This ``forward'' error calculator of the Astrometrical Operations computes variations in the baseline length and optical path difference (OPD) given variations in the telescope coordinates and star positions. This is correlated with but not the same as answering the question how errors in the baseline and OPD propagate backwards to errors in the star coordinates.

Graphical User Interface, Applet

Fields above the "Update" button are editable after the telescope stations have been selected. Fields below the "Update" button are not editable with the exception of the MIDI subsection. Image snapshots can be generated with xwd(1) and printed after using convert(1), or running the appletviewer(1) and using its print option.

The Paranal Origin of (U,V,W) coordinates for generic sky chart calculators are 70° 24' 17.953'' West, 24° 37' 38.782'' South.


Optionally edit the set of station coordinates with their geodetic parameters (longitude in degrees, latitude in degrees, including their signs, altitude above the tangential plane of the geoid) and error estimates. Nonzero error estimates must follow the values separated by "+-". The name "ZE" at the end of the list refers to the nominal origin of the array; for the VLTI this is the U=V=W point. Names "Ke1" and "Ke2" have been intialized with the Keck coordinates.

Optionally set the model of the Earth flattening and radius to the values selectable from the WGS84 or two IAU conventions. The 1/f entry for the inverse of the flattening factor and equatorial radius are only editable if the selector "others" has been chosen. (For comparison: see D Egger's Location Observer applet.)

Select stations for telescope 1 (T1) and 2 (T2), specify two star coordinates for the primary (PS) and secondary (SS) star with associated error bars. These are apparent coordinates, proper motion already included. Type in a local sidereal time between 0 and 86400 seconds with an error bar separated from its reference value by a +- sign. (The default represents the time the GUI is started at the location of the telescope array.) Click on "Update below!" to compute

The square plot at the bottom shows a green circle symbolizing a diameter of 2 arcsec (radius of 1 arcsec) on the sky in the x-y FITS coordinates of the MIDI detector. North (N), East (E) and projected baseline (b) directions to T2 are also marked with green lines (and these may occur twice if hybrid telescope pairs are selected) as explained in the reference given above. Red symbols show the primary star (PS) and the secondary star (SS) at a location compatible with the star orientation and field orientation angles. (This plot does not yet take into account optical trains that use the star separator or the differential delay lines which may be installed at some time in the future.) Blue lines of equal differential delay run perpendicular to this direction of the projected baseline at a stride [micron per line] that can be selected to the right of the graph by editing the blue number. Optionally a brown rectangular grid of the detector pixel mesh can be added for the two different MIDI cameras. Changing the zoom factor helps to locate the SS if the star separation is larger than 1 arcsec.

Mathematics of Error Model

Calculations are based on linear error propagation of maximum, correlated errors. The model represents telescopes and delay lines in vacuum. Note that OPD's are signed variables: the definition here is OPD=OPL(T1)-OPL(T2) and the value is positive if the star is closer to T2 than to T1. The Azimuths are 0 in the North direction and becoming positive when turning to the West. Subtract this value from 180 degrees (modulo 360) to obtain the values reported by the ISS in ISS AZ FITS header keywords. The color of the output field of the star separation changes if the separation becomes larger than 2 arcmin. The color of the altitude output field z changes if the zenith distance becomes larger than 60 deg. Limitations by the skyline of neighbouring domes (see the issshadow files in my VLTI web page) are not considered. If the external OPD becomes too large for compensation by the main delay line ranges, the field of the OPD and DOPD is colorized to indicate that restriction. This is an estimate based on a simple geometric model, and the issgui files in the VLTI web page should be consulted to obtain more accurate pointing limits.

Richard J Mathar,