C1 Analogue and Digital Signals

C2 Data capture and CCDs

C2.1 Capacitance

When electric charge is added to a conductor, the electric potential of the conductor rises. For a specific conductor it is found that if the charge is doubled then the potential is also doubled; if the charge is tripled then the potential is also tripled etc. In other words, the potential of the conductor is proportional to the charge on the conductor, so the ratio of the charge to the potential is a constant. This constant is called Capacitance.

If the charge is measured in Coulombs and the potential is measured in Volts, then the unit of capacitance is the Farad. The Farad (F) is a very large and impractical unit and more realistic units are the µF, nF and pF.

The capacitance of a conductor will be dependent upon its size and shape and it will also be affected by how near it is to other conductors.

C2.2 Charge Coupled Device (CCD)

Charge Coupled Devices (CCDs) were originally used as analogue memory units within the music industry for generating delays and echoes. They were often called Bucket Brigade Devices or Analogue Shift Registers, because of the way in which they operated. Electric charge is passed from one element of the device to the next much like a line of people could pass buckets containing water from one to the next to douse a fire.

Experiments on making light sensitive CCDs which could be used to capture images resulted in the first image forming CCDs being made in 1973 which contained more than 10,000 separate picture elements or pixels.

An individual pixel element consists of three sections as shown in the diagram below.

The white bars represent electron-collecting zones of low electric potential, created below an array of electrodes formed on the surface of very thin semiconducting silicon (5 - 8µm). These electron collecting zones are called the potential energy wells and are where photoelectrons are collected.

The coloured bars are zones of higher electric potential that act as barriers to keep the electrons in the potential energy wells. The heights of these potentials can be changed by means of three sets of electrodes shown as green lines which run across the surface of the chip and work together to move the electrons in the potential well along the channels. The electrons are kept from moving side-ways by permanent barriers called channel stops (thick black lines).

The pixels are laid out in closely spaced columns or channels, as shown in the diagram below, which shows a section of three columns each with three pixels, giving 9 pixels in total.

C2.3 Light and pixels

Photons have energy that is proportional to the wave frequency. For an individual photon its energy is given by E=hf, where h is Planck's constant and f is the wave frequency. In a CCD being exposed, photons enter the chip from the rear. When a photon strikes the silicon, it is very likely to interact with an electron in the thin layer of silicon (approximately 8µm) and give sufficient energy to the electron to displace it from the silicon lattice. This creates an electron-hole pair. The displaced electron, or photoelectron, is collected in the nearest potential well while the hole created by the loss of the electron is eventually filled by an electron from the silicon substrate. The more photons which strike the silicon, the more electron-holes produced and so the more electrons stored within each potential well.

C2.4 Digitized images on a CCD.

A CCD is an array of pixels. Each pixel can be thought of as a person holding a bucket containing the charge created by the exposure of the pixel to light. In order to extract the information from the buckets, each person passes their bucket onto the next person along the CCD, as shown in the diagram below.

The first line shows the initial state with the coloured bucket three from the left hand side. The second line shows position of the coloured bucket after the first swap. The free bucket at the right hand side contains the charge which is then digitised. The potential formed by the charge is amplified and converted into a digital signal by an Analogue to Digital Converter (ADC). After each swap, the buckets move one place further to the right.

Since the data is presented sequentially to the ADC, by knowing how many shifts have occurred, the position of each data value can be mapped to a position within the image.

Consider a CCD where the maximum output voltage from a pixel, after amplification, is 0.8V. If this is to be converted into a 3-bit binary number, then there will be 8 different quantisation levels as shown in the table below.

e.g. The voltage at the output is 0.42 V. This falls in the quantisation level represented by 4 and will give a digital signal of 100.

C2.5 Quantum efficiency of a pixel.

An ideal light detector would generate a measurable response for every photon which struck it, without introducing noise or other spurious signals. Such a detector would have a Quantum efficiency of 100%.

Quantum efficiency is a measure of the sensitivity of a light detector. Many photoelectric materials typically emit an electron for every 5 to 10 incident photons and so therefore have a quantum efficiency of between 10 and 20%.

Quantum efficiency is defined as the ratio of the number of photoelectrons emitted to the number of photons incident on the pixel.

The Quantum efficiency of modern CCDs can be as high as 90%.

C1.6 Magnification

CCDs are frequently used as the image sensor in optical instruments. The optical instrument will have a system of lenses which will produce an image onto the surface of the CCD of an object.

The linear magnification is defined as the length of the image on the CCD divided by the length of the object.

Consider a tree that is 3m in height. When viewed through a camera, the height of the image of the tree on the CCD is 6mm. What is the magnification of the optical system?

C2.7 Resolution on a CCD

For two points on an object to be resolved when viewed via a CCD it is necessary for the images of these points on the CCD to be at least two pixels apart.

Consider the situation below where a star gives rise to an image on a CCD. The graph shows the charge (number of electrons) in the pixels viewed across the image.

If a second star is near to the first, then it will produce a similar charge distribution across the pixels. If the image of the second star falls on adjacent pixels, then the charge distribution below will result.

As can be seen, there is little evidence from the resulting charge distribution that there are two stars. The charge distribution would suggest just one larger and brighter star.

If the image of the second star is two pixels away from the first image then the charge distribution below will result.

In this diagram it can be seen that the two images will be able to be resolved.

C2.8 Image quality

An ideal detector would have a quantum efficiency of 100%; that is it would generate a measurable response for every photon that struck it, without introducing noise or spurious signals. In addition it would be sensitive to light of all colours and it would give an accurate value for the brightness of the light at every point in a scene. It could be used for both very long and very short exposures and it would be able to measure accurately both dim and bright objects in the same picture. Finally it would be able to accurately record the positions of the incoming photons accurately.

