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        Sagnac Interferometer / Fibre-Optic Gyroscope (FOG):          
      Sagnac loop Length (m) Refractive Index of fibre  
      Loop radius (m) wavelength of light  
      number of loops tangential v due to earth:    
      frame Velocity w (m/s) z-axis = vertical m/s  
      Rotational velocity v (m/s) z-axis = NS m/s  
      area of loop (m2): z-axis = EW 0 m/s  
    Wind: Arm 1 forward Time Arm 2 return Time Time round trip: Time Difference Blue -Red  
    0 Fringe Difference:  
      Arm 1 forward Time Arm 2 return Time Time round trip:  
      Arm 1 forward Time Arm 1 forward Time Time round trip: Time Difference Blue-Red  
    90   Average frame velocity is 2V/p per arm.  
    90 Fringe Difference   Frame velocity for g is 2V/p per arm  
      Arm 1 forward Time Arm 2 return Time Time round trip:   General Equation per arm:    
      (p*r * g)/( c/n +/-( 2/p)(w/n2)+/- v/n2)    
      Earth Rotational Velocity: Lorentz Contraction g :    
      Latitude (degrees): min. 0= YES, 1 = No  
        DFringe due to g :  
      ................Earth Rotation Values: ................ ......Regular Rotation/Translation Values:......  
      Using Eq. 1 Method: Using Eq. 1 Method: Using Eq. 2 Method: Using Eq. 2 Method:  
      DFringe due to Earth Rot. : Dt due to Earth rot. : z-axis = vertical z-axis = vertical  
      z-axis = vertical 4WAsin(lat)/c2 DFringe due to frame vel. w: Dt due to frame velocity w:  
      z-axis = NS 4WAcos(lat)/c2 z-axis = vertical z-axis = vertical  
      DFringe due to rot. vel. v: Dt due to rot. velocity v:  
      z-axis = EW no W in this plane  

    A Sagnac Inteferometer is a rotation detector, but it is incapable of detecting its linear movement in space. 

              This webapp is setup using two methods of calculating the effect of motion on the fringe shift seen in a Sagnac interferometer. Equation 1 method is the most common

              method, using the angular velocity and area of the loop to determine the fringe shift. Supplied herein is a second method (Equation 2) which uses addition of velocities (based

              on the equations of Lorentz) to calculate the fringe shifts expected. Conditions similar to the Michelson-Gale experiment are pre-loaded to demonstrate that the fringe shifts

              expected for the Earth's rotation alone (z-axis = vertical) using Eq.1 and Eq.2 match to a good approximation. The use of the Equation 2 method allows for the convenient

              addition of the Lorentz contraction factor to see how a real Lorentz contraction of the path would affect the fringe shift. The Lorentz contraction fringe shift is the only visible effect

              related to the translational velocity. Eq.2 allows for the expression of the time difference in terms of velocities of light differences around the paths as seen by an observer at rest

              with the interferometer. The red and blue columns are for calculating the time of light propagation for each arm. The Eq.2 method also allows for the effect of the translational velocity

             of the interferometer, and show that this velocity is undetectable (cancels around the arms) as with other interferometers. The latitude parameters are for inputting your latitude on the

             Earth's surface. Once this is done, the Earth rotation values will be calculated automatically for three different axis alignments of the interferometer (Vertical, NS and EW). All the

             other user input parameters control the Regular Rotation/Translation values calculated using the Equation 2 method. This includes loop length (circumference of the light path), frame

             velocity (how fast the device is moving in a straight line), rotational velocity (how fast the device is rotating around its axis), the refractive index of the light path (for example, fibre optic

             cable is RI= 1.467), the wavelength of the light in meters, and whether or not to assume a real Lorentz contraction of the path (YES/NO, calculated in a separate box). Click on the

             calculate button after inputting the test values. Various input values can be tried to see how it effects the propagation time difference for two counter-propagating beams of light in the

             loop, and how much of a fringe shift this results in when the interference pattern is viewed at the detector.

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