The electromagnetic spectrum is the reflected energy, and where it lies within the electromagnetic spectrum. Electromagnetic energy is all around us and is constantly striking objects. The energy is then reflected, absorbed, or transmitted from those objects back to our recording sensor, such as a camera. The energy that is reflected is what it appears as in the picture.

The intensity is the product of photon energy and photon flux. It is sometimes called optical energy flux.

 

 

The Brewster angle is the angle at which the reflectance of the air-liquid surface vanishes for light polarized linearly in the incidence plane

Harrison Anak Mattiew A17SC0047

• The angle of the incidence for which the reflected beam is completely polarized is called the polarizing angle, θp
• Brewster's law relates the polarizing angle to the index of refraction for the material
n=sin θp/cos θp=tan θp
• θp may also be called Brewster's angle

The essence of Faraday effect or Faraday rotation is that it shows the interaction between light and a magnetic field in a medium.

The basic structure of an optical fiber consists of three parts; the core, the cladding, and the coating or buffer. The core is a cylindrical rod of dielectric material. Dielectric material conducts no electricity. Light propagates mainly along the core of the fiber. The core is generally made of glass. The core is described as having a radius and an index of refraction n1. The core is surrounded by a layer of material called the cladding. Even though light will propagate along the fiber core without the layer of cladding material, the cladding does perform some necessary functions.

The cladding layer is made of a dielectric material with an index of refraction n2. The index of refraction of the cladding material is less than that of the core material. The cladding is generally made of glass or plastic. The cladding performs the following functions:

-Reduces loss of light from the core into the surrounding air.

-Reduces scattering loss at the surface of the core.

-Protects the fiber from absorbing surface contaminants.

-Adds mechanical strength

For extra protection, the cladding is enclosed in an additional layer called the coating or buffer. The coating or buffer is a layer of material used to protect an optical fiber from physical damage. The material used for a buffer is a type of plastic.

The buffer is elastic in nature and prevents abrasions. The buffer also prevents the optical fiber from scattering losses caused by microbends. Microbends occur when an optical fiber is placed on a rough and distorted surface. 

SINGLE MODE OPTICAL FIBRE

-Supports only one mode 

-Smaller core diameter 

-Transmission losses 

-Has higher bandwidth 

-Used for long distance communication 

-They are mostly made from glasses 

-They are by default step index 

With a graded-index fiber, the light follows a more curved path. The high-order modes spend most of the time traveling in the lower-index cladding layers near
the outside of the fiber. These lower-index core layers allow the light to travel faster than in the higher-index center layers. Therefore, their higher velocity compensates for the longer paths of these high-order modes. A good waveguide design appreciably reduces modal dispersion.

Material dispersion contributes to group delay distortion, along with waveguide delay distortion, differential mode delay, and multimode group delay spread.

The output from a fiber laser can be either continuous wave (CW) or pulsed. Pulsed fiber lasers are created by modulating the loss of the laser cavity, and the pulsewidth is determined by the temporal profile of the loss modulation and the chromatic dispersion of the cavity.

If your application is laser cutting of metals, you’ll most likely need a high-power CW (continuous wave) fiber laser. For other materials like plastics and rubber, it can be one or the other.

The main difference that determines the type of materials each laser can process is the wavelength. A fiber laser usually has a wavelength of 1,060 nm while CO2 lasers have wavelengths in the 10,600 nm range. In general, fiber lasers have many advantages over CO2 lasers.

Mitigating these effects in an optical fiber is one of the most critical requirements for fiber laser.

A hemispherical fiber distribution separates the transmitting and receiving fibers into two distinct groups, with one half of the probe tip composed of transmitting fibers and the other half all receiving fibers.  Hemispherical probe tips offer a long range, but low displacement sensitivity.

A concentric transmit inside fiber distribution contains a group of transmitting fibers located at the center of the probe tip surrounded by a concentric group of receiving fibers.  This fiber optic probe arrangement offers an intermediate choice between the high-sensitivity/short-range random probe fibers and the long-range/low-sensitivity hemispherical probe fibers. Because of their symmetric arrangement this style of probe is less affected by tilted targets.

where n_eff is the effective refractive index of the fiber core, and
λ_B is the wavelength of the light reflected by the Bragg grating.

Therefore, the Bragg grating wavelength λ_B can be expressed as

Note that the Bragg grating wavelength is the function of the effective index and the period of the grating.

