CLASSIC Data Reduction Pipeline


The CLASSIC / CLIMB data reduction software is maintained by Theo ten Brummelaar. Please see his website for download and installation instructions.

Example CLASSIC data on Kappa Ser from 2018_05_11

The steps below show an example of how to process data using the CLASSIC/JOUFLU reduction pipeline called redfluor.  Typing "redfluor -V" at the command line prompt will give the version of the code and list the available options that can be used with the code.

$ redfluor -V
VERSION: V3.1 Wed Feb 28 14:48:15 PST 2018
usage: redfluor [-flags] ir_datafile
Flags:
-a        Toggle apodize for FFT (ON)
-A        Use shutter sequence A for noise (TRUE)
-b        Bootstrap to estimate the Median Error (OFF)
-c        Force this to be treated as CLASSIC data (OFF)
-d[0,1,2,3,4]    Set display level(1)
-D[Dir]        Directory for results (Basename)
-e        Toggle edit scans (ON)
-E[min_weight]    Edit scans by fringe weight (OFF)
-f        Force this to be treated as JOUFLU data (OFF)
-F[env_mult]    Change # of envelopes to include (3)
-g        Toggle GTK (OFF)
-h        Print this message
-H[n]        Set percentage definition of high frequency (20)
        Use 0.0 to force using upper integration limit.
-i        Toggle manual integration range (OFF)
-I[start-stop]    Set integration range of data (AUTO)
-j        Toggle adjusting filter width using Vg (ON)
-J        Toggle ignoring photometric data (OFF)
-k[0,1]    Set method of calculating Kappa (KAPPA_BY_SCAN)
            0 - Calculate for each scan.
            1 - Calculate for total mean.
-l[freq-fwhm]    Use low pass instead of Wiener filter (0).
-L        Toggle use photometry for noise estimate (OFF)
-O        Toggle Photometry Only (OFF)
-o[n_sigma]    Number (float) of standard deviations for outlier removal (OFF, <=0 to turn off)
-M        Use weighted mean (ON)
-p        Toggle use postscript (OFF)
-P[smooth_noise_size]    Change noise PS +-smooth size (5)
-q        Toggle ignore off star data (OFF)
-Q        K band shutter background percentage (3.63%)
-R        Toggle remote mode (OFF)
-s[spec-chan]    Change spectral channel (0=ALL)
-S[smooth_signal_size]    Change +-smooth size (1)
-t[start,stop]    Truncate scans (OFF)
-u        Toggle noise PS multiplier (OFF)
-U[freq]    Set DC suppression frequency (20.0 Hz)
-v        Toggle PLPLOT verbose mode (OFF)
-V        Toggle REDFLUOR verbose mode (OFF)
-x        Toggle use dither freq for fringes (OFF)
-X[stddevmult]    Set stddev multiplier (3)
-y        Toggle use fringe signal for waterfall (OFF)
-Y        Toggle use filter for waterfall (ON)
-z[pixmult]    Set pixel multiplier (2)

The README file in the reduceir software package includes a detailed description for these options.  Redfluor uses the PLPLOT package to produce the plots it makes, and therefore will also understand any standard Plplot command line arguments. For example, it would be very common to use:

redfluor -dev xwin

on an X windows machine, or

redfluor -dev psc

to produce a color postscript output.

A common way to invoke redfluor is:

redfluor -dev xwin -D/home/schaefer/chara/classic/2018/2018_05_11 -d2 -o3.0 2018_05_11_HD_139087_ird_001.fit

where -D indicates the directory path to save the reduced files, -d2 displays an intermediate amount of plots, and -o3 removes outliers that are more than 3 standard deviations away from the median visibility.  The data file to be processed is 2018_05_11_HD139087_ird_001.fit.  This command would need to be run for every data file collected.

The first step of the redfluor pipeline will show a waterfall plot of the fringe envelope over time (with time running vertically).  On a night of good seeing, the fringe waterfall will be concentrated in the center of the scan window.  On a night with bad seeing, the waterfall will look more like a scatter plot, with the position of the fringes bouncing back and forth across the scan window.  If there are any gaps in the fringes (vertical regions where the fringes disappear), then these scans should be removed by entering "e" on the command line and clicking on the region to edit.

Fringe editing.

