Jeff Meisner's Interferometry Page

Presentations
Papers
Abstracts
VINCI links:
      Observation logs and statistics
      Diameter determinations
Links
Contact info

Presentations (some with anotations, most directly from powerpoint files)


Diameter determinations from VINCI using global calibration solutions
Poster presented at the
workshop entitled:
The power of optical/IR interferometry: recent scientific results and 2nd generation VLTI instrumentation
held in Garching, Germany, 4-8 April 2005
View Abstract
PDF file of Poster
We were also allowed to submit a 2 page (!) paper for this conference.
Here is the 3 page "paper" I submitted in postscript format.


MIDI data reduction, analysis and science workshop 2004:
Presentation on ESO MIDI Data Reduction System (pipeline)

Presentation given 14 October 2004 in Leiden as part of MIDI data reduction workshop
PDF file produced from presentation


Conceptual Design Review PRIMA Astrometry Operations and Software
29 Sep 2004 through 1 Oct 2004

Presentation given concerning dispersion and fringe tracking between bands
Includes the "famous" dispersion animations
Powerpoint file used in presentation (no annotations)


Understanding visibility functions
Presentation/tutorial covering the calculation of visibility functions for various object profiles.
Raw powerpoint file without anotations


Data reduction, calibration, and stellar diameter results using VINCI
J. Meisner
Annotated slides from a presentation made at the September 2003 Workshop
Long Baseline Interferometry in the mid-infrared, Ringberg Castle near Munich.
PDF File


Direct detection of exoplanets using long-baseline interferometry and visibility phase
J. Meisner
Presentation made in Leiden 27 June 2003 based on a poster presented at XIXth IAP Colloquium "Extrasolar Planets : Today and Tomorrow" held in Paris, 30 June - 4 July 2003
View Abstract
Slide show presentation (PDF file)


Real-time control systems for a ground-based nulling interferometer: requirements and configurations
J. Meisner
View Abstract
Presented at GENIE workshop, 3 - 6 June 2002, Leiden
Annotated version of slides from presentation (pdf)



Publications

Note: these are published papers for which I was the primary author or played a major role in preparing.
Other papers which may contain my name can be found using an ADS Abstract Service query.

Coherent integration of complex fringe visibility employing dispersion tracking
J. Meisner, R Tubbs, W. Jaffe
View Abstract
Proceedings SPIE v5491
Interferometry conference, Glasgow, July 2004
Postscript File


Direct detection of the disk around HR 4049
Bakker, Eric J.; Meisner, Jeffrey A.; Percheron, Isabelle; Dominik, Carsten
View Abstract
Proceedings SPIE v5491, p35
Interferometry conference, Glasgow, July 2004


Scientific and technical results from VINCI using coherent estimation of fringe visibility
J. A. Meisner
View Abstract
Proceedings of the workshop at JENAM 2002, The Very Large Telescope Interferometer: Challenges for the Future
Astrophysics and Space Science, v286, p119
Postscript File


Dispersion affecting the VLTI and 10 micron interferometry using MIDI
J. Meisner, R. S. Le Poole
View Abstract
Published in proc. SPIE 4838
Postscript File


Direct detection of exoplanets using long-baseline interferometry and visibility phase
J. Meisner
In J.-P. Beaulieu, A. Lecavelier des Etangs, and C. Terquem, editors, Extrasolar Planets: Today and Tomorrow, volume 321 of ASP Conference Series, pages 125–126, 30 June - 4 July
For much more detail on this subject than they let me write in the paper, see my associated
presentation.
Or you can read the two-page "paper" that they allowed to be published.


Fringe Tracking and Group Delay Tracking Methods for MIDI
Jeffrey Meisner
View Abstract
Published in the proceedings of the 36th Liege International Astrophysics Colloquim (2001):
"From Optical to Millimetric Interferometry: Scientific and Technological Challenges"
Postscript File


Spatial Filters for Astronomical Interferometry using Discrete Optical Components
Jeffrey A. Meisner
View Abstract
Published in the proceedings for the
NOVA/LEIDEN/NEVEC/ESO/ESA Workshop on Space and Ground Based Optical/InfraRed Interferometry, Leiden, The Netherlands, September 18-22, 2000
Postscript File

Related paper:
Spatial Filtering with Pinholes for MIDI (unpublished)
Postscript File


Coherent estimation of complex fringe visibility: a generalized approach,
Jeffrey Meisner
View Abstract
Published in Proc. SPIE 4006, pp 1068, Astronomical Interferometry,
Proceedings of the conference "Interferometry in Optical Astronomy," held March 26 - 29, 2000, Munich, Germany
Postscript File


