Overscan and bias

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In an attempt to provide an estimate of the value produced by an empty or unexposed pixel within a CCD, calibration measurements of the bias level can be used.1 Bias or zero images allow one to measure the zero noise level of a CCD. For an unexposed pixel, the value for zero collected photoelectrons will translate, upon readout and A/D conversion, into a mean value with a small distribution about zero.2 To avoid negative numbers in the output image,3 CCD electronics are set up to provide a positive offset value for each accumulated image. This offset value, the mean "zero" level, is called the bias level. A typical bias level might be a value of 400 ADU (per pixel), which, for a gain of 10e-/ADU, equals 4000 electrons. This value might seem like a large amount to use, but historically temporal drifts in CCD electronics due to age, temperature, or poor stability in the electronics, as well as much higher read noise values, necessitated such levels.

1 For more on bias frames and their use in the process of CCD image calibration, see Chapter 4.

2 Before bias frames, and in fact before any CCD frame is taken, a CCD should undergo a process known as "wiping the array." This process makes a fast read of the detector, without A/D conversion or data storage, in order to remove any residual dark current or photoelectron collection that may have occurred during idle times between obtaining frames of interest.

3 Representation of negative numbers requires a sign bit to be used. This bit, number 15 in a 16-bit number, is 0 or 1 depending on whether the numeric value is positive or negative. For CCD data, sacrificing this bit for the sign of the number leaves one less bit for data, thus reducing the overall dynamic range. Therefore, most good CCD systems do not make use of a sign bit. One can see the effects of having a sign bit by viewing CCD image data of high numeric value but displayed as a signed integer image. For example, a bright star will be represented as various grey levels, but at the very center (i.e., the brightest pixels) the pixel values may exceed a number that can be represented by 14 bits (plus a sign). Once bit 15 is needed, the signed integer representation will be taken by the display as a negative value and the offending pixels will be displayed as black. This is due to the fact that the very brightest pixel values have made use of the highest bit (the sign bit) and the computer now believes the number is negative and assigns it a black (negative) greyscale value. This type of condition is discussed further in Appendix.

To evaluate the bias or zero noise level and its associated uncertainty, specific calibration processes are used. The two most common ones are: (1) overscan regions produced with every object frame and (2) usage of bias frames. Bias frames amount to taking observations without exposure to light (shutter closed), for a total integration time of 0.000 seconds. This type of image is simply a readout of the unexposed CCD pixels through the on-chip electronics, through the A/D converter, and then out to the computer producing a two-dimensional bias or zero image.

Overscan strips, as they are called, are a number of rows or columns (usually 32) or both that are added to and stored with each image frame. These overscan regions are not physical rows or columns on the CCD device itself but additional pseudo-pixels generated by sending additional clock cycles to the CCD output electronics. Both bias frames and overscan regions are techniques that allow one to measure the bias offset level and, more importantly, the uncertainty of this level.

Use of overscan regions to provide a calibration of the zero level generally consists of determining the mean value within the overscan pixels and then subtracting this single number from each pixel within the CCD object image. This process removes the bias level pedestal or zero level from the object image and produces a bias-corrected image. Bias frames provide more information than overscan regions, as they represent any two-dimensional structure that may exist in the CCD bias level. Two-dimensional (2-D) patterns are not uncommon for the bias structure of a CCD, but these are usually of low level and stable with time. Upon examination of a bias frame, the user may decide that the 2-D structure is nonexistent or of very low importance and may therefore elect to perform a simple subtraction of the mean bias level value from every object frame pixel. Another possibility is to remove the complete 2-D bias pattern from the object frame using a pixel-by-pixel subtraction (i.e., subtract the bias image from each object image). When using bias frames for calibration, it is usually best to work with an average or median frame composed of many (10 or more) individual bias images (Gilliland, 1992). This averaging eliminates cosmic rays,1 read noise variations, and random fluctuations, which will be a part of any single bias frame.

Variations in the mean zero level of a CCD are known to occur over time and are usually slow drifts over many months or longer, not noticeable changes from night to night or image to image. These latter types of changes

1 Cosmic rays are not always cosmic! They can be caused by weakly radioactive materials used in the construction of CCD dewars (Florentin-Nielsen, Anderson, & Nielsen, 1995).

indicate severe problems with the readout electronics and require correction before the CCD image data can be properly used.

