Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.mrao.cam.ac.uk/projects/OAS/publications/fulltext/spie4838-162-letter.ps Äàòà èçìåíåíèÿ: Wed Feb 20 16:41:17 2013 Äàòà èíäåêñèðîâàíèÿ: Sat Mar 1 03:28:55 2014 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: earthed atmosphere

Fringe envelope tracking at COAST
Nathalie D. Thureau ay , Roger C. Boysen a , David F. Busher a , Christopher A. Hani a , Ettore
Pedretti bz , Peter J. Warner a and John S. Young a
a Astrophysics Group, Cavendish Laboratory, Madingley Road, CB30HE, Cambridge, UK
b Harvard-Smithsonian Center for Astrophysics, 60, Garden Street, MS20, Cambridge,
MA 02138, USA
ABSTRACT
We report on a new fringe envelope tracking system installed at the Cambridge Optical Aperture Synthesis
telescope (COAST). This currently uses the existing photon-counting avalanche photo diode (APD) detector
system to allow real-time fringe tracking on up to 3 baselines simultaneously. This system has been recently
tested on the sky and has proved to successfully track the fringe envelope on a 38m baseline. The algorithm
based on an envelope method has also been implemented and tested at the Infrared-Optical Telescope Array
(IOTA) interferometer.
Keywords: interferometry, fringe envelope tracking
1. INTRODUCTION
COAST 1 is an imaging interferometer which provides fringe visibility measurements that can be used to re-
construct images. It is a Y-shaped array which consists of 5  40cm telescopes. It has two beam combiners,
one operating in the visible part of the spectrum (650 1000nm), the other one operating in the near infrared
(1:3 2:2m) (see Fig. 1). The equalisation of the optical paths is carried out by four delay lines, each consisting
of a roof mirror mounted on a motorised trolley running on 30m rails.
In order to obtain interference between any two telescopes, the dierence in optical path travelled by the two
beams of light must be matched to less than the coherence length of the light being observed, typically a few
microns. For ground-based long-baseline optical and infrared interferometers, the Earth's atmosphere introduces
random path-length uctuations of many tens of microns with a timescale as short as a few milliseconds.
The basic idea for a fringe envelope tracking system at COAST was to have a system that can take the output
of any of the beam combiner in order to sense and correct atmospherically-induced disturbances to the optical
pathlength inside the interferometer.
The results presented in this paper concentrate on the implementation of the fringe envelope tracker for the
visible beam combiner. We present the principle of the system, its implementation at COAST and the rst tests
carried out on the sky.
2. DESCRIPTION OF THE HARDWARE
The light beams coming out from the telescopes are fed into the delay lines where the optical paths are equalised
by moving the trolleys. Their positions are controlled by a two stage system. The high frequency errors are
corrected by moving the voice-coil-controlled roof mirror with respect to the trolley. The low frequency large
displacements are provided by motion of the trolleys. The accuracy of the trolley position is ensured by the use
of a laser interferometer system.
The beams are then fed into one of the two beam combiners which can accept up to 4 beams. Each combiner
generates four collimated outputs that are focused onto single pixel detectors which record the photon counts
versus time. In the visible, the detectors are optical APDs 2 , whereas in the near infrared, they are single pixels
y Marie Curie postdoctoral fellow, z Smithsonian Predoctoral Fellow
Further author information: (Send correspondence to N.D.T)
N.D.T.: E-mail: thureau@mrao.cam.ac.uk

