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Linearity of CCD: how to determine

Costruire una curva di linearità della propria camera CCD è un'operazione abbastanza semplice e diventa una necessità, se non un obbligo, per chi desidera utilizzare i propri strumenti astronomici alla misura fotometrica di qualsiasi sorgente celeste.
Esistono vari metodi più o meno rigorosi per determinare la linearità di un sensore CCD: ad esempio " In situ CCD testing " di T.M.C. Abbott ne utilizza uno particolarmente sofisticato utilizzato negli osservatori professionali: il sito inoltre è una sorgente di informazioni and useful ideas for those who want to characterize a CCD camera for astronomical use.
We use a slightly simpler procedure that will be sufficiently accurate for our purposes: we can be divided into three main steps: setup of the instrumentation, the acquisition and data processing.


INSTRUMENT SETUP The setup tool is normally used for the acquisition of FLAT FIELD configuration " DOME-FLAT" or one where you use a screen opal and / or reflective and a source of artificial light outside.
not required to use filters (unless it is necessary to mitigate the source luminosa) ma è importante che il binning sia impostato alla massima risoluzione ( 1 x 1 ). Il CCD deve essere ad una prefissata temperatura, preferibilmente vicina alla temperatura usuale di lavoro. E' quindi necessario attendere che tutto quanto sia in condizioni termicamente stabili, a maggior ragione se il CCD non è termoregolato elettronicamente: generalmente occorre attendere 30-40 minuti dall'accensione della camera CCD . Evitate di eseguire la sequenza di immagini flat in ore della serata che comportano delle escursioni termiche di qualche grado come poco dopo il tramonto o l'alba.
Puntate il telescopio verso lo schermo illuminato e fate alcune esposizioni di prova aumentando gradualmente il tempo d'esposizione: per ogni immagine selezionate una finestra di all'incirca 300x300 pixel nella zona centrale dell'immagine e, utilizzando le funzioni statistiche del software individuate qual'è il valore medio (in ADU) dei pixel che compongono il riquadro fino a raggiungere la saturazione del convertitore analogico-digitale (65536 per un 16 bit, 32768 per un 15 bit ecc.).
Se utilizzate Astroart potete aprire la finestra delle statistiche dell'immagine (o del riquadro selezionato) attraverso il comando Visualizza > Statistiche , mentre per selezionare sempre lo stesso rettangolo, una volta impostate le coordinate o manualmente o con il mouse, è sufficiente premere su ogni immagine la [Ctrl] + [R].
It 'important to reach saturation with certainty because we want to establish the exact limits of our tool: without exaggerating of course submitting to a light exposure throughout the sensor: a need for particular caution illuminated CCD as the sensor SITE ' s Apogee Ap7p that may be damaged even by simple exposure to daylight.
Suppose we have reached saturation levels with an exposure of 35 seconds and proceed with the acquisition of the frames.

ACQUISITION OF FRAME
We have established with evidence that the integration time leads to saturation most of the pixels in the frame of the box chosen. We recall that this time in our example is 35 seconds but may of course vary depending on your setup instrumental.
We can now proceed with the acquisition sequence of frames needed for our analysis.
aim is to adopt a sequence of frames (call them flat field) with integration time gradually increasing to reach 35 seconds with 1 second integration step. If the time limit of 35 seconds for your instrumental setup much larger, eg. > 60 seconds, you can increase the integration step, taking it to 2-3 seconds to lower the total amount of frames to be measured. For
each step should then resume its dark frames plus a flat field by one second with its dark frame duration of 1 second. In short, putting in brackets in the second period of integration, the sequence would be:

FLAT (1), DARK (1), FLAT (1), DARK (1), FLAT (2), DARK (2), FLAT (1), DARK (1), FLAT (3),
DARK (3), FLAT (1), DARK (1 ),... FLAT (35), DARK (35), FLAT (1), DARK (1). The