Producing a histogram of a typical averaged bias frame will reveal a Gaussian distribution with the mean level of this distribution being the bias level offset for the CCD. We show an example of such a bias frame histogram in Figure 3.8. The width of the distribution shown in Figure 3.8 is related to the read noise of the CCD (caused by shot noise variations in the CCD electronics (Mortara & Fowler, 1981)) and the device gain by the following expression:

Note that a is used here to represent the width (FWHM) of the distribution not the usual definition for a Gaussian shape. For example, in Figure 3.8, a = 2 ADU.

1.00E5

80000

60000

40000

20000

T | i-1 i | r i i | i i i | i i r j_i_i_I I I _i_i_I_i_i_i_I_i_i_ ' I _i_i_L

1012 1014 1016 1018 1020 1022

Fig. 3.8. Histogram of a typical bias frame showing the number of pixels vs. each pixel ADU value. The mean bias level offset or pedestal level in this Loral CCD is near 1017 ADU, and the distribution is very Gaussian in nature with a FWHM value of near 2 ADU. This CCD has a read noise of 10 electrons and a gain of 4.7e-/ADU.

3.8 CCD gain and dynamic range

The gain of a CCD is set by the output electronics and determines how the amount of charge collected in each pixel will be assigned to a digital number in the output image. Gain values are usually given in terms of the number of electrons needed to produce one ADU step within the A/D converter. Listed as electrons/Analog-to-Digital Unit (e-/ADU), common gain values range from 1 (photon counting) to 150 or more. One of the major advantages of a CCD is that it is linear in its response over a large range of data values. Linearity means that there is a simple linear relation between the input value (charge collected within each pixel) and the output value (digital number stored in the output image).

The largest output number that a CCD can produce is set by the number of bits in the A/D converter. For example, if you have a 14-bit A/D, numbers in the range from zero to 16 383 can be represented.1 A 16-bit A/D would be able to handle numbers as large as 65 535 ADU.

Figure 3.9 provides a typical example of a linearity curve for a CCD. In this example, we have assumed a 15-bit A/D converter capable of producing output DN values in the range of 0 to 32 767 ADU, a device gain of 4.5e-/ADU, and a pixel full well capacity of 150 000 electrons. The linearity curve shown in Figure 3.9 is typical for a CCD, revealing that over most of the range the CCD is indeed linear in its response to incoming photons. Note that the CCD response has the typical small bias offset (i.e., the output value being nonzero even when zero incident photons occur), and the CCD becomes nonlinear at high input values. For this particular CCD, nonlinearity sets in near an input level of 1.17 x 105 photons (26000 ADU), a number still well within the range of possible output values from the A/D.

As we have mentioned a few times already in this book, modern CCDs and their associated electronics provide high-quality, low-noise output. Early CCD systems had read noise values of 100 times or more of those today and even five years ago, a read noise of 15 electrons was respectable. For these systems, deviations from linearity that were smaller than the read noise were rarely noticed, measurable, or of concern. However, improvements that have lowered the CCD read noise provide an open door to allow other subtleties to creep in. One of these is device nonlinearities. Two types of nonlinearity are quantified and listed for today's A/D converters. These are integral non-linearity and differential nonlinearity. Figure 3.10 illustrates these two types of A/D nonlinearity.

1 The total range of values that a specific number of bits can represent equals 2(number of blts), e.g.,

214 = 16384. CCD output values are zero based, that is, they range from 0 to 2<number of bits) - 1.

Fig. 3.9. CCD linearity curve for a typical three-phase CCD. We see that the device is linear over the output range from 500 ADU (the offset bias level of the CCD) to 26 000 ADU. The pixel full well capacity is 150 000 electrons and the A/D converter saturation is at 32 767 ADU. In this example, the CCD nonlinearity is the limiting factor of the largest usable output ADU value. The slope of the linearity curve is equal to the gain of the device.