Figure 1. The 4-way all-in-one visible and near infrared beam combiners.
from a NICMOS III detector. 3
By sweeping the roof mirror position back and forth, we change the optical path length, producing temporally
encoded interference fringes. The path length is varied in a symmetric triangle wave of frequency 5Hz, meaning
that there are 10 sweeps per second. The temporal modulation in the fringe pattern intensity appears as a sinc
function, "the fringe envelope", multiplied by a cosine function, "the fringes". The centre of the fringe envelope
indicates the position of the roof mirror which equalises the optical path between the dierent beams. The length
of the sweep is typically 60 microns which is longer than the coherence length of the optical lter bandpasses
( 20 40nm bandpass corresponds to  40 80 fringes at 800nm) used for fringe tracking.
For closure phase measurements, the light from three telescopes is combined simultaneously. The path length is
modulated in a similar fashion as before, but at a dierent speed in each arm. This serves to separate the fringes
from each baseline in frequency (see Fig. 2).
In the optical band, we use the APD output signal for fringe tracking. It consists of a stream of digital pulses
(a) (b)
Figure 2. (a) Optical path delay as a function of time for a 3-beam temporally-scanned combination. Each line represents
the path delay in one arm. Plain line: trolley 1 with a zero sweep amplitude, dashed line: trolley 2, dotted line: trolley
3. The fringes appear at 1 (beams 2 and 3), 2 (beams 1 and 2) and 3 (beams 1 and 3) times the fundamental fringe
frequency. (b) The corresponding power spectrum. The three peaks due to the fringes on three dierent baselines can
clearly be seen. The higher the sweep amplitude, the higher the fringe peak frequency.

corresponding to photon arrival times. The pulses are counted by an ISA card in the PC. A driver running under
RT-Linux (real-time Linux) reads the 4 counters at 200-microsecond intervals and saves the readings to a memory
buer. Every sweep (i.e. every 100ms) the data is transferred to a data manager which makes data available to
a normal user-space Linux process where the fringe envelope tracking software is installed. At COAST we use
dierent lters in front of the dierent APDs, which enable us to use broadband lters for fringe tracking and
narrowband lters for science observations.
3. OVERVIEW OF THE FRINGE ENVELOPE TRACKING SYSTEM
We give in Fig. 3 a block diagram representation of the fringe envelope tracking software. This diagram sum-
marises the main functions involved in the fringe envelope tracking process.
A set of detectors records the intensity coming out from either the visible or the infrared beam combiners. The
fringe tracking software send a data request to the data manager via a socket link. If data are available, the data
manager sends back a chunk of data and a header which include all the information relevant for the interpretation
of the data by the tracking system.
Then the program extracts the signal from the APD used for fringe tracking. It computes the power spectrum
of the interferogram and performs a test on the power spectrum to check the presence of the fringe peak(s) in
the power spectrum. If no fringe peak can be detected, the program processes the next data until a fringe peak
has been found. However, if a fringe peak is detected, it calculates the fringe envelope and estimates its mean
position.
The COAST control software "ApdGui" provides a real-time display with interactive plots of either the raw
data, the power spectrum or the fringe envelope. Thus we got a real time visual display of the current fringe
packet position.
The envelope position is computed using the algorithm described below and this is converted into trolley osets
which are made available to the trolley controller through a serial port link. The trolley controller reads the
serial line and places the values in the common data area and a ag is set. An interrupt routine is called every
0.2ms and every 0.2ms the position of each trolley is updated. Any osets from the envelope tracking system
are added to the trolley positions.
This closed loop system works as an integral controller which output is proportional to the integral of the er-
ror with time. The gain of the control can be adjusted, so as to adapt the system to dierent light level or
atmospheric conditions.
Figure 3. Block diagram of the fringe envelope tracking software
4. DESCRIPTION OF THE SINGLE-CHANNEL ENVELOPE DETECTION
ALGORITHM
We give in this section a detailed description of the algorithm used to calculate the fringe envelope and nd the
null-OPD (Optical Path Delay) point in a fringe packet.