Fiber Bragg grating can be used as a MUX/DEMUX (multiplexer/demultiplexer) device in WDM systems for extracting a signal (channel) with a particular wavelength from a stream of signals (channels).

The fiber Bragg grating will typically have a sinusoidal refractive index variation over a defined length. We have seen the definition of Bragg wavelength λ_B from the previous section.

The wavelength spacing between the first minima, (as shown in above figure), or the bandwidth
 Δλ is given by,

where
 δn₀ is the variation in the refractive index (n₃-n₂), and
η is the fraction of power in the core.

The refractive index has two primary characteristics, the refractive index profile, and the offset. Typically, the refractive index profile can be uniform or apodized, and the refractive index offset is positive or zero.

There are six common structures for Fiber Bragg Gratings;

The circuit that combines signals at the source (transmitting) end of a communications link is known as a multiplexer. It accepts the input from each individual end user, breaks each signal into segments, and assigns the segments to the composite signal in a rotating, repeating sequence. The composite signal thus contains data from multiple senders. At the other end of the long-distance cable, the individual signals are separated out by means of a circuit called a demultiplexer, and routed to the proper end users. A two-way communications circuit requires a multiplexer/demultiplexer at each end of the long-distance, high-bandwidth cable.

If many signals must be sent along a single long-distance line, careful engineering is required to ensure that the system will perform properly. An asset of TDM is its flexibility. The scheme allows for variation in the number of signals being sent along the line, and constantly adjusts the time intervals to make optimum use of the available bandwidth. The Internet is a classic example of a communications network in which the volume of traffic can change drastically from hour to hour. In some systems, a different scheme, known as frequency-division multiplexing (FDM), is preferred.

Each device is assigned a time slot where the TDM will accept an 8 bit character from the device. A TDM frame is then built and transmitted over the circuit. Another TDM on the other end of the circuit de-multiplexes the frame.

 
Wavelength division multiplexing (WDM)

 

In early WDM systems, there have been 2 IR channels per fiber. At the destination, the IR channels were demultiplexed by a dichroic (two-wavelength) filter with a cutoff wavelength some midway between the wavelengths of the 2 channels. It before long became clear that quite 2 multiplexed IR channels might be demultiplexed victimization cascaded dichroic filters, giving rise to coarse wavelength-division multiplexing (CWDM) and dense wavelength-division multiplexing (DWDM). In CWDM, there square measure sometimes eight completely different IR channels, however there will be up to eighteen. In DWDM, there will be dozens. as a result of every IR channel carries its own set of multiplexed RF signals, it's on paper potential to transmit combined information on one fiber at a complete effective speed of many hundred gigabits per second (Gbps).

The use of WDM will multiply the effective information measure of a fiber optic communications system by an outsized issue, however its value should be weighed against the choice of victimization multiple fibers bundled into a cable. A fiber optic repeater device known as the Er electronic equipment will build WDM a cheap long-run answer. 

working of Wavelength division multiplexing (WDM)

 
Wavelength division multiplexing (WDM)

Q. what one can do with wavelength division multiplexing ?

Answer:

 

            Using wavelength division multiplexing (WDM) technology several wavelengths, or light colors, can simultaneously multiplex signals of 2.5 to 40 Gbps each over a strand of fiber. Without having to lay new fiber, the effective capacity of existing fiber plant can routinely be increased by a factor of 16 or 32. Systems with 128 and 160 wavelengths are in operation today, with higher density on the horizon. The specific limits of this technology are not yet known.

WDM increases the carrying capacity of the physical medium (fiber) using a completely different method from TDM. WDM assigns incoming optical signals to specific frequencies of light (wavelengths, or lambdas) within a certain frequency band. This multiplexing closely resembles the way radio stations broadcast on different wavelengths without interfering with each other (see Figure 1-7). Because each channel is transmitted at a different frequency, we can select from them using a tuner. Another way to think about WDM is that each channel is a different color of light; several channels then make up a “rainbow.”

 

Basics of Multiplexing

Difference between Multiplexing and Multiple Access

Comparison in FDM and synchronus TDM and statistical TDM

How Multiplexing of signals in Fiber Optical cable is done?

Dense wavelength division multiplexing works on the same principle as CWDM, but in addition to the increased channel capacity, it can also be amplified to support much longer distances.