Use of a Seeing Monitor to Determine the Velocities of Turbulent Atmospheric Layers
Richard Roosen, Jeffrey Meisner
View Abstract
Working on the Fringe: Optical and IR Interferometry from Ground and Space. Proceedings from ASP Conference Vol. 194. Edited by Stephen Unwin and Robert Stachnik. p.303
("Working on the Fringe" conference, sponsored by JPL, May 24-27 1999, Dana Point, CA)
Postscript File


Concentration of Starlight from Large Apertures into a Single Spatial Mode for Long-Baseline Interferometry
Jeffrey Meisner
ASP Conference Series #174, p193 (1999)
(Contribution to symposium on interferometry and adaptive optics, ASP meeting, June 28 - July 1 1998, Albuquerque)
Long unpublished Version in HTML format
(Depending on your browser and installed fonts, you might have some problems with certain characters in the text! However the display equations are in graphic format and will come through fine.)
Published version: postscript file
View Abstract


Coherent integration of fringe visibility employing probabilistic determinations of atmospheric delay
Jeffrey Meisner
Paper in HTML format
(Depending on your browser and installed fonts, you might have some problems with certain characters in the text! However the display equations are in graphic format and will come through fine.)
View Abstract
Proc. SPIE v 3350, p294 (1998)


Atmospheric delay tracking in a long-baseline optical stellar interferometer,
Jeffrey Meisner
View Abstract
Optical Engineering v35, #7, pp. 1927-1935 (1996)
Scanned paper now downloadable


Estimation and tracking of atmospheric delay noise in a long-baseline optical stellar interferometer and determination of the expected estimation error, Ph.D. Thesis, Univ. of Minnesota (1995)
View Abstract
Online version in pdf format now available, courtesy Richard Mathar.



Abstracts:

Diameter determinations from VINCI using global calibration solutions
J. Meisner

ABSTRACT
VINCI is the test and commissioning instrument of the VLT interferometer (VLTI). It operates in the K band (2.0 - 2.4 microns) using delay-scanning. Optical fibers serve as spatial filters, beam combiner, and photometric pick- offs. Although intended as a test and commissioning instrument, VINCI has produced many scientifically useful results during its 4 years of operation resulting in well over a dozen papers in refereed journals.

Visibilities from VINCI raw data are obtained using coherent integration. These raw visibilities are interpreted using a global solution algorithm which simultaneously solves for calibration (transfer function) fluctuations and stellar diameters. Using this system, 15500 successful visibilities have been processed on 296 objects, including science objects and calibrators. Half of these objects were successfully observed at least 15 times and on at least 5 separate nights, providing a fruitful database for cross-calibration.

The standard approach to calibration based on observations of "calibrator" stars having assumed diameters, is challenged in the present work. No a priori diameters are input to the algorithm, which relies on baseline diversity to simultaneously solve both for diameters of stars having well-behaved characteristics, and a quasi-static transfer function subject to various hardware fluctuations. The success of this approach depends on a diversified schedule of observing the same target on different nights in conjunction with a mixture of other targets, so that all visibilities can be "cross-calibrated."

The results thereby obtained consist mainly of uniform disk diameters, but additionally the algorithm detects specific departures from that model. In about 20 cases, we detect a "zero- baseline power" significantly smaller than unity, probably due to circumstellar emission. Diameter variations of several pulsating stars were also observed. Visibilities beyond the first null were obtained for several objects, thus directly constraining the magnitude of limb-darkening in these cases. Among the uniform disk diameters obtained, about one third had formal errors of better than 1%.


Coherent integration of complex fringe visibility employing dispersion tracking
J. Meisner

ABSTRACT
We discuss methods of interferometric data reduction using coherent integration of fringe visibility. Unlike incoherent estimation techniques which discard the phase of interference, coherent integration retains as a complex quantity the contribution from each frame (or scan). In order to integrate these coherently, one must apply an OPD correction (or ``phase reference'') to compensate for random atmospheric pathlength fluctuations.

In an instrument with substantial bandwidth, it is also necessary to correct for fixed and random dispersion. The integrity of phase functions obtained is dependent on correct modelling of fixed optical phase functions (obtained from a calibrator observation), dispersion from air filled delay-lines (calibratable in principle), and averaging over time to reduce the effect of random atmospheric water vapor dispersion.

