This tool is designed to create the artificial, nevertheless photometric
realistic, frames. They are intended for modelling of various observation
effects as well as for testing purposes.
Synopsis
munipack artificial [.. parameters ..]
Description
Artificial frames are created by artificial photons having origin
in physical principles and mathematical formulas rather than in nature.
This approach can be very useful for understanding
of true nature of many effects which can be else encountered
only after long period of an observational experience.
There is list of currently implemented features:
Quantum efficiency of detector, telescope parameters.
Point spread functions (PSF): Gaussian, Moffat and seeing.
Background noise
Light curves: plain wave, Algol-like, δ Cep and user defined
Field stars: by a catalogue or generated randomly.
The frames are generated:
on base of catalogue stars which simulates nearly real field or
on base of randomly generated positions and magnitudes of stars.
Modelling of Telescope Properties
The properties of star images can be easy simulated for
various quantum efficiency η of a detection apparatus (including
detector itself), an exposure duration and a telescope diameter.
Both angular resolution and collecting area of a telescoped
are proportional to diameter.
The parameter --airy can set it directly, but
better way is set diameter (via --diameter in meters)
which sets both diffraction limit and input area.
Modelling of Extinction
An observed light intensity I(X) passing the clear (no clouds) Earth's
atmosphere is attenuated proportionally of air-mass X according
to the formula
I(X) = I0 e-k(X-1)
where I0 is an extra-atmospheric intensity.
The extinction coefficient k depends on a spectral band.
Modelling of seeing
Turbulent motion in atmosphere creates large cells
which slightly reflect light rays. The nature of turbulent
motion is totally chaotic. There is a formula describing
effect of chaotic moving of picture of a star due atmosphere
during long exposures. It modelled star profile as function
of air mass.
r'0 is an actual radius of stars at air-mass X,
while r0 is the one at zenith.
Modelling of Star Profiles
These profiles known as point spread functions (PSF) are available:
Seeing spread function which convoluted diffraction pattern of
telescope aperture and Gaussian spread by seeing. It is the best
method for simulation of any star natural profile.
Moffat profile
which is commonly used for rough description of observed profiles.
Gaussian profiles exp(-r2/r20)
which is the basic estimator. It is ideal for
theoretical work, the practical use is limited on extra-atmospheric
applications, such as spacecraft or Moon base observatories, without
image perturbations by the seeing.
Gauss
Moffat
seeing
The plain diffraction pattern, representing response of an input aperture
of a telescope without atmosphere seeing, can be generated as seeing spread
with zero seeing parameter. It is difficult to expose it, even in laboratory,
due to limited dynamical range of detectors.
The distribution of seeing is supposed as Gaussian and convoluted
with actual diffraction profile. There are two methods convolution
implemented:
Direct convolution -- diffraction profile is randomly shifted
in both directions and the result is accumulated. This slow method
gives slightly asymmetrical frames and is intended for
simulating of short exposures.
Fourier convolution -- this method generates both diffraction profile
and Gaussian with the Fried's width. The profiles are convoluted
with help of convolution theorem and
FFT. This method is fast and results are perfectly smooth.
All stars, on the image, are modelled with the same profile.
Star fields
Field stars are generated by a random number generator
in case if no -c option is presented. Catalogue
star coordinates and magnitudes are used otherwise.
Coordinates of the stars has
uniform distribution in ranges given by frame size.
The standard Fortran random number generator, with no initial seed, is used.
I derived the rough approximation
of the observed (surface) distribution of stars by brightens
from DR1
by Gaia mission:
Σ(m) = 10-4 · e1.1m [□°]
The quantity describes probability to found counts of stars
of given magnitude per square degree.
The distribution approximation must be considered as an effective description.
Stars are distributed over our sky very non homogeneously. Standard galaxy
textbooks (like Binney's & Merrifield's
Galactic Astronomy)
gives more extensive description with references.
Models of light curves
The artificial tool has three models of light curves included. The model
of the pulsating star δ Cep (data computed by Mérand et al.)
and the eclipsing binary star Algol (observed by Kim, Ho-Il). Both the curves has been approximated by
Fourier series. The last model is a simple cosine wave.
The approximation of light curves of δ Cep and Algol.
There is also possibility to define own
Fourier series
approximation of light curves which is suitable for wave-like patterns.
Do create a FITS table with format similar to fourier.lst.
The table contains real Fourier coefficients an, bn.
If the coefficients are estimated from measured data with noise,
any appearance of high-order terms indicates inappropriateness of Fourier approximation.
I can't recommend use on curves with sharp edges as Algol-like objects has.
