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ST-7e CCD Tests, Gain, ReadOut Noise, Dark Current

A series of tests were performed using my ST-7e CCD camera on 2008-11-21 / 22, with the goal of characterising the performance the camera to confirm its general health and provide parameters to input into advanced photometric SNR calculations.

Whilst a Non-ABG (non anti-blooming) version was originally ordered, it has been assumed that the actual version of ST-7e camera received was an ABG (anti-blooming) camera since it has never displayed blooming spikes on any bright star.  This ABG behaviour has been particularly beneficial over the years, though the ABG / non-linear impacts on photometry has slightly concerned me.

Camera Expectations

The ST-7e camera is 16 bit

The camera uses a KAF-0400 CCD and compared to the Non-ABG version is understood to have 70% less collecting area due the drain circuitry and up to 50% lower quantum efficiency. However at the same time the camera should have 50% less dark current. For the same exposure length the Non-ABG version will have 40% lower magnitude error than the ABG version of the camera.
[Technical Note at http://www.mirametrics.com/tech_note_antibloom.htm ]

The full well capacity is understood to be 50,000 e- for the ABG camera (compared to 100,000 e- for the Non-ABG camera). At 1x1 binning and the quoted gain of 2.3 e-/ADU the expected saturation level is understood to be ~20,000 ADU for the ABG camera (compared to ~40,000 ADU for the Non-ABG version)
[ST7 specifications at  http://www.phys-astro.sonoma.edu/observatory/documentation/st7_specifications.html ]

The camera is specified to have a dark current of 1e¯/pixel/sec at 0° C
[ Specifications for the current ST-7e camera (using the KAF-0402ME CCD chip) are at http://www.sbig.com/sbwhtmls/st7.htm ]

Elsewhere I have seen that the KAF-0400 CCD chip has a read-out noise of only 13 e-/pixel, with a dark current Given by the equation
    N_d (e^-/pixel/sec ) = 9.47x10¹³ x T^1.5 x exp(-11230/T)  with T in deg K  (degK=273+ degC)
[ http://www.astrosurf.com/audine/English/intro/intro5.htm ]

Saturation Level

At 1x1 binning, saturation level in the camera was measured to be around 32,000 ADU.  This compares with an expected figure of ~20,000 ADU.

At 2x2 binning, saturation level in camera is ~ 65,000 ADU. This compares well with the expected value of ~65,000 ADU

Basic CCD Test

A basic CCD test was conducted based around the methodology given in "The Handbook of Astronomical Image Processing", Section 8.2 by Richard Berry and James Burnell  [http://www.willbell.com/aip/index.htm]

• Camera turned on and allowed to reach thermal equilibrium at -25 deg C
• 2 flat frames obtained using the same identical integration time, and using 2x2 binning (F1 and F2)
• 2 bias frames taken (B1 and B2)
• 1 dark frame taken with 60s integration time (D)

The flats were taken using white illuminated board on the wall of the observatory and a tungsten light source, with the integration time selected to provide a suitable Flat Frame count; around 50% of saturation level. 2x2 is the normal binning mode that I use for taking light frames at night.   Frames were also collected at 1x1 and 3x3 binning for comparison.

In practice 3 flat, 3 bias and 3 dark frames were taken allowing 3 pairs of bias and flat frames to be created.
 

Manipulation of Frames  (Mean and Standard Deviation)

Frames were analysed using AIP4WIN. (AIP4WIN software is available with the "The Handbook of Astronomical Image Processing". It has superior analysis tools compared to those of CCDsoft ) 

The two bias frames were added together and the mean pixel value was measured  μ_(B1+B2). Next one bias frame was subtracted from the other and the standard deviation measured  σ_(B1-B2).    The left-hand image below shows features in the total bias. The right-hand image below shows that subtracting one bias frame from the other removes any features in the bias leaving the total noise in the two bias frames. The noise is √2 times the noise in a single bias frame

Sum of two bias frames		Difference between same two bias frames
CCD Support Frame 2x2 binning (#224803 + 224804)		CCD Support Frame 2x2 binning (#224803 - 224804)

The two flat frames were added together and the mean pixel value was measured  μ_(F1+F2). Next one flat frame was subtracted from the other and the standard deviation measured  σ_(F1-F2).   The left-hand image below shows features in the total flat. The right-hand image below shows that subtracting one flat frame from the other removes any features in the flat leaving the total noise in the two flat frames. The noise is √2 times the noise in a single flat frame.

