Experimental Efforts to Study Core-collapse SNe and...

CCD Characterization

Semiconductor-based detector for astronomical observations

CCD Components

Scientific CCD

Charge Coupled Devices (CCDs)

CCD Characteristics & Parameters

What sort of things can you imagine regarding CCD Characteristics and Parameters?


What sort of things can you imagine regarding CCD Characteristics and Parameters?

Sensitivity, Noise, Pixel Numbers, Saturation, etc


CCD is a capacitor. Does this statement make sense to you?

CCD is structurally a 2D (sometimes 1D) array of thousands to millions of “metal insulator semiconductor photosensitive capacitors” (= pixels). Bias voltage is applied across the pixels.



Q = C V = N e-

Q: total storable charge in pixel C: capacitance of pixel V: applied bias voltage N: number of total electrons

that can be stored in pixele-: electron charge

Therefore, the total number of photo-electrons that can be stored in pixel is dependent on C & V. If C & V are small, one cannot observe bright sources or cannot expose long.

“Q determines full well capacity which is the maximum number of electrons that can be stored in a pixel: e.g., N 100,000.”

Photo-electrons are transferred along the column first by changing the gate voltage and then transferred horizontally by serial shift register. Therefore, the pixels are read out successively, not independently. They are connected each other, and it is why the device is called CCD.

CCD: array of interconnected capacitors (= pixels)

Charge Coupled Devices (CCDs)How are electrons transferred in CCDs?

After transferred by the serial shift register, the charges are converted to voltages by amplifier by adding (small) bias voltage. The converted voltages are eventually converted digital number by analog-to-digital (A/D) converted and stored as image.

Charge Coupled Devices (CCDs)How are electrons transferred in CCDs?

CCD Operation

Exposure: collecting photo-electrons in pixel;

Photo-electrons moved to the electrode of pixel;

Electrons transferred along column and then

horizontally through pixels;

Electrons transferred to the output amplifier;

Amplifier converts the charges to output voltages;

Output voltages converted to the digital number by

A/D converts;

Converted numbers (DN) stored in the computer as image.

Quantum Efficiency (QE):

QE = (# photo electrons)/(# incoming photons)

80 % for most of modern CCDs

Different CCDs have different QEs.

QE is dependent on wavelength and temperature.

CCD Characterization:Quantum Efficiency, Charge Transfer Efficiency, Full Well Capacity, Gain and Digital Number, Digitization Error, etc

Charge Transfer Efficiency (CTE):

CTE = (electrons transferred) / (electrons produced)

~ 0.99

Full Well Capacity:

= the amount of charge (or number of electrons)

that a CCD pixel can store

: depends on CCD, but usually 100,000 electrons


Data (or Digital) Number (DN): digitized data number in computer after A/D converter; it is proportional to the intensity of incoming light, in principle

(incoming photons)

→ (photo electrons: current)

→ (voltage after amplification)

→ (digital number after A/D converter)

A/D converter: 14-bit, 15-bit, 16-bit resolution

e.g., 16-bit: 0 – 65535, so CCD with 16-bit A/D

converter has DN between 0 and 65535


Gain: the number of electrons (or the amount of voltage)

needed to produce 1 digital number (DN)

Example: A CCD has 150,000 e full well capacity and 15-bit A/D converter. What’s the gain of this CCD if it provides the maximum dynamic range? (Note that not all CCDs provide the maximum dynamic range.)


Gain: the number of electrons (or the amount of voltage)

needed to produce 1 digital number (DN)

Exercise: When is a CCD image saturated? Describe this with the aforementioned CCD characterization parameters.

Example: A CCD has 150,000 e full well capacity and 15-bit A/D converter. What’s the gain of this CCD if it provides the maximum dynamic range? (Note that not all CCDs provide the maximum dynamic range.)

Gain = 150000/215 ≈ 4.6

Digitization Noise: the degeneracy in the number of electrons that produce the same digital number due to gain. If the gain is 1, there is no digitization noise.

“Low gain for fainter objects, high gain for bright ones”


Basic Processes of CCD Observations – Flat Fielding

Each CCD pixel has a different sensitivity.

How do we calibrate it?




By observing a light source with a uniform brightness to create a pixel sensitivity image “Flat Fielding”

“Flat Fielding Image” is often obtained by taking an exposure to a reflective light off a dome screen (see left) illuminated by a bright light source with a uniform illumination.




