{{2005 International Linear Collider Workshop - Stanford, U.S.A.}}\\ %% Please keep this conference title here \vspace{12pt} Frequency Scanned Interferometry for ILC Tracker Alignment
Hai-Jun Yang$^*$
Sven Nyberg
Keith Riles$^\dagger$
In this paper, we report high-precision absolute distance and vibration measurements performed with frequency scanned interferometry using a pair of single-mode optical fibers. Absolute distance was determined by counting the interference fringes produced while scanning the laser frequency. A high-finesse Fabry-Perot interferometer was used to determine frequency changes during scanning. Two multiple-distance-measurement analysis techniques were developed to improve distance precision and to extract the amplitude and frequency of vibrations. Under laboratory conditions, measurement precision of $\sim$ 50 nm was achieved for absolute distances ranging from 0.1 meters to 0.7 meters by using the first multiple-distance-measurement technique. The second analysis technique has the capability to measure vibration frequencies ranging from 0.1 Hz to 100 Hz with amplitude as small as a few nanometers, without a {\em priori} knowledge. A possible optical alignment system for a silicon tracker is also presented.
fsi-tracker-alignment.tex
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\title{{\small{2005 International Linear Collider Workshop - Stanford,
U.S.A.}}\\ %% Please keep this conference title here
\vspace{12pt}
Frequency Scanned Interferometry for ILC Tracker Alignment
} %% Paper title goes here

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\author{Hai-Jun Yang$^*$, Sven Nyberg, Keith Riles$^\dagger$
\\($^*$ yhj@umich.edu, $^\dagger$kriles@umich.edu)
}

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\affiliation{Department of Physics, University of Michigan, Ann Arbor, MI 48109-1120, USA}


\begin{abstract}
In this paper, we report high-precision absolute distance and vibration
measurements performed with frequency scanned interferometry 
using a pair of single-mode optical fibers. Absolute distance was determined 
by counting the interference fringes produced while scanning the laser frequency. 
A high-finesse Fabry-Perot interferometer was used to determine frequency 
changes during scanning. Two multiple-distance-measurement analysis techniques 
were developed to improve distance precision and to extract the amplitude
and frequency of vibrations.
Under laboratory conditions, measurement precision of $\sim$ 50 nm was achieved for 
absolute distances ranging from 0.1 meters to 0.7 meters by using the first
multiple-distance-measurement technique. 
The second analysis technique has the capability to 
measure vibration frequencies ranging from 0.1 Hz to 100 Hz with amplitude
as small as a few nanometers, without a {\em priori} knowledge.
A possible optical alignment system for a silicon tracker is also presented.
\end{abstract}

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% instrumentation, fringe analysis, interferometry, vibration analysis


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\section{Introduction}

The motivation for this project is to design a novel optical
system for quasi-real time alignment of tracker detector elements
used in High Energy Physics (HEP) experiments. A.F. Fox-Murphy {\em et.al.}
from Oxford University reported their design of a frequency
scanned interferometer (FSI) for precise alignment of the ATLAS
Inner Detector \cite{ox98,ox04}. Given the demonstrated need for
improvements in detector performance, we plan to design an
enhanced FSI system to be used for the alignment of tracker
elements in the next generation of electron positron Linear
Collider detectors. Current plans for future detectors
require a spatial resolution for signals from a tracker detector,
such as a silicon microstrip or silicon drift detector,
to be approximately 7-10 $\mu m$\cite{orangebook}. To achieve this
required spatial resolution, the measurement precision of absolute
distance changes of tracker elements in one dimension should be on the order of 1
$\mu m$. Simultaneous measurements from hundreds of interferometers
will be used to determine the 3-dimensional positions of the
tracker elements.