To achieve the best performance, it is necessary to include a dispersion tracker as well as tracking achromatic OPD, applying each as a phase correction as a function of time and of optical frequency. Using MIDI, the N band instrument of the VLTI, which has a wide bandwidth, it is often possible to uninterruptedly track random dispersion fluctuations over an observation. Plots of dispersion fluctuations due to water vapor above the VLTI are shown, which are used (along with OPD tracking) to coherently integrate raw frames from that instrument.

The resulting complex visibility includes a unique phase delay signature reflecting the source structure. A residual ``water-vapor-like'' phase may be present due to unmonitored humidity in the delay line paths, and to incomplete averaging of (nominally zero-mean) atmospheric water vapor fluctuations. Nevertheless, the use of visibility phase results corrupted by random dispersion is possible.


Direct detection of the disk around HR 4049
Bakker, Eric J.; Meisner, Jeffrey A.; Percheron, Isabelle; Dominik, Carsten

ABSTRACT
We present direct detections of the spatial extent of the circumbinary disk around HR 4049 and its companion. Observations were obtained with the ESO Very Large Telescope Interferometer using the VLT Interferometric Commissioning Instrument (VINCI) at 2 micron and the Mid Infrared Instrument (MIDI) between 8 and 12 micron. A single uniform disk model fit to the VINCI data gives an angular diameter of 27 milli-arcseconds. After taking into account the contribution from an unresolved central star we find that the observed visibilities indicate a second component with a spatial extent of 37 milli- arcseconds (which is identified as the circumbinary disk). The MIDI interferometric spectra show features which are due to PAH emission lines (8.6 and 11.3 micron). The visibilities of the emission lines indicate that the spatial extent in the lines (50 to 60 milli-arcseconds) is larger than in the continuum (35 to 45 milli-arcseconds). This leads us to propose a three emission components model to explain the interferometric observations: a central unresolved star, a 37 milli-arcseconds circumbinary disk and polar lobes emitting in the PAH bands with a size of 50 to 60 milli-arcseconds.


Direct detection of exoplanets using long-baseline interferometry and visibility phase
J. Meisner

ABSTRACT
There are several programs involving long baseline interferometry in the search for dim exoplanets and brown dwarfs orbiting around bright stars. These involve either ground-based observations, or space- based observations which will be more sensitive. Three techniques will be employed: indirect detection using precision narrow-angle astrometry; direct detection using nulling interferometry; and direct detection using visibility amplitude and/or phase.

We shall limit our discussion to the third method, in which the effect of a dim companion modulates the visibility function by a small amount. For a brightness ratio A (generally A < .001), the magnitude of the visibility amplitude and phase variations will be of order A, and A radians, respectively. It is expected that the small phase variations will be more detectable than the amplitude variations due to symmetry constraints. This phase can be observed in two ways.

Using a three-telescope interferometer, the closure phase can be computed by integrating the triple product of the three raw visibilities. In principle, this estimator needs no calibration, and will be sensitive when the star-planet separation exceeds .25 * lambda/B. Spectrally resolved interferometry will allow a spectrum of the planet's radiation to be directly obtained. It should be noted that closure phases measured with current interferometers have error levels an order of magnitude larger than required for planet detection, however no fundamental limitation appears to prevent the required improvement.

The alternate method of observing phase is to observe tiny changes in the phase delay of interference as a function of wavelength, the so-called "differential phase" method. This method is particularly sensitive in the case that a planet's radiation has sharp spectral features within the interferometer's passband. But even with a smooth spectrum, a planet can be resolved when the separation multiplied by the fractional bandwidth is somewhat in excess of .25 * lambda/B. Such an observation requires careful phase calibration of the instrument using observation of unresolved or symmetric calibration sources. Furthermore, random atmospheric dispersion due to water vapor inhomogeneities, acts as an additional source of interference, which must be tracked and removed. The remaining phase signal which cannot be absorbed by an arbitrary amount of differential water vapor dispersion, can solve for the planet's brightness ratio and separation.

We present the mathematical basis for these techniques, sensitivity estimates, and mention plans for the VLTI to perform such observations using the MIDI (mid infrared) and AMBER (near infrared) instruments.


Scientific and technical results from VINCI using coherent estimation of fringe visibility
J. A. Meisner

ABSTRACT
Although primarily intended as a test and alignment instrument in order to commission the VLTI, VINCI has taken useful scientific data in its first year and a half of operation. Our results employ coherent integration of fringe visibility in which the actual amplitudes of the raw scans are combined linearly after correcting for the position of the fringe within each scan. In addition to reducing the effect of noise compared to incoherent integration, the result contains a broader range of information, including an estimate of the complex visibility spectrum.