Note. The Fourier approximation gives very good approximation
of Cepheids but is not very suitable for Algoids. The spline approximation
can be recommended in that case.
Universal flux-time pattern is implemented as a time series table.
It can represent a periodic object like Algol star or exoplanet transition,
but it can also model an non periodic behaviour like a supernova explosion
or an optical afterglow. The usage is described in
Light Curves section of Overview.
Watermark
Every generated frame is marked by a symbol which indicates
its artificial origin to prevent potential confusion.
The mark can not be hide.
The method used to spread diffraction pattern (useful with --psf SEEING only):
FFT (fast, smooth), RANDOM (slow, natural look) or AUTO (the RANDOM
is selected for exposures shorter than 3 seconds)
--hwhm hwhm
Half with of half of maximum of spread Gaussian in pixels. It represents
half of seeing parameter. The parameter is common for all PSF.
--airy airy
Radius of Airy spot in pixels. It is useful for seeing PSF.
This parameter can be also set by --diameter.
--beta β
Value of β exponent of Moffat profile (β > 0, β ≠ 1).
--maglim mag
Sets the most faint stars on frame for random generated field stars.
This option is active only when star catalogue (by -c,--cat)
is not used.
--lc-model [Cepheid|Algol|wave]
The light curve model: `Cepheid' means light curve of δ Cep, `Algol' means β Per,
`wave' means cosine function.
This parameter is mutually exclusive with --lc-table, --lc-fourier.
--lc-table file
The light curve model is determined by an smoothing spline
interpolation in a table. The table is represented
by the passed FITS file (see
Time Series Table for format description).
This parameter is mutually exclusive with --lc-model, --lc-fourier.
--lc-fourier file
The light curve model is given by the coefficients
of Fourier series listed in the FITS file.
This parameter is mutually exclusive with --lc-model, --lc-table.
--lc-mag mag, --lc-amp amp
The mean magnitude of the variable source.
The relative amplitude of light curve. For example, 0.1 (10%) means
cca 0.1 magnitude. The amplitude is ignored with conjunction of
--lc-table.
--lc-jd0 jd0, --lc-per period
Time elements of the light curve: jd0 is a reference time in
Julian date (exact meaning depends on the kind of the curve), period in
days. Don't use modified JD.
--lc-ra α, --lc-dec δ
A Right Ascension and Declination of the variable source. If the coordinates
are undefined, the centre of projection (as --rcen, --dcen)
is used.
--back-level B
Sets level of background as a positive number.
--back-noise b
Sets noise of background. If not given (or negative value passed), the
square root of the background level is used.
--back-grad-x bx, --back-grad-y by
Background gradient in counts per pixel. It can simulate a light
pollution (by Moon).
--area area
The detection area of a simulated telescope in square meters.
It is 1m² by default (see --diameter option).
This is equivalent area for 56 cm (22 inch) diameter telescope.
--diameter diameter
Sets diameter (twice of radius) of a telescope in meters. If set,
the area (--area) and Airy radius (--airy)
is (re-)defined.
--exptime time
The exposure time of generated frames in seconds.
--qeff η
The quantum efficiency of a whole apparatus (0 ≤ η ≤ 1).
--atmosphere
Switch-on modelling of the atmosphere. The model includes
both extinction and seeing.
--extk k
Monochromatic extinction coefficient. Setting on zero effectively
suppress of the extinction determination.
--long λ, --lat φ
Geographic coordinates of a station in degrees (-east, +north).
Brno has coordinates --long -16.6, --lat +49.2.
--date YYYY-MM-DD, --time HH:MM:SS
Date as YYYY-MM-DD and time as HH:MM:SS of (initial) frame.
--count #
Total count of generated frames.
--timestep time
Time delay between simulated exposures in seconds.
-f, --filter filter
Simulated filter.
-c, --cat file
Input catalogue with star positions and magnitudes.
--fov fov
Field of view in degrees.
--rcen α, --dcen δ
Centre of the field of view in Right Ascension and Declination
in degrees.
--scale s
Scale of the frame in degrees per pixel.
--angle φ
Angle of rotation of the frame around the centre in degrees.
Clockwise direction is positive.
The table has similar format as the time-series table.
It contains magnitudes (optionally, with errors)
with columns: TIME,MAG,MAGERR.
Records in the table must be sorted in time-increasing
order. Overview does demonstrate usage.
Table of Fourier coefficients
This table contains two valid columns with
Fourier series
approximation of a light curve. The columns are: first is the real
and second the imaginary part of Fourier complex coefficient.
The text file fourier.lst demonstrates
an instance of data (NAXIS2 must be updated when modified). A FITS file,
required by --lc-fourier, will be created as