Lecture 4:

Optics

The Electromagnetic Spectrum - An electromagnetic (EM) wave is comprised of an oscillating electric field and a magnetic field. EM waves propagate through a vaccuum at around 3x108 meters/sec or 186,000 miles/sec.

Electromagnetic Waves

Different EM waves are characterized by their rates of oscillation which can be quantified as the frequency of the EM wave measured in Hertz or cycles/per second. The distance traveled by the wave during one period of its oscillation is called the wavelength. Radio waves range from several hundred meters down to less than 1 meter in length; radiant heat (infrared energy) is comprised of EM waves measured in millionths of a meter or microns and can range from a few hundred microns down to around 1 micron; visible light is measured in Angstroms or nanometers (1x10-9 meters) and ranges from between 780 and 380 nanometers.

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The Electromagnetic Spectrum

When we refer to visible light we mean light that is visible to humans, however electro-optical components and some animals can see in the near-IR and ultra-violet (UV) regions of the spectrum. Photoresistors and photovoltaics can be made that respond to IR, NIR, visible and UV wavelengths.

The Visible Spectrum

Sources of Light - Sources of light can be natural or artificial. The distribution of energies at the various wavelengths is referred to as the spectral power distribution of the light source.

Spectral Responsivity - The sensitivity of a light sensor as a function of the wavelength of the light is called the spectral responsivity of the sensor. It is important to match the spectral responsivity of the light sensor to the spectral power distribution of the light source.

Blackbody - A blackbody radiator is a theoretical material that reflects emits 100% of its thermal energy as radiant energy.

Color Temperature - Color temperature refers to the heat of a light source. As color temperatures vary, so does the distribution of energy at each wavelength. This distribution is quantified by Planck's Law.

Some Basic Principles

Plank's Law

Planck's Law gives the relationship between the spectral power distribution of a blackbody radiator and its temperature. The distribution of EM energy emitted from a blackbody as a function of wavelength for various temperatures is shown below.

The nature of light and the visible spectrum one of the three factors that permit us to see colors and light. The second factor has to do with the interaction of light and matter, for when we see an object as blue or red or purple, what we're really seeing is a partial reflection of light from that object. The color we see is what's left of the spectrum after part of it is absorbed by the object.

First, let's look at the general properties of light interacting with matter. When light strikes an object it will react in one or more of the following ways depending on whether the object is transparent, translucent, opaque, smooth, rough, or glossy:

It will be wholly or partly transmitted.

It will be wholly or partly reflected.

It will be wholly or partly absorbed.

Interaction of Light & Matter

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Transmission takes place when light passes through an object without being essentially changed; the object, in this case, is said to be transparent:

Transmission

Some alteration does take place, however, according to the refractive index of the material through which the light is transmitted.

Refractive Index is the ratio of the speed of light in a vacuum to the speed of light in a given transparent material (e.g., air, glass, water). For example, the RI of air is 1.0003. If light travels through space at 186,000 miles per second, it travels through air at 185,944 miles per second—a very slight difference. By comparison, the RI of water is 1.333 and the RI of glass will vary from 1.5 to 1.96—a considerable slowing of light speed.

The point where two substances of differing RI meet is called the boundary surface. At this point, a beam of transmitted light (the incident beam) changes direction according to the difference in refractive index and also the angle at which it strikes the transparent object. This is called refraction.

Light striking the surface of an object straight on (that is, at normal incidence) will pass through without refraction (as in the illustration above). But light striking at any other angle will be refracted as well as partially reflected:

The RI of a substance is further affected by the wavelength of the light striking it. The RI of a transparent object is higher for shorter wavelengths and lower for longer ones. This is most apparent in the refraction of a light beam through a prism. The red end of the visible spectrum does not refract as much as the violet end. The effect is a visible separation of the wavelengths. The rainbow is another example, where sunlight is refracted through raindrops in a manner similar to the refraction of light through a glass prism.

If light is only partly transmitted by the object (the rest being absorbed), the object is translucent. The degree of absorption is the only essential difference. Light transmitted through a translucent object reflects and refracts according to the same principles as light transmitted through a transparent object.

