basic working of fog

8/10/2019 Basic Working of Fog

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BASIC WORKING OF FOG



S AGNAC EFFECT:-

• Light beams propagating in opposite direction experiences a path length difference , w

proportional to the rotation rate.

The wave travelling in direction of rotation is clock

wise wave, which will travel more path.

is the distance that the mirror has moved in that same time

The wave travelling in opposite direction of

rotation is counter clock wise, which will travel

less path.



Time difference between the two waves is:

The phase shift produced between the two waves is,

Sagnac effect in a medium,

Where the velocity of light and velocity of a medium must be taken into

consideration.



the speed of light should be increased when "dragged" along by the water

decreased when "overcoming" the resistance of the water

Fizeau equation for speed of light is given as

Magnitude of drag was very much lower then expected by Fizeau.

Differential length of Sagnac effect in a medium is identical to that of in vacuum



TWO BEAM INTERFEROMETRY:

Sagnac effect can be observed in this phenomenon, the

phase shift produced between the two light waves due to

rotation is similar to that of Sagnac phase shift.

• Output fed to detector, the detector try to estimate the

optical intensity as a function of omega which is also a

function of differential length.

OPTICAL FIBER IMPLEMENTATION:-

• The 3 mirror system is replaced by an optical fiber to

improve the sensitivity of the interferometer.

• By implementing N turns, the corresponding diff-

length , phase shifts are enhanced by N times.



P ASSIVE RESONATOR METHOD:-

Light with a frequency f enters the resonator at one mirror, along

directions and exits at other mirror.

In absence of rotation resonance frequencies are identical due tochange in perimeter.

In case of rotation the perimeter observed by both wave are differ

which will in turn create a frequency difference.

In case of optical implementation the perimeter is changed by n ti

, which will reduce the frequency difference.



RING LASER GYRO:-

• Optical amplifier included into the resonator.

• In absence of rotation the laser frequency remains

constant.

• In presence of rotation, the time differencebetween the waves introduces slight change in

frequency.

• A beat pattern of waves is observed at the output

side.

Problems in fibre optic implementation:-

•

Simultaneous bi-directional lasing is not possible.



IMPLEMENTATION OF TWO BEAM INTERFEROMETRY FIBER OPTIC

GYRO:-

• In absence of rotation output of detector is

maximum, and output drops with omega.

• To identify the magnitude and direction ofrotation phase modulator is introduced at the

coupler.

• If PSD output is directly used, it is called open-

loop.

• If PSD output is used to generate the phase

shift which is fed back to optic chip, it is calledthe closed loop.



Other non reciprocal sources:

1. Polarization effects.

2. Back reflection.

3. Temperature effect.4. Offset errors of electronic devices.

Parameters that influence the closed loop operation:-

1. Source wavelength changes

2. Temperature control over the coil



IMPLEMENTATION OF PASSIVE RESONATOR FIBRE OPTIC GYRO:-

• Counter clock-wise wave was detected bydetector 1 and used in locking the laser

frequency at the resonance.

• Clock- wise wave was detected by detector 2

and used to identify magnitude and direction

of gyro.

• By closing the second loop it is possible tochange the laser frequency in clock wise. Which

can produce a precise frequency difference

between both the waves.

• Other non reciprocal effects still exists…..



Closed loop approach.

• A phase difference is introduced to nullify the total phase differenc

between the interfering optical waves.

• Advantages in closed loop approach rotation signal is independe

optical intensity and gain of electronic components.

• Disadvantage in this is identifying the exact electronic optical elem

that produces the phase shift.

• Generally frequency shifters and phase modulators are used to

produce the required phase shift.



Phase modulator is located at asymmetrical position in gyro loop.

T is the transit time.

To avoid gyro switching between + or – 90deg, a phase bias of 90

is fed to change the operating point.

Ideal form of producing the phase difference is a continuous phas

ramp in time.

By varying the phase ramp the differential phase can be varied.

which in turn helps making the net difference zero.



• Producing infinite phase ramp is not possible. So

to avoid that problem periodic ramp with finite

duration is used.

• The output of phase modulator is taken as the gyrooutput. This approach is called gated phase

modulation approach.



FREQUENCY SHIFTER

Frequency shifter is placed at one end of gyroscope loop.

Both the waves are induced with frequency shift. The shift in the f

induces a differential phase shift = . is the transit time of light through the fibre.

In a closed loop gyro we always try to maintain the total differential

shift zero. i.e.:- Δ = +Δ =0.

Where the frequency becomes Δf=Δ/2 and Δf=(DΩ/nλ ).

Observations:-1) diff. freq depends on the D, n, λ but not on the optical intensity and

electronic components.

2) Scale factor similar to the RLG.

3) Dependence on ‘n’ causes instability of scale factor for a high rotati



ANALOG SERRODYNE PHASE MODULATION:-

Different waveforms are used for the modulation

1. Saw tooth wave

2. Asymmetric triangular wave

Saw tooth wave for phase modulation:-

1. It should have a large frequency band width to accommodate th

modulated wave.



CONT…

The diff. phase shift produced during time period Δ(t)=2f

Basing on fm(freq of saw tooth wave ) or T(time period of ramp sign

one can calculate the rotation rate i.e. Δf=(DΩ/nλ ).

Caution: finite fly-back time will introduce errors in the scale factor.

Drawback: demand of high bandwidth cannot be introduced in the f

optic.



SINUSOIDAL MODULATION:

Sinusoidal approximation of saw tooth wave is applied to the

gyroscope. In turn it produces a sine phase diff modulated wave.

But, it is not useful at constant rotation rate.

Solution: if the negative half cycle of sine is turned of and we can

produce time averaged signal which can be used null the rotation



ASYMMETRIC TRIANGULAR WAVEFORM:

Triangular waveform with asymmetry in time is used.

The operating point of gyro is made to alter between two symmet

points.

Two differential phase shifts induced for two time periods.

i.e.: Δ=2(m) / T1 and Δ= - 2(m) / T2.

The rotation rate is given as (r)= (T1-T2)/(T1+T2).



CONT…

Observations:

1. measurement of rotation does depend on modulation amplitudthe transit time.

2. Scale factor is independent of the refractive index.



OPEN LOOP APPROACHES:-

They do not use phase shifters but they need the quadrature pha

information. (i.e. differential phase shift values of sine and cosine

between two waves.)

Basic method by sinusoidal modulation, where detector current is

proportional to cosine(r) and sine(r) harmonics.

Basic method lacks accuracy and complex in measurement.

Other methods :

1. Synthetic heterodyne

2. Digital phase locked loop



Synthetic heterodyne:-

• It converts the rotation information into phases of low frequency

signal.

• By amplitude modulation operating at (Fm) of detector current it

produces sidebands signals of Fm.



CONT..

Band pass filter generates output at frequencies 2Fm

i.e. : I1=(IK/2)cos(2*Fm*t+(r)) and I2=(IK/2)cos(2*Fm*t-(r

By using these two signals one can measure the rotation rate.



DIGITAL PHASE LOCKED LOOP:

Optical phase shift is measured by closed- loop digital electronic

circuit. The spacing between the pulses reflects the optical phase shift.

Phase shift equation= (r)= tan^-1[Sx (2/T)/Cx(2 /T)]



THANK YOU

source

detector

Fibre coil

Phase modulator

Fb

GATE

PSD

Servo

Adjustablephase

modulator

basic working of fog

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