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(Entire section in one PDF file).

Basic Principles and Properties

Detectors work because they are made of some material which interacts with photons. Consider three general types

In a photon counting device, some fraction of incident photons hit a photosensitive material and eject a photoelectron. This electron is amplified numerous times to create a large ``swarm'' of electrons which is detected as a pulse. Thus, photons are ``counted'' as they come in. Simple photomultipliers do not retain any information about the location on the detector where the photon hits. There are some modern devices, however, called microchannel plates, which are essentially arrays of small photomultipliers where positional information can be obtained; one of the more common of these is called a MAMA (multi anode microchannel array), and exists in several instruments on the Hubble Space Telescope. Traditional photomultipliers were the workhorse of photometry from the 50's to the late 70's. More recently, a more sensitive type of photon counter, called an avalanche photo-diode, has been used.

Photon collecting array detectors are the most common for optical and near-infrared detectors today. In these devices, incoming photons create photoelectrons which are trapped in local potential wells. The amount of energy needed to eject a photoelectron depends on the type of material used. In the optical, silicon provides a good choice, but the excitation energy for silicon is too high to be used in the infrared. In the IR, various different substances are used, including HgCdTe, InSb, and PtSi. After a specified amount of time, the photoelectrons are ``counted''. The method by which this is done differs between different types of arrays. In CCDs, the charge is physically clocked down columns of the device, a single row at a time (a parallel transfer) then read out of serial register; CCDs are inherently asymmetric in rows and columns. In IR devices, each pixel is read individually, in sequence.

Detectors are characterized by a variety of different important quantities:

Other possible effects/issues:

Understand the basic types of detectors: photon counters...
... resolution elements, readout noise, dark current, linearity.}


In array detectors, after the charge is collected and read out, it is sent through a chain of electrons which digitizes the signal, often after amplifying it. The digitization is made by a device known as an A/D convertor; these work by comparing an input signal with a set of reference voltages which successively differ by factors of two. Thus an input signal is translated into a series of bits depending on whether the input voltage exceeds a series of reference voltages. Typical A/D correctors in use in astronomy consider 16-bits. The digital signal which comes out of the CCDs is variously referred to as counts, digital numbers (DN), or analog-to-digital units (ADU). The number of output counts is related to the number of input counts by a constant which depends on the amplification in the electronics. The amplification factor is known by most people as the gain, but astronomers define the gain of a device by the number of input electrons divided by the number of output counts (i.e., the inverse gain); this ``astronomers'' gain is specified in units of e-/DN. Because the number which we receive from the electronics chain differs from the number of input electrons (i.e, the number of detected photons), the calculation of noise must take this into account. The photon counting noise (rms) is given by the square root of the number of detected photons. The number of detected photons is given by GC, where G is the (inverse) gain and C is the number of detected counts. Consequently, the noise in electrons is $ \sqrt{{GC}}$, and in units of counts is given by $ \sqrt{{C/G}}$. This is apart from readout noise; the latter is usually specified in units of electrons, giving a total noise in electrons of $ \sqrt{{GC+\sigma_{rn}^2}}$, or, in units of counts, by $ \sqrt{{C/G+\sigma_{rn}^2/G^2}}$.

A/D converters can only measure a positive incoming signal. At low light levels, the true input signal can be negative in the presence of readout noise. To avoid trucation of the negative signals, a constant voltage, called the bias, is added to the signal before it passes through the A/D. This bias must later be removed to preserve the correct count ratios between different sources; this is generally accomplished in CCDs by using the overscan region of the image.

A/D convertors can introduce small systematic errors in recorded count rates if the reference voltages are not carefully controlled.

Understand how digitzation works. Know what the gain is....
...calculate noise in both units of detected electrons and in counts.}

Dynamic range

A detector system can be characterized by its dynamic range, which is the ratio of the signals of the brightest and faintest sources which can be detected (with some definition of ``detection''). At the bright end, the system is limited by either the full well of the detector (or the number of electrons at which the detector goes significantly non-linear), or alternatively by the limitation of the A/D convertor (e.g., if an A/D convertor has 16 bits, you can never see counts higher than 216 - 1 = 65535. At the faint end, the system is limited either by the bias level, the A/D convertor (you can't detect less than one count), or by the readout noise (source buried by readout noise cannot be detected). The gain of a system is often set to maximize the dynamic range; if the readout noise is $ \sim$ 10 electrons, one can maximize dynamic range by digitizing the signal by several electrons/DN if the detector has sufficient full well.

