intensity modulation - University of Washington

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Intensity Modulation

Wei-Chih WangDepartment of Mechanical Engineering

University of Washington

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Why Intensity Modulation

• Simple optical setup • Broadband or mono-chormatic light source• Less sensitive but cheaper to make

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Intensity (Amplitude) Sensors

In this case, the signal to be measured (the measurand), intensity (amplitude) modulates the light carried by an optical fiber or waveguide. For this class of sensors a normalized modulation index (m) can be defined as

where, ∆ I = change in optical power as a result of modulation by the measurand; I0 = optical power reaching the detector when there is no modulation; and P = perturbation (measurand).

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Intensity Sensors

The sensor response expressed as a differential voltage per unitchange in measurand is given by

Where q = detector responsivity (A/W); R = load resistance.m= normalized modulation index

S = q Io R m

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Limits on Performance

1. Signal voltage ~ noise voltage

The minimum measurable quantity in the shot noiselimit is given by,

id2 = 2eBId “white noise”

With light: id2 = 2eBIp

where e = electronic charge and B=detection bandwidth.

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Noise in photodetectors

hυ detector electronics

Radiation noise(quantum noise)

Nλ Ip

Internal detectornoise

System noise OutputSignal Ip

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Four noise sources often encountered in connection with optical detectors.

•Johnson noise

•Shot noise

•1/f noise

•Photon noise

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Sources of internal detector noise

Johnson (thermal) noise

1. All resistive materials2. Depends only on temp. and bandwidth of measuring system

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The Johnson noise contribution is provided by the shunt resistance of the device, series resistance and the load resistance. The Johnson noise (thermal noise) is given by:

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Johnson noise is generated by thermal fluctuations in conducting materials. It is sometimes called thermal noise. It results from the random motion of electrons in a conductor. The electrons are in constant motion, colliding with each otherand with the atoms of the material. Each motion of an electron between collisions represents a tiny current. The sum of all these currents taken over a long period of time is zero, but their random fluctuations over short intervals constitute Johnson noise.To reduce the magnitude of Johnson noise, one may cool the system, especially the load resistor. One should reduce the value of the load resistance, although this is done at the priceof reducing the available signal. One should keep the bandwidth of the amplification small; one Hz is a commonly employed value.

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Shot noise

• Seen in photodiodes under reverse bias (dark current noise) with no photon input,

I = Isat (eqV/kt –1) = -Id (dark current)

id2 = 2eBId “white noise”

With light: id2 = 2eBIp (a function of

light instead)

where e = electronic charge and B=detection bandwidth.

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The term shot noise is derived from fluctuations in the stream of electrons in a vacuum tube. These variations create noise because of the random fluctuations in the arrival of electrons at the anode. The shot noise name arises from the similarity to thenoise of a hail of shots striking a target.In semiconductors, the major source of shot noise is random variations in the rate at which charge carriers are generated and recombine. This noise, called generation-recombination or gr noise, is the semiconductor manifestation of shot noise.Shot noise may be minimized by keeping any DC component to the current small, especially the dark current, and by keeping the bandwidth of the amplification system small.

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1/f noise

Larger noise powers at lower frequencies.No theory: not well understood.Seems to be related to contacts, surfaces, other potential barriers

If2 ~ I2B/f

B = bandwidth f = frequency

Usually much smaller than shot noise except at very low frequency

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The term 1/f noise (pronounced one over f) is used to describe a number of types of noise that are present when the modulation frequency f is low. This type of noise is also called excess noise because it exceeds shot noise at frequencies below a few hundred Hertz.The mechanisms that produce 1/f noise are poorly understood. The noise power is inversely proportional to f, the modulation frequency. This dependence of the noise power on modulation frequency leads to the name for this type of noise.To reduce 1/f noise, an optical detector should be operated at a reasonably high frequency, often as high as 1000 Hz. This is a high enough value to reduce the contribution of 1/f noise to a small amount.