FLAT FRAME FRAME and DARK taken from 1 second between each progressive integration are needed to ascertain that there are substantial variations in the behavior of the CCD camera during the entire sequence. Take all these manually
frame is without a doubt What boring but now almost all acquisition programs have the ability to create scripts. Here is an example for those who use Astroart:

'**********
'Variables
'**********
$ folder = "\\ LINTEST \\" EXP_NUM = 35 'seconds maximum exposure
T_EXP_DARK = 0' set to zero exposure of dark
darkname $ = "DDs" 'string of first names dark frame
T_EXP_LIGHT = 0 'set to zero the display of flat
lightname$ = "FFs" 'stringa iniziale del nome dei flat

'************************
'Inizio ciclo esposizioni
'************************
for i=1 to EXP_NUM
Camera.Binning(1)
T_EXP_LIGHT = i
T_EXP_DARK = i

'Esposizione dei light frames
'******************************
Camera.Start (T_EXP_LIGHT)
Camera.Wait
Image.Save ("F: \\ Cavezzo" + folder lightname $ + $ + str $ (i) + ". Fit")

'Exposure of dark frames
'******************************
Camera.Start (T_EXP_DARK, 0)
Camera.Wait
Image.Save ("F: \\ Cavezzo" + folder darkname $ + $ + str $ (i) + ". fit")

'exposure to the flat 1s
'******************************
Camera.Start (1)
Camera.Wait
Image.Save ("F: \\ Cavezzo" + $ folder + "FLAT1-" + str $ (i) + ". Fit")

'Exposure of the dark frame from 1s
'******************************
Camera.Start (1.0)
Camera.Wait
Image.Save ("F: \\ Cavezzo" + $ folder + "dark1-" + str $ (i) + ". fit")

the next

'************************
'End cycle exposures
'************************

In our example, the frames are saved in F: \\ Cavezzo \\ LINTEST but intuitively customize the process to suit your needs.
should be noted that the workbooks, where the frames that are saved during the execution of the script, must already exist, otherwise you will get an error message.

DATA PROCESSING
At this point, we will have 140 files in the folder LINTEST that correspond to the same frame: 35 frames FFsXX, with its 35 dark DDsXX e 35 frame da 1 secondo FLAT1-XX con i 35 dark DARK1-XX, dove XX è il progressivo di ripresa che nei primi due casi coincide anche con il tempo d'integrazione.
La prima cosa da fare è creare un master DARK FRAME con i 35 DARK FRAME da 1 secondo (DARK1-XX) e sottrarre questo master ad ognuno dei FLAT FIELD da 1 secondo (FLAT1-XX) salvando il file risultante. Con Astroart l'operazione è immediata impostando la finestra del preprocessing in questo modo:



Una volta lanciato il pretrattamento ci troveremo nella stessa cartella 35 nuovi file FLAT1-XX_P con il suffisso P che andranno analizzati con la funzione statistica Visualizza > Statistiche after selecting the central rectangle of 300 x 300 pixels (this is convenient to use the keyboard shortcut [Ctrl] + [R]: the program will always select the last marquee saved).

data to be entered for each frame are the mean and standard deviation as indicated in the figure below:


It should now write data to an Excel sheet for convenience I have already set up a link to download http://users.libero.it/mnico/linearita_AP7p.xls . After completing this first set of data sheet will assume the following aspect:


remain to fill the second and third column of the spreadsheet. The procedure is slightly longer: you need to load one frame at a time with its dark FFsXX DDsXX, subtract the latter FFsXX frame, click once with [Ctrl] + [R] analysis of the rectangle of 300 x 300 pixels and open the statistics window with View> Statistics .
For these frames must be recorded on the sheet on the mean and standard deviation to the full compilation of the Excel spreadsheet. The last two columns to the right, headed in orange, those are calculated: the first by multiplying the average value of control by one second flat FLAT (1) for the second exposure Exp (s) while the second is the ratio of normalization R (s) = Flat (s) / [Flat (1) * Exp (s)]: more than R (s) is close to 1 the better the behavior of linear CCD camera. Here

hours on a graph the average value of FFsXX (second column, or Flat (s)) as a function of R (s). For our example, the graph looks like this:


