Coordinates

Coordinate systems in astronomy can be complicated, AstroPhot is no different. Here we explain how coordinate systems are handled to help you avoid possible pitfalls.

For the most part, AstroPhot follows the FITS standard for coordinates, though limited to the types of images that AstroPhot can model.

Three Coordinate Systems

There are three coordinate systems to think about.

1. world coordinates are the classic (RA, DEC) that many astronomical sources are represented in. These should always be used in degree units as far as AstroPhot is concerned.

2. plane coordinates are the tangent plane on which AstroPhot performs its calculations. Working on a plane makes everything linear and does not introduce a noticeable projection effect for small enough images. In the tangent plane everything should be represented in arcsecond units.

3. pixel coordinates are specific to each image, they start at (0,0) in the center of the [0,0] indexed pixel. These are effectively unitless, a step of 1 in pixel coordinates is the same as changing an index by 1. AstroPhot adopts an indexing scheme standard to FITS files meaning the pixel coordinate (5,9) corresponds to the pixel indexed at [5,9]. Normally for numpy arrays and PyTorch tensors, the indexing would be flipped as [9,5] so AstroPhot applies a transpose on any image it receives in an Image object. Also, in the pixel coordinate system the values are represented by floating point numbers, so (1.3,2.8) is a valid pixel coordinate that is just partway between pixel centers.

Transformations exist in AstroPhot for converting world to/from plane and for converting plane to/from pixel. The best way to interface with these is to use the image.world_to_plane for any AstroPhot image object (you may similarly swap world, plane, and pixel).

One gotcha to keep in mind with regards to world_to_plane and plane_to_world is that AstroPhot needs to know the reference (RA, DEC) where the tangent plane meets with the celestial sphere. AstroPhot now adopts the FITS standard for this using image.crval to store the reference world coordinates. Note that if you are doing simultaneous multi-image analysis you should ensure that the crval is same for all images!

Projection Systems

AstroPhot currently only supports the Gnomonic projection system. This means that the tangent plane is defined as “contacting” the celestial sphere at a single point, the reference (crval) coordinates. The tangent plane coordinates correspond to the world coordinates as viewed from the center of the celestial sphere. This is the most common projection system used in astronomy and commonly used in the FITS standard. It is also the one that Astropy usually uses for its WCS objects.

Coordinate reference points

There are three coordinate systems in AstroPhot: world, plane, and pixel. AstroPhot tracks a reference point in each coordinate system used to connect each system. Below is a summary of the reference coordinates and their meaning:

1. crval world coordinates on the celestial sphere (RA, DEC in degrees) where the tangent plane makes contact. crval always contacts the tangent plane at (0,0) in the tangent plane coordinates. This should be the same for every image in a multi-image analysis.

2. crtan tangent plane coordinates (arcsec) where the pixel grid makes contact with the tangent plane. This is the pivot point about which the pixelscale matrix operates, therefore if the pixelscale matrix defines a rotation then this is the coordinate about which the rotation will be performed. This may be different for each image in a multi-image analysis.

3. crpix pixel coordinates where the pixel grid makes contact with the tangent plane. One may think of the referenced pixel location as being “pinned” to the tangent plane. This may be different for each image in a multi-image analysis.

Thinking of the celestial sphere, tangent plane, and pixel grid as three interconnected coordinate systems is crucial for understanding how AstroPhot operates in a multi-image context. While the transformations may get complicated, try to remember these contact points:

• crval is in the world coordinates and contacts the tangent plane at (0,0) in the tangent plane coordinates.

• crtan is in the tangent plane coordinates and contacts the pixel grid at crpix in the pixel coordinates.

What parts go where?

Since AstroPhot works in multiple reference frames it can be easy to get lost. Keep these basics in mind. The world coordinates are where catalogues exist, so this is the coordinate system you should use when interfacing with external resources. The tangent plane coordinates are where the models exist. So when creating a model and considering factors like the position angle, you should think in the tangent plane coordinates. The pixel coordinates are where the data exists. So when you create a TargetImage object it is in pixel coordinates, but so too is a ModelImage object since it is intended to be compared against a TargetImage. This means that any distortions in the TargetImage (i.e. SIP distortions) will show up in the ModelImage, but aren’t actually part of the model. This can manifest for example as a round Gaussian model looking elliptical in its ModelImage because there is a skew in the CD matrix in the TargetImage it is matching. In general this is a good thing because we care about how our models look on the sky (tangent plane), not strictly how they look in the pixel grid.