Reflection  - As we've seen above, light that strikes a transparent object is transmitted in part and reflected in part. But when light strikes an opaque object (that is, an object that does not transmit light), the object's surface plays an important role in determining whether the light is fully reflected, fully diffused, or some of both. A smooth or shiny surface is one made up of particles of equal, or nearly equal, refractive index. These surfaces reflect light at an intensity and angle equal to the incident beam:

Reflection

Most commonly, light striking an opaque object will be both reflected and scattered. This happens when an object is neither wholly glossy nor wholly rough.

Finally, some or all of the light may be absorbed depending on the pigmentation of the object. Pigments are natural colorants that absorb some or all wavelengths of light. What we see as color, are the wavelengths of light that are not absorbed.

Absorption

The wavelengths of light that concern us most are the red, green, and blue wavelengths. These are the basis for the tri-stimulus response in human vision, as well as a significant part of color reproduction.

Vision

After all consideration has been made to the nature of the light and the spectral reflectance of the object being viewed, how you see color depends on the combination of three distinct stimuli of the retina. For this reason, human vision is often referred to as a tristimulus response.

This aspect of seeing color was well described by British physicist James Clerk Maxwell who wrote in 1872,

We are capable of feeling three different color sensations. Light of different kinds excites these sensations in different proportions, and it is by the different combinations of these three primary sensations that all the varieties of visible color are produced.

Maxwell's studies, along with those of Thomas Young and Hermann von Helmholtz, form the basis for all currently held views on human color vision.

The Human Eye

The CIE (Commision Internatinale de L'Eclairage) Standard Observer Curve - This curve shows that humans are most sensitive to green light and least sensitive to red and blue.  This curve also closely matches the sensitivity of the monochromatic sensor used in black-and-white film and in black-and-white video cameras.

Spatial Acuity - Another measure of your vision is the spatial resolution or acuity.  This is what is measured by the standard eye chart.  Your ability to resolve (recognize) objects at a distance is typically stated in relative terms.  For example a person with normal sight is said to have 20/20 vision.  This means that your ability to regonize images (at 20 feet) is what is normal for humans.  A person with 20/400 vision is able to recogize objects at 20 feet that are recognizible at 400 feet by a person with "normal vision".

What is really being measured here is the angular resolution, or the ability to resolve two lines separated by a given angle.  As range to the test object increases the effective angular separation decreases.

The sharpest vision (for normal 20/20 vision) or highest angular resolution is around 1 line-pair per arcmin or 1/60 of a degree.  Human visual acuity drops off quickly as we move away from the visual axis.

The image transmitted from the eye to the visual cortex of the brain undergoes a form of compression.  This natural image compression takes  the form of a band-pass filter.

Lateral inhibition and excitation together lead to a bandpass characteristic of the contrast sensitivity function of the human visual system.

This image compression is lossy. One of the functions of the visual cortex is to reconstruct the image from this compressed information.  Usually this reconstruction works well but we can set up examples the illustrate the limitations this processing using some simple optical illusions.

Visual Image Compression

Optical Illusions

Sitting within 2 feet of this image, try to count the black dots at the intersections of the gray lines. The width of the gray lines is less than your visual acuity in your peripheral vision but greater than your visual acuity in the region of sharp focus.  Therefore you will experience a "ringing" in the image near an abrupt change in contrast in your peripheral vision.

The gray lines in the image below are all horizontal and parallel to each other.  The skewed alternating black and white boxes interfere with our ability to properly reconstruct this image.

Finally, we can test our ability to correctly process moving images.  Look at the black dot in the center of the image below as you move your head toward and away from the image.

Evolution of the EyeOne of the most straightforward examples of biological evolution is the eye. From the mostly non-directional light sensor to human sight and beyond, a clear continuous process of adaptation and emerging complexity can be traced from the Cambrian Explosion to now.

Focal Length & Field of View

Electromagnetic Waves & the EM Spectrum

Plank's Law

Basics of Light

Refractive Index

The Human Eye

CIE Standard Observer Curve

Spatial Acuity

The Visual Cortex and Image Compression

Optical Illusions

The Evolution of the Eye

Focal Length & Field of View

Summary