Most of the points are lying on the line R (s) = 1, as expected, and is clearly the beginning of the collapse of linearity about 60,000 ADU. However, some points deviate from the true values \u200b\u200beven lower: a careful analysis of the behavior the CCD camera showed that in reality are due to poor temperature control of the CCD, which has slightly changed the average dark current during the rapid succession of exposures of 1 second.
To further ensure that the changes were not due to discontinuity in the linearity of the CCD camera can be useful to analyze the graph of the standard deviation of FLAT (s) depending on the FLAT (s) itself:


There are still a couple discontinuity (the points should all be equally spaced on the same line as the increase of exposure is more than 1 second) but still show the discontinuity over 60,000 ADU.
Discontinuities are minimum, averaging below '1.4%, as can be calculated through the same spreadsheet.

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Contrail before 1995, III

Two more pictures of contrails taken many years ago. Are contained in a study of 1972 ; complete reference: RG Knollenberg, "Measurement of the growth of the ice budget in a persisting contrail," Journal of the Atmospheric Sciences, vol. 29, 1972 .

Note that the second shot to the concept of "persistent trail, often flaunted as a symptom of something strange ; actually 'a thing normally seen in any scientific study - so it' s true that many studies that, starting from the consideration that many long contrails remain in heaven, evolving into cirrus clouds, we deal with the impact on climate due to a possible increase in cloudiness' because of the contrail.

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Linearity of the CCD: the problem

And 'one of the main advantages of CCD sensors. Indeed, it is the characteristic that makes our CCD sensor and a measuring instrument not just a simple "camera" digital.
Linearity means that there is a simple linear relationship between the input value (the electric charge collected in each photoelement) and the output value (the number assigned to each pixel that composes the final image).

There are two important limits defined by the elements of its CCD sensor input and output elements of the CCD camera: the first is the Full Well Capacity photoelements of making up the sensor while the second is the type of analog to digital converter (or ADC Analog to Digital Converter) used by the CCD camera.
E 'so easy to see that there are two levels of saturation : the first is the ability to collect individual photoelements electrons that make up the CCD, the second is given by the resolution (in bits) of the analog-digital converter.

To fix ideas, always consider the example of the CCD camera sensor with Apogee Ap7p SITE supplied Astronomical Observatory of Cavendish. The size of 24 microns square photoelements have a Full Well Capacity of about 300000 electrons as the analog to digital converter has a resolution of 16 bits, corresponding to 65535 ADU (2 ^ 16).
If we build a graph with the x-axis input data, the number of electrons contained in photoelement, and the ordinate the output value, the number of ADU of the corresponding pixel of the image, these two limits are represented by the saturation two blue lines, respectively (x = 300000) and red (y = 65535).

A CCD camera is not professional but good quality present a curve similar to the linear graph above where the green lines is precisely the section where the camera behaves in a linear fashion while the orange, which starts at around 250,000 photoelectrons captured by photoelement, is the non-linear stretch which is lost by the photometric quality of the chamber.
We note that the same graph gives us a couple of notes: we know from analytic geometry that the equation of a line has an expression:

Y = mX + c where

m is the slope, or the slope of the line and c is the so-called known term, namely ntercetta with the y-axis. Well, the slope m (equal to the tangent of the angle that the line of linearity underlying the x-axis) is no more che l'inverso del gain, mentre c è l'offset della camera CCD (che nel caso della Apogee Ap7p è posto a circa 3080 ADU).

Notiamo immediatamente un'altra cosa importante: il tratto non lineare inizia prima che la curva di linearità raggiunga uno qualsiasi dei due livelli di saturazione: dunque l'operatore non ha nessuna avvertenza o segnalazione di quanto sta avvenendo. Per questo è importantissimo determinare in modo sperimentale le coordinate del punto P.