The University of Michigan group constructed two demonstration
Frequency Scanned Interferometer (FSI) systems with laser
beams transported by air or single-mode optical fiber
in the laboratory for initial feasibility studies.
Absolute distance was determined by counting the interference
fringes produced while scanning the laser frequency\cite{stone99}.
The main goal of the demonstration systems was to determine the
potential accuracy of absolute distance
measurements that could be achieved under controlled conditions.
Secondary goals included estimating the effects of vibrations and studying
error sources crucial to the absolute distance accuracy.
The main contents of this proceedings article come from our published paper\cite{fsi05}.
However, new material in this paper includes a description of a dual-laser system and 
a possible optical alignment for a silicon tracker detector.


\section{Principles}

The intensity $I$ of any two-beam interferometer can be expressed as
$$
\begin{array}{c}
I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos(\phi_1 - \phi_2)
\end{array}
\eqno{(1)}
$$
where $I_1$ and $I_2$ are the intensities of the two combined beams,
and $\phi_1$ and $\phi_2$ are the phases.
Assuming the optical path lengths of the two beams are $L_1$ and
$L_2$, the phase difference in Eq.~(1) is
$\Phi = \phi_1 - \phi_2 = 2\pi |L_1 - L_2|(\nu/c)$,
where $\nu$ is the optical frequency of the laser beam, and c is
the speed of light.

For a fixed path interferometer, as the frequency of the laser is
continuously scanned, the optical beams will
constructively and destructively interfere, causing ``fringes''.
The number of fringes $\Delta N$ is
$$
\begin{array}{c}
\Delta N = |L_1 - L_2|(\Delta\nu/c) = L\Delta\nu/c
\end{array}
\eqno{(2)}
$$
where $L$ is the optical path difference between the two beams,
and $\Delta\nu$ is the scanned frequency range. The optical path
difference (OPD for absolute distance between beamsplitter and retroreflector)
can be determined by counting interference fringes while scanning the laser frequency. 

\begin{figure}[htbp]
\centerline{\scalebox{0.5}{\includegraphics{figure1.eps}}}
\caption{Schematic of an optical fiber FSI system.}
\end{figure}

\section{Demonstration System of FSI}

A schematic of the FSI system with a pair of optical fibers is shown in Fig.1.  
The light source is a New Focus Velocity 6308 tunable laser 
(665.1 nm $<\lambda<$ 675.2 nm). A high-finesse ($>200$) Thorlabs SA200
F-P is used to measure the frequency range scanned by the laser. The free 
spectral range (FSR) of two adjacent F-P peaks is 1.5 GHz, which corresponds 
to 0.002 nm. A Faraday Isolator was used to reject light reflected back into
the lasing cavity. The laser beam was coupled into a single-mode optical fiber
with a fiber coupler.
Data acquisition is based on a National Instruments DAQ
card capable of simultaneously sampling 4 channels at a rate of 5 MS/s/ch with
a precision of 12-bits.  Omega thermistors with a tolerance of 0.02 K and a
precision of 0.01 $mK$ are used to monitor temperature.  The apparatus
is supported on a damped Newport optical table.

In order to reduce air flow and temperature fluctuations, a transparent plastic
box was constructed on top of the optical table. PVC pipes were installed to 
shield the volume of air surrounding the laser beam. Inside the PVC pipes, 
the typical standard deviation of 20 temperature measurements was about $0.5 ~mK$. 
Temperature fluctuations were suppressed by a factor of approximately 100 by 
employing the plastic box and PVC pipes.

Detectors for HEP experiments must usually be operated remotely for 
safety reasons because of intensive radiation, high voltage or strong magnetic
fields. In addition, precise tracking elements are typically surrounded by
other detector components, making access difficult. For practical HEP application
of FSI, optical fibers for light delivery and return are therefore necessary.

The beam intensity coupled into the return optical fiber is very weak, requiring
ultra-sensitive photodetectors for detection. Considering the limited laser beam 
intensity and the need to split into many beams to serve a set
of interferometers, it is vital to increase the geometrical efficiency.
To this end, a collimator is built by placing an optical fiber in a ferrule 
(1mm diameter) and gluing one end of the optical fiber to a GRIN lens. 
The GRIN lens is a 0.25 pitch lens with  0.46 numerical aperture, 1 mm diameter 
and 2.58 mm length which is optimized for a wavelength of 630nm. 
The density of the outgoing beam from the optical 
fiber is increased by a factor of approximately 1000 by using a GRIN lens. 
The return beams are received by another optical fiber and amplified by a 
Si femtowatt photoreceiver with a gain of $2 \times 10^{10} V/A$. 