 

# Processing file 2018_05_11_HD_139087_ird_001.fit
# Vel = 425.0 Lambda = 2.1 BP = 199.2
Move on, zoom in, Zoom out, Edit, Redraw or Clear (m/z/Z/e/r/c)? e
Click on the start of the edit.
Click on the end of the edit.
Move on, zoom in, Zoom out, Edit, Redraw or Clear (m/z/Z/e/r/c)? m

Next the routine will show plots of the photometry (raw and background subtracted).  The first three segmented areas show the light from Beam 5, darks (shutters closed), and the light from Beam 6.  The next ~ 200 scans are the fringe data (light from both telescopes with fringes).  The second set of ~ 200 frames are light from both telescopes but without fringes (carts moved away from the fringe position).  The final three segmented areas used to be another shutter sequence, but are now sky frames where the telescopes are moved off the star and the sky background is recorded.  The sky frames were added to the observing sequence after it was found that the shutters inside the lab contribute thermal heat in the K-band, which is particularly important when observing faint targets.  The last shutter sequence should be checked to make sure that the telescope moved off the star during the sky frames.  If you see light during the last sequence and the data were recorded using the new off-fringe and star sequence (e.g., the fits header keyword CC_SEQ = 'OFF_FRG_AND_STAR'), then you will need to run redfluor using the -A flag to use only the first shutter sequence instead.

Photometry and Kappa Matrix.


Hitting enter in the terminal window will bring up the next window showing the power spectra for the dark frames, fringe frames, telescope A, and telescope B.  In the example below, the fringe peak shows up at 160-240 Hz.  Peaks in the dark frames would indicate the presence of electronic noise, whereas peaks in the shutter A or shutter B frames would likely indicate an oscillation of the telescope (e.g., the small peak at ~ 260 Hz in shutter B).

Power Spectra.


Hitting enter in the terminal window will bring up the next window showing the off-fringe power spectra (light from both telescopes but without fringes), the signal/noise estimate, and the noise subtracted power spectrum of the signal.  The noise subtracted power spectrum will also show outlines of the fringe integration regions selected by the Gaussian fit to the fringe peak.

Noise Subtracted Power Spectra.


By default, the integration range is set by fitting a Gaussian to the fringe power spectrum peak.  If you want to select the integration region by hand, then set the -i flag.  Or if you want to define a fixed integration region for all stars in the data set, use the -I[start-stop] flag.  The automated integration region will be output to the terminal:

# Vel = 413.9 Lambda = 2.1 BP = 194.0 (193.0, 195.1)
# To get this integration range use
# -I146.82-241.30

Next is a plot of the low pass filter used to normalize the fringe signal.

Low pass filter.


Next the routine applies the sigma clipping algorithm if the -o flag is set.  The results from the outlier rejection are displayed.  If any data points are rejected they will be removed from the plot on the right.

Outlier Rejection.

 

# Calculating .........
# Rejected 0 scans due to low photometry.
# Rejected 0 scans due to being too close to the edge.
# Rejected 0 scans due to low weight.

The final plot will show histograms of the correlation and the fringe weights, the fringe waterfall, and the power spectra waterfall.

Histograms of the correlation and fringe weights.

 

# Results from FLUOR PS calculation method:
N_SCANS 201
# Detector 1 Detector 2 Combined
# Mean StdDev Mean StdDev Mean StdDev
Vg 404.268 15.575 407.158 15.698 405.880 15.234
T0_SCANS 21.8 21.6 22.3
T0_500NM 3.8 3.8 3.9
V2_SCANS 0.22248 0.09699 0.21254 0.10369 0.20418 0.09331
V2_CORR -1.18262
V2_CHI2 0.00225 0.00492
V2_SQRT 0.47168 0.20563 0.46102 0.22492 0.45187 0.20650
V_SCANS 0.45902 0.10883 0.44529 0.11969 0.43844 0.10960
V_NORM 0.46011 0.17201 0.44672 0.18679 0.43964 0.17224
V_LOGNORM 0.46157 0.09710 0.44893 0.10488 0.44133 0.09702
V2_MEDIAN 0.14754 0.09873 0.13858 0.09644 0.12813 0.09599
V_MEDIAN 0.38411 0.12971 0.37226 0.14757 0.35796 0.14248
Move on, toggle Log, zoom in, zoom out or zoom = 1 (m/l/z/Z/1)?


