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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.

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The Flat Field is an image of a perfectly uniform field of light intensity. The flat field is then used in the pretreatment of astronomical images to eliminate two major flaws: the difference in sensitivity that inevitably there may be another one-pixel CCD sensor and the various non-uniformity of field generated by the optical telescope and the dirt often can accumulate in the vicinity of the focal plane of our instrument.

We must say that is not a simple thing to achieve because you have to be really sure that the field of view is entirely consistent. There are essentially two ways to get it:

1. resume a sufficient area of \u200b\u200bthe sky luminosa durante l'alba o il tramonto ma lontani dal sole per evitare gradienti di luminosità (sky-flat);
2. riprendere uno schermo bianco ed uniforme allestito nelle pareti della cupola opportunamente illuminato (direttamente o indirettamente) con una sorgente luminosa bianca e costante (dome-flat).

Comunque la si ottenga l'immagine finale del FLAT FIELD deve avere una caratteristica molto importante: avere un elevato rapporto segnale-rumore. Ricordiamo infatti che ogni qualvolta faremo un'operazione matematica su due o più immagini (come la divisione del FLAT FIELD), i "rumori" presenti nelle immagini si sommeranno quadraticamente. Se avremo dei FLAT FIELD con un basso rapporto segnale-rumore, rischieremo di andare a peggiorare ancor di più le immagini che desideriamo correggere. In pratica occorre che il valore medio dei pixel che lo compongono sia almeno intorno ai 2/3 dell'effetiva dinamica dell'immagine. Se per esempio sappiamo che una camera CCD si comporta linearmente tra i valori di 3000 e 55000 ADU, il valore medio del FLAT FIELD può ragionevolmente attestarsi sui 35000 ADU o più (senza ovviamente superare i 55000 ADU).
Ricordiamo inoltre che occorre prendere una serie di FLAT FIELD (da combinare successivamente con una mediana ed ottenere così il MASTER FLAT FIELD) per ogni combinazione ottica utilizzata per le riprese delle immagini GREZZE. Vale a dire che se utilizziamo ad esempio tre filtri B V ed R per fare la tricromia di un oggetto celeste, need to resume after three sets of flat fields, one for each filter used. Not only that, if during the filming must change the focus of the instrument, necessarily need to resume the series of flat fields taken with the new configuration of fire. Basically, whenever you need to change the optical instrument, you must return the corresponding flat field for the optical configuration.

MASTER A typical flat-field taken with the Cavendish Centre in Newton 0.4m telescope. f/5.5 through the filter of the Johnson-Cousins \u200b\u200bV and the technique of SKY-FLAT. Note the remarkable uniformity of field, the presence of some grains of powder out of focus (with the classic form of a ring with a hole) and groups of pixels "cold."

Both methods for the acquisition of flat fields have their advantages and / or disadvantages that we discuss in brief. We remember only that it is necessary in both cases use the telescope in the firing position used to take pictures: it is saying that it is necessary to make a series of flat fields for each filter used.

SKY-FLAT

• should choose by an area of \u200b\u200bsky possible barren and return the set of FLAT-SKY or the pursuit off or telescopic rapidly changing field in a pose and the next in a way that it never the same field stars. This will allow us then, using the median of the series combination of SKY-FLAT, to obtain a master flat field without the disturbance caused by the presence of field stars.
• should be included in the narrow range of twilight and then the time available may be very little, especially if it is necessary to take many series of flat with different filters.
• During the twilight sky of the intensity changes rapidly with the risultato che otteremo delle serie di SKY-FLAT con valori medi anche molto differenti l'uno dall'altro: questo fatto falserebbe irrimediabilmente la successiva combinazione con mediana della serie per ottenere il MASTER FLAT FIELD. Ad esempio, l'eventuale presenza di stelle nelle singole immagini, non verrebbe eliminata con l'operazione mediana. Per risolvere questo problema, prima di applicare la combinazione a mediana, occorre riscalare tutte le immagini su uno stesso valore medio (ad es. con Astroart è possibile utilizzare una macro con il comando Immagine > Normalizza background ).
• Lo sky-flat ha la risposta spettrale più naturale per la correzione delle immagini con il MASTER FLAT FIELD: To get it you use the same light source used for RAW images the sky background or the same!
  

Here's what a typical SKY-FLAT taken together with other 9 to get the MASTER FLAT FIELD visible above.

DOME-FLAT

• The main disadvantage of the dome-flat is that you must equip themselves and strive to obtain it: the solutions are many and depend very much on the instrumentation that we have and how we structured our osservatorio, ad esempio se siamo fortunati possessori di una struttura fissa con cupola oppure abbiamo un piccolo osservatorio mobile attrezzato per spedizioni outdoor. In quest'ultimo caso può essere utile il progetto di Giovanni Benintende visibile al link http://www.astrogb.com/art_flatbox.htm .
• Nel caso dell'Osservatorio di Cavezzo invece, in prossimità dell'apertura della cupola viene allestito uno schermo di plexiglass simile al vetro smerigliato: una sogente di luce bianca esterna viene accesa ad una distanza sufficiente ad illuminare lo schermo in modo adeguato ed uniforme. A questo punto è possibile puntare il telescopio sullo schermo (dal quale è distante poche decine di centimetri) e riprendere le sequenze di dome-flat con il tempo d'esposizione necessario ed in tutta tranquillità.
• Un altro svantaggio, forse maggiore del primo per chi fa fotometria, è dato dalla risposta spettrale della sorgente di luce utilizzata che non sarà mai in grado di riprodurre esattamente quella del fondo cielo.