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Noise spectrum

1/f

shot

Johnson

frequency

MeasuredSquared noiseCurrentPer BW

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As an example: If a photodiode has a dark leakage current of 2 nA and a shunt resistance of 5E8 Ohms, and a responsivity of 0.5 A/W, and letting the bandwidth of the system be 1 Hz,

As an example: If a photodiode has a dark leakage current of 2 nA and a shunt resistance of 5E8 Ohms, and a responsivity of 0.5 A/W, and letting the bandwidth of the system be 1 Hz, Shot noise is the dominant component of the noise current of a reverse-biasedphotodiode. This is particularly true at higher voltages (at break down i.e.). If devices are operated in a photovoltaic mode with zero bias, the Johnson noise dominates, as dark current approaches zero. When operating in the zero bias mode the noise current is reduced such that the NEP, and hence the minimum detectable signal, is reduced in spite of some loss of absolute sensitivity.

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Macrobend(intrinsic)

A large-scale bend that is visible; for example, a fiber wrapped around a person's finger. To prevent macrobends, all optical fiber (and optical fiber cable) has a minimum bend radius specification that should not be exceeded.

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Macro-bend losses are losses observed when a fiber is bent to a radiusof several centimeters. Large bending loss occurs at a critical bending radius of

where n1and n2 are the indexes of refraction of core and cladding and λis the operating wavelength. The optimum conditions for a largebending radius occur when refractive index difference between core and cladding is small or operating at a long wavelength.

Rc =3n1

2λ4π n1

2 − n22( )3/ 2

Macrobend(intrinsic)

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. Under the condition which a /R∆ is to remain small, the light intensity attenuation is equal to

where r is the core radius, and a specifies the shape of index of refraction (for a parabolic profile, a = 2 and for a step profile a = ∞,) R is radius of curvature of the bend, ∆ is the relative refractive index difference between core and cladding. Based on the above equation, it is apparent that the bend loss can be enhanced with a smaller refractive index difference between core and cladding or by using a larger core radius of the guide.

∆+

=Rr

aaRB 2

2)(log10γ

Macrobend

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WWaveguide Sensor Arrayaveguide Sensor Array

•Higher spatial resolution (250µm x 250µm)

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pressure

bend loss

dimmer

dimmer

Basic Pressure Sensor Design Basic Pressure Sensor Design

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Basic Shear Sensor DesignBasic Shear Sensor Design

original position sheared position

sensor layers

shear displacement

applied shear force

high compliance

sensor mesh

applied compression force

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Microbend loss sensor(intrinsic)

In an optical waveguide, a sharp curvatures involving local axial displacements of a few micrometers and spatial wavelengths of a few millimeters. microbending can cause significant radiative loss and mode coupling.

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Microbend Sensor(intrinsic)

* fiber experiences multiple bends* lower order guided modes are converted to higher order modes and are eventually lost by radiation

Multimode fiber

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Microbend Theory

For pressure sensor, the transmission coefficient for light propagating through the bend fiber changed by the amount of applied pressure is equal to [1]

PkAxTP

lAE

kAxTT fp

s

ssfp ∆

∆∆

≅∆+∆∆

=∆ −− 11)( (1)

Where Ap is area under the load, kf is the bent fiber force constant and As, Es, ls are cross sectional area, Young’s modulus and length of the mechanical deformer. The approximation is assume the deformer’s AsEs/ls is much smaller than the fiber’s kf.

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For the optical portion of the modulation index ∆T/∆x, the loss occurs when wave number of the spatial distortion is equal to the difference in wave number between the modes. The period microbending induced along the fiber axis couples power between modes with longitudinal propagation constant is [1]

Λ

=−πββ 2

nm (2)

where each mode has propagation constant )cos(1 mm kn θβ = , with mθ representing the angle which the mode’s equivalent rat makes with the fiber axis, n1 core refractive index, and k is free space propagation constant, Λ is the mechanical distortion wavelength. Based on WKB approximation, the distance in β space between adjacent guide modes in a fiber is given by [2]

222/1

12

2+−

+

∆

+=−=

αα

ααββδβ

Mm

rmm (3)

where m is the order of modal group and M is total number of modes, α is a constant ( 2=α for parabolic index fiber, ∞=α for step index fiber), r is the core radius and ∆ is the fractional difference in refractive index between core and cladding [2]:

12 1

212

1

22

21 ⟨⟨∆

−≅

−=∆ for

nnn

nnn

where n1 and n2 are refractive indices for core and cladding.

