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Image Formation: Seeing is believing.
For a general introduction to the field of optics, you may like to visit the HyperPhysics Light and Vision pages, where many terms are defined and explained in an extremely comprehensive manner.
Image from space shuttle
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This is a very special time, in that the field of optical engineering is expanding as rapidly and with as much impact as transistor technology was seen to achieve during the 1960 & 70s. |
What is an image, what makes up an image and how does the eye interpret what it sees?
Essentially an image is the conversion of the optical rays entering the eye into brain.
The Human Eye
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The human eye is a very special lens. It is a high resolution, very intelligent device. |
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The eye is a complex optical system with many interfaces, but it may be considered as a simple refractive surface that can change its curvature The nodal point of this simple optic system is situated 7 mm behind the anterior corneal surface and 17 mm in front of the retina. |
The insect eye
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Image of the construction of the eye. |
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The image that the fly is looking at. |
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How the image is perceived through the eye of the fly. |
Computational demands of vision
We can calculate what constitutes a typical image as seen by the eye. The problem until recently has been that there is so much information in each image that processing and manipulating brings virtually all computers to their knees.
 | Average image is approximately 7,000 x 2,000 pixels = 14 Mpixels. |
| Typical digital camera have a maximum resolution of 2,000 x 1,000 pixels. |
| Photographic film has a resolution of 4,000 x 4,000 pixels. |
| However the eye has a sensitivity of 12-14 bits and a framing rate of 10 frames/sec. |
| Which is 14 x 2 x 10 M byestes/s. |
| Approximately 300Mbyes /sec. |
Why does a Magnifying Lens make things look bigger?
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This is a question where the "light as geometrical rays" approach works quite nicely, as shown in the picture below. Many optical instruments bend rays in a similar manner to "fool" the visual (eye/brain) system into seeing a virtual image like this (it is "virtual" because it cannot be projected like a real image -- the focusing ability of the eye is a required part of such an optical system). |
Wavefronts and rays
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Wave fronts from a point source are spherical surfaces of constant phase. Rays are lines that are normal to these wave fronts, showing the direction of energy flow at one particular point. |
Snell's law and refraction
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Snell's Law was discovered in 1621 -- It precisely defines how light is bent, or refracted, when it passes through a boundary between two media of differing index of refraction (n), such as air and glass or air and water (the angles theta-i and theta-t are the incident and transmitted angles, respectively). We notice refraction when we look at an object that's under water: |
In a sense, all of geometrical optics is contained in Snell's simple expression.
Types of Lenses
Lenses come in many shapes and sizes, and many optical systems make use of multiple lens elements to bend the light in just the right way to form images as required while minimizing aberrations. A basic distinction is between a positive (focusing or converging) lens and a negative (diverging) lens:
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Positive or converging lens: |
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Negative or diverging lens: |
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Although these particular examples are symmetric in shape (front and back curvatures are equal but opposite in sign), most lens elements are not symmetric. The curvatures, glass properties, and thickness all affect the way that the lens alters the path of light passing through it. Determining these parameters (usually for a number of lenses working together) is the job of the optical designer.
Spot Diagrams
Spot diagrams are graphs that show where rays from a point object will fall on the image surface (they must fall close together if the lens is to form a good image). The graph is usually highly magnified (as if you looked at the image spot through a microscope), and its shape can indicate the type and amount of aberration in the lens. Perhaps most distinctive is the aberration coma, whose name is fairly descriptive.
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Coma looks like a comet: |
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Spherical aberration is circular and concentrated at the centre: |
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Simple astigmatism shows X-Y asymmetry : |
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This one has higher order astigmatism mixed with other aberrations: |
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This is an off-axis point for glass singlet, and astigmatism gives the overall shape. The prism-like dispersion of glass focuses the red, green, and blue wavelengths differently. This is called chromatic aberration: |
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Spherical Aberration
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Spherical aberration results from the geometry of the REFRACTION and REFLECTION of rays. It prevents a converging lens or mirror from bringing parallel rays into perfect focus, because the focal length for rays focused by the central part of the lens differs from that for rays focused by the outer parts. For the spherical reflector shown above, two parallel rays enter from the left (from a point source located a very large distance to the left, such as a star). The ray near the edge (red) crosses the axis (black line) closer to the mirror than the lower (blue) ray. We say the outer ray "focuses short." If the spherical surface is turned into a parabola, both rays would focus at the same distance from the mirror. |
Hubble Space Telescope
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The Hubble Space Telescope (HST) is a large astronomical telescope that orbits the earth, allowing it to view distant objects without the disturbing effects of earth's atmosphere. An error was made in the fabrication of its large primary mirror, and unfortunately this error was not discovered until the HST was in earth orbit. The resulting spherical aberration prevented the HST from forming ideal images. Discovering the exact nature of the problem and inventing a fix required the work of many optical engineers, scientists, and designers from many organizations (including ORA). The repair mission to install "corrective lenses" restored the HST to nearly its design performance. For more information on the HST (and a lot of fascinating educational material on astronomy and other related subjects), visit the Web site at the Space Telescope Science Institute. |
Limit of Resolution :
This is a fundamental issue in the design of any optical systems. It restates the principle that the spatial temporal envelope, also known as the uncertainty principle, is finite. What you see is not what you get.
In other words whenever you make a measurement or try to record an event it is not possible to accurately completely record that event, only represent it.
We can illustrate one aspect of this by investigating the Rayleigh criteria.
We can use the limit of resolution to calculate the optical resolution of the human eye.
| s = 1.21 l F
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What defines the resolving power of an optical system.
The resolving power can be defined in two ways.
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The Rayleigh criteria considers two point sources being imaged through an imaging system. The limit of resolution is when the two points can no longer form two distinct images. |
There are two categories of resolution. Those caused by geometric distortion and that created by the wavelength of light. The latter criteria is known as the diffraction limit.
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