St. Louis Public Schools



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Digital Technology

9. A digital camera is used to photograph an object that is 3.0 x 10-1 m2 in area. The image that is focused onto the CCD is 4.5 x 10-3 m2. What is the magnification of the camera?

Binary Numbers: numbers expressed using base 2

Example:

Analogue and Digital Signals

1. On a DVD, the pits are much closer together (a tighter spiral) so more pits can be etched onto a disk. As a result, laser light with a shorter wavelength needs to be used to store and retrieve the data.

2. The DVD may also use multi-layer data storage techniques. For example, a 2-layer DVD doubles the amount of information that can be stored on it.

Storing and Retrieving Digital Information (CDs and DVDs)

Decimal Numbers: numbers expressed using base 10

Examples:

Least-significant bit (LSB):

Most-significant bit (MSB):

|Method of storage |Typical information |Overview of process |Analogue or Digital|

|Photocopying |Text or pictures |Optics and electrostatics used to fix powder to paper |Analogue |

|LPs (vinyl) |Music or speech |Sound variations stored as grooves in vinyl |Analogue |

|Cassette tapes |Music or speech |Sound variations stored in magnetic fields on tape |Analogue |

|Floppy disks |All forms |Bits stored as variations in magnetic fields on disk |Digital |

|Hard disks | | | |

|CD, DVD |All forms |Bits stored as series of optical bumps to be read by laser |Digital |

Analogue (analog) signal: a potential difference that varies continuously with time

Digital signal: a potential difference that is either High (1) or Low (0)

5. What is an advantage of using a CCD with a higher quantum efficiency?

Pixel: the smallest area on the silicon or semiconductor chip that can detect a photon and behaves as a small capacitor.

1. The graph shows how the analogue voltage of a signal varies with time. Convert this to a digital signal using a sampling rate of 10000 Hz.

1. Determine the number of separate bits needed to represent the phrase: I love IB Physics!

Sampling: In order to convert an analogue signal (voice, music, pictures, etc.) into a digital signal that can be stored on a digital device (CD, DVD, computer hard drive, flash drive, etc.), the signal voltage is measured at regular time intervals (sampled). The measured value is then converted into a binary number and stored as bits.

Advantages of digital storage of information over analogue storage

Implications for society of ever-increasing data storage capabilities

4. A certain digital X-ray machine uses a CCD that has a quantum efficiency of 85%. Determine the number of X-ray photons needed to build up a charge of 7.2 nC on one pixel in the CCD array.

Charge-Coupled Device (CCD): a silicon chip used to digitally record an image focused onto its surface.

NOTE: CCDs are used for image capturing in a large range of the electromagnetic spectrum. They are used in digital cameras, video cameras, medical X-ray imaging, and telescopes, such as the Hubble Telescope.

Capacitance

Image capture:

1) When photons are incident on a pixel, each photon releases one electron.

This is due to

2) Each pixel acts as a capacitor in that it stores the charge built up by the incident photons. Potential difference is then built up across the pixel as more photons are incident on it.

Thus, the amount of potential difference on a pixel is proportional to

3) An electrode then measures the potential difference developed across each pixel and converts it into a digital signal which is stored in memory.

4) The position of the pixel is also stored.

6. The quantum efficiency of the pixels in a certain CCD is 40%. How much potential difference is built up across a single 35 pF pixel in 5 ms if photons are incident on it at a rate of 4.5 x 106 s-1?

Formula:

Resolution: the ability to distinguish between two sources of light

Applied to CCD:

11. The CCD of a digital camera has a square image collection area that measures 25 mm on each side and a “resolution” of 5.0 megapixels. An object that is photographed by the camera has an area of 4.6 x 10-3 m2. The image formed on the CCD has an area of 1.0 x 10-4 m2.

a) Calculate the magnification.

b)

Some advantages of using CCDs compared with the use of film:

a) Each photo does not require film and is thus cheaper and uses less resources/produces less waste.

b) Traditional film has a quantum efficiency of less than 10% while CCDs can have quantum efficiencies of over 90%. This means that very faint images can be photographed with CCDs.

c) The image is digital and can be stored and edited more easily.

d) Storage takes up less space.

e) Images can be viewed immediately with no processing time delay.

f) Storage, archiving, and retrieving a large number of photos is easy and efficient.

|Digital cameras |Very convenient to take and share photographs, but image quality can be less than that of traditional film unless the |

| |camera is of high quality (more expensive). |

|Video cameras |Digitized images are usually better quality than analogue images stored on magnetic videotape and are easier to store |

| |and transport. It is possible to continuously record video without interruption during playback. Searches are faster |

| |and easier to perform. Digital storage is fast and utilizes re-usable media, an advantage for security cameras. |

|Telescopes |Sensitivity of CCDs is better than traditional film and allows for detailed analysis over a range of frequencies. |

| |CCDs also allow for remote operation of telescopes, both ground-based and in orbit, like the Hubble space telescope. |

|Medical |Digital X-rays have better contrast and can be processed, allowing for enhancements and detailed study. Information |

|X-ray imaging |can be quickly shared between hospitals and more easily stored and retrieved. |

Example: What wavelength of laser light should be used to read the data shown encoded at right?

