Independent Researcher, Poland
Received date: March 31, 2016; Accepted date: July 29, 2016; Published date: August 03, 2016
Citation: Kecman M (2016) Sagnac Effect and Fiber Optic Gyroscopes. J Phys Math 7:189. doi: 10.4172/2090-0902.1000189
Copyright: © 2016 Kecman M. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Sagnac effect (Sagnac interference) is well described by the author Anderson. There is the original paper translated into English. The generally accepted interpretation is based on different trails (The difference in the length of roads caused by peripheral speed). Interference fringes are evenly lined with dark stripes, move with the changing angular velocity. Theoretical calculations given significant deviations from the experimental results. Experimental data suggest: Sensitivity (accuracy) of the device is proportional to the square of the length of optical fiber. The official interpretations (and others) argue: Sensitivity is proportional to the length of the optical fiber. Exposed is a mathematical analysis of the experimental data.
Sagnac; Optical gyroscope; Quadratic regression
Sagnac experiment was published 1913 years by the Author which is precisely described device and method of measurement [1,2]. The calculation and experimental results are consistent. Figures 1 and 2 show a model for calculating the phase shift. Sagnac has introduced a surface A due to deviations of the measurement results. On his drawing device is a hatched area . It is better to agree with the measurement of 2π R to model. Sagnac wrote:” After many runs, I have always observed the sense to change as expected (Table 1).
n=[0.5/(Bias)] × [0.027/(Scale f)].
Table 1: Bias data is reduced to the same peripheral speed, and on the same scale factor.
At the end of the twentieth century made sophisticated optical gyroscope. The device had no moving parts (elements). Optical cable, laser, electronics, and software enable high-precision devices.
Calculate k1give us a sum of squared deviations is minimal.
k1=0.033 Calculate thesum of the squareddeviations: F1=330
4.2Quadratic regression (QuadReg)
y=k2x2 calculate k2 give us a sum of squared deviations is minimal as shown in Tables 2 and 3.
Table 2: Sum of squared deviations.
|205||1||42025||62500||3906 × 106||-1.16||1.35|
|300||2.5||90000||225000||8100 × 106||-0.61||0.372|
|420||5.6||176400||9877840||31117 × 106||-0.5||0.25|
|700||15||490000||8183000||240100 × 106||-0.2||0.04|
|1200||50||1440000||72000000||2073600 × 106||-0.23||0.053|
Table 3: illustration of quadratic regression.
From thisdF/dk2=0 get:
F2 << F1 from which it follows that the quadratic regression much better fit with the experimental data.
Predict the sensitivity of optical fiber length L=5000 m.y=0.0000346*50002=856. Bias is 0.00058°/h, and this is one revolution in 70 years. Is necessary revision of theoretical explanations for Sagnac effect? The new theory must contain a square dependence of sensitivity on the length of the fiber. Additional experimental design is also essential. Serious hypothesis will be given.
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