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Contrail before 1995 before 1995 Contrail II

Continues Wheeled material that shows how contrails are known - and photographed - a long time. Another documented example and 'an article dating back to 1974 , dedicated to the analysis of a series of observed contrails in the skies of America; complete reference: TG Konrad, JC Howard, "Multiple Contrail Streamers Observed by Radar", Journal of Applied Meteorology, vol. 13, 563-572, 1974 .

Without discussing the article, reporting directly to a series of photos in it (with captions):

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I continue with the recovery of materials relating to research on the contrail (condensation trails) in past decades. And I 'have seen, among many supporters of the alleged evidence of "chemtrails", a strong increase in the use of the argument that before a certain date (1995) basically there were no contrails in the sky. Until you get to real challenges, retrieve old photos to show you they were contrails (not counting the obvious point, namely that in the past decades the traffic was much less than today).

As already ' I started doing this blog, the answer to this question is 'much more' simple. In fact in the scientific literature over the years there 'has been a growing attention to the phenomenon of condensation trails, mostly out of concern that with the increase in air traffic, the relative increase in contrail formation could lead to climatic changes ( leading to increased cloud cover, thus blocking a certain percentage of solar radiation). In many studies published even before the '90s, is a clear indication of condensation trails, how are visible and common, but how often is persistent over time.

Turning to practical examples, in a study of 1975 proposes the study of the contrail found in some satellite images of the island of Cyprus (full reference: Joseph JH, Levin Z, Y, Mekler, G Ohring, J. Otterman, "Study of contrails Observed from ERTS-1 satellite imagery", J. Geophys. Res, 1975, vol. 80, no. 3, 366-372 ). , The article reports - should be repeated - explicitly as the contrail formation of both normal and as the trails can be persistent enough to develop into cirrus clouds:

in Some Areas of heavy jet traffic, contrails released by a number of Aircraft May spread to cover a portion of the sky With thin cirrus-type clouds. The Possibility That May Such contrails lead to an increase in the average amount of high cloudiness and that such an increase of clouds may affect the earth's weather and climate has been raised [Murcray, 1970; Machta and Carpenter, 1971].

A parte questo, nel paper si ritrova una delle immagini satellitari usate:


Per la precisione, si noti che le immagini sono state prese nel 1972.

Un altro esempio e' uno studio del 1970 , sempre focalizzato su come le scie di condensazione possano influire sul clima (reference completa: PM Kuhn, "Airborne Observations of Contrail Effects on the Thermal Radiation Budget",Journal of the Atmospheric Sciences, 1970, vol. 27, 937-942 ). Anche in questo caso vale la pena di estrarre alcuni passaggi che rendono palese come le contrail fossero abbondantemente note, osservate e studiate:

The spreading out of jet contrails into extensive cirrus sheets is a familiar sight. Often, when persistent conditions exist from 25,000 to 40,000 ft, several long contrails increase in number and gradually merge into an almost solid interlaced sheet.

Nell'articolo si riportano dunque alcune fotografie di contrail, in territorio statunitense, come ad esempio:


La foto risale al 1969.

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The dynamic range

Il range dinamico di una camera CCD indica la capacità di distinguere oggetti molto luminosi e molto deboli nella stessa immagine. I costruttori di CCD definiscono matematicamente il range dinamico con il seguente rapporto:

DR = FWC / RON

dove abbiamo indicato il range dinamico con DR , la full well capacity con FWC e il readout noise con RON , entrambi espressi in elettroni per fotoelemento quindi il range dinamico è una quantità adimensionale. Più questo numero è elevato, maggiore è la capacità della camera CCD di distinguere differenti livelli d'intensità luminosa. Chiaramente per aumentare il range dinamico è necessario agire o sulla qualità del sensore (ovvero con un basso RON ) o sulla dimensione dei photoelements its component which is closely linked to the FWC .