\section{Multiple-Distance-Measurement Techniques}

For a FSI system, drifts and vibrations occurring along the optical
path during the scan will be magnified by a factor of $\Omega =
\nu / \Delta \nu$, where $\nu$ is the average optical frequency of the laser
beam and $\Delta \nu$ is the scanned frequency range. For the full scan of
our laser, $\Omega \sim 67 $. Small vibrations and
drift errors that have negligible effects for many optical
applications may have a significant impact on a FSI system.
A single-frequency vibration
may be expressed as $x_{vib}(t) = a_{vib} \cos(2\pi f_{vib} t + \phi_{vib})$,
where $a_{vib}$, $f_{vib}$ and $\phi_{vib}$ are the amplitude, frequency and phase of the
vibration, respectively.
If $t_0$ is the start time of the scan, Eq.~(2) can be re-written as
$$
\begin{array}{c}
\Delta N=L\Delta\nu/c+2[x_{vib}(t)\nu(t)-x_{vib}(t_0)\nu(t_0)]/c
\end{array}
\eqno{(3)}
$$
If we approximate $\nu(t) \sim \nu(t_0) = \nu$, the
measured optical path difference $L_{meas}$ may be expressed as
$$
\begin{array}{c}
L_{meas} = L_{true} - 4 a_{vib} \Omega \sin[\pi f_{vib}(t-t_0)] \times \\
\sin[\pi f_{vib}(t+t_0)+\phi_{vib}]
\end{array}
\eqno{(4)}
$$
where $L_{true}$ is the true optical path difference in the absence of 
vibrations. If the path-averaged refractive index of
ambient air $\bar{n}_g$ is known, the measured distance
is $R_{meas} = L_{meas}/(2\bar{n}_g)$.

If the measurement window size $(t-t_0)$ is fixed and the window used to
measure a set of $R_{meas}$ is sequentially shifted, the
effects of the vibration will be evident. 
We use a set of distance measurements in one scan by successively shifting the 
fixed-length measurement window one F-P peak forward each time. 
The arithmetic average of all measured $R_{meas}$ values in one scan is taken to be the
measured distance of the scan (although more sophisticated fitting methods
can be used to extract the central value). 
For a large number of
distance measurements $N_{meas}$, the vibration effects can be greatly suppressed. 
Of course, statistical uncertainties
from fringe and frequency determination, dominant in
our current system, can also be reduced with multiple scans.
Averaging multiple measurements in one scan, however, provides similar precision
improvement to averaging distance measurements from 
independent scans, and is faster, more efficient, and less 
susceptible to systematic errors from drift.
In this way, we can improve the distance accuracy dramatically if 
there are no significant drift errors during one scan, caused, for example, 
by temperature variation. 
This multiple-distance-measurement technique is called 'slip measurement
window with fixed size', shown in Fig.2. However, there is a trade off in that the
thermal drift error is increased with the increase of $N_{meas}$
because of the larger magnification factor $\Omega$ for a smaller
measurement window size.

\begin{figure}[htbp]
\centerline{\scalebox{0.35}{\includegraphics{figure2.eps}}}
\caption{The schematic of two multiple-distance-measurement techniques.
The interference fringes from the femtowatt photoreceiver and
the scanning frequency peaks from the Fabry-Perot interferometer(F-P)
for the optical fiber FSI system recorded simultaneously by DAQ card
are shown in black and red, respectively. The free spectral range(FSR)
of two adjacent F-P peaks (1.5 GHz) provides a calibration of the scanned frequency range.}
\end{figure}

In order to extract the amplitude and frequency of the vibration, another 
multiple-distance-measurement technique called 'slip measurement window with 
fixed start point' is used, as shown in Fig.2. In Eq.~(3), if $t_0$ is fixed, the 
measurement window size is enlarged one F-P peak for each shift, an 
oscillation of a set of measured $R_{meas}$ values indicates the amplitude 
and frequency of vibration. 
This technique is not suitable for distance measurement because there
always exists an initial bias term, from $t_0$,
which cannot be determined accurately in our current system.

