Read Noise and Gain of the ACA Primary CCD

Summary

Using fiducial light data, we empirically determine the read noise and gain of the ACA Primary CCD. The read noise is 14.9 electrons (well within the budgeted value of 25 electrons) and the gain is 5.9 electrons/DN. The value of gain differs from the Ball specification of 5.0, but there is no operational impact and no need to adjust any mission planning or CXCDS database values.

Introduction

The ACA CCD is a counting device which is expected to obey the basic statistical relationship

   Variance(electrons) = Read_Noise^2 + Poisson_Counting_Noise^2
                       = Read_Noise^2 + Pixel_Value(electrons)
                       = Read_Noise^2 + DN * Gain


   Variance(DN)        = Variance(electrons) / Gain^2

                         Read_Noise^2      DN
                       = ------------  +   ----
                         Gain^2            Gain

Here the term Read_Noise includes all sources of fixed gaussian noise, including electronic and quantization noise. DN is the digitized pixel output from the analog to digital converter which is telemetered. It is assumed that the electron is the basic quantum for which Poisson counting noise applies.

By plotting pixel variance (in DN) as a function pixel value, it is possible to independently determine the Read_Noise and Gain from the slope and intercept.

Analysis

The fiducial lights present a convenient way to estimate pixel variance, since they are bright and the fid light images move only very slowly during an observation. This means that the input signal to a particular pixel is nearly constant and it is possible to calculate a meaningful variance as a function of pixel intensity. However, even the fid lights move enough to affect the variance somewhat, so a more robust method is to calculate the variance of the differences of adjacent readouts (in time) for a pixel. This value is divided by 2 to recover the expected variance of the pixel time history:

  pixel(i,j,k) = k'th sample in time of pixel at image location i,j

  Variance(DN)(i,j) = Variance ( pixel(i,j,1:n-1) - pixel(i,j,0:n-2) ) / 2

In order to exclude non-gaussian outliers (particularly from cosmic ray hits), we first applied a 2-pass sigma-clip filter with a rejection limit of 4-sigma.

A total of 18 fiducial light images were processed, each containing 64 pixels. The image below shows a scatter plot of pixel variance in DNs as a function of the mean pixel value (DN).

This linear plot is zoomed in to show the non-zero intersection with the origin, but the best fit line (in red) was calculated using the full dataset. Using the fitted intercept and slope, the read noise and gain are calculated to be:

   Read_Noise = 14.9 electrons
   Gain       = 5.9 electrons/DN

The value of the gain is significantly different from the value of 5.0 supplied by Ball. The blue dotted line in the above plot shows the expected variance for a gain of 5.0. The origin of this discrepancy is not clear. However there are no immediate operational impacts since the actual value of gain is only important for estimating counting noise. Mission planning star selection and ground aspect processing are only weakly dependent on this noise, and there is no compelling reason to adjust the gain (and accordingly the magnitude calibration values).

The image below shows the full dataset on a log-log scale. The value of Read_Noise^2 has been subtracted so that the linear relationship (in log-log space) over nearly three decades in pixel value is seen.

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Last modified:12/27/13