The final results are output to the screen and stored in the .info files in the directory created for each data file.  The results consist of a variety of visibility estimators.  Currently, it is recommended to use V2_SCANS which is the weighted mean of the visibilities for all scans.  The three sets of numbers listed for each estimator give the visibility and error recorded for pixel 1, pixel 2, and the difference signal.  The default is to use the difference signal, however, comparing the values obtained individually from the two readout pixels could provide an estimate of systematic offsets.

Calibration

Use calibir to use the calibrator stars to calibrate the system visibility and correct the visibilities measured for the science target.  The calibir program reads the INFO files in the directories in the current location.  The routine calibrates the science target using the nearest neighbor calibrators observed before and after the science target.  If the alignment changes between a calibrator and neighboring science target, then these observations should be moved to different directories to avoid calibrating across a jump in the system visibilities.  If NIRO alignments occurred between two calibrators, then it should be OK to calibrate all of the data in one directory since calibir uses only the nearest neighbors.

A common way to call calibir is as follows:

calibir -F -i -s1.1368-0.1069,1.0644-0.1001 -BV2_SCANS HD_141477 HD_139087 HD_142244

where -F saves the output to an OIFITS file based on the name of the object, -i selects objects based on the "ID" name listed in the INFO file, -s sets the calibrator diameters (uniform disk diameters in the K-band of θ = 1.1368 ± 0.1069 mas for HD 139087 and θ = 1.0644 ± 0.1001 mas for HD_142244 estimated by JMMC/Searchcal), and -BV2_SCANS sets the visibility estimator to "V2_SCANS" for both the target and the calibrators.  After the flags, the science target ID is listed, followed by a listing of the calibrators in the same order as their diameters in the -s flag.  Calibir outputs a plot of the calibrator visibilities (green, blue points), and the raw (red) and calibrated (yellow) visibilities of the science target.  In this example sequence, a NIRO alignment was done after every C1-O-C2 set.

Calibir calibration plot.


By default, the calibrated data are saved to an oifits file with the name 2018_05_11_HD_141477_001.fits. The oifits files can be fit using various data analysis software or read directly into programming languages like IDL.


OIFITS Utitlities

There are a few oifits utilities included in the reduceir package that can be used to manipulate, view, and analyze data.  For instance, oifits-merge can be used to merge multiple OIFITS files on the same target (e.g., merge observations from different nights) and oifud can be used to fit simple geometries like a uniform disk to the visibility data:

oifud 2018_05_11_HD_141477_001.fits

 

oifud interface.

 

Uniform disk fit.

How to Extract OIFITS Data Using IDL Utilities


Download the IDL OIFITS Library
- maintained by John Monnier at the University of Michigan.

Inside the IDL OIFITS Library are two test files called testdata.fits and bigtest.fits.  The bigtest.fits contains several tables to demonstrate the full richness of the OIFITS data format, although the values are nonsensical.

Read the OIFITS Tables

The routine "read_oidata" will provide an inventory of the tables contained in the OIFITS file and read in those tables:

IDL> read_oidata, 'testdata.fits', oiarray, oitarget, oiwavelength, oivis, oivis2, oit3, /inventory
This file Satisfies the requirements of the OI_DATA format
Inventory:
OI_ARRAY: 1
OI_TARGET: 1
OI_WAVELENGTH: 1
OI_VIS: 1
OI_VIS2: 1
OI_T3: 1
Unknown Tables: 0

IDL> print, oivis2(0).time, *oivis2(0).vis2data, *oivis2(0).vis2err
82810.000 0.67700000 0.064000000

However, the visibility data are stored as pointers when using read_oidata.  To extract and manipulate the data, use the routines extract_vis2data and extract_t3data described below.

Extract Visibility Amplitudes:

IDL> extract_vis2data, file='bigtest.fits', vis2data

The data are stored in arrays of structures.  To view the contents of the file, use the "help" command with the "/structure" flag:

IDL> help, vis2data, /st
** Structure <1474b28>, 26 tags, length=224, data length=207, refs=1:

OI_REVN INT 1
DATE_OBS STRING 2004-01-11
ARRNAME STRING CHARA_2004Jan
INSNAME STRING  CHARA_MIRC
EFF_WAVE DOUBLE 1.4000000e-06
EFF_BAND DOUBLE 5.0000001e-08 
WAVE_ID INT 
TARGET_ID  INT 0
TARGET  STRING 'alp_ori'
RA DOUBLE 0.0000000
DEC  DOUBLE  10.000000 
EQUINOX FLOAT 2000.00
TIME DOUBLE 0.0000000
MJD DOUBLE 0.0000000
INT_TIME DOUBLE 2.0000000
VIS2DATA DOUBLE 0.0000000
VIS2ERR DOUBLE 0.020000000
UCOORD DOUBLE 0.0000000
U DOUBLE 0.0000000
V DOUBLE 0.0000000
SFU DOUBLE 0.0000000
BASELINE DOUBLE 0.0000000
PA DOUBLE 0.0000000
STA_INDEX INT Array[2]
FLAG BYTE 70