\section{Absolute Distance and Vibration Measurement}

The typical measurement residual versus the distance
measurement number in one scan using the above technique is shown in Fig.3(a), where
the scanning rate was 0.5 nm/s and the sampling rate was 125 kS/s.
Measured distances minus their average value for 10 sequential scans
are plotted versus number of measurements ($N_{meas}$) per scan in Fig.3(b).
The standard deviations (RMS) of distance measurements for 
10 sequential scans are plotted versus number of measurements ($N_{meas}$) per scan in Fig.3(c).
It can be seen that the distance errors decrease with an increase of $N_{meas}$.
The RMS of measured distances for 10 sequential scans
is 1.6 $\mu m$ if there is only one distance measurement per scan ($N_{meas}=1$).
If $N_{meas}=1200$ and the average value of 1200 distance measurements
in each scan is considered as the final measured distance of the scan,
the RMS of the final measured distances for 10 scans is 41 nm for the distance of
449828.965 $\mu m$, the relative distance measurement precision is 91 ppb.

\begin{figure}[htbp]
{\scalebox{0.35}{\includegraphics{figure3.eps}}}
{\scalebox{0.375}{\includegraphics{figure6.eps}}}
\caption{Distance measurement residual spreads versus number of distance measurement 
$N_{meas}$ 
(a) for one typical scan, 
(b) for 10 sequential scans,
(c) is the standard deviation of distance measurements for 10 sequential scans
versus $N_{meas}$.
The frequency and amplitude of the controlled vibration source 
are 1 Hz and 9.5 nanometers, 
(d) Magnification factor  versus number of distance measurements,
(e) Distance measurement residual  versus number of distance measurements,
(f) Corrected measurement residual  versus number of distance measurements.}
\end{figure}


The standard deviation (RMS) of measured distances for 10 sequential scans 
is approximately 1.5 $\mu m$ if there is only one distance measurement per scan
for closed box data. By using the multiple-distance-measurement 
technique, the distance measurement precisions for various closed box data
with distances ranging from 10 cm to 70 cm collected in the past year
are improved significantly; precisions of approximately 50 nanometers are
demonstrated under laboratory conditions, as shown in Table 1. 
All measured precisions
listed in Table 1. are the RMS's of measured distances for 10 sequential scans.
Two FSI demonstration systems, 'air FSI' and 'optical fiber FSI',
are constructed for extensive tests of multiple-distance-measurement technique, 
'air FSI' means FSI with the laser beam transported entirely in the ambient atmosphere,
'optical fiber FSI' represents FSI with the laser beam delivered to the interferometer 
and received back by single-mode optical fibers. 

\begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline
Distance & \multicolumn{2}{|c|}{Precision($\mu m$)} & Scanning Rate & FSI System \\ 
\cline{2-3}
(cm) & open box & closed box & (nm/s) & (Optical Fiber or Air) \\ \hline
10.385107 & 1.1 & 0.019 & 2.0 & Optical Fiber FSI \\ \hline
10.385105 & 1.0 & 0.035 & 0.5 & Optical Fiber FSI \\ \hline
20.555075 & - & 0.036, 0.032 & 0.8 & Optical Fiber FSI \\ \hline
20.555071 & - & 0.045, 0.028 & 0.4 & Optical Fiber FSI \\ \hline
41.025870 & 4.4 & 0.056, 0.053 & 0.4 & Optical Fiber FSI \\ \hline
44.982897 & - & 0.041 & 0.5 & Optical Fiber FSI \\ \hline 
61.405952 & - & 0.051 & 0.25 & Optical Fiber FSI \\ \hline
65.557072 & 3.9, 4.7 & - & 0.5 & Air FSI \\ \hline
70.645160 & - & 0.030, 0.034, 0.047 & 0.5 & Air FSI \\ \hline
\end{tabular}
\caption{Distance measurement precisions for various setups using the 
multiple-distance-measurement technique.}
\end{table}