The dynamic range is also expressed in decibels:

Note that the readout noise to be used for this calculation is not usually indicated in the data-sheet of the sensor (also called RON "On-chip, generally less the total readout noise of the entire CCD camera). The type of readout noise that we used in the calculation is exactly what the total given in the specifications of the chamber. Just to be clear is that we actually measured previously with the analysis of the bias frame.

Example: to focus the telescope di Cavezzo è posta una telecamera Apogee Ap7p con sensore SiTE. I fotoelementi quadrati di dimensione 24 micron hanno una Full Well Capacity di circa 300000 elettroni. Il readout noise della camera CCD è di 11,9 elettroni. Calcolarne il range dinamico.

DR = 300000/11,9 = 25210

Con questa camera CCD è possibile riprendere sorgenti luminose che differiscono tra loro di oltre 25000 volte (con una pellicola fotografica per esempio la differenza si riduce a 100 volte).
La dinamica misurata in decibel si calcola facilmente:

DR db = 20 log (300000/11,9) = 20 log(25210) = 88.0 db

This report also gives an indication of the minimum level of digitization that is to apply for the best use of the sensor: in the following table we see that the CCD camera in the previous example is one of the 14 and 15 bits. Apogee's engineers have opted for an A / D converter with 16-bit and setting the gain to 4.5 e-/ADU.


The fact that they have a CCD camera "16-bit" is misleading and might think you have the ability to shoot images with a range of more than 65,000 levels of gray. In fact, as we have seen from the example above, the dynamics in the specific case of Apogee Ap7p is "only" 25,210 levels and is only determined by two characteristics full well capacity and readout noise .

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Study on the contrails of 1970

Molto spesso I find phrases given to the effect that contrails created by aircraft have increased exponentially, filling the sky, which now appear clearly too profusely, suggesting - or explicitly saying - that in an unspecified past were not so '. Obviously, such claims are never accompanied by objective data or evidence (I 'by obvious considerations on change of entity' in air traffic over time). So, as you can 'make an idea of \u200b\u200bthe situation?

As a first contribution to tackling this question, report a 1970 publication: B. Wallace Murcray,
"On the Possibility of weather modification by aircraft contrails" (full reference: MURCRAY, W.B., 1970: ON THE POSSIBILITY OF WEATHER MODIFICATION BY AIRCRAFT CONTRAILS. Mon. Wea. Rev., 98, 745–748. )

Riporto il paragrafo introduttivo di questo studio:

Aircraft contrails first attracted public attention during
World War II; but as air traffic has built up to its present
level, they have come to be accepted as part of the environment.
Even during World War II, it was difficult to watch
the cloud cover laid down by a large bomber formation
without wondering what it might be doing to the weather;
at present, there is widespread belief among the general
public and some feeling among scientists (Fletcher 1969,
Reinking 1968, Livingston 1969, and Schaefer 1969) that
contrails are increasing cloudiness, if nothing more, in
some regions. The writer himself has seen instances in
which a single contrail seemed to grow until it became an
overcast covering the whole sky. If the contrail were indeed
responsible, which is by no means certain, this would
constitute definite proof that contrails are capable of a
significant effect on local weather, and even possibly on
global climate, if such occurrences are widespread and
frequent. It seems worthwhile, in view of all this, to
consider quantitatively whether or not there is reason to
believe contrails are capable of exerting a significant influence
on weather.

Even without retrieving other parts of the document, that 'emerging and' quite pronounced. Contrails are certainly not something that 'suddenly appeared in recent years. The author shows how since the Second World War had something particularly eye-catching, so then it becomes something "to be accepted as part of the environment", an event that is so 'normal to be perceived as an integral part of the environment that we surroundings. Recalling that the writing and 'in 1970, it is clear that the trails are a phenomenon present, famous and known for some time, or rather, when and' developed the technology of aviation. Not only that: it is also reported that contrails can essere persistenti, ed evolversi fino a diventare vere e proprie nuvole. Questa osservazione e' molto rilevante, dato che un'altra accusa che ho spesso incontrato riguarda il fatto che le scie di "oggi" restino visibili a lungo e che si espandano progressivamente, dunque per questo non siano normali scie di condensazione. In realta', anche per questo punto e' noto da tempo, e da tempo studiato, il fatto che le contrails possano essere persistenti, ed evolversi allargandosi fino a non essere riconoscibili rispetto ad altre normali nuvole.