Such an estimator is thus sensitive to instrumental phase and spectral characteristics, including the variable component of dispersion introduced by the excess air paths in the delay lines. Calibration of such instrumental effects demonstrates the ability to detect source phase at a fine level as will be required for direct interferometric detection of extrasolar planets.

We present diameters for five stars obtained by observing the visibility null in their correlated spectra. Using coherent integration we have also observed the peculiar correlated spectra seen in many Mira variables, possibly due to changes in the apparent diameter with wavelength. Calibration of the zero-baseline power from o Ceti is used with other interferometric observations of this star over a period of 90 days to plot diameter variations associated with its pulsation cycle.


Dispersion affecting the VLTI and 10 micron interferometry using MIDI
J. Meisner, R. S. Le Poole

ABSTRACT
A wideband interferometer is sensitive to the effects of longitudinal dispersion which affect the interfering light beams unequally. At shorter wavelengths the major effect of dispersion is from dry air itself, while at mid infrared wavelengths the effect of water vapor is dominant. MIDI, the future 10 micron instrument of the VLTI, will experience significant effects from the imbalances in the water vapor content affecting the paths of the two interfering beams. This imbalance will include terms due to the unbalanced air paths in the delay line, random atmospheric humidity fluctuations in the lines- of-sight to the star, and random humidity variations inside of the VLTI delay line tunnels.

Large amounts of dispersion, if not monitored, can reduce the accuracy of measured visibility amplitudes. Measurements of the visibility phase as a function of wavelength will be highly sensitive to dispersion. This will then become a source of noise in results dependent on the phase of interference, such as imaging of non-symmetric objects, or detection of faint companions. In addition to dispersion over the 7 - 14 micron region detected by MIDI, observations using phase tracking with detection in the near IR, could be catastrophically affected by differential phase delays between the 2 micron and 10 micron bands.

Dispersion measurements from VINCI observing in the K band, both due to dry air and to water vapor, are presented. Combining VINCI results with published data from millimeter wave measurements leads us to expect atmospheric differential water vapor fluctuations to exceed 1 mole/m^2 rms over typical baselines. Specific effects from such a level of unmonitored dispersion variations are presented, which demand corrective action. Various solutions to monitor water vapor dispersion in realtime are considered.


Fringe Tracking and Group Delay Tracking Methods for MIDI
Jeffrey Meisner

ABSTRACT
The tracking of the white light (central) fringe in a broadband optical/IR interferometer, allows the possibility of long coherent integrations of fringe visibility. Fringe tracking involves the determination of absolute OPD offsets (not just narrowband phase) and either real-time correction of the interferometer's delay lines, or determination of the estimated OPD time series to be applied to the interferometric data off-line to effect coherent integration of fringe visibility. Algorithms of this sort will be included in the data reduction software package being developed for MIDI, the 10 micron interferometric instrument of the VLTI.

Group-delay tracking is a technique which is somewhat more robust than true phase tracking, but supplies a cruder estimate of OPD variations. Such incoherent techniques are useful for coarse adjustments to an interferometer's delay lines, and will be part of the real-time software operating in support of the MIDI instrument. General characteristics of both estimators are compared as regards sensitivity, detection bandwidth, and behavior in response to dispersion.



Spatial Filters for Astronomical Interferometry using Discrete Optical Components
Jeffrey A. Meisner

ABSTRACT
Spatial filtering of received optical radiation is used to select a single spatial mode from which interference can be obtained. By constraining the radiation to a single mode, as is done by the antenna in radio interferometry, a definite relationship is established between the initial power in the interfering beams, the strength of the interference signal, and the underlying correlation (fringe visibility), thus providing a means of calibration which is insensitive to variations in the atmosphere. In the case of an infrared interferometer operating at longer wavelengths where the system noise level is dominated by background (thermal) radiation, the spatial filter serves a second purpose: that of rejecting (as much as possible) background radiation responsible for the noise level, while accepting most of the coherent power in a single mode. These criteria are quantified in order to evaluate the performance of proposed spatial filter designs.

While a single-mode waveguide (optical fiber) has excellent properties in relation to both criteria, it may not be the ideal solution in all cases, particularly at longer wavelengths where suitable materials may be unavailable. Instead, concepts for spatial filtering using discrete optical components are analyzed. Although the proposed configuration is highly wavelength dependent, one possibility for a wideband implementation is discussed as well.



