Simulation Options on the Web
Interface
This section offers a section-by-section, option-by-option
overview of the web interface, how the various options relate to the
set-up of the simulation, and occasionally going into detail about
any assumptions that the OST makes behind the scenes.
Instrument
Figure 1. Array Selection
The first menu on the web interface allows the user to select
which array on the ALMA site they wish to simulate. Included in the
menu are two possibile realisations of the
Early Science array
(with maximum baselines of 125 m and 400 m), the full 50-antenna ALMA and the Atacama Compact Array (ACA).
Although the full ALMA undergoes a continuous reconfiguration process
and does not have a fixed array layout there is only a single option
in the menu for this instrument. This is because the OST will select
an appropriate configuration for the full array based on the
subsequent resolution requirements of the simulation. There are 28
possible configurations which are consistent with those supplied
within the CASA distribution.
Sky Setup
Figure 2. The sky setup options on the OST front-end.
This section is where the user specifies the properties of the
source, namely its position and the
ideal sky brightness
distribution that will be observed by ALMA.
Source Model
The drop-down menu in this section contains all the source models which are currently part of the OST Library. There are a variety of options here, ranging from a simple central point source to morphologically complex structures. The Library is assembled from a combination of existing observations and the results of astrophysical simulations.
The single option in this menu which does not select a pre-existing
source model is
Uploaded FITS file which notifies the OST that the
user has submitted a custom sky model. There are numerous things to
consider when preparing a source model FITS file, and some hints for
this process are presented in
the FITS section.
Upload a FITS file
Clicking the
Browse button here will bring up a file
selection box and allow the user to supply an arbitrary source model
in FITS format only. Many parameters in the header of the FITS file
will be overridden by the options that the user subsequently selects
on the OST interface, however there are some parameters which must be
valid in order for the OST to process the file successfully,
specifically the angular scale of the pixels and the brightness unit
(Jy/pixel). These are discussed in
the FITS section.
Declination
The string in this field specifies the source Declination. It must be formatted correctly, including the leading
+ or
- sign. The value entered here will replace the value in the header of any FITS file that is uploaded and will also be used for any source model selected from the Library.
The Right Ascension field is conspicuous by its absence. The OST does not require the user to specify this value, relying instead on the user to supply an
Hour Angle value (Section ??) which determines the time of the observation relative to the transit time of the source.
Image Peak / Point Flux
The user can arbitrarily scale the brightness of the source
model by entering a non-zero value in this field. The original image
Ix,y is scaled according to:
Eqn. 1
where
P is the value entered in the field and
M is the original maximum value of the image. Entering a value of zero means that no image scaling will be applied. It is therefore not possible to scale an image such that all pixels are zero. The value entered in this field also controls the brightness of the point source if the user selects that particular source model. If a simulation of a pure noise field is required then this can be accomplished by selecting the point source model and
applying a flux of zero. There is also a small drop down menu which selects the unit of the value entered: Jy, mJy or
μJy.
Observation Setup
Figure 3. The observation parameters the OST front-end.
This section contains options for choosing frequency setup,
observation duration, resolution con- siderations and a simple
mosaicking model.
Central Frequency in GHz
As the name implies, this is the central frequency of the
observation in GHz, which should be within the ranges of bands 3 - 10
of ALMA. The OST will return an error if the user attempts a
simulation outside these ranges.
Bandwidth
This field also has a small menu which selects the unit of the specified bandwidth. Note that the OST is currently only a single channel simulator. For spectral line detection simulations it is recommended that the user selects representative channels from the sky model and submits these as separate simulation jobs with appropriate channel widths entered in the bandwidth field.
For high-sensitivity pseudo-continuum applications then the user can enter a large bandwidth here which will be reflected in the calculated noise in the final map.
Note that the CASA simdata task allows the automatic processing of spectral line cubes, and thus may be a better option for larger-scale line simulation work.
