A5 Resolution

What is Resolution? Refers to the sharpness and clarity of an image. You would have come across resolution in the for of pixels in cameras, televisions and printers but resolution of optical instruments is also very important in our lives. While resolution of light can be associated with non coherent white light. To make life easy we will only consider monochromatic (coherent)light, such as that produced by a laser, in this powerpoint.

Resolution and the Airy Disk This phenomenon is caused by diffraction or scattering of the light. The central maximum of the Airy patterns is often referred to as an Airy disk, which is defined as the region enclosed by the first minimum of the Airy pattern and contains 84 percent of the luminous energy. These Airy disks consist of small concentric light and dark circles as illustrated in Figure 3. This figure shows Airy disks and their intensity distributions as a function of separation distance.

Rayleigh Criterion The Rayleigh criterion specifies the minimum separation between two light sources that may be resolved into distinct objects. The central region of the profile, from the peak to the first minimum, is called the Airy disk. It has an angular radius given by: b sinθ = 1.22λ or θ =1.22λ/b or using the small angle approximation that sin θ ≈ θ (where θ is measured in radians). b = circular aperture width (m) λ = wavelength of monochomatic light. (m)

I resolve that you can call me Baron! If we have two point or more point sources very close together, their Airy disks will overlap. It is only possible to resolve a pair of sources if the central peaks of the two diffraction patterns are no closer than the radius of the Airy disk. This is known as the Rayleigh Criterion and was named for John William Strutt, the 3rd Baron Rayleigh.

Well Resolved These two stars are clearly resolvable, as their Airy disks do not overlap. Well Resolved

These two stars are not resolvable. These two stars are just resolvable - although the Airy disks overlap, they are separated by more than the Airy disk radius. These two stars are not resolvable. Just Resolved Not Resolved

An example Problem What is the Rayleigh criterion for diffraction- limited vision for an iris diameter of 5 mm and a wavelength of 500 nm? λ = 5 x 10-7 m b = 5 x 10-3 m θR = 1.22 λ/b ΘR = 1.22 (5x10-7) 5x10-3 θR = 1.22x10-4 rads

Practical Devices that involve diffraction and resolution These include CDs and DVDs Electron Microscopes Radio Telescopes

Compact Discs - CDs The maximum amount of information that is stored depends on the size and method used for recording. A CD can store up to 74 minutes of music, so the total amount of digital data that must be stored on a CD is: 783,216,000 bytes To fit more than 783 megabytes (MB) onto a disc only 4.8 inches (12 cm) in diameter requires that the individual bytes be very small.

Cd structure Diagram of CD layers. A. A polycarbonate disc layer has the data encoded by using bumps. B. A reflective layer reflects the laser back. C. A lacquer layer is used to prevent oxidation D. Artwork is screen printed on the top of the disc. E. A laser beam reads the polycarbonate disc, is reflected back, and read by the player.

Extra for the interested CD data are stored as a series of tiny indentations known as “pits”, encoded in a spiral track moulded into the top of the polycarbonate layer. The areas between pits are known as “lands”. Each pit is approximately 100 nm deep by 500 nm wide, and varies from 850 nm to 3.5 µm in length. The optical lens of a CD drive. The distance between the tracks, the pitch, is 1.6 µm. A CD is read by focusing a 780 nm wavelength(near infrared) semiconductor laser through the bottom of the polycarbonate layer. The change in height between pits and lands results in a difference in intensity in the light reflected. By measuring the intensity change with a photodiode, the data can be read from the disc.

DVDs A DVD is very similar to a CD, but it has a much larger data capacity. A standard DVD holds about seven times more data than a CD does. This huge capacity means that a DVD has enough room to store a full- length, MPEG-2-encoded movie, as well as a lot of other information. Here are the typical contents of a DVD movie: Up to 133 minutes of high-resolution video, in letterbox or pan-and-scan format, with 720 dots of horizontal resolution (The video compression ratio is typically 40:1 using MPEG-2 compression.) VCD has a resolution of 352 x 288, while DVD has a resolution of 720 x 480. Soundtrack presented in up to eight languages using 5.1 channel Dolby digital surround sound. Subtitles in up to 32 languages DVD can also be used to store almost eight hours of CD-quality music per side.

Electron microscope For light microscopy the wavelength of the light limits the resolution to around 0.2 micrometers (10-6) In order to gain higher resolution, the use of an electron beam with a far smaller wavelength is used in electron microscopes. High Resolution Transmission Electron Microscopes TEM (HRTEM) has allowed the production of images with sufficient resolution to show carbon atoms in diamond separated by only 0.89 ångström (89 picometers 10-12m) and atoms in silicon at 0.78 ångström (78 picometers 10-12m)at magnifications of 50 million times. The ability to determine the positions of atoms within materials has made the HRTEM an important tool for nano- technologies research and development.

Radio telescopes A radio telescope is a form of directional radio antenna used in radio astronomy and in tracking and collecting data from satellites and space probes. In their astronomical role they differ from optical telescopes in that they operate in the radio frequency portion of the electromagnetic spectrum where they can detect and collect data on radio sources. Radio telescopes are typically large parabolic ("dish") antenna used singularly or in an array.

The size of the dish limits the resolution possible. This is why arrays of several radio telescopes linked together to create a virtual radio telescope with greater diameter and with a greater ability to resolve astronomical objects. For example the Very Large Array (VLA) (below) in Socorro, New Mexico has 27 telescopes giving 351 independent baselines at once to achieve resolution of 0.2 arc seconds.