Non solo: questi elementi fanno modo che sin dai tempi di questo scritto ci sia posti il dubbio dell'impatto ambientale del traffico aereo e delle scie di condensazione che creano; quello che in maniera intuitiva and little depth is observed from Murcray, will be 'the subject of many investigations in the future. In fact there are many studies since the early '90s, I found (I will report 'depth in the future) and deal with the impact of contrails on clouds, and thus the possible contribution to climate change, particularly how they can participate in the so-called Greenhouse Effect.

conclusion, in summary: those who say that the wakes formed by the planes are a recent phenomenon, or is otherwise relevant become a phenomenon recently, makes a mistake, those who argue that the contrail must necessarily be small and vanish soon time (otherwise you are expected to be something "different"), he lies.

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How to calculate the gain and readout noise

Now that we know the meaning of gain and readout noise to a CCD camera, we see how we can determine the value if these quantities were not reported in the literature that accompanies our device.

There is a very simple and quick to make, though not very accurate, however we will give a reliable estimate of these two quantities.

Once installed on the CCD camera telescope, simply take two flat field, [F1] and [F2] and two BIAS FRAME [B1] and [B2]. ( Note: always use this convention to indicate a "frame" of the CCD camera, or that to enclose the identifier in square brackets: it is an array of numbers and not a single numerical value, this will be useful for easy reading of the mathematical formulas used here ).

The only important warning about the flat field: they shall not be a sky-flat in the highly unlikely the two flat field will have exactly the same illumination as will have been taken at different times and therefore with a luminosity del cielo differente. E' necessario riprendere due flat field con la tecnica del dome-flat ovvero utilizzando una sorgente luminosa stabile e costante.

Una volta ripresi e salvati su disco i due flat field e bias frame, utilizzando Astroart possiamo aprire le finestre della statistica per ogni frame ed annotarne il valore medio: indicheremo questi valori ripettivamente con avg[F1] , avg[F2] , avg[B1] e avg[B2] .

A questo punto sottraiamo un flat field con l'altro, cioè utilizzando il comando Matematica > Sottrai di Astroart eseguiamo l'operazione [F1]-[F2] . We'll get a completely black frame looking as if all the pixels have a null value: in fact they are the thresholds for display of the image that must be regulated and do it quickly and automatically, simply click your mouse on the bar status of the image. You should get a representation of the "noise map " in the flat field as in the image below.

However it is not the graphical representation we are interested because its numerical value: return to open the annotiamoci statistics and the standard deviation: the denote by ds ([F1] - [F2]) . Repeating the same steps for the two bias frames will get the value ds ([B1] - [B2]) .

Now we have all the information needed to apply the following formula to calculate the gain:

while applying the following to calculate the readout noise:

always remember that the gain is expressed in electrons / ADU and the readout noise is expressed in electrons.

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The "gain" and "full well capacity"

Before setting out the important subject of gain of a CCD camera, we introduce an equally important characteristic of a CCD: the Full Well Capacity . The photoelements that make up the matrix of a CCD can be viewed as microscopic containers of electrons: the number of electrons that can fit in each photoelement is usually indicated by the manufacturers of CCD with the term Full Well Capacity (FWC). The analogy of the container is more suitable if we think that the larger the size of photoelement, the greater its ability to contain electrons. So for example a sensor KAF-0401E of Kodak composed photoelements 9 micron square of side a FWC of about 100000 and the sensor-SITE Room Apogee Ap7p has photoelements square size of 24 microns with a FWC of about 300,000 e-. E ' clear that when a light sensor is no longer able to contain electrons, the CCD camera will no longer be able to count them: the system has reached saturation. But that is another topic that we will see later.

