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Äàòà èçìåíåíèÿ: Mon Sep 17 19:47:53 2007 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 19:32:07 2012 Êîäèðîâêà: |

Basic algorithms of program.

1) Measurement. The basic task of this algorithm is
measurements of coordinates of objects with a best possible accuracy. Usually
this accuracy makes 0.1 - 0.02 pixels.

The described algorithm is suitable for measurements of complex images of
stars.

The input information is:

a) the zero-based number of stars in the complex (multicentric) image,b) set of preliminary coordinates -x, for all stars, index_{i}, y_{i}iis number of a star,c) values of brightnesses for pixels -I(xindex_{j}, y_{j}),jis number pixel.

The program uses two profile for measurements of the images of objects.

The profile of Lorenz is

_{},

and the profile of Moffat is

_{}

here

_{}

and

_{}.

WhereI(xis brightness of pixel with coordinates_{j}, y_{j})x,_{j}, y_{j}jis index of pixel belonging to the aperture;i- index of a star in the complex image;N -number of stars in the complex image, for the single images N=0;x- coordinate of the star with the zero index;_{0}, y_{0}_{}- distance between zero's and i's star,_{}- positional angle of the direction the zero –i's star;A, B, C, D, E,_{}are determined at measurements. The parameters have the following sense:Ais the size of the image;B –ovality of the image on an axis Y;C –brightness of the image at the centre;D –free term;E– ovality of the image in any direction.

These parameters are calculated by a nonlinear method of a least squares.The
main output parameters of this algorithm are *x _{i}, y_{i}*;
where the index

The modes of operations of algorithm are set in "

"

Aperture" is radius of the aperture in pixels."" is initial value

Exponent of power_{}.

"Exponent of power is variable"If it is off,_{}have constant value.

"Elliptic images" if it is off, E=0.

"Floating aperture"if this mode is on, at ending iterations the algorithm will be repeated, but already with the measured values of coordinates as initially.

"Common A, B" is the parameters A, B will be common for all stars of multicentric image.

"Centration of aperture" is at marking of the frame will be is made centration of the aperture on the nearest local maximum.

"Profile of Lorenz", "Profile of Moffat" is switch between profiles.

2) Calculation of coordinates. The input information is:

a)

xare measured coordinates of a reference stars,_{k},y_{k}k=1,2 … M,whereMisnumber of the reference stars.

b)_{}are equatorial coordinates and proper motions of the reference stars,

c)xare measured coordinates of objects_{l},y_{l}l=1,2 … S, whereSnumber of objects,

tis epoch of observations.

If it is taken into account refraction:

e)T, Pare temperature and pressure of air.

f)_{}are longitude and latitude of observatory.

At the first step the proper motions are taken into account:

_{}

Here _{}_{} are equatorial coordinates of the
star at epoch of observations; t0 is epoch of the catalogue.

If it is necessary to take into account refraction, the equatorial coordinates
are translated into horizontal:

_{}

where _{}are zenithal distance and azimuth of
the star, _{} are hour angle of the star.

Further:

_{}

here *t* is temperature in degrees C^{o}, *P* is pressure
in millimeters of a mercury pole.

And back from horizontal to equatorial:

_{}

If refraction it is not taken into account, it is simple _{}, _{}.

A tangential coordinates are calculated for the reference stars:

_{}

where _{} are coordinate of the centre of the
frame.<br>

Systems of the equations is solved by the method of a least squares:

_{}

here *d* is order of the astrometric solution.

The program prints at a moment of calculation of coordinates the following
values:

*M _{x}, M_{y}*are scales X and

_{}

Finally, we obtain equatorial coordinates (_{}) of objects:

_{}

If it is taken into account refraction; the transition to horizontal coordinates is made; the amendment for refraction added to zenithal distance; and the transition back to equatorial coordinates is made Let's note, this the formula:

_{}

In this case, there is the equation.

The modes of this algorithm are set in "**Properties\Calculation of
coordinates**".