> 360 URLs

WELCOME-to williamson-labs.com --HOME

> 90 Subjects

BOOKS:

LINKS:

DEMO of OPTICS for EEs

The four main constituents of Optics are:
Reflection, Refraction, Wave theory & Quantum theory

Light Source

Object S at f₁
S: Source

Lens, thin
Double Convex (DCX)

Image P at f₂
P: perfect image

Light from the Light Source Reflects off of the (object S)
Some of the Reflected Rays are gathered by the Lens
The Lens Refracts those Rays and Focuses them onto the (image P)

NOTES:
1)_ For simplicity, the above illustration is for only one "Point" on the imaged object.
Imagine a similar diagram for every point on the surface of the object

2)_ The location of image is called the Focal Plane. It is made up of thousands of focused points of light, equal to the number of points on the object surface. [1]

3)_ Notice there is an Inversion of the Image through the single lens.

[1] The number of points imaged by the lens is limited by the "Diffraction Limit."

PREFACE
(Along with the Introduction, the part everybody Skips)

Optics for EEs, is one in the © Intuitive Concepts Series.

The philosophy behind the © Intuitive Concepts Series is to convey the concepts of a particular subject with a Minimum of clutter.

The idea is to communicate a Concept on an Intuitive level; leaving the reader "Feeling" the subject matter.

Too often a subject is confused by DETAILS interjected at the wrong time. Many details are better left to later--when the reader is ready and willing to know them... In fact, so many of these details take care of themselves as the concepts start to solidify.

The heart of the © Intuitive Concepts Series is the use of graphics and animations to convey, on a visceral level, the ideas and concepts needed by the reader.

If a Picture is worth a thousand & twenty-four words; how many words is an Animation worth?

For the over three thousand year History of OPTICS, as well as, present day--and the future, see: the Introduction page.

....

Prologue
(A.K.A., BS)

Optical Fibers, Optical Storage, and the ultimate, Optical Computing

Data transport using Soliton Pulses in Dispersion-Shifted Fiber
Single Fiber: Errorless data transmission: 50 Gb/s, at over 19,000 km, No Repeaters

Undersea Fiber Optic Cable: TAT-14 (map)

The 15,000-mile cable, which incorporates dense wave division multiplexing (DWDM) with 16 wavelengths of STM-64 per fiber pair, is operating at a protected capacity of 640Gbps, with a total capacity of 1.3 Tbps; enough to transmit the content of more than 400 full length movie DVDs every second.

Repeaters that amplify light using Erbium-doped Fiber Light Amplifier EDFA
40 THz bandwidth (12.5⁶ bibles/sec)

10 Fsec pulses from Erbium-doped Fiber LASER
   Pulse widths ~ 10 Femtoseconds (10^-15 sec)
   Light travels 1/8th the thickness of a sheet of paper in 10 Fsec.
   1 Fsec is to one second as one second is to 32 million years.

The next generation of computing--Optical Computing, will have CPU operations and bus speeds measured in THz, data paths >>kbytes wide. Logic operations will occur in ‘optical space’ as Soliton wave packets interact algebraically/logically--the operations happen outside of silicon. The hardware: sub-micron LASERS communicating across sub-micron 'free space,' both transferring and processing data, stored in Terra Byte optical storage. [_*]

Notes:
Today
Tomorrow
[_*] Forecasting the future of technology is a Fool's Errand.

For the over three thousand year old History of OPTICS, as well as, present day--and the future, see the Introduction page.

.....

...

DEMO of OPTICS for EEs

Incident light rays

The angle of the Reflected rays is equal to the angle of the Incident rays.

When looking at one's self in the mirror--our right is now on our left, why then aren't we upside down?

The mirror is believed to be the first optical device, dating back to 1900 B.C.

Early mirrors were made of polished copper, bronze, and later, of speculum, a copper and tin alloy. Hence the term specular: See below.

Specular Reflection

Diffuse Reflection

Specular (shinny) Surface

Diffuse Surface

Retro-Reflector

Reflecting Mirrored Surface

Reflecting Prism with mirrored sides

Normal of Reflection The angle of the Reflected rays is equal to the angle of the incident rays. NORMAL

Second-surface Mirror
with Internal Reflections cause "ghosting."

First-surface Mirror
No Internal Reflections

Reflective Layer on Back side of Glass,
with protective over-coating on the back.

Reflective Layer on Front Surface This type of mirror is preferred in optical instruments; however,
It is delicate, and subject to scratching.

Critical Angle

When is a transparent surface (glass) a mirror or a window? "It all depends on how you look at it."

