Digital technology

14.1 Analogue and digital signals

Conversion of binary to decimal

Examples

Solve problems involving the conversion between binary numbers and decimal numbers. Students should be aware of the term bit. An awareness of the least-significant bit (LSB) and most-significant bit (MSB) is required. Problems will be limited to a maximum of five bits in digital numbers.

Most and Least significant bit Significant Figures We shall define significant figures by the following rules.3 1. The leftmost nonzero digit is the most significant digit. 2. If there is no decimal place, the rightmost nonzero digit is the least significant digit. 3. If there is a decimal point then the right most digit is the least significant digit even if it is a zero. 4. All digits between the least and most significant digits are counted as significant digits.

Specimen paper 38. The binary equivalent of the number 12 is A. 1010. D. 0101. Q’s 1,2 from worksheet

Bits and bytes A bit is the smallest unit of digital information, represented as a 0 or a 1. A byte is an eight bit word

Describe different means of storage of information in both analogue and digital forms. Students may consider LPs, cassette tapes, floppy disks, hard disks, CDs, DVDs, and so on.

How A Compact Disc Works Hyperlink Video

Pits and bumps

Reading a CD λ/4 depth, so that the wave travels λ/2 further, and destructively interferes As the disk rotates, the laser reflects off the sequence of bumps and lower areas into a photodector The photodector converts the fluctuating reflected light intensity into an electrical string of zeros and ones The pit depth is made equal to one-quarter of the wavelength of the light When the laser beam hits a rising or falling bump edge, part of the beam reflects from the top of the bump and part from the lower adjacent area Light reflecting from the top and bottom of the pit is a half-wavelength out of phase, so the intensity drops.

Reading a CD The bump edges are read as ones (i.e. no light). The flat bump tops and intervening flat plains are read as zeros Explain how interference of light is used to recover information stored on a CD. Students must know that destructive interference occurs when light is reflected from the edge of a pit. Calculate the wavelength of laser that must be used for a bump height of 125ηm.

Specimen paper 39. The depth of a “pit“ on a CD is 150 nm. The wavelength of the laser used to read the information on the CD must be A. 6 00 nm. B. 450 nm. C. 300 nm. D. 150 nm.

Solve problems on CDs and DVDs related to data storage capacity. Use the information in the diagram to estimate the number of bits of information that can be stored on a CD. If a 16 bit number code is used, how much information can be stored? Q’s 10,11

DVD data density DVD CD The pits are a different size and spacing, allowing a higher data density

Analogue and digital signals In the Beginning: Etching Tin. Thomas Edison is credited with creating the first device for recording and playing back sounds in 1877 His approach used a very simple mechanism to store an analogue wave mechanically. In Edison's original phonograph, a diaphragm directly controlled a needle, and the needle scratched an analogue signal onto a tinfoil cylinder Hyperlink

Record player

Analogue signal Voice pattern Pure note

DAC The analogue wave can be represented by a series of 1’s and 0’s                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      

Sampling rate The higher the sampling rate, the better the approximation to the analogue signal                                                                                                                                                                                                                                  Q’s 5,6

Digital magnetic storage The 1’s and 0’s are stored as a series of north's and south's of the single domain particles on the tape or disc.

Discuss the advantage of the storage of information in digital rather than analogue form. Students should consider quality, reproducibility, retrieval speed, portability of stored data and manipulation of data. Quality Depends on sampling rate, but can be indistinguishable from the input Virtually indistinguishable from the input, but liable to corruption. i.e. higher S/N ratio Reproducibility Each retrieval almost identical Subject to wear and damage from each use. Retrieval speed Easy to search around within a film Hard to search through a video tape. Portability Usually small Larger for the same data

Discuss the implications for society of ever-increasing capability of data storage. Teachers should consider moral, ethical, social, economic and environmental implications. Cost Privacy Ownership of data Accessibility

Tsokos Page 461 Q’s 1-19

Data capture; digital imaging using charge-coupled devices Define capacitance A capacitor is a device that can store charge (it has a “capacity”). Capacitance is defined as “the charge stored per volt”

Describe the structure of a charge‑coupled device (CCD). Students should know that a CCD is a silicon chip divided into small areas called pixels. Each pixel can be considered to behave as a capacitor. Q’s 12,13,14. (with next slide)

Capacitance Capacitance is defined as “the charge stored per volt across the plates” and is measured in Farads: Q V Capacitance = charge displaced C = Q (in F) voltage across plates V Therefore 1 Farad = 1 CV-1. The Farad is a large unit so capacitance is usually expressed in μF, nF or pF. A capacitor stores 1200 μC for a charging voltage of 6V. What is its capacitance? Another capacitor stores 1000 μC and has a capacitance of 25 μF. What is the charging voltage? If a 500 μF capacitor is charged by a voltage of 10V what charge will it store?