Several technical improvements can be obtained by optical connections within CAN bus systems with the use of an optical transceiver, such as secure separation of high voltages and insensitivity to electromagnetic interference (EMI). 

2) It's the easiest network topology for connecting computers or peripherals in a linear fashion.
3) It requires less cable length

In a ring network, packets of data travel from one device to the next until they reach their destination. Most ring topologies allow packets to travel only in one direction, called a unidirectional ring network. Others permit data to move in either direction, called bidirectional.

The major disadvantage of a ring topology is that if any individual connection in the ring is broken, the entire network is affected.

Ring topologies may be used in either LANs (local area networks) or WANs (wide area networks). Depending on the network card used in each computer of the ring topology, a coaxial cable or an RJ-45 network cable is used to connect computers together.

Disadvantages of Ring topology:

Ex: Let’s say A, B, C, D, and E are a part of the ring network. The data flow is from A towards B and henceforth. In this condition, if E wants to send a packet to D, the packet must traverse the entire network to reach D.

In a full mesh topology, every computer in the network has a connection to each of the other computers in that network. The number of connections in this network can be calculated using the following formula (n is the number of computers in the network): n(n-1)/2

In a partially-connected mesh topology, at least two of the computers in the network have connections to multiple other computers in that network. It is an inexpensive way to implement redundancy in a network. If one of the primary computers or connections in the network fails, the rest of the network continues to operate normally.

Connector loss: 0.15dB

Splice loss: 0.15dB

Amplifier gain: 10dB

Fiber optic loss: 0.2 dB/km

The total attenuation of this link is the sum of:
- Fiber optic loss : (30km + 50km) x 0.2dm/km = 16dB
- Attenuation of connectors: 4 x 0.15 dB = 0.60dB
- Attenuation of splices: 5 x 0.15 dB = 0.75 dB

Total Attenuation for this link: 17.35 dB

Total gain generated by optical amplifier: ?

The receiver's sensitivity at the end of the optical fiber link:
Pr=??

 

1)   Image distance = object distance

2)  Image is virtual (no actual rays intersect to build the image)

3) Image cannot be projected on a screen.


b)  Image of an extended object on a plane mirror. All the properties are the same as that of the point object.

1)  Image size = object size or magnification = 1

2)  Transverse orientation of image and object are the same.

3)  A right‐handed object has a left‐handed image.

4)   Image location does not depend on the observer.

c)  The mirror does not lie directly below the object. We can extend the mirror to construct the image.


d) Multiple images of a point object from direct reflections and multiply reflected light rays.

≈ θ ≈6⁰ ≈ 0.1 radians, we can observe an image of S at S’.
From Snel's law for paraxial rays we can write:


n1 tan θ1 = n2 tan θ2 analogous to n1(x/s) =
 n2 (x/s')

Location of the image point:
s' = (n2/n1) s

-If n₂> n₁ then s ' > s and the image forms below the object point. Apparent depth is larger than the reality (seeing objects from a pool) .

-If n₂ < n₁ then s ' < s and the image forms above the object point.

Apparent depth is smaller than the reality (looking into water).

                                                      

From the figure we can write:

θ=α + Φ; 2θ = α + α'

The relationship has to be independent of the ray we choose to trace so we have to eliminate θ between the two equations:We get:  α - α' = -2 Φ
Now applying the paraxial approximation;

For real objects and images the distances are positive.

For the virtual objects and images the distances are negative. Or: real positive, virtual negative

Radii of curvature are positive when C, center of the sphere, is to the right of V, vertex equivalent to convex mirror and are negative when C is to the left of V equivalent to the concave mirror.

Focal lengths of the spherical mirrors are the image distance for the object at infinity and object distance for the image at infinity (figures). Notice symmetric appearance of the conjugate points in the formula.

The general equation for the spherical mirrors:
1/s +1/s' = 1/f
f = -R/2 ===== >0 concave mirror, <0 convex mirror.
Signs of s and s' are determined from the convention.

For flat mirror R approches infinity, and s = -s ' a virtual image

(+) when image and object have the same orientation. (‐) when image and object have opposite orientation. Goal: find a relationship between the image height to the object height as a function of the object and image location. We build the construction and conclude using the law of reflection that:

ho/s = hi/s'

Then, we define lateral magnification: /m/= hi/ho = s'/s

since the image is virtual its distance will be negative, we need a negative sign in the formula.