How often have we looked at ourselves as we passed a store's display window?
We could both see ourselves and inside.

Glass panes are "two-way" mirrors; of course, real two-way mirrors have coatings that determine the ratio of reflection to transmission.

We have trouble seeing the fish for the "glare,"
but that #*@' fish always seem to see us!

DEMO of OPTICS for EEs ORDER

The key to understanding Lenses, is to understand the refraction of light, as well as, the "Index of Refraction" (represented by n) of different transparent media.

Refraction:
Refraction is what happens to light rays that enter into one transparent material from another material of different density, or index of refraction (n), e.g., Air to Glass.

In essence: the velocity of light, c, in free space, (where n = 1.000000 for a vacuum) is~300 million meters per second. When that light enters the atmosphere it is slowed in velocity, by a slight amount determined by the index of refraction of Air (n = 1.000293). When that light enters, say glass, it is slowed by a considerable amount (where n = 1.517 for crown glass).

Each time the light crosses an interface--as the light rays change velocity--the rays also change direction: they diverge. The angle of divergence is dependent on several things: the difference in "n" of the two bounding media (air - glass), the angle of entry at the interface, and the wavelength (frequency), of the light rays (dispersion).

** divergence = a deviation from a course or standard GLOSSARY

Classic Illustration of Refraction in Action:

Refraction and various Angles of Incidence in Glass Plates

Assorted Indices of Refraction



Plane Waves impinging the Air-Glass interface	Reflection, Refraction & Internal Reflection

Refraction and various Angles of Incidence in Glass Prisms

Index of Refraction,-n

DEMO of OPTICS for EEs

Index of Refraction
Index of Refraction (n) is the numeric representation of a transparent material's ability to Refract, or bend light rays.

The denser the material, the greater the index. A Vacuum has the lowest index of refraction, n = 1.0000, Air is n = 1.000293, Water n = 1.333, crown glass with n = 1.517, and Diamond is near the highest with n = 2.416 (Gallium phosphide n = 3.50).

Index of Refraction (n) Illustrated

Divergence

Examples of interfaces between various refractive indices.


Glass > Air	Glass > Water	Glass = Fluid

Notice that due to no differing refractive indices there are no visible interfaces in the Glass = Fluid example.

The figure illustrates divergence's dependence on angle of incidence.	(colors used for clarity)
Notice the lack of divergence when the light ray is perpendicular to the plane of the glass surface.

--Material (Media)	--n
Vacuum	1.000000
Air	1.000293
Water	1.333
------Ice	1.310
Ethyl Alcohol	1.360
Plexiglas	1.51
Boro-silicate crown glass	1.517
Gelatin	1.530
Light flint glass	1.588
Dense flint glass	1.649
Zircon	1.923
Diamond	2.416
Rutile	2.907
Gallium phosphide	3.500

Mirage caused by air density variation

Hot roadway and cool air above, refract the light causing the view to be displaced. Because the observer is looking at a low grazing angle, the image is actually a reflection of the scene.

Now to add another Ingredient:

..Dispersion

As has been mentioned, among the several things that affect the angle of divergence of refracted light is, wavelength. This effect is called Dispersion; and is illustrated in the adjoining figure.

Note that red light is affected less than blue light. Blue light is more energetic than red light.

Refractive Prism

Prisms as a Lens
To better Illustrate the Refraction of Light by a Lens

As the next step to understanding the operation of a Lens,
lets look at the action of discrete glass segments--Prisms--functioning as a Lens.

DEMO of OPTICS for EEs ORDER

Prisms as a Positive Lens		Prisms as a Negative Lens
	The faces of each prism is flat
Converging light rays mean a Positive Lens		Diverging light rays mean a Negative Lens

REMEMBER:	Positive lenses make it look BIGGER
	Negative lenses make it look smaller

Animation showing light rays entering and exiting the curved surfaces of a lens.

Notice that the deviation of the light rays takes place at the surface boundaries (interfaces) only.

DEMO of OPTICS for EEs

"Normal"

GLOSSARY:..

Normal: "perpendicular to a tangent at a point of tangency." The NORMAL is a line of reference that is perpendicular to the surface of the optic at the point of reference.


Normal of Reflection	Normal of Refraction

some Lens Types


PCX (+)	DCX (+)	PCV (-)	DCV (-)

Plano Convex	Double Convex	Plano Concave	Double Concave

(+)	(+)	(+)	(+)

Positive Meniscus	Doublet Cemented	Aspheric

DEMO of OPTICS for EEs ORDER

Thin Lenses

DEMO of OPTICS for EEs

.
.

