©  1999 -  2014  Questions or Comments about this Site webmaster
BOOKS:
LINKS:
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."
 
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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.
 
 
.....

 
 
 

 

  ...

 
 
 
 

 
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 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!
As you look through a glass pane, and rotate it: at the extremes, you either see only reflections or only what is on the other side. Between theses extremes, you see varying ratios of same.

There are coatings that can be deposited on glass (called "half-silvered mirrors") which pre determine the ratios of Reflectance & Transmittance.

 
Reflectance & Transmittance
The sum at any given point is ~ 1; that is,
what is not reflected is transmitted.
   
 More Mirrors:- See Reflecting Telescopes  
   
..
 
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
 |_ = 0º    
     
     
Plane Waves impinging the Air-Glass interface
Reflection, Refraction & Internal Reflection
Refraction and various Angles of Incidence in Glass Prisms
     
 
 
   
..

Index of Refraction,-n

 
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. 
Assorted Indices of Refraction
 
Inhomogeneous medium
   Take a LASER, a Fish Tank, add Sugar & water, and stir:  you now have a demonstration of light refraction through a 'graded' medium.
   As the sugar in solution settles out, the index of refraction at the bottom of the tank is denser (higher) than at the top. Hence, the LASER beam bends more towards the bottom.
 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. 
 
Prisms as a Positive Lens
 Converging light rays mean 
a Positive Lens
Notice the slight angular differences between the inner and outer prisms  The faces of each prism are flat


 
Prisms as a Negative Lens
 Diverging light rays mean 
a Negative Lens
Notice the slight angular differences between the inner and outer prisms
The faces of each prism is flat
.
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.
 

 
 
   
..
..
"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
Normal for Convex Surface
Normal for Concave Surface
..
 
   
..

FYI:- Lens Types

 
PCX (+)
DCX (+)
(+)
PCV (-)
 DCV (-)
(+)
Plano Convex
Double Convex
Compound
Plano Concave
Double Concave
Triplet
           
  (+)
 (-)
 (+)
(+)
(+)
(+)
Positive Meniscus
Negative Meniscus
 Doublet Cemented
Doublet Air Spaced
 Doublet Air Spaced
Aspheric
           
 
 
 
   
..

Thin Lenses

 
 
 
   
..

Thick Lenses

 
 
 
   
..

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. 
Parallel to Converging;   Diverging to Parallel;-----
Parallel to Converging
Diverging to Parallel
   
 
 
 
 Parallel to Diverging
Converging to Parallel
 
 DCV
 
 
Parallel to Diverging
Can be used for LASER beam expanders
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).. 
   
Single Double Convex (DCX) lens
From Diverging Circular Waves |-| to a Plane Waves |-| then back to Converging Circular Waves
 
 
 
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APPLICATION
Relay Lens accommodates Narrow-band Dielectric Filter
Hasting Triplet Dielectric Filter Hasting Triplet
The center frequency of an interference filter can be shifted a small percentage by tilting the filter some small amount from the perpendicular. This allows the "fine tuning" of very narrow-band filters. Likewise, as the optical bandwidth decreases, it’s view angle also decreases, that is, it passes parallel rays more readily than off-axis rays.   See example
 
 
..

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
   
 Refractive Prism illustrates Dispersion
 Another Refractive Prism illustrates Dispersion
 Lens undergoing CA
Achromat
Chromatic Aberration in Lens
Achromat corrects for Chromatic Aberration
Using Glass of two different n
 
 .  
Spherical Aberration  (SA)
   
Geometrical Distortion  Aperture
 Spherical Aberration  Spherical Aberration Correction
 
 
 
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. 

It seems timely to mention the reason for using mirrored optical systems instead of lensed systems. All lenses suffer from chromatic aberrations (color errors; Dispersion); mirrors do not. Of course, there are means for reducing these aberrations to acceptable levels by the use of achromatic lenses, coatings, etc. When greater precision and fidelity are required, the use of mirrors is then appropriate.  However, even in a mirrored system there is inevitably some refractive lens or lenses, e.g., a telescope eyepiece.