Based on our studies, the slow fluctuations are reduced to a negligible level by using 
the plastic box and PVC pipes to suppress temperature fluctuations.
The dominant error comes from the uncertainties of the interference fringes 
number determination; the fringes uncertainties are uncorrelated for multiple 
distance measurements. In this case, averaging multiple distance measurements
in one scan provides a similar precision improvement to averaging distance measurements
from multiple independent scans. But, for open box data, the slow fluctuations 
are dominant, on the order of few microns in our laboratory. The 
measurement precisions for single and multiple distance open-box measurements 
are comparable, which indicates that the slow fluctuations cannot be adequately suppressed by using
the multiple-distance-measurement technique.
A dual-laser FSI system\cite{coe2001} intended to cancel the drift 
error is currently under study in our laboratory .


In order to test the vibration measurement technique, 
a piezoelectric transducer (PZT) was employed to produce 
vibrations of the retroreflector. For instance, the frequency of the controlled 
vibration source was set to $1.01 \pm 0.01$ Hz with amplitude
$9.5 \pm 1.5$ nanometers. The magnification factors,
distance measurement residuals and corrected measurement residuals for 2000
measurements in one scan are shown in Fig.3(d), Fig.3(e) and Fig.3(f), respectively.
The extracted vibration frequencies and amplitudes using this technique,
$f_{vib} = 1.025 \pm 0.002$~Hz, $A_{vib} = 9.3 \pm 0.3 $ nanometers,
agree well with the expectation values.

In addition, vibration frequencies at 
0.1, 0.5, 1.0, 5, 10, 20, 50, 100 Hz with controlled vibration amplitudes ranging from 
9.5 nanometers to 400 nanometers were studied extensively using our current
FSI system. The measured vibrations and expected vibrations all 
agree well within the 10-15\% level for amplitudes, 1-2\% for frequencies,
where we are limited by uncertainties in the expectations.
Vibration frequencies far below 0.1 Hz can be regarded as slow fluctuations, 
which cannot be suppressed by the above analysis techniques. 

Detailed information about estimation of major error sources for the absolute distance
measurement and limitation of our current FSI system is provided elsewhere\cite{fsi05}.

\section{Dual-Laser FSI System}

A dual-laser FSI system has been built in order to reduce drift error and slow 
fluctuations occuring during the laser scan. Two
lasers are operating simultaneously, the two laser beams are coupled into one optical
fiber but isolated by using two choppers. 
The principle of the dual-laser technique is shown in the following.
For the first laser, the measured distance $D_1 = D_{true} + \Omega_1 \times \epsilon_1$,
and $\epsilon$ is drift error during the laser scanning.
For the second laser, the measured distance $D_2 = D_{true} + \Omega_2 \times \epsilon_2$.
Since the two laser beams travel the same optical path during the same period,
the drift errors $\epsilon_1$ and $\epsilon_2$ should be very comparable.
Under this assumption, the true distance can be extracted using the formula
$D_{true} =  (D_2-\rho \times D_1)/(1-\rho)$, where, $\rho = \Omega_2/\Omega_1$, 
the ratio of magnification factors from two lasers.

The laser beams are isolated by choppers periodically, so only half the fringes are
recorded for each laser, degrading the distance measurement precision.
Missing fringes during chopped intervals for each laser must be
recovered through robust interpolation algorithms. 
The chopper edge transitions make this interpolation difficult. 
Several techniques are under study.

