Issue translating World Coordinate system to cartesian coordinate

Question

I have two fits images from the WFC3 that I am trying to combine with a C# program. When I try to combine multiple images I don't think the values I am getting for my x/y coordinates (calculated from Right Ascension/Declination) are correct. I am expecting a final image that is about the same width as the two images combined, but it turns out to be about the same width and about twice the height. I know the final image should be about double the width of a single image because I manually combined the images in photoshop and the final image was about twice as wide as either of the two original images.

NOTE: when I say "image" they are fits images, so they are just a bunch of single values in a file, so to combine them I create a new file and initialize the correct number of single values (width * height) to zero, and then fill in the values from the images I am using to combine. They are not jpg or tif or png.

I am using the following formula to change from world coordinate system to cartesian: formula is (since distance is the same for everything): x = cos(dec) * cos(ra) y = cos(dec) * sin(ra)

I get the right ascension and declination from the header in the fits file.

For the final image dimensions, I calculate the distance between x1 and x2 and create a new image that is 1/2 image 1 width + distance + 1/2 image 2 width. For the final height I do a similar calculation with y and image heights.

The images do also have a rotational component, but I am ignoring that as both images share the same rotation. This could be part of my problem.

public const double PixelsPerArcSecond = .039; // per WFC3 spec from Nasa

public static ImageDataModel Combine(List<ImageDataModel> inputImages)
{
    //  Right ascension is CRVAL1
    //  Declination is CRVAL2

    //  formula is (since distance is the same for everything):
    //     x = cos(dec) * cos(ra)
    //     y = cos(dec) * sin(ra)

    ImageDataModel returnImage = new ImageDataModel();
    ImageDataModel bm = inputImages[0];

    double x1, y1, x2, y2;

    x1 = Math.Cos(bm.CRVAL2) * Math.Cos(bm.CRVAL1);
    y1 = Math.Cos(bm.CRVAL2) * Math.Sin(bm.CRVAL1);

    int mult = 4; // todo: set this based off of the bitpix of the incoming images.

    for (int i = 1; i < inputImages.Count; i++)
    {
        ImageDataModel cm = inputImages[i];

        x2 = Math.Cos(cm.CRVAL2) * Math.Cos(cm.CRVAL1);
        y2 = Math.Cos(cm.CRVAL2) * Math.Sin(cm.CRVAL1);

        double dx = x1 - x2;
        double dy = y1 - y2;

        int distX = (int)((dx * 3600) / PixelsPerArcSecond);
        int distY = (int)((dy * 3600) / PixelsPerArcSecond);

        // This is what I expect to be wider than tall, but the converse is true.
        int w = Math.Abs(distX) + (bm.ImageWidth / 2) + (cm.ImageWidth / 2);
        int h = Math.Abs(distY) + (bm.ImageHeight / 2) + (cm.ImageHeight / 2);
        // This is where the two images are combined into the final image.
        ImageDataModel imd = CombineTwoImages(bm, cm, i, w, h, mult);
        bm = imd;
    }

    return returnImage;
}

I am expecting an image that turns out like this:
http://wierdling.net/stack-overflow-images/ManuallyCombined.png

But getting this:
http://wierdling.net/stack-overflow-images/CombinedTest.png

The stats for the first image are: Width = 4139, Height = 4535, RA = 350.1584456860353 (CRVAL1), DEC = 61.16155335032816 (CRVAL2), ORIENTAT = -125

The stats for the second image are:Width = 4139, Height = 4535, RA = 350.1159150008405 (CRVAL1), DEC = 61.19543100394401 (CRVAL2), ORIENTAT = -125

The final expected width is close to 7733 with a height near 4773.

The final actual width is 4284, and the height is 7662.

Does anyone have any insight into what I am doing wrong?

The full source code for the program can be downloaded from https://bitbucket.org/wierdling/fitscombiner/src/master/

It currently only works with WFC3 data, and the program is very much a work in progress.

Answer 1

I think that your image program already does the rotation and you should do it too.

If I rotate the coordinates you calculated by 125 degrees and then calculate how far away the coordinate x1 is from the left side and the same for x2 and the y coordiantes I get a width of 6725 and height of 6166.

Not perfect but I think it goes in the right direction.

Hope that helped.

    public static ImageDataModel Combine(List<ImageDataModel> inputImages)
    {
        //  Right ascension is CRVAL1
        //  Declination is CRVAL2

        //  formula is (since distance is the same for everything):
        //     x = cos(dec) * cos(ra)
        //     y = cos(dec) * sin(ra)

        ImageDataModel returnImage = new ImageDataModel();
        ImageDataModel bm = inputImages[0];

        double x1, y1, x2, y2;

        x1 = Math.Cos(bm.CRVAL2) * Math.Cos(bm.CRVAL1);
        y1 = Math.Cos(bm.CRVAL2) * Math.Sin(bm.CRVAL1);
        var values = Rotate(0 - bm.Orientation, x1, y1);
        x1 = values.x;
        y1 = values.y;
        int mult = 4; // todo: set this based off of the bitpix of the incoming images.

        for (int i = 1; i < inputImages.Count; i++)
        {
            ImageDataModel cm = inputImages[i];

            x2 = Math.Cos(cm.CRVAL2) * Math.Cos(cm.CRVAL1);
            y2 = Math.Cos(cm.CRVAL2) * Math.Sin(cm.CRVAL1);
            var values2 = Rotate(0 - bm.Orientation, x2, y2);

            x2 = values2.x;
            y2 = values2.y;

            double dx = x1 - x2;
            double dy = y1 - y2;

            int distX = (int)((dx * 3600) / PixelsPerArcSecond);
            int distY = (int)((dy * 3600) / PixelsPerArcSecond);

            double width = (1.0 + x1) * (bm.ImageWidth / 2) + (1.0 - x2) * (cm.ImageWidth / 2) + Math.Abs(distX);
            double height = (1.0 + y1) * (bm.ImageHeight / 2) + (1.0 - y2) * (cm.ImageHeight / 2) + Math.Abs(distY);
            // This is what I expect to be wider than tall, but the converse is true.
            int w = Math.Abs(distX) + (bm.ImageWidth / 2) + (cm.ImageWidth / 2);
            int h = Math.Abs(distY) + (bm.ImageHeight / 2) + (cm.ImageHeight / 2);
            // This is where the two images are combined into the final image.
            ImageDataModel imd = CombineTwoImages(bm, cm, i, w, h, mult);
            bm = imd;
        }

        return returnImage;
    }

    private static (double x, double y) Rotate(int angle, double x, double y)
    {
        double rad = Math.PI * angle / 180.0;

        return (x * Math.Cos(rad) - y * Math.Sin(rad), x * Math.Sin(rad) + y * Math.Cos(rad));
    }