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
Spherical Mirror Aberrations
..
   
SA Corrective Systems:
 Parabolic Mirror
 Schmidt Optical System
Aberration Free, the Parabolic Mirror
The Schmidt Optical System employs a Corrector Plate that compensates for the Aberrations inherent in Spherical Mirrors.
 
 
-More on Telescopes
   
Coma
Astigmatism
Petval Field Curvature
Distortion
 
 
   
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Pinhole Camera

A Lens-less Camera
 
Object
Pinhole Camera 
 Image
pinhole = Very Small 
     
 Image
pinhole = Small 
 Image
pinhole = Medium 
 Image
pinhole = Large 
 
   
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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.
   
------------------------Camera Principles
    Image, 
     Focal Plane, 
     Film
Lens
Shutter, 
Aperture
Object
   
 Camera Focal Plane
 
 Lens system in need of a "Field Flattener"
Results of a Spherical Focal Plane
Improved image fidelity requires
greater camera lens complexity
 Results of flattened Focal Plane
 
 
 
..

Light- Propagation--->

 
Diffraction
 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. 
   
Interference
Plane Waves
 

Apertures

Diverging 
Near Field waves

Projection Screen

A Plane Wave wave front impinges upon three apertures, the resultant three diverging Near-field waves project outward onto a screen. Because all three waves have phase coherence, as can be seen on the projection screen, an Interference pattern results from Constructive and Destructive Interference. That is to say: light waves are adding and subtracting from one another.    --Pretty neat, eh? 
 
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
Keck Telescopic Interferometer
Interferometer measuring phase coherent starlight
 
Radio Telescope Interferometer
Part of VLBI Very Long Baseline Interferomtry
Orbital SAR Interferometry  nasa
Synthetic Aperture Radar Images of  the Landers 1992 earthquake zone, show crustal shift. Interferogram is created by differentiation between before and after passes.
   
  LINKS:

Interferometry Cambridge
Interferometry Keck
    Interferometry Links

VLBI NASA
SAR
Airborne SAR
 

 
 
   
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Special Applications

 
Relay Lens accommodates Narrow-band Dielectric Filter
by converting diverging rays to parallel rays
Hasting Triplet
Dielectric Filter
Hasting Triplet
In interference filters,  as the optical bandwidth of the filter decreases, its view angle also decreases, that is, it passes parallel rays more readily than off-axis rays. 

Also, attendant to that, center frequency of an interference filter can be shifted by a small percentage by tilting the filter some small amount from the perpendicular. This allows for "fine tuning" very narrow-band filters.

Main Entry: in·ter·fer·ence 
Pronunciation: -'fir-&n(t)s 
Function: noun Date: 1783 
1 a : the act or process of interfering b : something that interferes : OBSTRUCTION 
2 : the mutual effect on meeting of two wave trains (as of light or sound) that constitutes alternating areas of increased and decreased amplitude (as light and dark lines or louder and softer sound).

For more information on interference filters

 

 
 
 
   
....
LINKS: Tutorials Optics & LASERs Magazines
Organizations & Societies      
..SMPTE Glenbrook.k12: Refraction .Edmund Scientific .Hot List
..SPIE
The International Society for Optical Engineering 
Refraction Demo interactive Java applet MWK Industries Laser Focus World
 ORNL (DoE) Imaging Page      
 Optical Society of America, OSA physicsweb.org/ VLAB/  Edmund Optics
C a m e r a s
NASA MSFC Coherent Lidar/Diffractive Optics Team  JML TechManual Melles Griot Kodak
   Interferometry Cambridge .Hamamatsu RITRONICS 
   Interferometry Keck . Sony
    Interferometry Links    
.HISTORY
  . JML Optical Camera & sensors
.A Fiber-Optic Chronology   Products by Manufacturer:
     
 MISC
MPJA
 
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