\section{A Possible Silicon Tracker Alignment System}

One possible silicon tracker alignment system is shown in Fig.4.
The left plot shows lines of sight for alignment in R-Z plane of the tracker barrel,
the middle plot for alignment in X-Y plane of the tracker barrel,
the right plot for alignment in the tracker forward region.
Red lines/dots show the point-to-point distances need to be
measured using FSIs. There are 752 point-to-point distance
measurements in total for the alignment system. More studies
are needed to optimize the distance measurments grid.

\begin{figure}[htbp]
%{\scalebox{0.55}{\includegraphics{figure1.eps}}}
{\scalebox{0.23}{\includegraphics{sd-barrel-alignment-xy.eps}}}
{\scalebox{0.23}{\includegraphics{sd-barrel-alignment-z.eps}}}
{\scalebox{0.23}{\includegraphics{sd-forward-alignment.eps}}}
\caption{A Possible SiLC Tracker Alignment System.}
\end{figure}

% If you have acknowledgments, this puts in the proper section head.
\begin{acknowledgments}
This work is supported by the National Science Foundation and the Department of Energy of
the United States.
\end{acknowledgments}

%%\bigskip
%Electronic address: $^*$yhj@umich.edu, $^\dagger$kriles@umich.edu

\begin{thebibliography}{99}
%%Do not include separate BibTeX files; if BibTeX is used, paste the output here.

\bibitem{ox98} A.F. Fox-Murphy, D.F. Howell, R.B. Nickerson, A.R. Weidberg, 
``Frequency scanned interferometry(FSI): the basis of a survey system for ATLAS
using fast automated remote interferometry'',
Nucl. Inst. Meth. A383, 229-237(1996)

\bibitem{ox04} P.A. Coe, D.F. Howell, R.B. Nickerson,
   ``Frequency scanning interferometry in ATLAS: remote, multiple, simultaneous and precise distance measurements in a hostile environment'', Meas. Sci. Technol.15 (11): 2175-2187 (2004)

\bibitem{orangebook} T. Abe {\it et.al.}, American Linear Collider Working Group, 
``Linear Collider Physics, Resource Book for Snowmass 2001'', 
hep-ex/0106058, SLAC-R-570 299-423(2001) 

\bibitem{stone99} J.A. Stone, A. Stejskal, L. Howard, 
``Absolute interferometry with a 670-nm external cavity diode laser'',
Appl. Opt. Vol. 38, No. 28, 5981-5994(1999)


\bibitem{fsi05} Hai-Jun Yang, Jason Deibel, Sven Nyberg, Keith Riles,
``High-precision Absolute Distance and Vibration Measurement
using Frequency Scanned Interferometry'', physics/0409110,
to appear in Applied Optics, July, 2005.

%\bibitem{dai98} Dai Xiaoli and Seta Katuo, ``High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry'', Meas. Sci. Technol.9, 1031-1035(1998)

%\bibitem{barwood98} G.P. Barwood, P. Gill, W.R.C. Rowley, 
%``High-accuracy length metrology using multiple-stage swept-frequency interferometry
%with laser diodes'', Meas. Sci. Technol. 9, 1036-1041(1998)

%\bibitem{bechstein98} K.H. Bechstein and W Fuchs, 
%``Absolute interferometric distance measurements applying a variable synthetic wavelength'',
%J. Opt. 29, 179-182(1998)

%\bibitem{thiel95} J. Thiel, T. Pfeifer and M. Haetmann,
%``Interferometric measurement of absolute distances of up to 40m'', Measurement 16, 1-6(1995)

%\bibitem{kikuta86} H. Kikuta, R. Nagata, 
%``Distance measurement by wavelength shift of laser diode light'', 
%Appl. Opt. Vol. 25, 976-980(1986)

\bibitem{coe2001} P. A. Coe, 
``An Investigation of Frequency Scanning Interferometry for the alignment
of the ATLAS semiconductor tracker'', Doctoral Thesis, 
University of Oxford, 1-238(2001)

%\bibitem{otsuka2002} K. Otsuka, K. Abe, J.Y. Ko, T.S. Lim, 
%``Real-time nanometer-vibration measurement with a self-mixing microchip solid-state laser'',
%Opt. Lett. Vol. 27, 1339-1341(2002)

%\bibitem{schott96} SCHOTT'96 for Windows Catalog Optical Glass, 
%Schott Glaswerke Mainz, Germany, 1996, 
%http://us.schott.com/sgt/english/products/catalogs.html

%\bibitem{peck72} E. R. Peck, K. Reeder, ``Dispersion of air'', JOSA 62, 958-962 (1972) 

%\bibitem{ciddor96} P.E. Ciddor, 
%``Refractive index of air: new equations for the visible and near infrared'',
%Appl. Opt. Vol. 35, 1566-1573 (1996) 

\end{thebibliography}


\end{document}

physics0506197.extracted_bib
\begin{thebibliography}{99}
%%Do not include separate BibTeX files; if BibTeX is used, paste the output here.