History of the CCD In 1969 Willard S. Boyle and George E. Smith, while working at Bell Laboratories, designed the first Charge Coupled Device (CCD), a working version was produced just a year later. The CCD has become the bedrock of the digital imaging revolution including digital photography and video. In January 2006 they have been honored with the Charles Stark Draper Prize which is presented by the National Academy of Engineering.

Explain how incident light causes charge to build up within a pixel Students are required to use the photoelectric effect.

How Does a CCD Work? 1.Charge Generation is via the photoelectric effect N.B. Charge produced is proportional to the intensity of the light (Silicon bandgap is 1.14 eV. Therefore easily absorbs photons of energy 1.1 to ~4 eV (1,100 to 300 ηm)). 2.Each pixel “fills” with photoelectrons i.e. the charge across each capacitor increases.

Outline how the image on a CCD is digitised. Students are only required to know that an electrode measures the potential difference developed across each pixel and this is then converted into a digital signal. The pixel position is also stored.

Define quantum efficiency of a pixel. Quantum efficiency is the ratio of the number of photoelectrons emitted to the number of photons incident on the pixel. Now do question 17.

Quantum Efficiency Above you see several quantum efficiency curves of different types of CCDs as a function of the wavelength. The large domain of wavelengths for the spectral response of CCDs becomes obvious.

Define magnification.

Resolution State that two points on an object may be just resolved on a CCD if the images of the points are at least two pixels apart.

Resolution and magnification ho=10m v =? hi=10µm u=50m Calculate the object distance (v). If the pixel width is 10µm, what is the smallest distance that can be resolved on the tree? Q’s 15,16,18 & 19.

Magnification question A satellite takes an image of the Earth. Each image covers an area of 100km2 and is recorded by a CCD of area 25cm2 (a) calculate the magnification of the system. (5x10-6) (b) The resolution of the system is 10m. Calculate the resolution of the pixels on the CCD (5x10-5m) Find the number of pixels on the CCD (4x106)

Discuss the effects of quantum efficiency, magnification and resolution on the quality of the processed image. Quantum efficiency – If this is low, then not all the photons will be recorded. Leads to a loss of detail. Different for different colours. Magnification – As the magnification increases, the image is projected onto a smaller area. This will eventually force photons from different areas of the object onto the same pixel. A larger CCD decreases this problem. Resolution- The greater the resolution, the more the detail that can be stored i.e. quality increases. But, more memory is needed.

Describe a range of practical uses of a CCD Students should appreciate that CCD’s are used for image capturing in a large range of the electromagnetic spectrum. They should consider items such as digital cameras, video cameras, telescopes, including the Hubble Telescope, and medical X-ray imaging.

List some advantages of CCDs compared with the use of film. The cost of each photo is cheaper. The QE of film is typically less than 10%. Therefore CCDs can capture images in darker conditions. The image can be enhanced electronically. Immediate viewing of the image. Easy to store a large number of photos, films etc…

Outline how the image stored in a CCD is retrieved. Apply voltages that make the charge move from one capacitor to the next (and hence the name charge coupled device. Push the charge from each pixel through the readout electronics in serial fashion. Convert the analogue signal (i.e.the voltage from a given pixel) to a digital number. This can be used to generate the intensity of that part.

Full-Frame CCD Operation Hyperlink

Colour images Unfortunately, each photodiode is colour-blind. It only keeps track of the total intensity of the light that strikes its surface. In order to get a full colour image, most sensors use filtering to look at the light in its three primary colours. Once the camera records all three colours, it combines them to create the full spectrum. Another method is to rotate a series of red, blue and green filters in front of a single sensor. The sensor records three separate images in rapid succession. This method also provides information on all three colours at each pixel location

Tsokos Page 468 Q’s 1-25.

Specimen paper 40. The amount of charge that builds on a pixel in a charged coupled device (CCD) is proportional to which property of the incident light? A Intensity B. Wavelength C. Frequency D. Amplitude

Specimen paper

Areas, not lengths.