1)        A ray parallel to the optical axis from the point p hits the mirror, reflects and passes through the focal point.

2)        A ray from point p passes the focal point and hits the mirror, is reflected parallel to the optical axis.

3)        A ray from point p passes through the center of curvature, hits the mirror, is reflected back at itself.

Our eyes generate real images from the diverging rays arriving at their lens on the retina. We can’t see the real images unless they are projected on a screen.

in the Snell's law with the value of the angles in radian we get: 
n1 (α -  Φ )= n2 (α' -  Φ )
Replacing the angles with their tan and assuming QV the axial distance is much less than s,s',R we find :

n1 (h/s-h/R) = n2 (h/s' - h/R), (n1/s) - (n2/s') = (n1 - n2/R )
With the sign convention real positive, virtual negative, and radii of curvature positive when C is to the right of V, and negative when C is to the left of V, the general formula is:
(n1/s') - (n2/s') = (n2-n1)/R
When R approaches infinity ,the spherical surface becomes a plane refracting surface:
s' = -(n2/n1)s     

n1/s1 + n2/ s'1= n2 - n1/R1 where 1 & 2 are subscripts

2nd surface:

n2 /s2 + n1/s'2 = n1 -n2/R2
where 1 & 2 are subscripts.

Assumption: both sides of the lens have the same refracive index.

2nd object distance:
 s₂= t- s'1
this produces a correct sign for the distance. 

where t is the thickness of the lens.

Neglecting t for the thin lenses:
s₂ = -s '1

Combine:
 -n2/s1' + n1/s'2 = n1-n2/R2,

n1/s1 - (n2-n1)/R1 + n1/s'2 = n1-n2/R2,

n1/s1 + n1/s'2 = (n1-n2)/R2 + (n2-n1)/R1,

1/s1 + 1/s'2 = (n2- n1)/n1 (1/R2 + 1/R1),

Finally,gives us the lensmaker's equation :

1/f = (n2- n1)/n1 ((1/R2 + 1/R1))

m = hi/ho = s '/s
With proper sign conventions :

m =- s '/s

m > 0 for images with the same orientation as objects.
 
m < 0 for inverted images.

Vergence is measured in unit of 1/m or Diopter: V= 1/s & V'= 1/s'

Refractive power of an optical system is P =1/f

Spherical lenses produce a point image for a point object (stigmatic).

Cylindrical lenses produce a line image for a point object (Astigmatic).

CL length of lens along the axis of cylinder 

From the similar triangles:
AB/CL =( s + s' )/s
AB =((s+ s')/s))CL

FIGURE 1

1)       Michelson‐Morley Interferometer, a two‐beam, amplitude division device.

2)       Fabry‐Perot interferometer a multiple beam, amplitude division device

  Used in applications such as proving special theory of relativity, measuring hyperfine structure in line spectra, tidal effect of the moon on the earth. Principle of operation is shown in the graph. In the graph of the interferometer the path difference between the beams traveling along the two
perpendicular paths is:
Δ(p) = 2d cos θ

(see the fig. b) where θ

measures the inclination of the beam with respect beam with respect to the optical axis.

For normal beam θ= 0

Δ(p) = 2d = m λ , d= m λ /2 for m= 0,1,2,3

will form constructive interference and will repeat every l/2 so long as d < Lc separation stays smaller than the coherence length.

In practice the light source emits a coherent beam of white light which is split by a half silvered mirror into two separate paths perpendicular to eachother. (The paths are shown here in green and red for illustrative purposes only). These two light beams impinge on two further mirrors (1 and 2), at right angles to eachother and are reflected back through the beam splitter which recombines them into a single beam and directs the beam into a detector.

If the difference in pathlengths between the two returning beams is an integral number of wavelengths then the two beams will arrive in phase, augmenting eachother, known as constructive interference, and the image detector will indicate a constant intensity spot of white light. If however the difference in pathlengths is not an exact number of wavelengths then the two beams will arrive out of phase with eachother and the light intensity will be reduced by destructive interference of the two beams and the imaging detector will show a sinusoidal interference pattern of light and dark fringes over the light spot, dependent on the differential pathlength.

