Exercise:

For what purposes do we make visual representations?

Visualisation is as old as humanityPaleolithic cave paintings, Lascaux, France, ca. 30000 years ago.

Image from http://www.culture.gouv.fr/culture/arcnat/lascaux/en/

Paleolithic figurine, “Venus of Willendorf,” ca. 25000 years old.

Image from Wikipedia

These are visual representations of objects that are remembered or imagined – products of abstract visualisation.

Human seeing is built of multiple components

Detection:

Light vs. dark

Motion, direction

Patterns, orientation

Edges

Contrast:

Gradients, shading

Relative distance & size

- parallax, stereopsis

Color discrimination

Object discernmentand

Object recognition, visual computation

Human seeing is built of multiple components: detection, contrast, object discernment

Human seeing is built of multiple components: object discernment

Spring peeper (frog), Pseudacris crucifer

Image from http://www.uri.edu/cels/nrs/paton/photo_sppe.htm

A classic illustration of object-background discrimination

Exercise:

What is an image?

Wavelength is inversely proportional to frequency: λ = c/ν Energy is directly proportional to frequency: E = hν and inversely proportional to wavelength: E = hc/λ

Most imaging depends on manipulating and detecting electromagnetic radiation

E-M radiation is is usually treated as propagating waves.

Refraction changes the direction of propagation at an interface

Light waves travel more slowly in media such as glass or water

Image from http://www.williamson-labs.com/optical-body.htmThis website has some nice introductory optics material.

Index of refraction is a measure of resistance to light propagation

Refractive index = speed of light in vacuum / speed of light in material

⇒Snell's law:

Index of refraction depends on wavelength, and is different for different materials

Wavelength dependence of refractive index for some glasses. This function is also known as a dispersion curve.

visible

Focus is a composite effect of refraction (or of reflection)

http://www.williamson-labs.com

from Hecht and Zajac, Optics

The focusing effect of a lens can reconstruct wavefronts from an object.

This is known as image formation.

1/f = 1/so + 1/s

i (the Gaussian Lens equation)

An image can also be formed by removing all the unfocused rays.

This is the principle of a pinhole camera.

This CCD pinhole camera is only $65 at spygadgets.com

Undesigned lenses can form images

Flower in the background imaged through hanging dew dropsFrom http://www.flickr.com/groups/macroviewers/discuss/72157594313729574/

Thus imperfect eyes can be useful.

Parabolic surfaces are used to focus radiofrequency signals and sunlight.

satellite communication: satellite dish antenna." Online Art. Encyclopædia Britannica Online. <http://www.britannica.com/eb/art-67385>.

Your home satellite dish has the shape of a part of a paraboloid. A radio telescope works the same way, but with a larger dish.

A cylindrical paraboloid reflector makes an effective solar heat collector. The center pipe usually has water or another fluid pumped through it.

Each point on a parabola will reflect normally-incident light to the parabola's focus point.

normal(=90°)

incidence

The surface formed by rotating a parabola about its axis is a

paraboloid.

axis

A parabolic refracting surface (e.g. a glass lens) will also focus parallel rays to a point.

A discontinuous array of reflectors can approximate a larger parabolic dish

The Solar One solar power stationBarstow, California, 1993

PIX Number 00036Sandia National LaboratoriesNational Renewable Energy LaboratoryU.S. Department of Energycopyright, U.S. Department of Energy

The Solar One mirror array as seen on Google Earth.

Likewise, a discontinuous array of refracting surfaces can approximate a lens

A Fresnel lens (right) has most of the refracting surface of a solid spherical lens (left).

A Fresnel lens can give the same focusing power with much less glass, so it can be much thinner and lighter.