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Geometric properties of sensors: 4 - The Field

Conoscendo il campionamento e il numero dei fotoelementi per lato, automaticamente conosciamo il campo coperto dal sensore utilizzando un determinato telescopio.

Esempio: al fuoco del telescopio di Cavezzo è posta una telecamera Apogee Ap7p con sensore SiTE 512x512 fotoelementi quadrati di dimensione 24 micron. Qual'è la dimensione del campo celeste coperta dal sensore?
Dagli esempi riportati nella sezione campionamento sappiamo che ogni fotoelemento copre 2.24 secondi d'arco di cielo per lato dunque avremo 512*2.24 = 1146.9 secondi darco = 19.1 primi d'arco per lato.

Esistono parecchi siti e programmi gratuiti per calcolare in modo semplice ed automatico il campionamento e/o il campo coperto da una determinata combinazione di telescopi e camere CCD commerciali. Uno dei migliori a mio avviso è CCDCalc di Ron Wodaski , scaricabile in questo link .

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BIAS FRAME

Il BIAS FRAME altro non è che un DARK FRAME , ovvero un'immagine CCD ripresa con tutte le ottiche coperte da uno schermo nero, con tempo d'esposizione nullo. In molte camere CCD, come nelle DSLR, il tempo d'esposizione nullo non esiste: in tal caso una buona approssimazione può essere il tempo minimo d'esposizione permesso dall'hardware o dal software. Ad esempio la camera Apogee Ap7p in dotazione all' Osservatorio di Cavezzo permette esposizioni minime di 0,02 secondi, quanto basta per rendere trascurabile la minima quantità di corrente di buio creata nei due centesimi di secondo d'esposizione. Piuttosto, è di gran lunga più importante la corrente di buio accumulata negli ultimi pixel scaricati durante necessary for the second reading of the CCD which is never instantaneous, especially when the chips are large (eg> 1 megapixel ): this may lead to the formation of a gradient of brightness in the vertical image.

As we have already seen the introduction of the dark frame, the main use of the bias frame is to get the THERMAL FRAME that is the only component of the CCD which is directly proportional to exposure time and / or temperature 'exercise of the CCD. From this you can "rescale" (multiplying the pixels for a suitable constant) a thermal frame of a given exposure time to obtain another with a different exposure time equivalent. However, when you have the possibility is always convenient to take the dark frames with the same exposure time used to shoot RAW images.

Another equally important use of the bias frame is that it gives us the opportunity to make an initial diagnosis of our CCD camera.

image above you can see a bias frame "ideal": a perfect carpet of uniform noise with no structure or change in brightness. The histogram is a thin bell symmetrically centered on the average value (in this case 3145). Drawing a vertical profile (using the command Visualizza > Profilo di Astroart ) si ottiene un grafico perfettamente orizzontale oscillante ancora una volta nell'intorno del valore medio precedente.

Nell'immagine sotto vediamo invece un BIAS FRAME un po' più realistico e con alcuni difetti non del tutto trascurabili: innanzi tutto, le prime 3-4 righe di pixel in alto sono più luminose, identificando una probabile zona di accumulo di cariche; in secondo luogo, al semplice colpo d'occhio, è evidente una "struttura" più o meno regolare a linee orizzontali generate da interferenze elettromagnetiche e un chiaro gradiente di luminosità che intensifica queste linee mano a mano ci si avvicina alle ultime righe in basso del BIAS FRAME. Queste righe are brighter because of the "hump" on the right of the bell visible in the histogram. Then plotting the vertical profile of the image is then even more clearly the presence of a gradient of brightness caused by the accumulation of heat load during the "download" image from the CCD to the PC.


It 'clear that the closer you get to the ideal situation and "best" is our CCD camera. But there is a fundamental parameter, intrinsically linked to the bias frame, which can give us a first important information on the images that we can achieve with our CCD camera: the readout noise or read noise. " As we shall see, the read noise is one of the main sources of noise present in a CCD image and is closely linked to the actual dynamics can be obtained by a CCD camera.

For now we see how we can estimate the readout noise of our CCD camera using a set of bias frame.

course all digital images "hide" between a pixel read noise: BIAS FRAME perfect is what comes closest to its structure, however, as we have seen, we can hardly get closer to perfection: there is always some unwanted signal interference . To minimize these unwanted signals can use a trick: we take some bias frame (a dozen could fit) the one teniamo da parte mentre degli altri nove otteniamo un "master" BIAS FRAME ovvero li combiniamo insieme facendone la mediana (ad es. utilizzando il comando Strumenti > Pretrattamento di Astroart ).

