|ASTAP astrometric solving method (plate solving)|
|1||Find background, noise and star level|
|2||Find stars and their CCD x, y position (standard coordinates)||Extract a similar amount
of stars for the area of interest from the star database that matches
the star density of the image.
Convert the α, δ equatorial positions into standard coordinates (CCD pixel x,y coordinates for optical projection) using the rigid method.
|3||Use the extracted stars to construct the smallest irregular tetrahedrons figures of four stars called quads. Calculate the six distances between the four stars in pixels and the mean x, y position of the four stars.||Use the extracted stars to construct the smallest irregular tetrahedrons figures of four stars called quads. Calculate the six distances between the four stars in pixels and the mean x, y position of the four stars.|
|4||Sort the six distances on size for each quad. d1 is the longest and d6 the shortest.||Sort the six distances on size for each quad. d1 is the longest and d6 the shortest.|
|5||Scale the six quad star distances as (d1, d2/d1,d3/d1,d4/d1,d5/d1,d6/d1). These are the image hash codes||Scale the six quad star distances as (d1, d2/d1,d3/d1,d4/d1,d5/d1,d6/d1)) These are the database hash codes|
|6||Find quad hash code matches where the five ratios d2/d1 to d6/d1 match within a small tolerance.|
|7||For the matching quad hash codes, calculate the longest side ratios d1database/d1image in ["/pixels]. Calculate the median ratio. Compare the quads ratios with the median value and remove quads outside a small tolerance.|
|8||From the remaining
matching quad hash codes, prepare the "A"
matrix/array containing the x,y center positions of the test image
quads in standard coordinates and the arrays Xref,
Yref containing the x, y center positions of the
reference image quads in standard coordinates.
A: Sx: Xref:
[x1 y1 1] [a] [X1]
[x2 y2 1] * [b] = [X2]
[x3 y3 1] [c] [X3]
[x4 y4 1] [X4]
[.. .. .] [..]
[xn yn 1] [Xn]
A: Sy: Yref:
[x1 y1 1] [d] [Y1]
[x2 y2 1] * [e] = [Y2]
[x3 y3 1] [f] [Y3]
[x4 y4 1] [Y4]
[.. .. .] [..]
[xn yn 1] [Yn]
Find the solution matrices Sx and Sy of this overdetermined system of linear equations.
The solutions Sx and Sy describe the six parameter plate solution Xref:=a*x + b*y + c and Yref:=d*x + e*y +f.
the solution and the equatorial center position of the reference image
the test image center equatorial position, α and δ can be
Make from the test image center small one pixel steps in x, y and use the differences in α, δ to calculate the image scale and orientation.
This is the final solution. The solution vector (for position, scale, rotation) can be stored as the FITS keywords crval1, crval2, cd1_1,cd1_2,cd_2_1, cd2_2.
© Han Kleijn, www.hnsky.org, 2018, 2022.
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