Background Subtraction with temperature scaling

A proper determination of the background is essential for measuring relative intensities.

During the data-taking of the Timing Counter the involved groups agreed on closing the beam blocker∼twice per day for a few minutes in order to take several background frames in a row. All beam pictures taken in between have to be corrected by those backgrounds.

Hence a stable background level is very important. As a measure for this the summed ADC values for all pixels in an image are drawn in gure 3.36. As seen from the plot the background intensity levels uctuate in time ranging from∼9.5·10⁶to∼1.5·10⁷ summed bitlevels. This would mean a severe drawback ruling out most of the captured frames

Figure 3.36.: The summed ADC values of the background images show signicant uctuations over time. However the temperature sensor mounted on the iDS camera housing shows a clear correlation with the background intensity levels.

for analysis unless being properly corrected for. The camera temperature read out by the AD590 is expected to be correlated with the intensity levels. Since the camera temperature can change within the 100 seconds exposure time, for example when the main door of the experimental hall is opened (see gure 3.37), the temperature that is assigned to a single frame is given by the integral for the exposure time of the linear interpolated temperature values. For the further evaluation the timeline plots for the status of the beam blocker, the magnetic eld and the LEM's rate are also linearly interpolated.

T_assign(f rame) = 1

t_{end f rame}−tstart f rame

·

Z tend f rame

tstart f rame

Tinterpolation(t)dt (3.15) Figure 3.38 shows the summed background intensity levels drawn against the integrated temperature. This also conrms the correlation between temperature and the background

Figure 3.37.: The time scale needed for the camera to cool down is of the same order of magnitude as the exposure time.

Figure 3.38.: The summed background intensity levels show a clear nonlinear correlation with the temperature and can therefore be tted by polynomial functions. The background frames taken with excited coils show a higher dark current level with a slightly dierent trend compared to background frames with COBRA OFF.

Table 3.4.: Polynomial functions and their coecients used to t the dark current levels: If it(T) =

level. There are two obvious main bands in which the points accumulate. Applying cor-responding cuts, the two main distinguishable types of (temperature|intensity) points can be identied. The lower band with many more points is identied as background frames taken while the coils of COBRA are not excited and vice versa. This means that the setup is sensitive to the magnetic eld. In principle the AD590 sensor could cause a similar eect by a B-eld dependent temperature read back. however, this can be ruled out as the major source since there are no temperature jumps of recognizable size in gure 3.36 observed while ramping up or down COBRA.

There is not only a gap between the backgrounds taken with "COBRA ON" (i.e. nominal current) and "COBRA OFF" but furthermore both bands have a dierent shape. This implies that the higher order dependence between the summed intensity I and the tempe-rature or the B-eld cannot be treated independently. A mixing term of the magnetic eld B and the temperature T would be required:

I(T, B) =f(T, B)6=g(T) +h(B)

with f, g, h being functions of temperature and/or the magnetic eld. However for a spatially stable camera position the B-eld contribution is constant and can therefore be absorbed in the coecients of two dierent polynomials that only show a temperature dependence. Hence both cases "COBRA ON" and "COBRA OFF" can be tted inde-pendently. Since we do not have the exact CCD and electronics temperature, we can not apply a common theory to describe the dark current [104]. Hence a 5^th order polynomial is tted to each, the COBRA OFF and the COBRA ON data points in order to evaluate the beam intensities. Dierent degree polynomials were tested in order to determine the best trade-o between good agreement and overtting. The resulting t parameters are summarized in table 3.4. Unfortunately the backgrounds taken with COBRA ON cover a smaller temperature range and less in number than those for COBRA OFF. An initial idea to put the camera in a thermal chamber at the end of the run and produce more back-ground frames covering a wider temperature was given up due to the strong dependence on the B-eld which can not be reproduced in the thermal chamber. In order to check

the validity of the ts all summed background intensity levels are normalized according to equation 3.16 and drawn in gure 3.39.

Inorm(f rame) = I(f rame)

I_{f it}(T_int(t(f rame))) (3.16) wherebyI_normis the normalized intensity,I(f rame)is the summed intensity of the frame, If it is the polynomial value with coecients an from table 3.4 and Tint(t(f rame))is the temperature derived from integration of the interpolated temperature values from data as in equation 3.15. The histograms in gure 3.40 show the deviations from 1 for the

norma-Figure 3.39.: Normalizing the background intensities assigned to the frames by the corresponding polynomial ts derived from gure 3.38 illustrates the strongly reduced residual uctuation of this method when compared to gure 3.36.

lized values for COBRA ON / OFF. The RMS values for the temperature normalization are 0.33% in the case of no current is applied to the COBRA coils and 0.78% with the nominal coil excitation. This does not only imply a higher dark current level when the coils are excited, which could be avoided in the future with a temperature stabilized ca-mera, but also a larger spread of the background intensities. The susceptibility to the eld of COBRA will strongly depend on the eld strength at the nal mounting position and the individual response of the camera electronics, which is dicult to predict. Therefore functionality tests are necessary when deciding on a new camera. Thorlabs, a candidate company, oer a loan of a temperature controlled CMOS camera [106] for careful tests, which are envisaged in the near future. The temperature scaling method shows a residual scattering < 1% RMS for the backgrounds taken with excited COBRA coils.

Applying this procedure to beam pictures with background subtraction allows the

ex-(a) Distribution of the temperature normalized

background intensities with COBRA OFF (b) Distribution of the temperature normalized background intensities with COBRA ON

Figure 3.40.: The noise levels of the dark frames after normalization correspond to RM Sdark,norm,COBRAOF F =0.33% andRM Sdark,norm,COBRAF F =0.78%.

traction of a beam intensity I∝µ which is approximately proportional to the number of incoming muons. The intensities have to be scaled according to equation 3.17.

I∝µ=If rame,beam− 1 n

X

n

If it(Tint(t(f rame, beam)))

I_{f it}(T_int(t(f rame, bkgd_n)))·If rame,bkgdn

(3.17) whereIf rame,beam is the intensity level of the beam picture under investigation,

I_{f it}(Tint(t(f rame, beam)))is the result of the background t function ("COBRA ON") for the integrated average temperatureT_intduring the exposure time of the beam picture from t(f rame, beam)−exposure timetot(f rame, beam), similarly forIf it(Tint(t(f rame, bkgdn))) the exposure time of the background frames. If rame,bkgdn are the intensities of the back-ground frames that are averaged for backback-ground subtraction. Equation 3.17 is only valid as long as the scintillator shows no degradation due to radiation damage. However since the number of muons also depends on the proton current and proton beam centring on TgE this information can be used to determine the radiation damage of the scintillation target. The required relationships between these quantities are derived in the following subsections.

3.5.3. Scintillation target proles and comparison with the APD scanner