The algorithm takes a fringe template which is a sinusoid modulated by a roughly Gaussian envelope (see Fig. 4.a)
and slides this template across the data, determining the correlation coeôcient as a function of the template
position. The frequency of the sinusoid is the central frequency of the fringes and the width of the Gaussian
corresponds to the inverse of the frequency range over which we wish to average. The width of the Gaussian will
hence correspond to the coherence time of the atmosphere (or the time taken to sweep through the coherence
envelope due to the optical bandwidth, if that is smaller).
The above operation corresponds to convolving the data with the template, which can be easily done in Fourier
space. The data is fast Fourier transformed and multiplied by the fast Fourier transform of the template. Fourier
transforming back to the time domain gives the correlation of the template with the data.
We can at once convolve with two templates simultaneously, namely the envelope multiplied a cosine function
and the envelope multiplied by a sine function, which corresponds to nding the real and imaginary parts of the
fringe phasor. Multiplying a one-sided Fourier window function is indeed equivalent to convolving with a real
cos function and an imaginary sine function. Taking the modulus squared of the resulting complex correlation
therefore gives the total fringe power in these two templates as a function of time. The resulting function is
a series of envelopes, which can be folded in time to give an average envelope, and this is what is plotted in
Fig. 4.b.
The same process is applied for the three beam case. Instead of using one single template, we use a template for
each available baseline. The central frequency of the template is adjusted so as to correspond to the frequency
xed by the sweep amplitude used for a given baseline. As a result, we obtain three envelope functions corre-
sponding to the three simultaneous fringe patterns. This algorithm realises a demodulation of the interleaved
fringe signal to restore the OPD information for dierent fringe frequencies.
Once the fringe envelopes have been computed, we apply a routine based on a centroid calculation to determine
the mean position of its centre. This mean position is then used as an estimate of the OPD.
In the one baseline case, we derive one OPD measurement and we have one trolley to move. Whereas in the
three baseline case, we got three OPD measurements and two trolleys to move. The extra bit of information
is used to better constrain the position of the two trolleys. Each trolley position is derived from the weighted
average of the three measured OPDs. This procedure is particularly useful in the case where the fringes on the
baseline we are supposed to track on, have a low contrast and can not be detected while the fringes are still
detected on the two other baselines (i.e. baseline bootstrapping).
(a) (b)
Figure 4. The template function (a). Example of intensity data and the resulting group-delay signal (b).
5. PRELIMINARY RESULTS
The algorithm has been intensively tested using an articial star to verify the stability of the system and to set
the parameters of the closed loop servo. When a suitable set of parameters was dened, the system was ready for
tests on the sky. The data analysed here were taken on the 14th of August 2002 with the centre and outer west
telescopes, providing a 38m baseline. We observed  Cygni which was chosen because it is a bright (V =1.25)

and not resolved target (angular size = 2.53 mas). The lters used in front of the four APDs were 905nm/50nm,
905nm/50nm, 830nm/40nm and 780nm/30nm. We used the data from an APD with a 780nm lter in front of
it for fringe envelope tracking. The mean photon rate was 1:5  10 5 photons/s.
We have recorded the data alternatively with and without using the fringe envelope tracker. We have represented
in Fig.5 the temporal variation of the envelope position for a few data les. Each plot represents 60s of data,
the envelope position being calculated for every second of data. This means that all the variations faster than
1Hz are averaged and do not appear on these plots.
The top panel represents a set of les recorded without the use of the fringe tracker. The fringe envelope motion
comprises a low frequency modulation with an amplitude of 40m and a period of several tens of seconds. As
well as a faster modulation with an amplitude of about 5 10m and a period of a few seconds. Another eect
observed if we do not track the fringes, but not illustrated here, is a slow drift of the fringe packet due to small
errors in the baseline solution. The low frequency of the fringe envelope motion arises from the fact we use a
long baseline. As a comparison, Fig. 6 represents the fringe envelope motion recorded while using the centre and
east telescopes providing a 10m baseline. The fringe envelope position appears to be pretty stable even without
fringe tracking.
The bottom panel in g. 5 represents a set of les recorded while we were using the envelope tracking system.
It appears that the fringe envelope low frequency displacements are very well corrected. The envelope position
uctuates around the null-OPD position. Nevertheless, the high frequency motion is still present with a slightly
reduced amplitude. This indicates that the servo is correcting atmospheric motions on timescale of order 5
seconds
Figure 5. Each plot represents 60s of data. They have been recorded with a 780nm/30nm in front of the APD on the
star  Cygni on the 14th of August 2002. The top plots have been recorded while not using the fringe tracking system.
The vertical axis has a 60m amplitude.
6. MULTI-CHANNEL ENVELOPE TRACKING
At the moment, the fringe envelope tracking system uses the signal from one single APD. However, we may want
to use all the available information to determine the trolley osets. The main diôculty arises from the use of
dierent spectral lters for the dierent APDs.