Ora sottraiamo la mediana dal singolo BIAS FRAME: ciò che otteniamo è un READ NOISE FRAME ovvero una riproduzione del solo rumore di lettura della nostra camera CCD (immagine sopra). Anche se purtroppo rimane amcora traccia delle strutture orizzontali causate dai disturbi elettromagnetici, queste in realtà sono di debole intensità come ci conforta la visione dell'istogramma rappresentato da una campana quasi perfetta. Come abbiamo già visto , la standard deviation, or the width of the bell, gives us a numerical estimate of the noise present in the frame, about 2.7 ADU (ADU is the unit used to denote the value of the pixel after scanning, or after processing by a potential difference to a whole number determined by the analog to digital converter of the CCD camera). But the read noise is usually reported by the manufacturers in electrons (per pixel) to transform the value from ADU to the corresponding electrons need to know the gain of the CCD camera, which is also often reported in the paper the characteristics of CCD camera, or how many electrons corresponds to an ADU. Ap7p supplied for Apogee Centre to Cavendish e-/ADU that the gain is 4.4 multiplied by 2.7 is approximately 11.9-and readout noise (the data-sheet says dell'Apogee 10.2 e-).

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Noise

brings us to introduce one of the most controversial topics for the young amateur digital noise.
One might be inclined to think that the dark frame is a form of "noise" to be removed from our raw images, not exactly. The dark frame is a signal: a sign of trouble but still a signal: the signal generated by dark current emitted by the CCD camera (or DSLR) at a given temperature and for a given exposure time. And luckily it's a sign! Luckily because, if we make the sensor work in the same conditions of exposure and temperature that we used to take the ' RAW image, this signal is "almost" perfectly reproducible.

But it is in that "almost" hiding, sneaky, the concept of noise .

provided evidence to back two dark frames in exactly the same conditions (same exposure time and same temperature). Now carefully analyze them pixel by pixel: are identical? Each pixel of coordinates (x, y) in the first dark frame has the same value in the corresponding pixel of the second dark frames? Certainly not. Of this we know it better by doing a simple subtraction: if we subtract the dark frame from the first second (or vice versa) will result in a new image with the pixel value around zero but not exactly all zero as you might expect.

Astroart has the essential tools for numerical analysis of the images as the histogram and the statistics window.

To better analyze this phenomenon we can generate a histogram: a histogram, the better we will see later, is a chart with the x-axis values \u200b\u200bof the pixels in the image in ascending order, and ordered the number pixel with that certain value. Well, the histogram of our image in the shape of a bell, with the peak at the value zero. This means that most of the pixels in the image have zero value, but many others have non-zero values, in the slightly greater than zero and some slightly less than zero. The bell shape is due to the fact that the more one deviates from the average pixel value (zero in this case), the lower the number of pixels in the image with that particular value. Ideally, if we had a perfect CCD camera, capable of playing two dark frames exactly alike, stealing from each other, we would get an image composed of all the pixels identically zero. It 's easy to see that the histogram of this image would be composed of a single column at the zero height equal to the number of pixels in the image. It is even more easy to deduce that the amplitude of the bell has a certain relation to the distribution of nonzero values \u200b\u200band thus is directly related to noise present in images taken with our CCD camera. The standard deviation , the statistics of the image shown in the box, it gives a direct measure of the dispersion of pixel values \u200b\u200bin the neighborhood of the average value (zero) and is therefore a quantity related to the "noise" image: the higher the standard deviation, the greater is the dispersion, the greater the "noise" that accompanies these images. Hence the concept of "noise" must be understood as a series of events that never allow the CCD to reproduce an image exactly equal to each other while operating in exactly the same conditions. In this case we used two identical dark frames but the same reasoning applies to any pair of FRAME taken using a CCD camera, two RAW images of any object in the sky, two flat field, two bias frame and so on.: We will never get two FRAME exactly equal to each other.
But what is worse is that we're going to do any math operation with the frames, such as the removal of DARK FRAME RAW image, so we're going to steal the map of thermal noise and BIAS RAW image, but also we're going to aggregate the noise in the two frames. What are the sources of noise and how can we do to minimize (note: we can only minimize and do not remove it entirely) the contribution of noise in the final image we will see in future posts.