Basic Principles and Properties

To illustrate basic terminology used for detectors, we will consider 3 examples of detectors: photographic plate, photomultiplier, and array detector.

Detectors work because they are made of some material which interacts with photons. An incoming photon generates a chemical reaction (photographic) or photoelectron. Photoelectrons are counted, either

• one at a time, usually with amplification, or
• by collection, then subsequent measurement.

In a photomultiplier, 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. Generally, 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, 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.

Array detectors are in more common usage 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:

• Quantum efficiency: fraction of photons detected. Of course, the quantum efficiency is usually a function of wavelength. Some typical values are:
  • photographic : $\sim$ 0.1 %
  • photomultiplier : $\sim$ 10 - 20 %
  • array detector : $\sim$ 20 - 90 %

• Size and resolution elements.
  • photographic: large size (many inches), good resolution.
  • photomultiplier: several inches, no resolution (although there are arrays of photomultipliers, e.g. MAMA)
  • array detector: individual detectors started out small but are continually growing. The largest current CCDs are around 2.5 inches square, whereas the largest IR arrays are roughly an inch square. Larger effective sizes are now available (for CCDs) because some modern devices are made to be ``buttable'', i.e. several can be placed side by side with only very small gaps between them. Pixel sizes of array detectors are typically 15-25 microns.

• Readout effects. The process of counting electrons is never totally exact, so noise is introduced. Generally this is at a level of 1-100 electrons rms. Readout effects can come in two different forms: pattern and random noise. The latter is what people usually refer to as readout noise. Pattern noise is noise which is introduced in the readout process but which has some spatiall correlation. Fixed pattern noise has the same spatial pattern over the detector from exposure to exposure, and thus can be corrected. If photon events are counted, rather than counting the number of photoelectrons, as is the case for a photomultiplier, there is no readout noise.

• Dark current. Electrons in a given substance will be moving around at speeds which are correlated with the operating temperature of the device. If there is enough thermal motion, an electron can actually be liberated from the substance and then counted as a (spurious) photon detection. This is called dark current. Devices with lower photoelectric threshholds (used at longer wavelengths) are more susceptible to dark current, thus they must be operated at a colder temperature. CCDs are typically operated betwee -70 and -120 C, IR arrays are operated colder (LN₂ = 77K, Liquid He =4K).

• Full well: maximum number of photons possible to detect.
  • photographic: limited by number of grains
  • photomultiplier: unlimited
  • array detector: $\sim$ 100,000 photons.

• Linearity: relation between number of output electrons and input photons. In a fully linear detector, this relation is linear, with the slope of the relation given by the quantum effeciency. An alternate way to consider nonlinearity is to consider that the quantum efficiency is a function of the count level.
  • photographic: nonlinear (characteristic curve)
  • photoelectric: linear except for dead-time correction. A dead-time correction applies for bright sources; if two photons arrive essentially simultaneously, they will only be counted as a single photon.
  • array detector: CCDs usually linear up to 50-90% of full well. IR arrays are usually slightly nonlinear over their entire range, but repeatably so.

• Reciprocity: sensitivity changes as a function of photon incidence rate. Exists in photographic plates, maybe in some array detectors? Dead-time correction is a reciprocity failure.

• Digitization. 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); the ``astronomical'' gain is usually 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 $\sqrt{{GC+R^2}}$ , or, in units of counts, by $\sqrt{{C/G+R^2/G^2}}$ .

  A/D convertors 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.

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

• 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 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.

• Defects. Most detectors are not perfect; there are often small regions which are unusable because of very low quantum efficiency, blocked columns, etc. Many devices are rejected for astronomical use because of too many defects.

• Modulation transfer function. In some detectors at some wavelengths, charge deposited at one location can be spread over a wider region, leading to degradation of image quality. This is often most notable at long wavelengths in CCDs, where one can see moderately large halos around point sources. This is usually due to the penetration of long wavelength photons to the substrate of the device from which they can be reflected back.

  A related effect is fringing on chips, which results from interference of monochromatic incident light that is reflected from the substrate, which is relevant because the night sky spectrum contains strong monochromatic features. Since the substrate surface is not perfectly flat, this can lead to irregular patterns in the background.

• Readout speed: typically 25 microsec/pixel for array detectors. However, the chips can in many cases be read at a variety of speeds. In general, when chips are read faster, the readout noise increases. Larger chips now often have multiple readout channels, so several regions of the chip can be read simultaneously, decreasing the total readout time.

• Saturation behavior. When full well is reached, the chip is said to be saturated. In some array detectors, especially CCDs, when a given pixel is saturated, additional charge often leaks into adjacent pixels, usually into adjacent rows rather than columns because of the construction of the CCD. Separately from detector saturation, one occasionally sees saturation of the readout electrons which can have the effect of a saturated pixel affecting the counts in subsequent pixels.

• Hysteresis generally refers to processes in which the prior exposure history of a detector affects subsequent exposures. A common example is residual image, in which an area of a detector which was subject to a very bright source in a previous exposure will continue to ``glow'' in subsequent exposures. Another form of hysteresis is so-called quantum efficiency hysteresis (QEH) in which the quantum efficiency of the chip changes as a function of previous exposure history. One manifestation of this effect has been used by astronomers, mostly with older CCDs; for some reason, when these CCDs were subjected to an extended influx of ultraviolet light, their optical quantum efficiency was found to be increased, and to stay increased at a stable level as long as the chip was kept cold. This led to the practive of ``UV-flooding'' CCDs as they were being cooled.