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In the case of parabolic index fiber, the equation (3) becomes,

r∆

=2δβ (4)

It shows that δβ is independent of order of mode since all modes are equally spacing in k space (to within WKB approximation). This means that an efficient coupling between modes can be achieved with just one single spatial period. Since numerical aperture is defined as

5.01

5.022

21 )2()(sin ∆≅−== nnnnNA oo θ (5)

the spatial period based on the above NA and ∆ is [2]

NArnr 122 π

π =∆

=Λ (6)

In the case of step index, modes are not equally spaced and

∆

=Mm

r2δβ (7)

The separation of modes in k space for step index is therefore depends on the order of the mode, m. Based on equation (2) and (7), we see larger the m, the smaller Λ and while lower order mode require larger period. The spatial period for highest order core modes coupled to radiated modes (assume m = M) is given by

NA

rnr 12 ππ≅

∆=Λ (8)

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The mechanical parameter also affects the outcome of the sensitivity of the sensor. The applied force and the resulted displacement ∆x are related by simple ∆F = kf ∆x. Considering the bent fiber or waveguide as a bar loaded at the center and clamped at its ends [4]

3

43Λ

=ηπ dE

k sf (9)

Where d is diameter of the fiber and η is the number of bent intervals.

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SMS Fiber Optics Sensor

The structure is composed of single mode leads and graded multimode sensor fiber.

Electrical Engineering and Computer ScienceLaboratory for Electro-Optics and Sensor SystemsSmetanova 17, SI-2000 Maribor, SLOVENIA

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Advantages

•higher sensitivity than classical microbend structures •use of shorter deformers •single mode leads, which eliminate intermodal interference problems •sensitivity of 120%/N by use of low-sensitivity standard multimode fiber •high insensitivity to macrobends


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Faculty of Electrical Engineering and Computer ScienceLaboratory for Electro-Optics and Sensor SystemsSmetanova 17, SI-2000 Maribor, SLOVENIA

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OTDR

Optical Time Domain Reflectometer (OTDR)

Intrinsic distributed sensors based on Rayleigh backscatter utilize either the measurand-dependent loss coefficient α(z) or backscattering coefficient r(z) mechanism in a single length of optical fiber which forms an extended sensor.

The backscattering method was invented by M. Barnoskim and M. Jensen in 1976

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OTDR

Position of the optical impulse in the fiber core at time t

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Basic Mechanisms of OTDR

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OTDR

•Coherent OTDR (CO-OTDR) - The week returned backscattered signal is mixed with a strong coherent local oscillator optical signal to provide coherent amplification •Correlation OTDR (COR-OTDR)

•COR-OTDR based on pseudorandom signal •COR-OTDR based on Golay code signal

•Low correlation OTDR (LC-OTDR) •Photon-Counting OTDR (PC-OTDR) •Optical Frequency-Domain Reflectometry (OFDR)

•OFDR with the frequency scanning (OFDR-FS) •OFDR with the synthesized coherence function (OFDR-SCF)

•Polarization OTDR (PO-OTDR)

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Proximity Sensor(extrinsic)

Liquid Level Sensors Distance Detection

tube-mountable liquid level detection

immersion type liquid level detection

Reflectivetype

Transmissivetype

By KEYENCE CORPORATION OF AMERICA

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Liquid level sensor(extrinsic)

A liquid-level sensor based on changes in the critical angle due to liquid level moving up to contact the sides of the prism (using total internal reflection in air).

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Displacement Sensor(extrinsic)

A change in the transverse alignment between two fibers changes the coupling and hence the power falling on the detector.

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Accelerometer or Pressure Sensor(extrinsic)

By W. Wang, UW

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Intensity modulation sensor(extrinsic)

A

B

C

D

Y

X

Figure 10. Quad cell photodiode position detector

Quadrant fiber detector

incoming coherentlight source

waveguide in motion

By W. Wang, UW

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Detector Scheme

X = ((IA+IB)- (IC+ID))/((IA+IB)+ (IC+ID))

Y= ((IA+IC)- (IB+ID))/((IA+IB)+ (IC+ID))

IA, IB, IC, ID are Intensity from fiber A, B, C and D.

intensity modulation - University of Washington

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