wiki:Equivalent Diameter

The Equivalent Diameter of RATIR on the 1.5-Meter Telescope

Why do we say that RATIR on the 1.5-meter telescope? is equivalent to a conventional single-channel imager on a 3.1-meter telescope?

The starting point is to realize that RATIR takes four images of an object simultaneously (say, in the r, i, Z, and J filters). Thus, it's like having four 1.5-meter telescopes observing the object. Summing the areas, these four telescopes would be equivalent to a 3-meter telescope observing the object in these four filters sequentially.

But 3 is not equal to 3.1, so where do we get the additional area?

The key point is that RATIR also takes two images of blank sky in addition to four images of the object. The ZY and JH detectors have split filters placed close to the focal plane, so for example while RATIR observes an object in Z and J it observes nearby sky in Y and H and vice versa.

In infrared imaging, one subtracts a mean sky image from each object image. The appropriate figure of merit is then

Merit = Telescope Area × Object Exposure Time ÷ (1 + 1 / N)

in which N is the number of sky images contributing to the mean sky image.

Let's consider a typical example, with 4 object images in Z, Y, J, and H. A single-channel imager would obtain three sky images for each object image and would have N = 3. (That is, it could use the other object images in the same filter as sky images.) RATIR would obtain seven sky images for each object image and would have N = 7.

If you do the math, you find that RATIR on the 1.5-meter telescope is equivalent to:

  • a 1.5-meter telescope imaging in r;
  • a 1.5-meter telescope imaging in i;
  • a 1.6-meter telescope imaging in Z and Y; and
  • a 1.6-meter telescope imaging in J and H.

Summing the areas, RATIR on the 1.5-meter telescope is equivalent to a conventional single-channel imager on a 3.1-meter telescope.

Last modified 2 years ago Last modified on May 21, 2015 3:29:26 AM