Then you can print, plot, and manipulate any of these arrays as follows:

IDL> plot, vis2data.sfu, vis2data.vis2data, psym=6, xtitle='Spatial Frequency', ytitle='V^2'

 

 

 

 

 

 

 

 

 

 

 

 

Extract Closure Phases:

IDL> extract_t3data, file='bigtest.fits', t3data

The data are stored in arrays of structures.  To view the contents of the file, use the "help" command with the "/structure" flag:

IDL> help, t3data, /st
** Structure <17fc358>, 39 tags, length=328, data length=313, refs=1:

OI_REVN INT 1
DATE_OBS STRING '2004-01-11'
ARRNAME STRING 'CHARA_2004Jan'
INSNAME STRING 'CHARA_MIRC'
EFF_WAVE DOUBLE 1.4000000e-06
EFF_BAND DOUBLE 5.0000001e-08
WAVE_ID INT 0
TARGET_ID INT 0
TARGET STRING 'alp_ori '
RA DOUBLE 0.0000000
DEC DOUBLE 10.000000
EQUINOX FLOAT 2000.00
TIME DOUBLE 0.0000000
MJD DOUBLE 0.0000000
INT_TIME DOUBLE 2.0000000
T3AMP DOUBLE 0.0000000
T3AMPERR DOUBLE 0.020000000
T3PHI DOUBLE 0.0000000
T3PHIERR DOUBLE 0.0000000
U1COORD DOUBLE 0.0000000
V1COORD DOUBLE 0.0000000
U1 DOUBLE 0.0000000
V1 DOUBLE 0.0000000
BASELINE1 DOUBLE 0.0000000
PA1 DOUBLE 0.0000000
U2COORD DOUBLE 0.0000000
V2COORD DOUBLE 0.0000000
U2 DOUBLE 0.0000000
V2 DOUBLE 0.0000000
BASELINE2 DOUBLE 0.0000000
PA2 DOUBLE 0.0000000
U3COORD DOUBLE 0.0000000
V3COORD DOUBLE 0.0000000
U3 DOUBLE 0.0000000
V3 DOUBLE 0.0000000
BASELINE3 DOUBLE 0.0000000
PA3 DOUBLE 0.0000000
STA_INDEX INT Array[3]
FLAG BYTE 70

Then you can print, plot, and manipulate any of these arrays as follows:

IDL> plot, t3data.mjd, t3data.t3phi, psym=6

Time Required for an Observation

A single interferometric observation consists of a calibrator-science-calibrator sequence.  The amount time to collect data on a star depends on the instrument, the seeing, and the brightness of the target.  Here are some guidelines for how long the observations will take:

  • For fast instruments like CLASSIC, CLIMB, JOUFLU, and PAVO, an observation on an individual target will take 5-15 min, so a single CAL-SCI-CAL set will take between 15 to 45 min.  Use the longer integration time for targets near the typical magnitude limit, the shorter integration time for stars ~ 2 mag brighter than the typical limit.
  • For MIRC, an observation on an individual target will take about 45 min, so a CAL-SCI pair will take about 1.5 hours.
  • For VEGA, an observation on an individual target will take 10-20 min, so a CAL-SCI-CAL set will take 30 min to 1 hour.

Each observation may produce between one to several dozen UV points, depending on how many telescopes are combined and the number of spectral channels in the instrument.  The number of calibrated observations needed to complete a program depends on the science objectives.  The table below gives estimates for the number of observations needed for typical science programs for each instrument:

 

