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ASTAP, the Astrometric STAcking Program, plate solver and FITS viewer




Brief description how the ASTAP plate solving works:


ASTAP  astronomical plate solving method
Image Star database
1 Find background, noise and star level Extract the α, δ position for stars of area of interest
2 Find stars and their CCD x, y position (standard coordinates) Convert the RA, DEC equatorial coordinates into standard coordinates (CCD pixel x,y coordinates for optical projection), rigid method
3 Find the stars to construct the smallest triangular pyramids. Record pyramid edges length and mean position (x,y) of  pyramids. Find the stars to construct the smallest triangular pyramids. Record pyramid edges length and mean position (x,y) of  pyramids.
4 Sort the six pyramid edges on length for each pyramid. e1 is the longest. and e6 shortest. Sort the six edges on length for each pyramid. e1 is the longest. and e6 shortest.
5 Scale the pyramid edges as (e1, e2/e1,e3/e1,e4/e1,e5/e1,e6/e1) Scale the pyramid edges as (e1, e2/e1,e3/e1,e4/e1,e5/e1,e6/e1)
6 Find pyramids matches where edges e2 to e6 match within a small tolerance.
8 For matching pyramids, calculate the ratio e1/e1 and find mean, σ (standard deviation) of e1. Remove outlier pyramids above 3* σ.
9 From matching pyramids, prepare the equations:
 
   x1,y1,1,xref1 or yref1
   x2,y2,1,xref2 or yref2
   x3,y3,1,xref3 or yref3
   x4,y4,1,xref4 or yref4
   ......                
10 Find solution vector in direction x and y using above equations using a least square fitting routine.

The two resulting solution vectors s:

x:=s[0]x+s[1]y+s[2]
y:=s[0]x+s[1]y+s[2]

Solution of an overdetermined system of linear equations according to the method of least squares using GIVENS rotations.
11 Convert the x,y position of the image center (standard coordinates) using the solution vector to equatorial α, δ position. This is the 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.

The following image shows the triangular pyramids used in an astronomical image:


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2018-5-5