I would like to simulate a telescope camera view, projecting (RA, Dec) coordinate sets to a 2D plane. So effectively the need is to convert Equatorial coordinates to (x, y) coordinates, when we can know how many degrees a single pixel spans. For convenience I'm using degrees for RA and Dec here, and the code is just pseudocode.
The following base information is provided as an example: Imaging equipment:
- Telescope focal length in mm (flen): 420
- Image resolution (widthPx, heightPx): 4000 * 3000
- Pixel size in microns (pxSize): 8
- Binning (bin): 1
So from my understanding we can calculate a few things from this for starters. The field of view in degrees should be:
fovW = radToDeg( 2 * atan((pxSize * bin * widthPx / 1000) / (2 * flen)) ) fovH = radToDeg( 2 * atan((pxSize * bin * heightPx / 1000) / (2 * flen)) )
And from this we could derive:
pixelsPerDegWidth = widthPx / fovW; pixelsPerDegHeight = heightPx / fovH;
For locations closer to the equator I can get some valid looking results using this formula:
deltaRa = starRa - imageCenterRa deltaRa = deltaRa > 180 ? 360 + deltaRa : deltaRa deltaDec = -1 * (starDec - imageCenterDec) posX = deltaRa * cosdeg(starDec) * pixelsPerDegWidth + 0.5 * widthPx posY = deltaDec * pixelsPerDegHeight + 0.5 * heightPx
With some catalog star positions projected using this formula, I can even get Astrometry.net solver to correctly identify the center position. However when we move to the poles this comes crashing down.
So let's go ahead and use a target center point near the pole:
- RA 30 degrees (imageCenterRa)
- Dec 89 degrees (imageCenterDec)
Let's also say that we have a hypothetical star at RA, Dec (220, 89.2) - this is close to the pole, and both the star and the pole gets included in the image. What kind of formula should we use to get the correct location and to draw the area correctly even in the polar regions?
I've been looking for an example for a while but haven't come up with any. I've seen some formulas that may be just the thing I'm looking for but my thick skull loves examples - hence why I included some exact numbers here, as I would love to see how this would be calculated in practice.
So to summarize: how would we calculate the (X, Y) coordinate in the image for the star at RA, Dec (220, 89.2)?