a) the zero-based number of stars in the complex (multicentric) image,

b) set of preliminary coordinates - x_i, y_i, for all stars, index i is number of a star,

c) values of brightnesses for pixels - I(x_j, y_j), index j is number pixel.

Where I(x_j, y_j) is brightness of pixel with coordinates x_j, y_j,

j is 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;

x₀, y₀ - coordinate of the star with the zero index;

 - 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:

A is 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 i is number of a star in the multicentric image.
The modes of operations of algorithm are set in  "Properties\Measurement":

"Aperture" is radius of the aperture in pixels."
Exponent of power" is initial value.
"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) x_k ,y_k are measured coordinates of a reference stars, k=1,2 … M, where M  isnumber of the reference stars.
b)  are equatorial coordinates and proper motions of the reference stars,
c) x_l ,y_l are measured coordinates of objects l=1,2 … S, where S number of objects,
t is epoch of observations.
If it is taken into account refraction:
e) T, P are 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_yare scales X and Y.  is angle of oblique frame. is orientation. These values are calculated by the formulas:

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".

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