The gain of a CCD camera is a number that expresses how many electrons per ADU in the image are generated from the same room. Recall that with ADU (Analog to Digital Unit ) denote the unit of luminous intensity of a pixel CCD. In practice the number corresponding to the pixels of a digital image.

The gain is a parameter that is set by the manufacturer of the CCD camera according to the choice the analog-digital converter: electrons captured during the exposure are converted to ADU integrity ADC (Analog to Digital Converter or analog to digital converter). The "accuracy" of this converter is measured in bits: the higher the number of bits of the converter, the greater the device's ability to distinguish the signal in electrons formed by the exposure of CCD 12 bit = 2 ^ 12 = 4096 values, 15 bit = 2 ^ 15 = 32768, 16 bit = 2 ^ 16 = 65536 values, etc. ..

A method for determining the gain to be used in a particular CCD camera is to compare the FWC photoelements of the sensor with the largest number that can count the analog-digital converter: thus, for example, assuming the sensor chamber SITE Apogee Ap7p (FWC = 300000 and-drive with a 16-bit), we have:

gain = 300000/65536 = 4.6 e-/ADU

And in fact in the data-sheet of the CCD camera are shown a gain of 4.4 e-/ADU: This value is then set correctly to take advantage of the characteristics of the analog-digital converter based on ability that each photoelement to collect electrons.

should make sure, however: the gain is also the minimum unit of discretization, namely that the system is unable to distinguish lower values \u200b\u200bto it (eg a number of electrons below 4.4 as above). This fact introduces a new concept of noise: the sound of discretization. The higher the gain, the greater the noise dicretizzazione. This type of noise can be important because it affects the precision of photometric measurements, especially in the faint and extended objects like comets and galaxies.

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The "readout noise "The Flat Field

The readout noise and readout noise is expressed in terms of electrons per pixel introduced into the final signal that occurred after the reading of the CCD. This is the first major source of "noise" with which we will inevitably coexist because generated by the same electronic components of the CCD camera.

Being a noise, can not have a precise value: mathematicians use to describe a particular function: the Gaussian curve or Gaussian :

Certainly at first sight, such a formula can be frightening, but " traduciamola "in a chart:

The chart above shows an example three Gaussians with the typical bell shape, all centered on the same average value (the Greek letter" mu ") zero, but of different sizes (the Greek letter sigma squared) that " variance. The variance is a measure of dispersion of data and there gives an immediate indication of the amount of "noise" in our data sample: the higher the variance, the wider the bell and noisier is the data in our possession. However, rather than using the variance, usually to indicate the dispersion of a set of data using its square root ("sigma") usually referred to as a standard deviation . All this we have seen in a simple practical application when we have addressed the topic of BIAS FRAME and in particular how to obtain the READ FRAME NOISE .

Returning to the formation of the readout noise, we can see that consists of two componenti:

1. la conversione di un segnale analogico in un numero non è mai perfettamente ripetibile: sia gli amplificatori integrati sul sensore che i convertitori analogico-digitali producono una distribuzione statistica di possibili risultati centrati su di un valore medio. Quindi anche nell'ipotetico caso di poter leggere lo stesso pixel due volte con la stessa identica carica, potrebbe produrre due valori leggermente differenti l'uno dall'altro.
2. l'elettronica stessa che compone la camera digitale può introdurre elettroni di disturbo nell'arco dell'intero processo di lettura e conversione portando inevitabilmente a fluttuazioni casuali del risultato finale di lettura.

La media di queste two components of uncertainty is what we call the readout noise. In the commercial
CCD readout noise can vary from 5 to over 20 e-/pixel. Obviously the lower this value the better the CCD camera in question. In particular, the CCD with a high readout noise are not suitable when you need to use the technique of the sum or average of multiple images to increase the signal to noise ratio: the final image will not have the same quality of a single long exposure of the same total time of integration, since each image will bring with them the contribution of the readout noise for each pixel that will contribute to the sum or average.