Fig. 3.9. CCD linearity curve for a typical three-phase CCD. We see that the device is linear over the output range from 500 ADU (the offset bias level of the CCD) to 26 000 ADU. The pixel full well capacity is 150 000 electrons and the A/D converter saturation is at 32 767 ADU. In this example, the CCD nonlinearity is the limiting factor of the largest usable output ADU value. The slope of the linearity curve is equal to the gain of the device.

A/D converters provide stepwise or discrete conversation from the input analog signal to the output digital number. The linearity curve for a CCD is determined at various locations and then drawn as a smooth line approximation of this discrete process. Differential nonlinearity (DNL) is the maximum deviation between the line approximation of the discrete process and the A/D step used in the conversion. DNL is often listed as ±0.5 ADU meaning that for a given step from say 20 to 21 ADU, fractional counts of 20.1,

Differential Nonlinearity (+/-0.5)

Input (electrons) Input (electrons)

Fig. 3.10. The two types of CCD nonlinearity are shown here in cartoon form. Differential nonlinearity (left) comes about due to the finite steps in the A/D conversion process. Here we see that the linearity curve (dashed line) cuts through each step at the halfway point yielding a DNL of ±0.5 ADU. Integral nonlinearity (right) is more complex and the true linearity curve (solid line) may have a simple or complex shape compared with the measured curve (dashed line). A maximum deviation (N) is given as the INL value for an A/D and may occur anywhere along the curve and be of either sign. Both plots have exaggerated the deviation from linearity for illustration purposes.

20.2, etc. up to 20.499 99 will yield an output value of 20 while those of 20.5, 20.6, etc. will yield an output value of 21. Astronomers call this type of nonlinearity digitization noise and we discuss it in more detail below. Integral nonlinearity (INL) is of more concern as it is the maximum departure an A/D will produce (at a given convert speed) from the expected linear relationship. A poor quality A/D might have an INL value of 16 LSB (least significant bits). The value of 16 LSB means that this particular A/D has a maximum departure from linearity of 4 bits (24 = 16) throughout its full dynamic range. If the A/D is a 16-bit device and all 16 bits are used, bits 0-3 will contain any INL at each ADU step. If one uses the top 12 bits, then bits 4-7 are affected.

How the INL comes into play for an observer is as follows. For a gain of say 5 electrons/ADU, an INL value of 16 can cause a nonlinear deviation of up to 80 electrons in the conversion process at its maximum deviation step (see Figure 3.10). Thus, at the specific A/D step that has the maximum deviation, an uncertainty of ±80 electrons will occur but be unknown to the user. This is a very unacceptable result for astronomy, but fine for digital cameras or photocopiers that usually have even higher values of INL caused by their very fast readout (conversion) speeds.

A good A/D will have an INL value near 2-2.5 LSB or, for the above example, a maximum deviation of only 10 electrons. While this sounds bad, a 16-bit A/D can represent 65 535 values making the 10 electrons only a 0.02% nonlinearity. However, a 12-bit A/D, under similar circumstances, would have a 0.2% nonlinearity. The lesson here is to use a large dynamic range (as many bits as possible) to keep the nonlinearity as small as possible. We can now obtain A/D converters with low values for INL and which have 18 bits of resolution. So for a given modern CCD, nonlinearity is usually a small but nonzero effect.

Three factors can limit the largest usable output pixel value in a CCD image: the two types of saturation that can occur (A/D saturation and exceeding a pixel's full well capacity; see Sections 2.2.4 and 2.4) and nonlinearity. For the CCD in the example shown in Figure 3.9, A/D saturation would occur at an output value of 32767 ■ 4.5 = 147451 input photons. The pixel full well capacity is 150000 electrons; thus pixel saturation will occur at a value of 33 333 ADU (150 000/4.5). Both full well and A/D saturations would produce noticeable effects in the output data such as bleeding or flat-topped stars. This particular example, however, illustrates the most dangerous type of situation that can occur in a CCD image. The nonlinear region, which starts at 26 000 ADU, is entered into before either type of saturation can occur. Thus, the user could have a number of nonlinear pixels (for example the peaks of bright stars) and be completely unaware of it. No warning bells will go off and no flags will be set in the output image to alert the user to this problem. The output image will be happy to contain (and the display will be happy to show) these nonlinear pixel values and the user, if unaware, may try to use such values in the scientific analysis.