Sum of two flat frames		Difference between same two flat frames
CCD Support Frame 2x2 binning, 2s, C Filter  (#224860 + 224861)		CCD Support Frame 2x2 binning, 2s, C Filter  (#224860 - 224861)

The first bias frame was subtracted from the dark frame to provide the dark (thermal) current recorded over the integration period (D-B).  The mean value was measured  μ_(D-B).

Calculation of Gain  (e-/ADU)

For a frame containing a high signal level such as a flat field frame, it can be expected to display Poisson statistics when measured in electrons,   i.e.  
         σ _electrons =  √μ _electrons
however since both σ and μ  have been multiplied by the conversion factor or gain, g (in e^-/ADU) we have actually measured
         g.σ _electrons =  √g.μ _electrons

solving for g
        g = μ _electrons   /  σ² _electrons

           g =  μ_{(F) ADU}   /  σ² _{(F) ADU}

A slightly more accurate figure for g can be obtained by subtracting the influence of the bias mean and noise

    g =  μ_(F1+F2) - μ_(B1+B2)          (in   e^-/ADU)
              _{-------------------------------}
                σ_(F1-F2) - σ_(B1-B2)   

 Calculations provided the following results

These figures compare with an expected gain value of 2.3 e^-/ADU. 

It is non clear why higher gain figures are calculated but is seems to be real (whilst an ABG version might have a different gain to a non-ABG version, it would be expected if anything to have been given a lower gain rather than a higher gain in view of it's smaller well capacity).

Calculation of Read-Out Noise (σ _ron)

The only source of noise in a bias frame should be the read-out noise. The sum of the readout noise in two bias frame has been measured from the standard deviation of the difference of two bias frames σ_(B1-B2).   And we know that this value is √2 times the noise in a single bias frame.  Therefore we can calculate readout noise as follows :

    σ_readout     =     g.σ_(B1-B2)     /   √2    [ in e^-/pixel ]

Based on measurements and the gain values calculated above, the following readout noise results were obtained based on the average of 3 tests :

These figures compare with an expected read-out noise of 15 e^-/pixel, and indicate that the camera is in good health.

A separate run in which Read-Out Noise was calculated for 2x2 binning at a 29 different set-point temperatures indicated a mean read-out noise of  14.1 +/- 0.2  e-/pixel 

Calculation of Dark Current

The mean dark current value of the 60s dark frame was converted to a dark current per second by dividing it by the integration time

    D _ADU  = μ_(D-B) / 60    [ in ADU/pixel/sec ]

or in electrons

    D _electrons = g.μ_(D-B) / 60    [ in e^-/pixel/sec ]

The following results were obtained based on 3 tests.

The figure of 0.43 compares with an expected dark current of  0.06  e-/pixel/sec  (based on expected 1 e-/pixel/sec at 0 degC and a 6 degC doubling rate temperature).   Notionally it would seem that the camera is underperforming in terms of dark current

Further Testing

A further sets of tests were carried out to understand the behaviour of the camera under various states of cooling.
 

Cool-Down / Warm Up

Using an automated routine developed for the task, sets of 3 bias and 3 x 60s dark frames were acquired at 1 degC intervals of set point temperature between -1 and -31 deg C , with 5 minute stabilisation periods after each temperature set-point change.

For each step the average cooling power (%) and ambient temperature were compiled from recorded data.   The cooling power is placed in the FITS header of each image, whilst ambient temperatures were taken from a log file of telescope tube temperatures recorded by Optec TCF focuser.   Ambient temperature remained at around +1 degC through the test.

At the end of the cool-down period. the routine was used to record 1 bias and 1 x 60s dark frame at 3 degC intervals between -29 and -5 degC, with 10 minute stabilisation periods after each temperature set-point change.

Read-out noise

For each temperature step the read-out noise was calculated from the standard deviation of the difference between pairs of bias frames (2x2 binning) and using a gain of 2.69 e-/ADU.   Average readout noise for the 29 steps was 14.1 +/- 0.2 e-/pixel. A graph of read-out noise vs CCD temperature is shown below.  As can be seen the data suggests that readout noise is pretty independent of temperature . However the mean bias itself is dependant on temperature and seems associated with dark current in the camera electronics as the bias frame is being read and counted.

Graphs of Mean Bias and Readout Noise vs CCD temperature  (S324)

Graphs of Mean Dark Value and Dark Current vs CCD temperature  (S324)

Graphs of Dark Current vs CCD temperature  with simple model curves (S324)

Graphs of Dark Current vs CCD temperature  with best fitting models (S324)

Gain Measurements / CCD Transfer Curves  (S324)

Linearity Tests (S324)

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