How does the laser detect the edge of pit?

Condition for destructive interference:

Path difference between two light beams:

Height (depth) of pit:

Reflection from the edge of a pit:

Retrieving information (“reading” a CD or DVD): In order to read the binary data stored on a CD, a laser is needed. The laser is shot through a diffraction grating which produces a central maximum beam to read the data by following the lands and pits in the long spiral track and two first-order maximum tracking beams to keep the central maximum beam on track. As the central maximum beam moves along the spiral track, it is reflected back by the metallic layer. The CD reader looks for either constructive or destructive interference between two successive laser beams reflected back to it.

| |Digital |Analogue |

|Quality |Output can be virtually indistinguishable from input |Output can be virtually indistinguishable from input but is|

| | |more liable to damage or corruption (eg. scratches on LPs) |

|Reproducibility |Use of laser ensures that each retrieval is virtually |Process of retrieval often affects quality of future |

| |identical since light does not damage surface |retrievals (eg. needle may scratch LP) |

|Retrieval |Very high speed |Slow retrieval speed |

| |Different sections can be accessed randomly (each is given |Data needs to be retrieved in sequential order |

| |a digital address) | |

| |Less noise/distortion (corruption) during playback | |

|Portability of stored data |Easier to transport |Storage devices usually take up much more space |

| |Takes up less space (eg. flash drives) | |

| |Less liable to damage | |

|Manipulation of data (editing) |Easily achieved with little corruption of data (eg. |All manipulation increases possibility of data corruption |

| |Photoshop) | |

|Moral/Ethical |Information that is potentially problematic can easily be shared (eg. terrorism, crime) |

| |Issues concerning ownership of electronic data (eg. piracy) |

| |Privacy concerns |

|Social |Use in documenting abuses of human rights |

| |Unequal access to the Internet |

| |Control of information and opinions |

|Economic |Quicker access to information needed to make economic decisions (eg. price comparisons) |

| |Rise of new businesses and decline of older ones |

|Environmental |Reduction in use of paper and other materials used traditionally to stored information |

| |Recycling of electronic junk is problematic due to more dangerous materials used in their manufacture |

| |Vast numbers of CDs and DVDs are produced so there is a problem of disposal since they are not biodegradable |

| |Manufacture of CDs and DVDs involves toxic materials and produces greenhouse gases |

How does laser light distinguish between a binary 0 or 1?

Reflection from a flat section between edges:

Why can more data be stored on a DVD than a CD if they are both digital storage devices?

|Decimal |Binary |

|0 |0 |

|1 |1 |

|2 |10 |

|3 |11 |

|4 |100 |

|5 |101 |

|6 |110 |

|7 |111 |

|8 |1000 |

|9 |1001 |

|10 |1010 |

|11 |1011 |

|12 |1100 |

|13 |1101 |

|14 |1110 |

|15 |1111 |

|16 |10000 |

|17 |10001 |

|18 |10010 |

|19 |10011 |

|20 |10100 |

|21 | |

|22 | |

|23 | |

|24 | |

|25 | |

|26 | |

|27 | |

|28 | |

|29 | |

|30 | |

|31 | |

Bit:

2) Convert the binary number 10011 to decimal.

1) Convert the binary number 101 to decimal.

Place Value:

3) Convert the decimal number 27 to binary.

Encoding text in binary

In computer code, each character of text (letters, spaces, and punctuation marks) is represented by two four-bit binary numbers, as shown by the chart at right displaying the current standard scheme known as the American Standard Code for Information Interchange (ASCII).

Example #1

Example #2

Sampling rate:

|Time (ms) |0.0 |

|Quantum efficiency |The greater the quantum efficiency, the greater the sensitivity of the CCD, therefore images can be recorded |

| |at lower light levels. Thus, the “signal strength” of the CCD is increased. |

|Magnification |A greater magnification means that more pixels are used for a given section of the image. The image will be |

| |more detailed. |

|Resolution |The greater the resolution, the greater the clarity of the image and the amount of detail recorded. |

Data Capture using CCDs

Capacitor:

Example:

1. The potential difference measured across a 100 pF capacitor is 25 mV. Determine the charge and number of electrons stored in the capacitor.

Formula:

Capacitance:

Units:

Structure of a CCD: The surface of a CCD is a silicon chip (made of a semiconductor material) that is divided into many small sections known as pixels (short for “picture elements”) arranged in a grid pattern. Each pixel can be considered to behave as a capacitor.

How many pixels are on a CCD in a typical digital camera?

Formula:

8. How tall is the image of a 1.2 meter person on the CCD of a digital camera if the camera’s magnification is 2.5 x 10-3?

Magnification –

c) Two small dots on the object are separated by a distance of 0.20 mm. Deduce whether the images of the dots will be resolved.

b) Estimate the length of a pixel on the CCD.

One star

10. A digital photograph is taken of a person whose eyes are 0.060 m apart. The distance between the eyes of the image incident on the CCD is 7.1 x 10-4 m. The CCD has an area of 4 x 10-4 m2 and contains 5 megapixels.

a) Calculate the magnification of the camera.

b) Calculate the length of one side of a pixel.

c) Determine whether the eyes of the person can be resolved in the image on the CCD.

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