution of the instrument \cite{ref2}. Any image formed on
the telescope's camera is a convolution of the ideal image with the
response of the optics. As such, the optical response of the
telescope should be optimised.


% INSTRUMENTATION

\section{Instrumentation}

A purpose-built, semi-automated alignment system (see Figure
\ref{fig1}) has been developed at NUI, Galway. Using this system, each
mirror facet can be individually aligned, thus bringing the entire
reflector into correct alignment. It comprises:

\begin{itemize}
\item A computer-controlled pan-tilt unit (PTU)
\item A laser and beam-splitter assembly
\item A SBIG ST-237A CCD camera
\item A translucent plastic screen
\end {itemize}

% Figure 1: Alignment system minus cover.

\begin{figure}
\begin{center}
\includegraphics [width=0.48\textwidth]{icrc0676_fig01}
\end{center}
\caption{The VERITAS Semi-Automated Alignment System (Cover removed for clarity)}\label{fig1}
\end{figure}

With the telescope at an elevation of 0$^\circ$, the system is set up
on a platform (or alignment tower --- see Figure \ref{fig2}) located
at twice the focal distance from the center of the reflector along the
optic axis. We refer to this location as the ``\textit{2f}'' point.

The PTU, controlled by a custom computer program, is used to direct
the outgoing laser beam onto each mirror facet in turn. Due to the
Davies-Cotton optics employed by the telescope reflector, the beam
reflected from the mirror should then return along its own outgoing
path when the mirror is correctly aligned. With all mirrors aligned in
this manner, light from a source at infinity should converge to a
point at the focal plane of the telescope.

Part of the laser beam is backscattered by the beam-splitter onto the
screen (\textit{i.e.} the reference beam). This gives a reference
point on the screen for the desired position of the reflected beam
when the facet is aligned correctly. Using an image of the screen
obtained by the CCD, the program can find the centroid locations of
both the backscattered and the reflected beams. These positions are
used to determine how far the reflected beam is from the reference
position on the screen and thus calculate what adjustments must to be
made to the facet mounting bracket in order to align the mirror
correctly. This is then repeated for all mirror facets on the
reflector. Once aligned, it is not necessary to re-align the facets
more frequently than once a year.

% Figure 2: T2 and the alignment tower.

\begin{figure}
\begin{center}
\includegraphics [width=0.48\textwidth]{icrc0676_fig02}
\end{center}
\caption{Purpose-built alignment towers have been constructed and
placed at the \textit{``2f''} point for each telescope. In this image, the
telescope is stowed (pointing north) and is not pointing at the
tower.}\label{fig2}
\end{figure}


% GRAVITATIONAL SLUMPING


\section{Gravitational Slump}

When the telescope moves in elevation, the optical support structure
(OSS) is subject to some slumping. As the OSS slumps, each of the
mirror facets moves by a small amount due to gravity. This puts the
telescope's optics increasingly out of alignment as the elevation is
increased, degrading the PSF at typical observing elevations. However,
this happens in a reproducible way and can be corrected for.

Measurements of the movement experienced by each mirror facet are made
by attaching a small, light-weight laser unit to each facet. The laser
beam is directed onto the focal plane of the telescope. A CCD image of
the focal plane is then obtained. The telescope is raised to an
elevation of 65$^\circ$ (the desired elevation of best focus) and
another image of the focal plane is obtained.

The amount by which the laser spot moves on the focal plane is
measured by comparing the images from the two different telescope
positions. The movement of the laser beam corresponds to the movement
of the mirror facet due to slumping of the OSS. This is repeated for
all mirror facets on the reflector. A file containing information
about the movement of each mirror (\textit{i.e.} bias file) is
generated for use by the alignment program so that the slumping effect
can be negated.

% Slumping vector image

\begin{figure*}[th]
\begin{center}
\includegraphics [width=0.65\textwidth]{icrc0676_fig03}
\end{center}
\caption{Gravitational slumping effects for Telescope 1
reflector. Mirror deflection is seen to be similar in the other
telescopes.}\label{fig3}
\end{figure*}

% BIAS ALIGNMENT

\section{Bias Alignment}

Once the movement of the mirrors with elevation is known (see Figure
\ref{fig3}), each mirror is then deliberately misaligned while the
telescope is at 0$^\circ$ elevation. The amount by which each mirror
is misaligned is equal in magnitude to the movement due to gravitation
slumping, but in the opposite direction. This intentional misalignment
of all mirrors is known as bias alignment. The technique was pioneered
on the Whipple 10m telescope \cite{ref5} \cite{ref6}.

The bias file, generated earlier, can now be used by the alignment
program. Once again, the back-scattered beam is used to define a
reference point on the screen for each mirror. The program then uses
the bias file to calculate where the reflected beam should be on the
screen in relation to the reference point when the mirror has been
moved to counteract gravitational slumping effects. This point will be
offset from the reference point by an amount which relates to the
movement of the mirror due to the slumping of the OSS when the
telescope was moved to an elevation of 65$^\circ$. The program outputs
the mounting bracket adjustments required to bring the reflected beam
to the new offset point on the screen. When completed for all mirror
facets the telescope's optics fall into optimum and correct alignment
at an elevation of 65$^\circ$.

% RESULTS

\section{Results}

In order to test the alignment, a CCD image of the focal plane is
obtained while the telescope is tracking a bright star. This is done
at a succession of elevations. This is done both before and after the
telescopes are bias aligned. Qualitative results may be seen in Figure
\ref{fig4}.

Figure \ref{fig5} shows the PSF\footnote{Full-width-half-maximum of a
fitted 2-D gaussian.} attained at a range of elevations, both before
and after bias alignment.

\begin{figure*}
\begin{center}
\includegraphics [width=0.60\textwidth]{icrc0676_fig04}
\end{center}
\caption{PSF before and after bias alignment. The line labeled
0.15$^\circ$ shows the angular size of the photomultiplier tubes which
comprise the camera on the VERITAS telescopes.}\label{fig4}
\end{figure*}

\begin{figure*}[th]
\begin{center}
\includegraphics [width=0.60\textwidth]{icrc0676_fig05}
\end{center}
\caption{FWHM of Telesope 1 PSF vs. elevation, before and after bias
alignment.}\label{fig5}
\end{figure*}

Before bias alignment, the PSF is seen to have its best value
(0.06$^\circ$) at an elevation of 0$^\circ$. The value then
deteriorates as the elevation increases to a maximum of 0.10$^\circ$
at around 70$^\circ$ elevation. This is what is to be expected from
gravitational effects before bias alignment is applied.

After bias alignment, the value for the PSF is optimized at around
65$^\circ$ elevation, to a value of 0.06$^\circ$. Either side of this,
the value only deteriorates slightly in the region where most
observations are taken. In the elevation range from 50$^\circ$ -
85$^\circ$, the PSF is always less than 0.075$^\circ$, or about half
the width of one PMT pixel in the Cherenkov imaging camera.

%BIBLIOGRAPHY

\bibliography{icrc0676}
\bibliographystyle{plain}

\end{document}