The quality of the image produced, therefore, by any light detection system depends upon six major criteria. These are quantum efficiency, noise level, dynamic range, colour response, photometric accuracy and geometrical stability.

Quantum efficiency is a measure of the sensitivity of the detector. Many photoelectric materials have quantum efficiencies of between 10 and 20%. Photographic film and the human eye both have quantum efficiencies of up to 2%. A CCD has a quantum efficiency of around 80%, so making it an efficient detector. This means that exposure times can be much smaller than with photographic film, so producing sharper images of moving objects. It also means, when used with astronomical telescopes, that more images can be captured within a given time.

The general term 'noise' refers to any process that contributes to errors of measurement or distortion of information. In photographic emulsion, the light sensitive particles are not uniformly distributed producing the effect known as graininess. Electronic detectors all generate noise as a result of the constant thermal agitation of their constituent atoms and molecules. This thermal noise can be reduced by cooling the detector, and in astronomy the CCDs are often cooled to -100°C or lower.

Colour response refers to the ability of a detector to respond to radiation of different wavelengths. The eye can respond to light of wavelengths from around 700nm to 450nm, with a quantum efficiency of greater than 0.1% while photographic film will respond to wavelength from 650nm with the same quantum efficiency. CCD imagers, on the other hand, respond to wavelengths from around 2000nm to 300nm with a quantum efficiency of greater than 0.1%, and so are extremely useful for producing images in the infrared as well as the visible spectra.

The dynamic range of a light detector is the ratio of the maximum detectable light intensity to the minimum detectable light intensity. The minimum is usually determined by the noise generated within the detector. The maximum is determined by the point at which the detector saturates (i.e. cannot produce a larger output). In a CCD imager, the upper limit of the dynamic range is established by the filling of the potential wells with electrons. Modern CCDs have dynamic ranges of around 10,000 compared to a photograph or a television system which has a typical value of around 100.

Photometric accuracy refers to the ability of a light detector to measure the exact brightness of an object. An accurate measurement of brightness requires that the detector responds in a known and reproducible manner, so that a given light input always gives the same output. In practice it is helpful if the detector's response is linear, or directly proportional to the input, since such a relation greatly simplifies the task of processing the image. The CCD imager is a linear device. Photographs, on the other hand, are inherently nonlinear and can only be used once. Their characteristics are not identical even for plates from the same batch of photographic emulsion.

Geometric stability refers to the ability of a detector to record the exactly position of an object. CCD imagers have exceptionally good geometric properties, since the individual picture elements are defined by the physical structure of the chip. The geometric stability of photographic plates is good but that of film is poor, along with the television type detectors.

C2.9 Practical uses and merits of using CCDs

Uses of CCDs

The use of CCDs is extensive now that the price of manufacture has fallen and their resolution has improved. Uses include the following and students are encouraged to research these applications themselves.

Digital video and still cameras, including camera phones etc

Telescopes, e.g. the Hubble telescope, where the Wide Field Planetary camera 2 contains four CCDs each containing 640,000 pixels.

Thermal imagers, e.g. used in medicine search for tumours by detecting areas of a patient's body which are hotter than the surroundings, and also by the emergency services to search for sources of fire.

X-ray imagers, e.g. used to capture X-Ray images in hospitals etc.

Advantages over photographic emulsion

There are many advantages of CCDs over photographic emulsion and students are encouraged to use the following examples as a guide to carrying out their own research

Reusable - once an image has been captured, the CCD can then be reset ready for the next image to be captured. Photographic emulsion is a 'one off' process and cannot be reused.

Greater sensitivity - modern CCDs are over 1000 million times more sensitive than the human eye

Greater colour response - modern CCDs will respond to electromagnetic radiation over a much wider range of wavelengths than either the human eye or photographic emulsion

Linear response - the output voltage from a CCD is proportional to the charge collected by each pixel, which in turn is proportional to the number of photons incident on the CCD. This is in contrast to many light detectors which have a logarithmic response.

C2.10 Retrieval of the image from a CCD

A CCD can be thought of as an array of shift registers. A picture is read out of the device by a succession of shifts through the imaging section, with all of the rows simultaneously moving one space at a time along the columns of the body of the device.

The diagram below represents a small segment near the edge of the device, with the output shift register being shown at the top.

In order to understand how the image is converted into a digital signal, consider the following series of diagrams. In the first diagram the section of the CCD has been exposed to light and each electron in each potential well is represented by *.

On the first shift, the voltage level of the next barrier towards the output shift register is lowered to the same level as the well. The electrons then divide between the two wells, as shown in the diagram below.

Finally, the voltage level of the original well is raised so that it becomes a barrier. The effect of this operation is to move the electrons one third of a pixel upwards, as shown in the diagram below.

This process is then repeated for each successive shift within the CCD.

The diagram below shows the position of the electrons after the next shift.

On the next shift the information passes out of the imaging section through an isolating region called a transfer gate into the output shift register, as shown in the diagram below. Electrons from pixels further in the body of the CCD now enter at the bottom of the diagram.

The same technique is now used to move the electrons along the output shift register and the next diagram shows the electrons moved towards the left.

An amplifier at the end of the output register measures each charge packet in turn and gives a corresponding voltage output. The process is repeated until the entire chip has been emptied of information.

C2.11 Problem solving on the use of CCDs

A selection of problems is given in the Student Work Book associated with this unit.