Thus it is very important to know the linear range of your CCD and to be aware of the fact that some pixel values, even though they are not saturated, may indeed be within the nonlinear range and therefore unusable. Luckily, most professional grade CCDs reach one of the two types of saturation before they enter their nonlinear regime. Be aware, however, that this is almost never the case with low quality, inexpensive CCD systems that tend to use A/Ds with fewer bits, poor quality electronics, or low grade (impure) silicon. Most observatories have linearity curves available for each of their CCDs and some manufacturers include them with your purchase.1 If uncertain of the linear range of a CCD, it is best to measure it yourself.

1 A caution here is that the supplied linearity curve may only be representative of your CCD.

One method of obtaining a linearity curve for a CCD is to observe a field of stars covering a range of brightness. Obtain exposures of say 1, 2, 4, 8, 16, etc. seconds, starting with the shortest exposure needed to provide good signal-to-noise ratios (see Section 4.4) for most of the stars and ending when one or more of the stars begins to saturate. Since you have obtained a sequence that doubles the exposure time for each frame, you should also double the number of incident photons collected per star in each observation. Plots of the output ADU values for each star versus the exposure time will provide you with a linearity curve for your CCD.

A common, although not always good, method of determining the value to use for the CCD gain, is to relate the full well capacity of the pixels within the array to the largest number that can be represented by your CCD A/D converter. As an example, we will use typical values for a Loral 512 x 1024 CCD in current operation at the Royal Greenwich Observatory. This CCD has 15-micron pixels and is operated as a back-side illuminated device with a full well capacity of 90 000 electrons per pixel. Using a 16-bit A/D converter (output values from 0 to 65 535) we could choose the gain as follows. Take the total number of electrons a pixel can hold and divide it by the total ADU values that can be represented: 90 000/65 536 = 1.37. Therefore, a gain choice of 1.4e-/ADU would allow the entire dynamic range of the detector to be represented by the entire range of output ADU values. This example results in a very reasonable gain setting, thereby allowing the CCD to produce images that will provide good quality output results.

As an example of where this type of strategy would need to be carefully thought out, consider a CCD system designed for a spacecraft mission in which the A/D converter only had 8 bits. A TI CCD was to be used, which had a full well capacity of 100 000 electrons per pixel. To allow imagery to make use of the total dynamic range available to the CCD, a gain value of 350 (~ 100000/28) e-/ADU was used. This gain value certainly made use of the entire dynamic range of the CCD, allowing images of scenes with both shadow and bright light to be recorded without saturation. However, as we noted before, each gain step is discrete, thereby making each output ADU value uncertain by ± the number of electrons within each A/D step. A gain of 350 e-/ADU means that each output pixel value has an associated uncertainty of upto ~ 1 ADU, which is equal to, in this case, upto 350 electrons, a large error if precise measurements of the incident flux are desired. The uncertainty in the final output value of a pixel, which is caused by the discrete steps in the A/D output, is called digitization noise and is discussed in Merline & Howell (1995).

To understand digitization noise let us take, as an example, a CCD that can be operated at two different gain settings. If we imagine the two gain values to be either 5 or 200 e-/ADU and that a particular pixel collects 26 703 electrons (photons) from a source, we will obtain output values of 5340 and 133 ADU respectively. Remember, A/D converters output only integer values and so any remainder is lost. In this example, 3 and 103 electrons respectively are lost as the result of the digitization noise of the A/D. More worrisome than this small loss of incident light is the fact that while each ADU step in the gain equals 5e-/ADU case can only be incorrect by < 5 electrons, the gain equals 200 e-/ADU case will be uncertain by upto 200 electrons in each output ADU value. Two hundred electrons/pixel may not seem like much but think about trying to obtain a precise flux measurement for a galaxy that covers thousands of pixels on a CCD image or even a star that may cover tens of pixels. With an error of 200 electrons/pixel multiplied by tens or many more pixels, the value of a galaxy's surface brightness at some location or similarly a stellar magnitude would be highly uncertain.