If the combination of the central frequency and bandwidth causes the requested frequency range to exceed the limits of an ALMA band then the OST will automatically truncate the bandwidth (and adjust the noise accordingly). If such a liberty is taken then the user will be notified.
Required Resolution in arcseconds
If the user has selected
ALMA in the instrument option then the value entered here will be considered, together with the frequency requirements, to select an appropriate ALMA configuration.
The maximum resolution
θ (in radians) of an interferometer is
approximately determined by:
Eqn. 2
where
c is the speed of light,
ν is the observing
frequency in Hertz and
B is the longest projected baseline in
metres. This equation is used to convert the required resolution into
a baseline requirement, which is then matched to the longest baseline
within the the 28 potential array layouts. Note that in practice the
resolution of an image rarely matches that of the longest baseline, as
the visibility measurements are generally weighted according to their local density in the uv plane. Since there are always more short baselines than long ones the practical resolution is generally less than the theoretical maximum.
Pointing Strategy
There are two options in this menu:
single and
mosaic. The field-of-view of a dish-based interferometer is a function of the diameter of the receiving elements
D and the observing frequency
ν. It is related to a function called the
primary beam which effectively dictates the sensitivity of the instrument as a function of angle. The sensitivity is maximum at the pointing centre and tapers off for off-axis directions. A rough estimate of the half-power level of this function for a parabolic antenna such as the type that ALMA uses is:
Eqn. 3
i.e. HPBW (half-power beam width) is the number of radians away from the pointing centre at which the gain of the array drops to 0.5.
Since ALMA operates at high frequencies its field of view is
correspondingly smaller than centimetre-wave instruments with
equivalent dish sizes. As such, mosaicked observations are likely to
be necessary. These consists of many individual pointings which are
overlapped in such a way that when combined they can cover a large
area of sky with approximately uniform sensitivity.
- The single option in this menu will therefore simulate a single pointing, i.e. the sky brightness will be attenuated by a model of the primary beam away from the pointing centre.
- The mosaic option will simply examine the sky area which
is to be simulated and return an approximate number of pointings,
based on a traditional hexagonal mosaic pattern, that would be needed
to cover the entire field with the required sensitivity.
Start Hour Angle
This value specifies the relationship between the start of the
observation and the source transit. Acceptable values are in the range
-12 to 12 hours. For example, if the user wishes to simulate a
two-hour observation with the source transiting in the middle then the
start hour angle needs to be set to -1.
On-source Time
This field specifies the duration of the observation, the units of which can be specified in the drop down menu. The maximum time that can be entered is 24 hours.
Phase Cycle
A new option for ALMA Cycle 1, this field specifies the on source time between cuts to a hypothetical phase calibrator
to better simulate the uv-coverage of a simulation. The OST does
NOT create a phase calibration simulation to
accompany your simulation, this is simply a time parameter for sectioning up the on source time.
On Phase
A new option for ALMA Cycle 1, this field specifies the time spent on a hypothetical phase calibrator at the end of each
on source cut (as specified by the Phase Cycle time see
above). Again the OST does
NOT create a phase calibration
simulation to accompany your simulation, this field is simply a time parameter for separating the on source time cuts.
Number of visits
If the user wishes to simulate either an observation that is longer than 24 hours, or a long observation which occupies a limited range of hour angles then this field can be changed to a value other than 1.
For example, a 100-day observation can be simulated by specifying a 24-hour track in the
on-source time field, and entering 100 in the
number of visits field.
Similarly, if there are strict hour angle requirements, e.g. only an hour angle range of +/-2 is acceptable but the user wishes to simulate 20 hours of observing then
start hour angle should be set to -1,
on-source time should be set to 2 and
number of visits should be set to 10.
It is worth bearing in mind when considering this option and the previous two that for certain Declination and hour angle combinations the source may well be below the horizon. The OST recongises that the Earth is opaque, and will naturally not consider such scans when calculating the noise in the map. It will however warn the user that the observing time that was requested has been shortened, and that the on-source time that was achieved may be at odds with what was requested.