By dividing source images with a Flat Fielding image.

Basic Processes of CCD Observations

Suppose that an observe took an image of a source with a CCD,

what kind of signals are included in the image?

A. Source signals: e.g., stars, galaxies, ……

B. Sky background: radiation from the Earth’s atmosphere

C. Thermal Noise (= Dark) of the CCD: note that thermal distribution of valence electrons in semiconductor

D. Bias for the CCD readout

A, B, C: proportional to the exposure time

D: independent of exposure time, when CCD is read


Observed Image =(Source + Sky)(CCD Sensitivity)(Exposure Time) (Dark for the same exposure time) (Bias)

Example:

For a given CCD pixel, if an observer obtain DN = 52 for dark measurement (= no light) from a CCD image with 10-sec exposure, what’s the DN from (pure) dark that can be obtained with 1-sec exposure? The bias is known to be 2 in DN.

Answer: Dark noise per second = (52 2) / 10 = 5/sec

Then, if the observe obtain DN = 702 from the same pixel in a flat-fielding exposure (by illuminating with a bright source), what’s the intensity of the flat-field per second obtained by the pixel after removing the bias and dark?

Answer: Intensity/second = [702 2 (5 50)] / 50 = 9



Continued ……

Now, if the observer has DN = 2002 from the same pixel by observing a star with 100-sec exposure, what’s the number after the flat fielding?

Answer: [(2002 2 (5 100))] / 100 / 9 1.67

Note: The exposure is the same for all the pixels in a CCD, but pixel sensitivity (= values for flat fielding) is different from a pixel to a pixel. So in the above Answer, dividing by 100 is not important when you compare values obtained with different pixels. However, dividing by 9 is critical.



CCD Observations: Signal and Noise

What kind of CCD noises do we expect?

CCD Observations: Signal and Noise

Noise from the object (e.g., stars, galaxies, …) brightness.

Noise from the sky background brightness.

Dark noise from the CCD (= Dark is not constant).

Readout noise from the readout electronics.

How accurately can we measure the object brightness?

How do we quantify the relevant uncertainties?

[1] If we take several measurements, we can in principle calculate the uncertainty of each noise.

[2] Or sometimes we can use their statistical properties (e.g., Poisson statistics).

CCD Random Noise There are basically two types of CCD random noise (): Photon noise (ph) from the “object, sky background, and dark noise.”

(This follows the Poisson statistics.) Readout noise (R) from “readout electronics.”

(Non-Poisson noise; e.g., 20 e per read)

CCD Noise (per pixel): 2 = ph

2 + R2

(ph is photon noise; R is readout noise.

Note the unit of , ph, and R is in unit of number of electrons.)

= G #(G is “Gain.” Number of electrons to increase data number by unity, e.g. 4. # is in unit of DN.)

ph2 = Nph,e = G Nph,# ( Poisson statistics!)(Nph,e is in unit of number of electrons; Nph,# is in unit of DN.)

G2 #2 = G Nph,# + R

2

#2 = Nph,#/G + R

2/G2

CCD Noise (in DN unit) is #

2 = Nph,#/G + R2/G2

# , Nph,# can be estimated from observed imagesG, R can be obtained by simple analysis known as

variance plot (or photon-transfer curve);

Bright images: photon-noise dominates;

#2 ≈ Nph,#/G

Short dark images: readout noise dominates;

# ≈ R/G

CCD Random Noise

[Data number] [Electron]

Variance Plot (= Photon-transfer Curve)log # = ½ log (Nph,#/G + R

2/G2) ½ log (Nph,#/G) photon noise regime log (R/G) readout noise regime

G and R can be obtained using variance plot of # and Nph,#.

Slope = 1/2

CCD Random Noise

Variance Plot or Photon-transfer Curvelog # = ½ log (Nph,#/G + R

2/G2)

Systematic errors that can affect the estimation of G and R?

CCD Random Noise


2/G2)


• Non-uniform illumination

CCD Random Noise


2/G2)



• Scalenoise (= QE variations)

CCD Random Noise


2/G2)



• Scalenoise (= QE variations)

• Nonlinearity.

“Image differencing” is a useful tool for removing systematic errors. But this is beyond the scope of the class.

CCD Random Noise

Experimental Efforts to Study Core-collapse SNe and...

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