Beam Combiner Number of Measurements in One Data Set Science Objective Recommended Number of Data Sets
CLASSIC, JOUFLU Each data set consists of one visibility measurement on a single baseline. Angular Diameter ~10 calibrated data sets on each baseline (2.5 - 7.5 hours per baseline).  Observations on two separate nights and on two different baselines are recommended to minimize systematics.  If the star is oblate, then a few baselines at different position angles should be selected.
Binary ~10 calibrated data sets on each baseline (2.5 - 7.5 hours per baseline).  To solve for the binary separation and position angle, then data should be collected on at least two perpendicular baselines.
PAVO Each data set consists of ~ 20 visibility measurements (in each spectral channel) on a single baseline. Angular Diameter 5-10 calibrated data sets on each baseline (2 - 7 hours per baseline).  Observations on two separate nights and on two different baselines are recommended to minimize systematics.  If the star is oblate, then a few baselines at different position angles should be selected.
Binary 5-10 calibrated data sets on each baseline (2 - 7 hours per baseline).  To solve for the binary separation and position angle, then data should be collected on at least two perpendicular baselines.
CLIMB Each data set consists of 3 visibility measurements on each of the 3 baselines and one closure phase. Angular Diameter Obtain ~ 10 calibrated data sets using three telescopes simultaneously (2.5 - 7.5 hours).  Although data is collected more efficiently with CLIMB, the visibility precision isn't quite as good as the 2-telescope combiners such as CLASSIC or JOUFLU. 
Binary Obtain 5-10 calibrated data sets using three telescopes simultaneously (2.5 - 7.5 hours).  In addition to the visibilities, the closure phase measurements provide an additional constraint on the binary separation.
Disks / Imaging Obtain ~ 5 calibrated data sets on each 3-telescope configuration (2 - 4 hours on each configuration).  Select several different 3-telescope configurations to fill in the sky coverage and to sample different spatial frequencies.
VEGA For calibrated V2 observations, each data set provides two visibility measurement on each baseline (one baseline for 2T, three for 3T, and six for 4T).  For differential measurements, visibilities and phases are measured as a function of wavelength across the spectral line relative to the continuum. Angular Diameter Obtain ~ 10 calibrated data sets on each selected configuration.
Spectral Studies Obtain a few repeated measurements on the selected configurations.
MIRC Each data set will consist of visibility measurements on up to 15 baselines across 8 spectral channels and closure phase measurements on up to 20 triangles also across 8 spectral channels. Angular Diameters, Circumstellar Disks A diameter or limb darkening measurement could be obtained with two calibrated data sets using all 6 telescopes simultaneously (~ 3 hours).  The second set can serve as a check on systematics.  For the size and orientation of circumstellar disks, 2-4 calibrated data sets are recommended to improve sky coverage (3 - 6 hours)
Binary 2-3 calibrated data sets using all 6 telescopes simultaneously (3.0 - 4.5 hours).  To solve for the binary position, a minimum of one calibrated 6T data set is required.  However,  to test systematics, two data sets are recommended.  For faint targets or for detecting faint companions, 2-3 sets are recommended to improve the signal-to-noise.
Imaging Complex Sources Imaging stellar surface features or structure within circumstellar disks requires collecting many calibrated data sets on multiple baselines during the night to fill in the sky coverage (~ 1 night per target or the number of hours in a night when the target is above ~ 30 deg elevation).

Companion Detection Limits


There are two ways that a binary star can be observed using an interferometer.  For binaries wider than the coherence length of the beam combiner, the binary will appear as a "Separated Fringe Packet" where a fringe is detected for each binary component.  The separation between the fringe packets gives the binary separation.  For a binary where the separation is smaller than the coherence length, then the two fringe packets from each component will overlap and a modulation can be measured in the visibilities and/or closure phases from the combined fringe packet.  The table below gives the separation range and magnitude sensitivities for binary companions resolvable using different beam combiners at the CHARA Array. 

Combiner Method Magnitude Difference Range of Separations* References
CLASSIC/CLIMB Separated Fringe Packets ΔK < 1.5 mag 8 - 80 mas Farrington et al. (2010); Raghavan et al. (2012)
CLASSIC/CLIMB Visibility and closure phase modulation ΔK < 3 mag 0.5 - 8 mas Schaefer et al. (2018)
MIRC Visibility and closure phase modulation ΔH < 6 mag 0.5 - 54 mas Gallenne et al. (2015)
PAVO Visibility modulation ΔR < 3 mag 0.2 - 50 mas  
* The Range of Separations is based on the longest 331 m baseline assuming the wavelength band identified in the Magnitude Difference column.  These separation ranges will scale by a factor of 331.0/B where B is the length of the baseline being used.  