Coherent estimation of complex fringe visibility: a generalized approach,
Jeffrey Meisner

ABSTRACT
The measurement of fringe visibility (correlation) in a long baseline optical/infrared astronomical interferometer may be performed through a coherent integration of noisy data if a measurement of the phase producing the interference is available. That phase reference can be applied in hardware by rapidly servoing a delay line, or may be applied offline to a data stream produced while the phase was being monitored. In a spectrally dispersed detection system, the same data may be used for atmospheric delay tracking as well as visibility estimation. In that configuration one measures not only the magnitude, but the phase of the visibility. The squared magnitude of the measured interference need never be formed, so that all averaging is performed on the unbiased measurements of complex correlation, optimally reducing the effect of measurement noise. However accurate results depend on careful modeling of the system and correction for a number of effects which are detailed in this paper. The results, supported by simulations, are applicable to visibility determinations in a wide range of astronomical interferometers utilizing analog detection or photon counting. In particular these methods are being developed and proposed for use with the MIDI 10 micron interferometric instrument being built for the VLTI.


Use of a Seeing Monitor to Determine the Velocities of Turbulent Atmospheric Layers
Richard Roosen, Jeffrey Meisner

ABSTRACT
Using the illumination of an arbitrary bright star, a schlieren optical system at the focus of a .75m telescope has been successful in imaging atmospheric turbulence. Such an apparatus translates the gradient of atmospheric phase variations into intensity variations. A CCD camera captures snapshots of the resulting pattern at a 60Hz frame rate.

Successive frames are later cross-correlated in order to extract the velocity vectors of winds affecting the turbulent layers responsible for astronomical seeing. The velocities of strong turbulent layers may be detected in as little as one second with the present apparatus, allowing the observation of transient atmospheric turbulent phenomena on such a time scale. Proposed enhancements would increase the sensitivity of the system to weaker features, and a system for simultaneously determining the altitude of the atmospheric layers associated with the wind velocities is suggested.

Due to its ability to identify the individual contributions of distinct atmospheric layers towards seeing, such an apparatus may have use as a realtime seeing monitor in conjunction with ground based interferometers and adaptive optics systems, as well as in statistical studies of seeing, site selection, and meteorological research.


Atmospheric delay tracking in a long-baseline optical stellar interferometer,
Jeffrey Meisner

ABSTRACT
The performance of a long-baseline optical stellar interferometer is greatly enhanced if the instantaneous atmospheric delay  tau(t), can be tracked to within a fraction of a wavelength, permitting coherent integration of the optical correlation (fringe visibility).  Real-time fringe- tracking involves a control system that servos a rapidly responding path-length compensator in real-time.

However precise delay-tracking can be achieved at somewhat lower signal levels by employing an off-line delay-tracking system, in which the raw data measured by the interferometer is stored for subsequent analysis.  Then the estimate of  tau  at time t, is based on data collected both before and after time t.

An optimum delay-tracking algorithm embraces the a priori statistics of the atmospheric delay process.  Rather than simply estimating tau at a point in time, a superior estimate of tau will be obtained by comparing all possible functions, tau(t), over a time period.  Using Bayes' theorem, the a posteriori probability density of any  tau(t) function can be determined.  An algorithm has been developed which determines one or more functions which maximize that probability.  Even the ambiguous estimates which result at lower signal levels, can be employed for the coherent integration of optical correlation.


Coherent integration of fringe visibility employing probabilistic determinations of atmospheric delay
Jeff Meisner

ABSTRACT
Coherent integration of fringe visibility in an optical stellar interferometer yields much higher signal-to-noise ratios is shorter integration periods for dim objects. Furthermore coherent integration, if performed simultaneously over multiple spectral channels, can yield direct determination of the phase of the visibility function, a quantity that is lost in incoherent integration. To perform coherent integration it is necessary to estimate the random atmospheric delay to well within a wavelength. That determination can be used either to compensate for the delay in hardware, or as a 'phase reference' for integration of fringe visibility with the correction applied in software. This paper primarily addresses the latter method, presenting algorithms for the proper estimation of optical correlation given the interaction between the statistics of the incoming light and the hardware. Of particular importance is the effect of error in the estimation of the atmospheric delay used as a reference phase. The author's previously published method for estimation of the atmospheric delay achieves well modeled error levels. In the case of very weak signal, even 'ambiguous' determinations of atmospheric delay can be used for phase referencing. The delay estimator may employ the same raw data used for estimation of fringe visibility.