Figure 6. Motion of the fringe envelope recorded on the 28th of August on  Lyrae. We used the centre and east
telescopes providing a 10m baseline and a 780nm/30nm lter in front of the APD. The average photon rate for this le
was about 1:75  10 5 photons/s. The plot represents 60s of data . The vertical axis has a 60m amplitude.
Fig. 7 represents the temporal variation of the fringe envelope motion recorded on the four APDs. Each data
point is the envelope position averaged over one second of data. The upper most curve is the plot of the envelope
position calculated with data from APD4 which was used for fringe tracking. We can see that the envelope
position recorded for this APD uctuate around the null-OPD position whereas the envelope positions estimated
with data from the other APDs are shifted from the null-OPD. The shift is larger as the wavelength dierence
between the spectral lters is bigger.
These shifts are due to the longitudinal dispersion eect which arises because we compensate the optical path
delay in the air and not in vacuum. The data represented in gure 7 lead to three dierent optical path dierence
estimates of 0m , 10m and 20m.
If we want to use this information for fringe tracking, we will either need to develop a model of the longitudinal
dispersion for COAST or use spectral lters which have bandpaths close enough for the dispersion eect to be
negligible. In both cases the use of the signal from the four APDs would provide a better estimate of the optical
path uctuations.
+2µm
­2 µm
APD4, 780nm
APD3, 830nm
APD2, 905nm
APD1, 905nm
Figure 7. Fringe envelope motion versus time. Each point represents the envelope position averaged over 60s of data. The
four curves represent the date coming out from the four dierent APDs. From top to bottom: APD4 with a 780nm/30nm
lter, APD3 with an 830nm/40nm lter, APD2 with a 905nm/50nm lter and APD1 with the same lter as APD2.

7. TEST AT IOTA
We have established a collaboration with the Infrared-Optical Telescope Array (IOTA) group for the development
of fringe tracking algorithms. The idea was to develop algorithms which can be tested and used both at COAST
and IOTA in order to carry out a study on their respective eôciency and limitations and establish which algorithm
is the most suitable for low light level observations.
E. Pedretti developed and installed the IOTA fringe tracking system. The algorithm he developed is based on
the measurement of the complex phase of the Fourier transform of the fringe pattern and is routinely used at
IOTA. This system will be described in a forthcoming publication.
Tests were carried out at IOTA to compare the two algorithms. They have been used to tack fringes on the star
 Vul, in the H band, with a 5.5m baseline. We represent in gure 8 the data recorded with the COAST algorithm.
The COAST algorithm behaved very well even if the IOTA algorithm proved to be less time consuming in its
execution.
No conclusion has yet been made regarding their respective eôciency since the two algorithms have so far showed
similar results for fringe tracking. Further investigation is required to quantify their eôciency.
(a) (b)
(c) (d)
Figure 8. Fringes from the IOTA IONIC3T combiner on the PICNIC camera recorded in the H band on the star  Vul
with a 5.5m baseline. (a) Fringe pattern recorded without fringe tracking. (b) Fluctuations of the position of the fringe
packet represented in (a). (c) Fringe pattern recorded while using the fringe envelope tracking developed at COAST. (d)
Corresponding fringe packet position.
8. CONCLUSION
We have been able to implement a fringe envelope tracking system at COAST. This system has been successfully
tried on the sky. It managed to keep the fringe packet around the null-OPD position.The next step will be to
enable the system to work with 4 incoming beams. In this case, we will have to compute 6 fringe envelopes to
derive 6 dierent OPDs and control three trolleys. We will also try the fringe tracker with data from the infrared
beam combiner. A detailed study of the performances and limitation of the dierent algorithms will be carried
out. The purpose of this study is be to determine the relative merits of the two algorithms and characterise their
performance at low light levels. According to the results we may decide to choose one or the other algorithm or
even switch from one to the other according to the observing circumstances.

ACKNOWLEDGMENTS
This research was made possible thanks to a Marie Curie Fellowship (within the Fifth Framework programme
"Improving Human Research Potential and the Socio-economic Knowledge Base) granted to N. D. Thureau
(contract HPMF-CT-200-00966).
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