\bibitem{ox98} A.F. Fox-Murphy, D.F. Howell, R.B. Nickerson, A.R. Weidberg, 
``Frequency scanned interferometry(FSI): the basis of a survey system for ATLAS
using fast automated remote interferometry'',
Nucl. Inst. Meth. A383, 229-237(1996)

\bibitem{ox04} P.A. Coe, D.F. Howell, R.B. Nickerson,
   ``Frequency scanning interferometry in ATLAS: remote, multiple, simultaneous and precise distance measurements in a hostile environment'', Meas. Sci. Technol.15 (11): 2175-2187 (2004)

\bibitem{orangebook} T. Abe {\it et.al.}, American Linear Collider Working Group, 
``Linear Collider Physics, Resource Book for Snowmass 2001'', 
hep-ex/0106058, SLAC-R-570 299-423(2001) 

\bibitem{stone99} J.A. Stone, A. Stejskal, L. Howard, 
``Absolute interferometry with a 670-nm external cavity diode laser'',
Appl. Opt. Vol. 38, No. 28, 5981-5994(1999)


\bibitem{fsi05} Hai-Jun Yang, Jason Deibel, Sven Nyberg, Keith Riles,
``High-precision Absolute Distance and Vibration Measurement
using Frequency Scanned Interferometry'', physics/0409110,
to appear in Applied Optics, July, 2005.

%\bibitem{dai98} Dai Xiaoli and Seta Katuo, ``High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry'', Meas. Sci. Technol.9, 1031-1035(1998)

%\bibitem{barwood98} G.P. Barwood, P. Gill, W.R.C. Rowley, 
%``High-accuracy length metrology using multiple-stage swept-frequency interferometry
%with laser diodes'', Meas. Sci. Technol. 9, 1036-1041(1998)

%\bibitem{bechstein98} K.H. Bechstein and W Fuchs, 
%``Absolute interferometric distance measurements applying a variable synthetic wavelength'',
%J. Opt. 29, 179-182(1998)

%\bibitem{thiel95} J. Thiel, T. Pfeifer and M. Haetmann,
%``Interferometric measurement of absolute distances of up to 40m'', Measurement 16, 1-6(1995)

%\bibitem{kikuta86} H. Kikuta, R. Nagata, 
%``Distance measurement by wavelength shift of laser diode light'', 
%Appl. Opt. Vol. 25, 976-980(1986)

\bibitem{coe2001} P. A. Coe, 
``An Investigation of Frequency Scanning Interferometry for the alignment
of the ATLAS semiconductor tracker'', Doctoral Thesis, 
University of Oxford, 1-238(2001)

%\bibitem{otsuka2002} K. Otsuka, K. Abe, J.Y. Ko, T.S. Lim, 
%``Real-time nanometer-vibration measurement with a self-mixing microchip solid-state laser'',
%Opt. Lett. Vol. 27, 1339-1341(2002)

%\bibitem{schott96} SCHOTT'96 for Windows Catalog Optical Glass, 
%Schott Glaswerke Mainz, Germany, 1996, 
%http://us.schott.com/sgt/english/products/catalogs.html

%\bibitem{peck72} E. R. Peck, K. Reeder, ``Dispersion of air'', JOSA 62, 958-962 (1972) 

%\bibitem{ciddor96} P.E. Ciddor, 
%``Refractive index of air: new equations for the visible and near infrared'',
%Appl. Opt. Vol. 35, 1566-1573 (1996) 

\end{thebibliography}