Number of Polarization
The receivers of ALMA record two orthogonal polarizations from
the incoming electromagnetic wave. By averaging both of these when
producing a map the signal to noise ratio may be improved by a factor
of sqrt(2). The OST presently only handles total intensity
simulations, so the noise consideration is the only reason for the
presence of this parameter.
Corruption - atmospheric conditions
Figure 4. Corruption Control.
Artifacts in an interferometric image derived from a genuine observation originate due to a variety of effects, including calibration errors, atmospheric effects and the thermal conditions of the receivers. Even in the case of a perfect observation, the latter is something that cannot be mitigated. The thermal noise introduced by the
system temperature is the absolute noise-floor in an interferometric map below which sources cannot be detected.
Many things contribute to the system temperature. The two major unwanted sources for ALMA are the temperature of the receivers themselves (
Trec) (which are cryogenically cooled in order to minimise their contribution), and the sky temperature (
Tsky) Even at the high and dry site at which ALMA is built the effects of the water vapour in the atmosphere can still be significant.
The RMS of the noise perturbation to the visibility, that is the single complex number which is the per-polarization, per-channel correlation product of a pair of antennas, is given in units of Janskys by:
Eqn. 4
where
kB is the Boltzmann constant,
Tsys
=
Trec +
Tsky is the system
temperature in K,
ηq = 0.9 and is an
efficiency term associated with digitization losses during
correlation,
Aeff =
ηa
×
Ageom is the effective area in m
2, equal to the aperture efficiency (assumed to be 0.9) multiplied by the geometric area of a single antenna,
Δν is the channel bandwidth in Hz and
Δt is the integration time per visibility in seconds.
The receiver temperatures are fixed per-band. is derived from a model of the atmospheric transparency at the ALMA site via:
Eqn. 5
where
Tatmos is the atmospheric temperature (assumed to be 260 K) and
γ is the transmission fraction.
The single menu option in the
Corruption section relates to
three levels of precipitable water vapour (PWV): 0.5, 1.5 and 2.5
mm. The atmospheric transmission fraction as a function of frequency for these three levels is shown in Figure 5. The corresponding atmospheric temperature profiles are shown in Figure 5.
Figure 5. Atmospheric transmission fraction at the ALMA site
asa functionof frequency for three column densities of percipitable
water vapour.
Interpolative functions are fitted to these plots so that the
transparency can be derived for arbitrary frequencies and the
corresponding sky temperature can be calculated via Equation 5 for
the selected level of PWV. To account for the variation of
Tsky within large bandwidths, the values are
calculated at ten points across the band and an average is taken. This value is then added to
Trec to form
Tsys for use in Equation 4.
Figure 6. Sky temperature at the ALMA site as a function of
frequency for three column densities of precipitable water vapour,
with an assumed atmospheric temperature of 260K.
Imaging
Figure 7. The imaging options on the OST front-end.
Imaging weights
As mentioned previously, the visibilities are gridded and weighted, prior to being Fourier transformed into a map. There are generally two extremes of weighting function. Natural weighting means the visibilities are weighted according to the number of measurements within a given region of the
uv-plane. As there is a higher density of points around the centre of the
uv-plane, which is occupied by the shortest baselines, the longest baselines which provide the highest resolution are downweighted. This weighting scheme provides the maximum sensitivity, but the resolution will be lower than that offered by the longest baselines.
Uniform weighting as the name suggests applies equal weighting to all visibilities, and offers the maximum resolution.
Briggs' (1995) weighting scheme represents an intermediate approach. Tuning of a parameter known as
robustness results in a sliding trade-off between uniform and natural weighting. The OST offers only the central value.
Preform deconvolution?
The image formed by Fourier transforming the visibilities is known as the dirty image, as it is convolved at all points with the point spread function of the array (known as the dirty beam). The shape of the dirty beam is directly coupled to the uv coverage of the observation. Deconvolution of the dirty image within the OST is performed by the CLEAN algorithm.
The CLEAN cycle is terminated when the theoretical noise limit in the map is reached.
