Analysis of Coadd Noise: Gain and Read Noise Derived From Coadd Noise Versus Background

T. Chester, T. Jarrett, S. Schneider

Thanks to G. Kopan, we finally now understand the noise in the coadds. We have derived the gain and read noise for each band using the noise measured in the coadded images in order to make sure we understand the noise in those images.

Ignoring any source contribution to the noise, the basic noise in the frames comes from two terms. The first term is the Poisson noise in the number of electrons produced by the background. The second term is the read noise. Hence in electrons the frame noise is:

sigma(frame)^2 = gain * (frame background) + sigma(read noise)^2 (in electrons),

where the gain is expressed in electrons per DN.

To convert to DN, we divide by the gain^2 to get:

sigma(frame)^2 = (frame background) / gain + sigma(read noise)^2 / gain^2

There are indeed many other sources of noise, but these are usually the dominant factors. Other sources of noise that sometimes may be important are:

• confusion noise at lower galactic latitudes;
• the error in estimating the dflat per-pixel offsets;
• any additional instrumental noise, such as the J-band jumps;
• electrical hum; and
• bias-reset variations.

In addition, airglow structure at H band may cause spurious source detections, especially of extended sources, that are not characterized by the noise term from the background.

These other noises may cause the values calculated below to be lower limits.

We asked G. Kopan to derive the gain from the frame noise and backgrounds, to make sure we were starting with truth. He plotted (frame background) / sigma(frame)^2 for one night, and found the following:

Note that these are values of the minimum gain, since the read noise and the airglow noise was not taken into account.

The coadd is produced by averaging 6 frames, which reduces the noise in the coadd by sqrt(6) compared to the frame noise. In addition, all fluxes are divided by 4 because the pixel area is reduced by a factor of four in the images, so that integrating over coadd pixels produces the same DN values as integrating over the frames. Finally, the Weinberg filter smooths the pixel values by a factor of 0.585341. Hence the coadd noise is then:

sigma(coadd)^2 = { 0.585^2 / (4^2 * 6) } * { (4 * coadd background) / gain + sigma(read noise)^2 / gain^2 }.

For completeness, the expression for the noise in an aperture of n pixels in the coadd is given below.

The square of the coadd noise is plotted versus coadd background for each band below. Also plotted are lines for different values of the gain and read noise.

From the plots, we derive the following values for the gain and read noise in each band:

Again, keep in mind that if there are other contributions to the noise, the value of the coadd noise due to background and read noise is lower than the obesrved value. This makes the computed gain to be a lower limit and the computed read noise to be an upper limit.

If the gain is the same in all bands, which does not have to be the case (see below), these data imply that the gain is probably around 8. The J data rule out a value of 7 for the gain unless the read noise is much lower than 50 electrons. The K data seem to rule out a value of 8 for the gain, but this may simply imply that there are other contributions to the K noise, such as the telescope thermal contribution seen in the prototype camera data.

The read noise must be less than about 60 electrons.

M. Skrutskie has improved his analysis tools in testing the southerm camera and found that the gain can indeed vary between the bands. He says that this is expected because the components of the array which ultimately determine the gain are not produced in such a way as to yield uniformity between devices. For the southern camera he finds the following:

Mike says that the nearly identical read noise is probably coincidental.

Mike's previous estimates of the northern camera numbers are very similar -- gain of 8-9 and read noise about 40.

Since the purpose of this investigation was to see if we understand the noise in the coadds, we conclude that to at least a first approximation, we do indeed understand it.

Noise In An Aperture Of n Coadd Pixels