 

Separated Fringe Packet Binaries

Separated Fringe Packet binaries can be detected by beam combiners like CLASSIC and CLIMB that scan through the fringe window. The minimum separation for this technique is set by the coherence length of the beam combiner given by λ2/Δλ, where λ is the central wavelength and Δλ is the width of the bandpass filter.  The maximum separation is set by the length of the dither scan.

  • For CLASSIC/CLIMB in the K-band (λ = 2.13 μm, Δλ = 0.3489 μm), the coherence length is 13.0 μm.

  • For CLASSIC/CLIMB in the H-band (λ = 1.6731 μm, Δλ = 0.2854 μm), the coherence length is 9.8 μm.

  • For CLASSIC, the short-scan length is 90 μm, medium-scan length is 120 μm, and long-scan length is 150 μm.

The separation in microns [ρ(μm)] can be converted to a separation in milli-arcsec [ρ(mas)] using the formula: ρ(mas) = 206.265 ρ(μm)/B(m) where B(m) is the baseline length in meters.  For the longest 331 m baseline at the CHARA Array using the longest dither scan, separated fringe packets can be measured with separations between 8-80 mas in the K-band.  Companions can be detected down to a magnitude difference of ΔK < 1.5 mag (Raghavan et al. 2012).

Examples of separated fringe packet binaries from Farrington et al. (2010).  The top three scans show the effects of changing the binary separation at a fixed magnitude difference of Δm = 1 mag.  The bottom three scans show the effect of changing the magnitude difference (Δm = 0.5, 1.5, and 2.5 mag) at a fixed separation.  The separation between the two fringes gives the projected separation of the binary along the baseline while the magnitude difference determines the ratio of the fringe amplitudes.

Modulated Fringe Packet Binaries

For binaries with overlapping fringe packets, the minimum separation is set by the resolution of the interferometer and is given by 0.5λ/B, where λ is the wavelength of light and B is the baseline length.  The resolution limit for the longest 331 m baseline at the CHARA Array is 0.20 mas in the R-band, 0.52 mas in the H-band, and 0.66 mas in the K-band.  The maximum separation that can be resolved is set by the coherence length of the beam combiner given by λ2/Δλ, where λ is the central wavelength and Δλ is the width of the bandpass filter. 

  • For CLASSIC/CLIMB in the K-band (λ = 2.13 μm, Δλ = 0.3489 μm), the coherence length is 13.0 μm.

  • For CLASSIC/CLIMB in the H-band (λ = 1.6731 μm, Δλ = 0.2854 μm), the coherence length is 9.8 μm.

  • For MIRC in the H-band (central λ = 1.62 μm, Δλ = 0.03 μm for the width of the 8 spectral channels), the coherence length is 86 μm.

  • For PAVO in the R-band (median λ = 716 nm, Δλ = 6.4 nm for the width of a spectral channel), the coherence length is 80 μm.

The separation in microns [ρ(μm)] can be converted to a separation in milli-arcsec [ρ(mas)] using the formula: ρ(mas) = 206.265 ρ(μm)/B(m) where B(m) is the baseline length in meters. The table at the top of the page lists the range of separations (in mas) that can be resolved by each beam combiner using the longest 331 m baseline

The faintest companion that can be detected using the modulated fringe packet technique can be estimated as follows:

  • For MIRC, Gallenne et al. (2015) determined a dynamic range of 1:200 (ΔH < 6 mag) for binaries with separations smaller than 50 mas.  The precision closure phases measured with MIRC (Zhao et al. 2011) provide good sensitivity to faint companions.

  • For CLASSIC, Schaefer et al. (2018) estimated a maximum magnitude difference of ΔH < 2.9 mag based on a typical 4.5% scatter in the visibilities.

  • For PAVO, an expected 5% precision on the calibrated visibilities would provide sensitivity down to ΔR = 2.7 mag.
Example visibility curve for a binary star. The separation between the peaks in the visibility curve provides a measurement of the binary separation while the minimum visibility reflects the flux ratio between the components

References:

Farrington, et al. 2010, AJ, 139, 2308
Gallenne, et al. 2013, A&A, 552, A21
Gallenne, et al. 2015, A&A, 579, A68
Raghavan, et al. 2012, ApJ, 745, 24
Roettenbacher, et al. 2015, ApJ, 807, 23
Roettenbacher, et al. 2015, ApJ, 809, 159
Schaefer, et al, 2018, ApJ, accepted
Zhao, et al. 2011, PASP, 123, 964

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