# Coordinates spaces and detector geometry

This revision applies to the software in observing-system s9; it does not apply to system s8.

## Complexity warning

To support all the various cameras and observing modes needed at ING, the system uses a very generalized system of coordinates to describe detector geometry.  The power of this system makes it complex to work with.

However, tools are on hand to make this easier. At this point, you should investigate the observing-system programme udas_geometry: that programme may tell you all you ever need to know about coordinates in UltraDAS.  Alternatively, see the pictorial examples below: these may explain sufficiently. If you really want to know the details, read on.

## Tedious details

Three coordinate systems are important when observing UltraDAS:
• Image coordinates ("i-space") describe what you get in the output (FITS) files. The first pixel in a FITS image is defined to be (1,1) in i-space, and the x-axis is the fastest-varying coordinate in the raster, as is standard for FITS.
• Readout coordinates ("r-space") describe the raster that is read out from one output of the detector, including both physical pixels and bias regions where appropriate. The pixel that comes out first in a readout from an output is defined to be (1,1) in r-space, and the x-coordinate of r-space increases along the serial register of the detector output.
• Detector coordinates ("d-space") describe how regions of the detector are related in physical space. D-space is contiguous across all physical regions of the detector and across all bias regions; i.e. all pixels, either physical or bias, have integer coordinates in d-space. The origin of d-space can be anywhere on or near the detector surface; usually, it is chosen to match the origin of r-space for one part of the detector.
D-space is important to you as an observer because all readout windows are set using d-space coordinates. The relationship between d-space, r-space and i-space is important because it relates known cosmetic features of the detector to pixel positions in the output image.

For simple, single-output cameras, i-space, r-space and d-space are usually the same thing. In some cameras, i-space is different to r-space because the data are re-oriented before filing. In multi-output cameras, there are multiple r-spaces and things can get quite complex.

Areas of these coordinate spaces are often expressed in IRAF's image-section notation: [x1:x2,y1:y2]  means the sub-raster running from pixel  x1 to x2 inclusive, and from pixel y1to y2 inclusive.

These are points to bear in mind:

• In an output image the first row and column of the raster are defined to be number 1 in i-space, not number 0. Similarly, in a readout, the first row and column are number 1 in r-space.
• There is one r-space for each channel of the image.  They all have different relationships to d-space.
• There is one i-space for each channel of the image; again they are all differently related to d-space.
• The i-spaces for some channels may never get used. Instead, the system may combine the pixels from those channels to make larger images in the ispace of one of the contributing channels.
• The i-space for a channel changes if you apply windows and/or binning.
This is a precis. For full details, see the document  INS-DAS-19 coordinate systems for UltraDAS .

## Graphic examples

The following pictures show how r-space, d-space and i-space are related for representative cameras.

In each picture, the light-sensitive areas are drawn in white and the bias regions, if any, in light grey. The legend on each section of the deetctor is in three parts:

1. Output-channel number / chip name / amplifier name.
2. Extent of the light-sensitve area, in d-space.
3. Extent in d-space of the area read out, including bias regions.
The axes are those of d-space.

The pictures, incidentally, are the output of the udas_geometry programme, which is working directly from UltraDAS' configuration database.  That is, the pictures are exactly how the DAS thinks the detector works, and do not involve a manual transcription of the geometry.

#### Tektronix CCDs

• All the tektronix CCDs have the same geometry.
• They have one output.
• D-space, r-space and i-space are identical.

#### EEV4280 CCD

• All the operational CCDs of this type have the same geometry.
• Some of the engineering devices may be set up differently.
• They use one amplifier (the left-hand one when the detector is viewed in d-space).
• D-space, r-space and i-sapce are identical.

#### INT Wide-Field Camera

• There is one output per CCD chip.
• For each chip, r-space and i-space are identical,
• The gaps between the chips are narrower than the bias strips, and the readout sections overlap in d-space.
• The picture shows the names of the actual CCD devices used (references to the silicon wafer on which they were made), but it is normal in observing to refer to them as chip 1, chip 2 etc. The chip numbers are the same as the channel numbers shown in the picture.
• Chip 2 has its r-space rotated 90 degrees relative to d-space, so its i-space is rotated through the same angle.
• The D-space orgin is at the bottom-left corner of the lit section of chip 4, not the corner of the bias strip.

#### INGRID

• There are four outputs.
• Because INGRID is an IR detector, there are no bias regions.
• The four quadrants are combined into one image before output.
• I-space is identical to d-space and to the r-space of quadrant 1.