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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.