Output Image Format
The OST can return the simulated and optionally-deconvolved
image in either FITS format or CASA image format. If the latter is
chosen then the image will be provided in a tar file.
Your e-mail address
Figure 8. One of the most important fields on the OST web form.
The final field on the web form is for the email address of the
user. An initial confirmation email will be sent to say that the
simulation job has been submitted successfully. A subsequent email
will be sent alerting the user when the job has been processed. This
email will contain a link to a webpage which will contain either the
results of the simulation or, in the event that the simulation fails
for a reason that the OST can recognise, an error message and a hint
on how to re-submit the simulation successfully.
The Results Page
Once the simulation is complete the user will receive an email
containing a link to the results page. All images on the results
page can be clicked to bring up the image in full-resolution.
Results Overview
Figure 9. The
Overview section of the results page.
The first section of the output page contains a few facts and figures about the simulation. Many of these simply repeat the parameters that were entered into the main OST front end, including the central frequency and bandwidth, the on-source time and the level of precipitable water vapour that was selected in the corruption section.
The
array configuration field will echo the instrument which was selected by the user, although in the case of simulations performed based on the full ALMA array it will also return the
out configuration which was chosen by the OST based on the resolution requirements.
Other parameters are derived from the outcome of the simulation itself. The theoretically-calculated RMS noise in an appropriately-weighted map is presented, which provides an immediate value for checking against RMS values measured from the simulated map itself.
The size (major- and minor-axis and position angle) of a two-dimensional Gaussian fitted to the central lobe of the PSF is also returned. This is essentially the resolution of the simulated observation. This Gaussian is also used as the
restoring beam during deconvolution.
If the user has uploaded a FITS file or selected a non-point-source model from the OST library then the
overview section will also contain two thumbnail images of the input model.
Histogram Equalization
When a sky image is rendered to appear on the results page it is done so with two different pixel intensity transfer functions. The image on the left will be a linear transfer function whereby the colour map is applied linearly to pixel values which range from zero to the maximum value in the image.
The image on the right will have been treated with an image processing
technique known as histogram equalization. Histogram equalization is an image processing technique which adjusts the pixel intensity histogram of an image such that it has a flat distribution. This is particularly useful for enhancing low level structure in images where the dynamic range is governed by a few very bright pixels.
Your Simulate Image
Figure 10. Thumbnail images of the final simulated image with
the FITS file download link on the left.
This section presents two thumbnails showing the final image (either the dirty image or the deconvolved image, depending on what was requested) with and without histogram equalization. In the left-hand column there is also a link to either the FITS file or the tar file containing the CASA format image.
Note that some browsers may attempt to render the FITS image, so it is
recommended that this link is right-clicked, and the file is saved to
disk manually.
Dirty Beam (point-spread function)
Figure 11. Thumbnail images of the dirty beam (point-spread function).
The pair of images in this section show the dirty beam, or array point spread function, on the same scale as the simulated image. The central peak of this image is the component to which a Gaussian is fitted in order to determine the parameters of the
restoring beam presented in the
overview section.
Coverage in the uv-plane
Figure 12. The
uv-coverage plot.
The
uv-plane coverage is determined by the layout of the antennas, hour-angle range, duration and frequency of the observation, and the declination of the source. The visibility formed by each baseline (and its complex conjugate) occupy a single point in the uv plane, representing the sampling of a single Fourier component of the sky brightness distribution. By adding more antennas, more baselines are formed and more Fourier components are measured per integration. Earth rotation changes the projection of the baselines on the sky, and further fills up the
uv-plane coverage. Projected baselines also change depending on the pointing direction, thus the source elevation affects the uv coverage.
The image presented in this section is derived by Fourier transforming the image of the dirty beam. The colour scale gives some impression as to the density of measurements at a given point in the
uv-plane.
Atmospheric Transmission
Figure 13. The atmospheric transmission again frequency for the
selected PWV levels. ALMA bands and the frequency setup of the
simulation are also shown.
