Tutorial:


AstroImageJ, Align and DrizzleIntroductionThis is an attempt from me to create a macro to AstroImageJ to align and stack sub images with a Drizzle function. Expect me to change and correct a lot here in the beginning. But follow it if you find it interesting to see how I develop the function and see if I reach the goal, a working Drizzle function! Drizzle:Drizzle is a way to increase the resolution of under sampled images, i.e. when you have big size pixels on a high resolution telescope. More information about Drizzle: Matrix:First we, especially me have to dig deeper in the mathematical word about matrices and transformation. Uses of matrices in the calculations can make it a lot easier to do it. Here you find deeper information:
Unit matrix, does nothing to the image.
Translation matrix, shifts the image in x and y axis.
Scale the x (W=width) and y (H=height) axis, many times W could set equal to H, symmetry.
Rotation matrix, rotate the image by angle v. Altogether this matrixes will correspond to: T_{1} T_{2} T_{3} T_{4} = T_{tot}
Translation, Scale and rotation matrices (functions) put together in one matrix. How to use T: X' = T X, T transform the coordinates of X to X'. X consist of one pixel coordinate, x_{ij} and y_{ij}, i=row and j=column. X' is the new coordinates. First we must find out what T is. To that we use our reference star as we get when we align our sub images. To X we put in our reference stars coordinates from our sub images. X' is the reference stars coordinates reference image (one of the sub images normally). One T matrix for each of your sub images will transform them to the reference image coordinates. The T_{tot} will do a affine transformation, all the three transformations above, to that we need three reference stars. It will not correct optical distortion.
Each column are the coordinates of the center of a reference star, x_{1}, y_{1} and x'_{1}, y'_{1} and so on should align on each other after the transformation (align) process. Inverse matrix:Now one problem, we need to know how to calculate the matrix T, its internal figures. X' = T X. With help of the invers matrix X^{1} we can get T alone on the right side, in matrix manipulation we normally can't change order of the matrices. It looks a bit strange if you are not used with it. X^{1} is of the construction that X^{1} X give the unit matrix I (I=1), se above. X' X^{1} = T X X^{1} = T I = T T = X' X^{1} Now we get one more problem, to calculate X^{1}. Later when we have find T values for each sub image we can put in each sub images coordinates one pixel by one to the transformation T matrix and get the new coordinates in the reference image. 
Ad / Annons:
Determinant:Determinant is another mathematical tool we need to find out the X^{1} that we need to calculate T. More information about Determinant: Coming more later. AstroImageJ doesn't have any matrix functions so I have to build loops to take care of that. Matlab which I have worked with earlier has most matrix function that is needed and everything get much easier. It will not be an easy task so this is a long time project. But if I succeed in this I can develop my own macros and do it exactly the way I want so it will be worth to spend that time on it, even better if I later can develop the functions in Java, but Java is new for me. 