Keck Interferometer Tutorial

Data Calibration

Update (July 2007): The KI team has investigated and quantified a flux bias in the visibility amplitude (see the flux bias memo for more details). This bias can be corrected using the -fluxBias command line option in wbCalib and nbCalib and we recommend that all KI data be calibrated with this option.

What is data calibration?

After you have obtained your level 1(L1) data, the next step in data analysis is to use your calibrator and target observations to produce calibrated visibilities, or level 2 (L2) data.

The visibility that KI measures on an astronomical object (Vm) is the product of the true object (Vt) visibility and a factor, called the system visibility (Vs), which represents the loss of coherence due to instrumental and atmospheric factors: Vm = Vt * Vs. In order to obtain the true object visibility, the system visibility must be estimated. The system visibility can be estimated using observations of stars of known size, and thus of known true visibility; or more typically using observations of unresolved stars, which have a true visibility of 1.0 and directly provide an estimate of the system visibility (Vm = Vs). Once the system visibility has been estimated, the calibrated or true object visibility is simply obtained as: Vt = Vm/Vs. (Note: the Keck Interferometer data reduction method uses visibility amplitude squared, rather than visibility amplitude, as the basic observable; a distinction with no consequences to the present discussion).

In general the system visibility is an instantaneous quantity, and may depend on other factors such as the object location in the sky (e.g. as the zenith angle increases, the atmospheric effects may become more severe) and the instrument configuration (e.g. integration time). Insuring that target and calibrators can be observed under the same instrument configuration (e.g. have similar magnitudes for the different sub-systems) and are close in the sky, is part of the planning process. Insuring that a target observation is bracketed by calibrator observations with a few minutes cycle time, so that a valid estimate of the system visibility can be formed, is the responsibility of the WMKO/NExScI staff executing the schedule.

How to calibrate your data

Your L1 data contains all that is needed to perform the calibration, and a variery of methods can be considered for estimating and applying the system visibility to produce calibrated data.

Although data calibration is not performed at the NExScI, we make available two software packages, wbCalib (for calibration of wide-band data) and nbCalib (for calibration of narrow-band data), which which greatly automate and simplify this process. The Calib packages take as input a L1 data file and a calibration script detailing which objects are targets and which are calibrators, and their estimated sizes, and produces one file of ASCII output containing the calibrated data, plus other very useful ancillary data, such as the spatial frequencies (u and v) corresponding to each calibrated visibility. The Calib packages also have a variety of options which apply corrections for potentially significant effects such as unbalanced fluxes between the two interferometer arms, or optical path jitter. Please refer to the help pages above for details on how to use those programs. Both packages can be downloaded from the NExScI software download page.

Troubleshooting your calibrated data

Once you have calibrated your visibilities, there are some simple checks you can do to insure that they are sensible:
  1. Plot the system visibility, it should be a smoothly varying function, with an average value between 0.6 and 0.8. The system visibility can change with time, for example it may decrease as the zenith angle increases, but abrupt changes are usually indicative of an instrument problem. In that case, inspect your data and observing logs.
  2. Note that if the calibrators are not unresolved, it is crucial to provide good estimates of their sizes in order to obtain a good estimate of the system visibility. A common way to verify this is to treat a calibrator as a target, and verify that you get the expected value of the calibrated visibilities (for example 1.0 for an unresolved calibrator). If not, then the calibrator sizes may need to be corrected.

Extracting astrophysical information from your calibrated data

Once the visibilities have been calibrated as outlined above, your KI data is ready for astrophysical interpretation. Typically this is done by assuming a simple target brightness (e.g. a binary, a uniform disk, a Gaussian disk, a ring, or a combination of those), deriving the corresponding visibility function, and fitting this function to the calibrated visibilities to extract some of the parameters that define the assumed brightness (e.g. binary separation, orientation, flux ratio; uniform disk or Gaussian diameters etc). Another typical approach is to add the visibilities to the global fitting of a more complex and physical model to a dataset which might also include spectro-photometric data, for example.

The NExScI distributes a tool for modelling interferometric observables, that can be used to compare the calibrated data with predictions from geometrical or physical models. Please see the Visibility Modelling Tool page.

Example

Suppose you have just retrieved your L1 data, containing some observations of one of your targets. The wide-band raw visibilities might look as in the plot below:


Clearly the above data shows that the source myTarget is clearly resolved, as its raw visibilities are much lower than those of the two calibrators used (HD157546 and HD174596).

The calibration script
We want to calibrate these wide-band data, and therefore will use the wbCalib program. As explained in detail in the user's manual, in addition to the input L1 SUM data, wbCalib requires a calibration script which informs it of the target and calibrator names, their astrometric information, and the calibrator angular sizes and errors, please see the Calib documentation for the detailed format specification. A calibration script for these observations would be as follows:

# Example calibration script for myTarget
myTarget
17 56 21.288 -21 57 21.880 -0.009 -0.040 0.01
---
2
HDC157546 17 24 37.040 -18 26 44.743 0.016 -0.008 0.02 0.17 0.1
HDC174596 18 52 08.375 -21 55 17.498 0.048 -0.048 0.01 0.21 0.1

Note that the getCal package contains a function that facilitates the generation of properly formatted calibration scripts.

Please pay particular attention to your choice of calibrator angular sizes and errors, as those will directly impact the resulting calibrated visibilities. While for observation planning it is acceptable to provide only approximate calibrator angular sizes, it is crucial to provide accurate estimates with realistic errors in the calibration step. Recall that in addition to providing stellar size estimates based on standard lookup tables for normal stars, the getCal package also contains routines to provide better estimates by fitting spectro-photometric data, see the getCal documentation for details.

Running wbCalib
If we save the above calibration script in a file called "example.calScript", and the L1 SUM data is in a file called "example.sum", then the command to run the calibration program would be:

wbCalib -WL -ratioCorrection example.calScript example.sum > example.wbcalib

A variery of command line options are available for both wbCalib and nbCalib. The NExScI science team has evaluated these options for KI data, and documented the recommended Calib settings. Note that the recommended settings for KI and PTI are not the same.

In the example above, we have told wbCalib that we want to use data from the white-light pixel, and to apply a correction for un-balanced fluxes between the interferometer arms. The calibrated data is now in the ASCII file called "example.wbcalib". Please see the wbCalib documentation for a detailed description of the output file fields. Using this file, a plot of the calibrated visibilities and errors versus UT time (columns 8, 9 and 5 respectively) is shown below:


Modelling the calibrated data
Suppose you know that the target above is an evolved star surrounded by a near-infrared emitting dust shell, and that you have independent evidence that the central star is unresolved and contributes 30% of the total K-band flux. You may then want to obtain a characteristic size for the dust shell being resolved by KI. Given what you know about the target, a reasonable model for this source would then consist of a point source plus an extanded component, represented for example by an uniform brightness. The plot below shows the model (and uncertainties) that would result from fitting such a model to the calibrated visbilities.


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Rafael Millan-Gabet, Sept 22 2003

last updated Nov 12, 2008