Know what dynamic range means.

Determining gain and readout noise

Consider an ensemble of measurements taken at a light level L. The noise in this ensemble should be $ \sigma^{2}_{}$ = LG + $ \sigma_{{rn}}^{2}$, where G is the gain and rn is the readout noise in electrons, and $ \sigma$ is the noise in electrons.

If you do this at a lot of different light levels, then you can plot $ \sigma^{2}_{}$ vs L, and the slope should give you G and the intercept rn2. However, remember that if you compute $ \sigma$ from the images, this gives $ \sigma$ in DN, so the slope will give you 1/G. This test is also excellent for checking the basic performancer of a detector. Deviations from nonlinearity can also usually be seen on such a plot.

However, in its most straightforward application the test is very time consuming and hard to analyze: you have to take many exposures at each different light level, and then determine a gain and readout noise for each pixel and look at them all. It is much easier just to use the set of all pixels as your ensemble at each light level. However, you can't do this directly, because each pixel may have a different sensitivity and different fixed pattern noise, so you're not measuring a true ensemble. If there is significant variation of sensitivity than you can't use a whole area at all, because the noise properties will vary across the area. You can avoid these problems by working with the difference between pairs of observations: if the light level is the same in the two images, then you'll be left with an image that only has noise.

Specifically, take a pair of images and form the difference. The expected noise is

$\displaystyle \sigma^{2}_{}$ = 2(LG + $\displaystyle \sigma_{{rn}}^{2}$)

where L is the light level, G is the gain, and $ \sigma$ is the noise in electrons. Since $ \sigma$(electrons) = G$ \sigma_{{DN}}^{}$, we have

$\displaystyle \sigma_{{DN}}^{2}$ = 2($\displaystyle {L\over G}$ + $\displaystyle {\sigma_{rn}^2\over G^2}$)

. You can directly measure $ \sigma$(DN) from your difference image. Make sure to do it over a region which doesn't vary significantly in light level. Now repeat the measurement at a variety of light levels and plot $ \sigma^{2}_{}$(DN) vs L. If you fit a line through this, the slope is 2/G and the intercept is 2$ \sigma_{{rn}}^{2}$/G2. If a straight line doesn't fit the points, then there is some sort of problem, which you should probably track down.

You can abbreviate this test if you just want to get an estimate of the gain and readout noise. First, take a pair of bias frames. These have light level of zero, so the noise from the difference just gives you $ \sqrt{{2}}$$ \sigma_{{rn}}^{}$. (Note that you still need to take a pair in case there is superbias structure). Then take a pair at a high light level; at this level the readout noise is probably negligible, and you can determine the gain from

G = 2$\displaystyle {L\over \sigma_{DN}^2}$

Understand how to determine gain and readout noise.



By the nature of their operation, there are some additional effects which are peculiar to CCDs. The unique feature of CCDs is that they are used as shift registers to transfer the charge through the detectors themselves in the process of readout. The parallel transfer efficiency (transfer efficiency from one row to the next) must be extremely good in order not to lose any significant amount of charge over the large number of parallel transfers which must be performed (especially in larger devices). For example, a charge transfer efficiency (CTE) of 0.999 per transfer, which sounds good, will result in a loss of 64% of the signal over 1024 transfers, or 83% of the signal over 2048 transfers! For detectors of these sizes, CTE's of order 0.99999 or better are required. Fortunately, they are achievable, though not trivially so; many devices are rejected because of inadequate CTE.

Charge transfer problems can lead to a variety of effects which are sometimes encountered by CCD users, especially those pushing for the most accurate photometry. An example of one such problem is known as deferred charge. This occurs because some CCDs transfer charge less efficiently at very low light levels. Essentially, this makes the detector non-linear at low light levels. Deferred charge can be corrected for if exposure levels are above the level where the nonlinearities are important. Alternatively, if low light levels are expected, detectors which exhibit this problem can be ``pre-flashed'' in which a background level of photons is put on the chip before the exposure is started; when one does this, however, one must pay the price of additional background noise.

CTE problems are apparently exacerbated by exposure to high energy photons, and, as a result, often plague space-based missions, where the CTE performance can degrade over time. There has been some technology development to mitigate this problem, but it is definitely an issue.

The quality of a CCD is generally specified by its quantum efficiency (as a function of wavelength), its readout noise, and charge transfer efficiency (though there are other figures of merit as well).