The gain of a particular CCD system is set by the electronics and is generally not changeable by the user or there may be but a few choices available as software options. How A/D converters actually determine the assignment of the number to output for each pixel and whether the error in this choice is equally distributed within each ADU step is a detailed matter of interest but lies outside the scope of this book. A discussion of how the digitization noise affects the final output results from a CCD measurement is given in Merline & Howell (1995) and a detailed study of ADCs used for CCDs is given in Opal (1988).

Major observatories provide detailed information to a potential user (generally via internal reports or web pages) as to which CCDs are available. Table 3.1 gives an example of some of the CCDs in use in various instruments at the European Southern Observatory (ESO) in Chile. When planning an observational program, one must not only decide on the telescope and instrument to use, but must also be aware of the CCD(s) available with that instrument. The properties of the detector can be the most important factor in determining the success or failure of an observational project. Thus, some care must be taken in deciding which CCD, with its associated properties, you should use to accomplish your science objectives.

In our above discussion of the gain of a CCD, we mentioned the term dynamic range a few times but did not offer a definition. The dynamic range of any device is the total range over which it operates or for which it is sensitive. For audio speakers this number is usually quoted in decibels, and

Table 3.1. Some CCDs available at the European Southern Observatory (ESO)

Instrument

Telescope

Type

CCD

Size

Pixel Size

Pixel Scale

Readout Time

Gain

Read Noise

Notes

(pixels)

(microns)

(arcsec)

(seconds)

(e"/ADU)

electrons

EMMI

3.6-m NTT

Spectrograph

MIT/LL

2048 x

4096

15

0.17

18—48

1.4

4

Thinned,

Red channel

back-side

EMMI

3.6-m NTT

Spectrograph

MIT/LL

1024 x

1024

24

0.37

40

1.4, 2.8

7

Thinned,

Blue channel

back-side

FORS2

8-m VLT

Imager/

MIT/LL

2048 x

4096

15

0.12

40

1.1

6

Deep Depletion,

Spectrograph

Red optimized

OmegaCam

2.6-m VST

Wide-Field

E2V

2048 x

4096

15

0.21

45

3

5

imager

this tradition has been used for CCDs as well. Keeping to the idea of decibels as a measure of the dynamic range of a CCD, we have the expression

D(dB) = 20 x log10(full well capacity/read noise).

Thus a CCD with a full well capacity of 100 000 electrons per pixel and a read noise of 10 electrons would have a dynamic range of 80 dB. A more modern (and more useful) definition for the dynamic range of a CCD is simply the ratio of the (average) full well capacity of a pixel to the read noise of the device, namely

D = (full well capacity/read noise). In the example above, D = 10000.

3.9 Summary

This chapter has concentrated on defining the terminology used when discussing CCDs. The brief nature of this book does not allow the many more subtle effects, such as deferred charge, cosmic rays, or pixel traps, to be discussed further nor does it permit any discussion of the finer points of each of the above items. The reader seeking a deeper understanding of the details of CCD terminology (a.k.a., someone with a lot of time on his or her hands) is referred to the references given in this chapter and the detailed reading list in Appendix A. Above all, the reader is encouraged to find some CCD images and a workstation capable of image processing and image manipulation and to spend a few hours of time exploring the details of CCDs for themselves.

As a closing thought for this chapter, Table 3.2 provides a sample of the main properties of two early astronomical CCDs and a few modern devices. The sample shown tries to present the reader with an indication of the typical properties exhibited by CCDs. Included are those of different dimension, of different pixel size, having front and back illumination, cooled by LN2 or thermoelectrically, and those available from different manufacturers. Information such as that shown in Table 3.2 can be found at observatory websites and in greater detail at CCD manufacturers' websites. Most have readily available data sheets for the entire line of CCDs they produce. Each example for a given CCD in Table 3.2 is presented to show the range of possible properties and does not imply that all CCDs made by a given company are of the listed properties. Most manufacturers produce a wide variety of device types. Appendix B provides a listing of useful CCD websites.

Table 3.2. Typical Properties of Two Old and Six Modern Example CCDs

Kodak

SITe

Sarnoff STA (WIYN) MIT/LL

Pixel Format

Pixel Size

(microns) Detector Size (mm) Pixel Full Well

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