ptc

EXPERIMENTAL SOLAR PHYSICS

CHARACTERIZATION OF A CCD CAMERA The Photon Transfer Curve

PURPOSE: To determine the foundamental parameters of the Photon Transfer Curve (hereafter PTC).

WHY THE PTC IS IMPORTANT IN YOUR LIFE: It allows to calibrate the CCD camera without knowing its technical specifications.

Experimental Solar Physics - Photon Transfer Curve

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FIRST OF ALL:

How to approach to a laboratory experiment?

1. Take a breath…

2. Study the topics covered in lectures before using a lab

3. Do not push buttons and turn knobs randomly

4. Is there a problem? Check the experimental set-up again (every part

of the experiment, software inputs, the experimenter, and so on… )!

5. Is there still a problem? Have some simply test to check what is

faulting

6. Is there still a problem? After having tried everything ask someone…


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SECOND:

How to approach to data analysis?

1. Organize the output data in a precise, clear, and possibly clever way

2. See points 4., 5., and 6. of the previous slide

Suggestion:

Take notes about everything you do (experimental set-up, problems encountered, how you resolved them, and so on…) because: 1) You might need to know what you did in a previous stage

2) You might need to know how a problem was resolved

3) You have to prepare a report


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Noise Sources: 1. Shot noise. Uncertanty in the photon counting. Ruled by Poisson

statistic 𝝈𝒔𝒉𝒐𝒕 = 𝑺

2. Dark Current. Thermal electron production noise. cooling

3. Non-uniformity. Intrinsic different pixel response to the same input. Flat Field: Response map to an uniform light

4. Read Out Noise (RON). Noise due to electron to signal (Voltage) conversion.

5. BIAS. Electronic offset. It allows to amplify even the weakest signals. acquire an image with closed shutter and exposure time = 0


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Photon Transfer Curve

CCD calibration consists in determining the parameters of the PTC. 𝑺𝑨𝑫𝑼 = 𝑮𝑵𝒆𝒍 + 𝒃 𝑆𝐴𝐷𝑈 : Signal in ADU 𝐺 : Gain (ADU / electrons) 𝑁𝑒𝑙 : Number of electrons in the package 𝑏 : bias

Parameters to be determined: 𝐺 & RON. (we’ll show why we don’t consider Dark & Non-Uniformity)


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Noise sources are independent, so

𝑁𝑡𝑜𝑡2 =𝑁𝑠ℎ𝑜𝑡

2 +(𝑅𝑂𝑁)2

Expressed in numbers of electrons. But CCD are read in ADU, so

(𝐺𝑁𝑡𝑜𝑡)2= (𝐺𝑁𝑠ℎ𝑜𝑡)

2+(G RON)2

with

(𝐺𝑁𝑡𝑜𝑡)2=𝜎𝑡𝑜𝑡

2

𝑁𝑠ℎ𝑜𝑡= 𝑁𝑒𝑙 =𝑥𝑛

𝐺

𝑥𝑛: mean signal in ADU. We find

𝝈𝒕𝒐𝒕𝟐 =𝑮𝒙𝒏 + (𝐆 𝑹𝑶𝑵)𝟐

Plotting 𝝈𝒕𝒐𝒕

𝟐 VS 𝒙𝒏 we obtain the PTC (linearity)


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ROADMAP: Verify the linearity AVERAGE-SIGNAL VS EXPOSURE TIME (that is why we

are acquiring at different exposure times).

Plot the PTC 𝝈𝒕𝒐𝒕𝟐 𝑉𝑆 𝑺 (in a log-log plot it is easy to see the different

regimes obtained by varying the exposure time)

In the linear regime determine G and RON by a linear fit

Write a report with • A brief theoretical introduction • Description of the experimental set-up • Description of the procedures • Results • Comments and conclusions


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To have the PTC in a graph we have to: Determine the BIAS image

Take 2 images 𝐼1 and 𝐼2 for each exposure time (from RON to saturation) and a

DARK frame

Consider the mean image 𝑆 =𝐼1+𝐼2

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Subtract BIAS image and the DARK frame

Calculate 𝑥𝑛 in a region free of artifacts (Region Of Interest, hereafter ROI)

Consider the image N =𝐼1−𝐼2

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Calculate the variance of N in the ROI and call it 𝜎𝑡𝑜𝑡

2 .


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Linear fit in the region dominated by Shot Noise G, RON

PSSSS! JUST REMEMBER… Images subtraction that leads to find the N image automatically exclude

BIAS and the noise that rise from pixel non-uniformity!

Why people work in linead regime? This part of the curve is dominated by the Shot Noise, so our noise sources appear to NOT DEPEND on the instrumental setup!!! They only depend on the source characteristics. This important region is called Shot Noise Limited

𝜎𝑡𝑜𝑡 ≅ 𝜎𝑠ℎ𝑜𝑡 = 𝑁𝑒

𝑙𝑛(𝜎𝑡𝑜𝑡) ≅1

2ln (𝑆)

The End

ptc

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