When used in the Michelson-Morley experiment, the two mirrors must be equidistant (d) from the beam splitter so that the pathlengths of the two beams are identical. In this case the expected interference pattern would instead be due to the time delay between the reference beam travelling at the speed of light perpendicular to the aether wind and the slower beam travelling along the direction of the aether wind. The delay results in a phase shift between the reference wave and the slower wave and when the two beams are combined an interference pattern will emerge in the detector representing this phase delay between the beams and consequently their difference in speed. The difference in the time the beams spent in transit would be observed as a shift in the positions of the interference fringes.

•  Describing a single optical element with a 2x2 matrix.

•  Analysis of train of optical elements by multiplication of 2x2 matrices describing each element.

*First and second principal points and principal planes. 
-The rays determining the focal points change direction at their intersection with the principal planes. 

-We define distances locating six cardinal planes with respect to the input and output planes.

-F1 and F2 are at f₁ and f2

from the principal points at H₁ and H2.

-F1 and F2 are at p and q

 from the reference input  and output planes.

 -r and s are disances of the reference input and output planes from the principal points at H1 and H2.
-v and w are distances of the reference input and output planes from the nodal points at N₁ and N₂

Sign convention:

(+) distance measured to the right of a reference plane

(-) distance measured to the

left of a reference plane 

 

-Ray tracing is following the actual path of each ray through the system using laws of reflection and refraction. Traditionally it is done by hand and graphically but today it is all computerized.

-It introduces a ray‐tracing technique that is often limited to meridional rays. Meridional rays are the rays that pass through the optical axis of the system.
-Meridional rays tend to stay in the meridional planes as the laws of refraction/reflection require them. 

-This limits our treatment to a 2‐dimensional space.

Skew rays are the ones that contribute to the image and do not pass the optical axis.
-Analysis of the skew rays require a 3‐dimensional treatment .

-Understanding aberrations require analysis of the non‐paraxial rays and skew rays. Design of the complicated lens systems require knowledge and experience with ray‐tracing techniques and optimizing performance of the system by changing system parameters and arriving at a perfect performance. 

-the focal length depends on refraction and the index of refraction

-Short wavelength has higher n and is refracted more than long wavelength

-The amount of chromatic aberration depends on the dispersion of the glass.

-If the index  is the same for all wavelengths, there is NO DISPERSION

-The n increases as wavelength decreases

-The idea is to use a lens pair – a strong lens of low dispersion coupled with a weaker one of high dispersion calculated to match the focal lengths for two chosen wavelengths. 

-Cemented doublets of this type are a mainstay of lens design 
Figure :Achromatic Doublets

 

 

-Aspheric Surfaces to the Rescue
- Aspheric lens has a non-spherical lens surface. The main advantage of aspheric lenses is its ability to correct for spherical aberration. Aspheric lenses allow optical designers to correct aberrations using fewer elements than conventional spherical optics because the former gives them more aberration correction than multiple surfaces of the latter. Given that, smaller amount of aspheric lenses can be substituted for many spherical lenses to achieve similar or better optical results, while reducing system size, simplifying the assembly process, and yielding imaging lenses that ultimately cost less and outperform assemblies made of traditional spherical components. 

-The coma flare, which owes its name to its cometlike tail, is often considered the worst of all aberrations, primarily because of its asymmetric configuration. 

-Coma is not well compensated for in the human eye.

-For lens systems, using best form lenses with non-spherical shapes can help. 

- It occurs when magnification varies with the distance of the object from the optic axis. 

-Problem only for high powers

-Tends to falsify the positions of objects and cause vertical lines to wave
- Aphakes.

-Minimized by very steep back base curves.

- Spherical Aberration

-  Oblique Astigmatism

-  Coma

-  Curvature of Field

-Distortion

- Post lasik increase in higher order aberrations

- Can be easily measured

- Wavefront guided correction available

Patient expectations 

-Shack elaborated on this in the 1980’s working for the air force

-Liang was the first to use the wavefront sensor to measure the human eye in 1994.
-By the late 1990’s commercial development was occuring.

-When wave encounters and obstruction, the direction of the wave changes.

This is called DIFFRACTION 

- Wavefront analysis describes the wave behavior of light in the eye

-Actual image displacement of the point source from foveola as it passes through the optical system of the eye compared to the ideal image. 

-Astigmatism

-Spherical Aberration

Coma

Custom does not correct for :

-Chromatic aberration

-Diffraction 

-Produces a “fingerprint” of the aberrations for an individual eye.

 

Into many sub-beams for measurement. Each lenslet focuses onto the 

Video sensor. We analyze the position of each spot.