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Artificial Frames

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:

The frames are generated:

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.

By Mr.Fries theory (very nice description has Electronic Imaging in Astronomy by Ian S. McLean), the seeing radius is modelled as

r'0 = r0 X0.6.

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:

GAUSS_PSF.jpeg
Gauss
MOFFAT_PSF.jpeg
Moffat
SEEING_PSF.jpeg
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:

All stars, on the image, are modelled with the same profile.

Modelling of Background

Background B(x,y) is modelled as a plane

b(x,y) = B0 + ΔBx (x - x0) + ΔBy (y - y0)

B(x,y) = N( b(x,y), Δb)

where B0 is a mean level (--back-level) at centre of the picture x0, y0, N(b, Δb) is a function which makes a noise with Normal distribution. The parameters are mean level b and standard deviation Δb (--back-noise). If Δb is not set, it is defined as Δb = √ B0. The optional gradient in background in counts per pixels is given by terms ΔBx, ΔBy (--back-grad-x, --back-grad-y). It can do modelling of a light pollution (by Moon). The common values for gradients are inside interval -1 … 1.

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.

lcapprox.svg
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.

Parameters

--psf [SEEING|MOFFAT|GAUSS]
Selects PSF function: SEEING (the best, slow, default), MOFFAT (commonly used), GAUSS (basic model, fast)
--spread [AUTO|FFT|RANDOM]
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.
--width width, --height height
Dimensions of output frame in pixels.

Examples

Common usage

  $ munipack artificial
  $ xmunipack artificial.fits

Overview comes with more useful examples.

Light curve table

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

  $ munipack fits --restore fourier.lst

See Also

Overview of Artificial sky, Artificial Sky … (seminary talk), Common options.