Geometric Optics

Geometric Optics
is that branch of optics dealing with the tracing of ray paths through optical systems.

Illustrations of Radiating & Plane Wave Light Wave Conversions

As the wave enters the glass with its denser index of refraction (n = 1.517) the waves slow down, and are transformed from circular waves to parallel or Plain Waves.

Because the plane Waves are orthogonal to the angle of incidence, upon exiting from the Plano surface of the lens, the Plane Waves remain unchanged; that is they project an image of source S as parallel waves (neither diverging or converging)..

~~~~The Way of Light Waves~~~~

Light starts out from a Point Source, diverging as ever increasing circular ripples. As the wave front propagates over distance it becomes flattened until for all intents and purposes, the wave front is parallel--a "Plane Wave."

If this wave front impinges upon an aperture of a certain size [2], the plane waves will undergo "Diffraction" where the aperture acts as a point source and emits the light energy escaping through the aperture as diverging Near-field waves; behaving the same as the original point source waves.

DEMO of OPTICS for EEs

Illustrations of Light Wave "conversions" by Plano Convex Lenses (PCX)

From source "S," a Diverging Circular Wave impinges upon the spherical or convex side of a Plano Convex lens.

Two Plano Convex (PCX) lenses

Source "S"

Slowed waves in Lens

Propagating Plane Waves -->
in Air

Slowed waves in Lens

Image "P"

From Diverging Circular Wave to a Plane Wave -->		--> From Plane Wave to a Converging Circular Wave
From source "S," a Diverging Circular Wave impinges upon the spherical or convex side of a Plano Convex lens.		Because the plane Waves are orthogonal to the angle of incidence (90º), upon exiting from the Plano surface of the lens, the Plane Waves remain unchanged; that is they project an image of source S as parallel waves (neither diverging or converging)..

Aberrations

*Aberrations Related to Wavelength*	Chromatic Aberration (CA)
*Aberrations Related to Geometry*	Monochromatic Aberrations: Spherical Aberration (SA), Coma, Astigmatism, Petval Field Curvature, Distortion

Chromatic Aberration (CA), Dispersion Related

Another Refractive Prism illustrates Dispersion

Achromat

Achromat corrects for Chromatic Aberration
Using Glass of two different n

Spherical Aberration (SA)

Geometrical Distortion

Spherical Aberration

DEMO of OPTICS for EEs

Spherical optics--lens or mirror--are the easiest to grind and polish. Unfortunately, they are not the ideal geometry for precision optical systems. For short focal lengths, where the curvature is the most severe, distortion or Spherical Aberrations are inevitable. For longer focal lengths, where the curvature is shallow, often they will suffice.

The ideal geometry is Aspheric, conforming to a Parabola; however, to grind and polish these shapes is not easy.
In the case of Lenses, aspheric lenses are amenable to casting ; also lenses can be made using Gradient-index (GRIN) technology. GRIN lenses attain the desired prescription by the proper mix of inhomogeneous materials.

In the case of Mirrored optics, the options are fewer, and more costly.

One approach that has been used for many years, is the Schmidt Optical System. The Schmidt uses a Spherical Mirror and a refractive aspheric correcting plate placed ahead of the primary and secondary mirrors.

The Spherical mirror has a focal point--for infinity, of half the radius of the sphere (R/2). Notice that any other point, is a focal point for either, beyond infinity or less than infinity; the radius being the extreme where the sphere focuses on itself (R/1).

Spherical Mirror ver Parabolic Mirror ver Corrected Spherical Mirror


Spherical Mirror Focal Points
..

Pinhole Camera

A Lens-less Camera


Object	Pinhole Camera	Image pinhole = Very Small


Image pinhole = Small	Image pinhole = Medium	Image pinhole = Large

DEMO of OPTICS for EEs ORDER

.
.

APPLICATION

Cameras
Lensed Cameras

Large Format Portrait Camera	35 mm Film Camera

Uses ground glass for focusing Note the image is inverted	Single Lens Reflex Through the view finder, the image is not inverted due to the action of the Penta prism; however, it is inverted on the film.

Light- Propagation--->

Diffraction

If this wave front impinges upon an aperture of a certain size [2], the plane waves will undergo "Diffraction" where the aperture acts as a point source and emits the light energy escaping through the aperture as diverging Near-field waves; behaving the same as the original point source waves.

Interference

Plane Waves

Apertures

Diverging
Near Field waves

Projection Screen

Example of two phase coherent waves Interfering

Interferometry

The above is related to the science of interferometry; which is used in extremely precise measurements—precision measured in fractional parts of wavelengths. See Spectrum