Concentration of Starlight from Large Apertures into a Single Spatial
Mode for  Long-Baseline Interferometry
Jeffrey Meisner

ABSTRACT
A long-baseline optical stellar interferometer requires a minimum level of optical power available from each arm in order to operate in the fringe-tracking mode which enables coherent integration of fringe visibility. That optical power must be concentrated in a single spatial mode in order to interfere coherently. However atmospheric seeing places a limit on the amount of optical power that will be accepted into a single spatial mode for apertures much larger than the Fried parameter, thus placing a magnitude limit on the coherent operation of the interferometer.

However the use of an adaptive optics system may enable larger apertures to concentrate greater amounts of optical power in a single mode, thus extending the magnitude limit of the interferometer. Aside from systems using laser guide stars, an adaptive optics system requires a feedback signal derived from the detection of a portion of the collected starlight in order to co-phase the sub-apertures. Increasing the portion of light directed to the feedback system will therefore allow the adaptive optics system to operate on dimmer objects.

On the other hand, the optical power which is sacrificed for the production of the feedback signal becomes unavailable for the ultimate use by the interferometer. However any light which would not successfully be concentrated into the output mode may be obtained "cost free." This observation leads one to different design criteria for an adaptive optics system used for concentrating light into a single mode, as opposed to one designed for high resolution imaging by a single large aperture.

The sensitivity limits and light concentrating power of any such adaptive optics system can be found by the analysis of a hypothetical guided wave optical circuit forming a binary tree structure. Optical power is concentrated from subapertures feeding the branches of the tree toward the root yielding starlight concentrated in a single mode which may supply one arm of a long-baseline interferometer. Concentration of light along the tree structure occurs at 2-input modules each of which are similar, and are optimized for maximum light concentration at each stage. The control system for each module operates independently of the others, and is optimized  on the basis of the power spectrum of phase noise expected for a given level of atmospheric turbulence. Performance limits are obtained for the resultant optical concentrating power as a function of incident flux, the Freid parameter, and the atmospheric coherence time parameter.
 


Estimation and Tracking of Atmospheric Delay Noise in a Long-Baseline Optical Stellar Interferometer and Determination of the Expected Estimation Error
Doctoral dissertation, University of Minnesota, 1995
Jeffrey Meisner

ABSTRACT
A long-baseline optical stellar interferometer is capable of performing superior measurements of optical correlation (or "fringe visibility") in much shorter observation times if the instantaneous atmospheric delay tau (t), can be accurately tracked to well within an optical wavelength. This permits coherent integration of the optical correlation, among other advantages.

The conventional approach to "fringe tracking" involves a control system that serves a rapidly responding path-length compensator in real-time. At marginal signal levels, the reliability of such a real-time delay- tracking system suffers. Precise delay-tracking can be achieved at somewhat lower signal levels by employing an off-line delay-tracking system, in which the raw data measured by the interferometer is stored for subsequent analysis. Then it is possible to estimate the delay error at time t using raw data collected both before and after time t, resulting in a superior estimate.

As opposed to point estimation procedures based upon the estimation of tau at a point in time, the optimum estimation of tau is based upon the comparison of all possible functions, tau(t), over a time period. Such a path estimation procedure fully incorporates the a priori statistics of the atmospheric delay process.

Solutions are found using an iterative procedure to maximize the a posteriori probability of the function tau(t), determined by employing Bayes' theorem. However there will be more than one local maximum of a posteriori probability. At lower signal-to-noise ratios it becomes increasingly difficult to differentiate among these multiple solutions, and the resultant estimate contains ambiguities. However by properly evaluating the array of solutions, sufficient information can be retained for the purpose of integrating the measurement of correlation. Very acceptable results are obtained at signal-to-noise ratios as low as 3.0, corresponding to 9 detected photons per T_0 with full optical correlation, |V| = 1. T_0 is defined as r _0/V_0) where r _0 is the Fried parameter, and V _0 is the velocity of the "wind" driving the atmospheric delay process according to the Taylor model. At this signal level the r.m.s. estimation error of the correctly identified solution is.7 radians.
 


Links

Leiden Observatory
Nova-ESO VLTI Expertise Centre (NEVEC)  homepage
VLTI Instrumentation
Optical Long Baseline Interferometry Newsletter
Massive Page of Interferometry Links (OLBIN)


Contact Info

Postal Address:
   Jeffrey Meisner
   Postbus 9513
   2300 RA  Leiden
   The Netherlands

Email: meisner@strw.leidenuniv.nl

PGP key for J. Meisner (or open as a text file)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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