CCDs can either be illuminated from the front side (where the electronics are implanted) or from the back side. To work efficiently when back-illuminated, the chips must be thinned by some process. Generally, thinned back-side illuminated chips have higher quantum efficiencies than front-side illuminated chips. However, the thinning process can be difficult, with a relatively high fraction of attempts at thinning ending in failure. Front-side illuminated chips not only have lower quantum efficiencies, but tend to have particularly poor blue response.

effect of thinning qe curves

An additional way to improve blue (or any) response is to coat the chip either with some sort of anti-reflection coating to minimize reflective losses, or with some sort of lumogen which converts blue (or UV) photons to longer wavelengths where the chip is more sensitive.

some qe curves E2V CCD selection guide

The quantum efficiency is never totally uniform over the entire chip. Pixel-to-pixel variations in q.e. are typically a few percent. Over larger scales, q.e. variations can be larger; larger q.e. variations are often found in thinned chips because the thinning process may be non-uniform. The variations in q.e. across the chip, along with possible differences in illumination pattern across the chip, leads to the necessity of flat-fielding.

An additional consideration rarely considered is whether there are quantum efficiency variations within each pixel. In the limit where sources are very well sampled (i.e. cover many pixels), these are irrelevant, but they would lead to direct systematic photometric errors in the situation where sources are undersampled. Little is known about the possibility of such variations in different devices, but it is likely that they exist at some level.

QE as a function of time, e.g. short term, long term, thermal cycling variations. Requirements for calibration. Of course, there may be other things in the optical system that lead to time-dependent sensitivity variations as a function of position, e.g. dust specks on the dewar window or filter.

The manufacture of CCDs, especially the low noise devices with high quantum efficiency that are needed by astronomers, is a complex procedure; only several manufacturers currently attempt this (e.g., E2V, STA, LBNL).

IR detectors

Infrared arrays operate under different principles than CCDs. First, a different material must be used, because silicon is not sensitive in the IR: PtSi, HgCdTe, InSb have all been used. Typical QE is not quite as good as that in typical CCDs, but it is constantly improving. Typical array sizes are also slightly smaller than currently available for CCDs.

In general, there is less experience with materials which are sensitive to infrared photons than there is with silicon. As a result, the infrared arrays cannot be used as readout registers in the way in which silicon arrays (CCDs) are. Instead, the IR arrays are generally coupled to a silicon array (a multiplexer). For some reason, they are generally not coupled to CCDs, however. Each pixel from the multiplexer array is read out individually, in sequence; charge is not transferred from one pixel to another. In IR arrays, each pixel can be thought of as a capacitor; as photons are detected, charge builds up on the capacitor. The amount of charge on the capacitor can be read out at any time, without affecting the accumulated charge. This leads to so-called nondestructive readouts for IR devices; a given pixel can be read out many times without removing the accumulated charge. The removal of charge is done in a seperate reset operation.

Before charge accumulation begins, each pixel is reset to some initial value. Because of thermal noise (often called KTC noise), however, it is not possible to know precisely what this initial value is from one reset operation to the next. This would introduce a fundamental uncertainty in the total charge measured if one only read each pixel once at the end of the desired integration period. To avoid this, most astronomical IR detectors perform doubly-correlated sampling, in which the array is read shortly after reset (non-destructively) and then again at the end of a specified integration period. The difference between the two readouts give the desired counts per integration period. To lower the effect of readout noise, it is possible that during each of these readouts, the chip is actually read several times; averaging the successive differences reduces the effective readout noise. This is known as Fowler sampling, whether the number of Fowler samples is the number of reads at the beginning and at the end of the exposure (so Fowler sampling of one is doubly-correlated sampling). Alternatively, one can do ``up the ramp'' (e.g. multiaccum) sampling as the exposure proceeds. Because each pixel is read in sequence, and only the time difference between the reads is relevant, many IR cameras are run without shutters.

See Rausher et al 2007.

More complex IR detector issues: nonlinearity, bias drifting, interpixel capacitance, etc.

QE differences between different types of IR devices: HgCdTe vs. InSb. Tuning long wavelength cutoff, e.g. in HgCdTe.

Subpixel QE.

UV and other detectors

Readout noise considerations more relevant because of low background, photon counting devices preferred, e.g. MAMAs.

next up previous
Next: Data Reduction: details and Up: AY535 class notes Previous: INSTRUMENTATION
Jon Holtzman 2017-11-17