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OptiSystem applications:Fiber optic gyroscope systems designDC detection method

FOG systems design

With ideal components, the output photo-generated current (I) is,

𝐼 = 𝐼𝑜 (1 − 𝑐𝑜𝑠𝜙𝑠 )(1)where φs is the Sagnac phase shift and Io is the current at zero angular speed given by𝐼𝑜 =𝜎𝑃2(2)P is the source optical power and σ is the photodetector responsivity (in our case this is equal to 1). The reason for dividing
the optical power by 2 in equation (2) is because half of the power is lost at the coupler. Once φ s is determined we can use

𝜙𝑠 =2𝜋𝐿𝐷Ω𝜆𝑐(3)where L is the length of the fiber, D is the diameter of the loop, λ is the wavelength of the source, to determine the angularspeed of the loop Ω. Notice that since equation (1) has a cosine relation, the DC technique cannot distinguish between
positive and negative velocities.
REF: http://www.jgorasia.com/Files/Spring10/Instrumentation/FOGreport.pdf (Accessed 24 Jan 2017)

Layout: I-FOG DC Detection

The Sagnac phase shift (resulting from angular rotation) isapplied to the CW direction and is calculated as follows:(8*pi* FiberCoilArea * NumberOfCoils * AngularVelocity )/(ReferenceWavelength* c)2Phase modulation method (1)FOG systems design

The DC method is not as accurate when trying to measure very low angular rotation rates and instead a phasemodulation technique is commonly used. For this configuration the photo-detected signal is given by [REF]:(4)

Choosing the phase modulator amplitudes as +/-0.9 rad gives the term Φm = 1.8 above for which J1(Φm) = 0.581517 ismaximized. We extract the Fourier cosine coefficient for modulation frequency ω m to give𝐼𝜔 = 𝐼𝑜 2𝐽1 1.8 sin(𝜙𝑠 )(5)which we can re-arrange to find 𝜙𝑠 and then use equation (3) again to find the angular velocity. Note that in this case,since equation (5) has a sine relation, we can determine both the magnitude and direction of the angular velocity.
In addition, in this situation, the zero velocity electrical current is not 𝐼𝑜 =𝜎𝑃𝜎𝑃
as in equation (2), but 𝐼𝑜 =because by28

the time the light has reached the photodiode, its power has been halved three times by the couplers.
REF: http://www.jgorasia.com/Files/Spring10/Instrumentation/FOGreport.pdf (Accessed 24 Jan 2017)
The photo-detected signal includes the DC term and all
harmonics resulting from the phase shift and modulated signal.
The harmonic of interest (to be measured) is at the signal
modulation frequency

Schematic of modulation technique (Source: REF)
upon which the OptiSystem design was built (Note:the Fiber polarizer was not included in the design)3Phase modulation method (2)FOG systems design

For the OptiSystem design below the angular velocity has been set to
7.27e-5 rad/s (rotation rate of the earth). The settings for the I-FOG areshown in the red box (under Global parameters). The Sagnac phase shift isapplied by using the Phase Shift Component and is calculated as follows:4 (LoopDiameter/2)FiberLengthAngularVelocity/( c)
Here we have used our C++ Component to calculate the angular velocitybased on the equations from the previous slide. The measured angularvelocity (shown as a result below the C++ Component) is 7.29e-5 rad/s

Layout: I-FOG Phase Modulation

The OptiSystem C++ Component can beused to access any OptiSystem signals andperform customized calculations.

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