The plots in this section show the atmospheric transmission fraction for the ALMA site as a function of frequency, delineated by the red line. The coloured regions on the left-hand plot correspond to bands 3 - 10 of ALMA, and these are numbered above. The right-hand plot shows a zoom-in on the specific band of the simulation. In both cases the vertical bright green line shows the frequency coverage of the simulated observation.
As mentioned in the
Corruption section, the atmospheric transmission is used to derive a sky temperature for noise calculation purposes, and the red trace in these plots varies depending on the level of PWV selected in the corruption menu.
Elevation vs Time
Figure 14. Elevation again Time.
The final plot shows the elevation of the source in degrees as a function of time for the duration of the observation. If the source drops below the elevation limit (currently 8 degrees) then the red line becomes fainter. Such scans do not contribute to the final image or noise measurement for obvious reasons.
Diagnostics
Presently this section simply contains the amount of time that the server took to process the simulation job from when it was picked up from the queue to when the
job complete email was sent. The time it takes to process a simulation job depends primarily on the length of the observation, the size of the image that is required, and whether or not deconvolution was requested.
Note that if an observation longer than 24 hours is requested it will not cause an increase in processing time as beyond this point the added noise is simply scaled accordingly (the
Δt term in Equation 4). This is valid as at this point the full range of spatial scales is sampled due to Earth rotation, and it also serves to keep the data volumes down.
FITS Requirements
FITS Header Keywords Required by the OST.
To function correctly the OST requires certain key FITS Header keyword parameters to be present these are listed below:
BUNIT: The physical units of the FITS image array values.
CDELTn*: Coordinate increment along axis n.
CROTAn: Coordinate system rotation angle.
CDn_n: Usually a matrix of four values which describe the mapping of the Coordinate system within the FITS image, i.e both increment and rotation. CDn_n matrix values and CDELTn and CROTAn are degenerate.
CTYPEn: Name of the CDELTn coordinate axis.
NAXIS: Number of axes.
NAXISn: Size of the axis n.
For more information on FITS keywords please see
this web page and
here for more on the CDn_n matrix.
Additionally the FITS keyword
BITPIX must conform to identifying float/double data type (
BITPIX=-32 or -64) not integer values (
BITPIX=8, 16 or 32). For examples please refer to
this webpage. This is a common problem when fits files have been generated from images using the GNU Image Manipulation Program (GIMP).
An experimental Python script has been created to check FITS headers and correct BITPIX values. It is available, along with more information,
here.
(* where n in an integer).
FITS Image Requirements.
File Size
Presently the maximum allowed image dimension is 2048 pixels. If a simulation job requires a larger image than this then the user is warned, but only the sky area corresponding to the central 2048 × 2048 pixel region is imaged from the simulated visibility set.
Thus the most computationally intense job that can be submitted to the server would be a 24-hour observation requiring the imaging and deconvolution of a 2048 × 2048 pixel image. Such a job would typically keep the server busy for around 15 minutes.
Rotation
Many astronomical instruments provide image files in which the 'x' and 'y' coordinate axes are not orientated with equatorial north corresponding to 'up' (and east == 'left'). For example see Figure 15.
Figure 15. Example of rotated image, Left: Image with orientated by pixel axis. Right: Image rotated such that equatorial north corresponding to 'up' (and east == 'left').
The OST does not rotate images, instead it assumes that an uploaded image does have equatorial north corresponding to 'up'. This may affect the representative nature of the output simulations for uploaded sky images which are rotated away from north== up by greater than ~30 degrees. This affect will be particularly pronounced in simulated observations at high and low declinations for sources which have extended emission in E-W directions as the synthesised beam will be elongated N-S.
As ALMA moves toward full science the orientation of an uploaded image for simulation will become less problematic as the beam will tend to be near round but this affect should be taken into account whenever you are using the OST for simulating images.
Fits images can be rotated prior to their use with the OST using e.g. PyFits, IDL, STARLINK etc.
