High precision time delay calibration system for range measurement by using phase stabilized optical fiber to eliminate temperature error
Introduction
The satellite range measurement system is a very precise phase meter. It measures the instantaneous phase difference between the internally-generated tone and the same tone echo-returned by the spacecraft. These measurements are performed at different frequencies, allowing to calculate the propagation time and consequently the distance. Ambiguity solving (such as ESA tone standards [1]) is determined by the minor tones while the measurement accuracy is determined by the major tone. Minor tones are derived from the major tone by frequency division. Before range measurement, a calibration of the system is required. The standard electric cables with different lengths are used to simulate the different distances for calibration. This method has some shortcomings, for a long range measurement distance calibration such as several kilometers, the volume of electric cable is large, and it is easy to receive electromagnetic interference.
Optical method such as by using optical fibers for calibrating the range measurement has its advantages over electrical method, including immunity to electromagnetic interference, capability of multiplexing, small size and light weight, and resistance to harsh environments.
For optical methods, the standard SMF is the key component to provide the optical time delay. This calibration system based on the Optical True Time Delay (OTTD) techniques which are used for Phased-Array Antennas [2], [3]. The electronic delay signal coming from the range measurement system is converted to optical delay signal and passes through the optical networks consisting of fiber switches and optical coils to generate the time delay. The delay is determined by the route chosen in the optical networks. Such delays can range from nanoseconds to milliseconds which equals to fibers length from several decimeters to hundreds kilometers. Than the optical delay signal is transformed to electronic signal and comes back to the range measurement system. This fiber based calibration system can be used to calibrate optical laser ranging systems, satellite ranging systems and other similar ranging systems. But, the SMF is sensitive to the environment temperature change, so the time delay accuracy of the system is affected by the temperature.
For the purpose of meeting the requirements of indoor and outdoor operations, the working temperature of satellite ranging calibration system should be from − 20 to 60℃. Although the optical fiber as the delay medium is installed in the instrument case, the system will still be affected by the temperature change of the external environment. So it is necessary to improve the optical fiber based satellite ranging calibration system to reduce the influence of temperature on the delay accuracy.
The method proposed by this paper is using the Phase Stabilized Optical Fiber to reduce the temperature effect in the range measurement calibration system to achieve high precision. The PSOF is a special fiber which minimizes the temperature dependence of transmission delay time. The fiber is buffered with a liquid crystal polymer jacketing, a material with negative thermal expansion coefficient [4]. It means that the PSOF has the lower thermal coefficient of delay than the SMF.
In order to verify the proposed method, the thermal coefficient of delay of PSOF and SMF are needed to be measured. The thermal coefficient of delay can be measured by using fiber optic Fabry-Perot interferometers methods [5], [6], fiber Bragg grating method [7] or optoelectronic oscillation (OEO) method [8].
Since the low coherence interferometry can reach high time delay resolution [9], in this paper, a low coherence interferometry is used to measure the delay time introduced by temperature. By measuring the thermal coefficient of delay of the PSOF compared with the SMF from −20 to 60℃, the results show the temperature dependence of transmission delay time of the two kinds of fibers are 8.073 ppm/K for SMF, 1.947 ppm/K for PSOF.
Section snippets
Materials and methods
The range measurement system and calibration system are shown in Fig. 1. In the range measurement system the Major or Minor tone is modulated on the Intermediate Frequency (IF) Carrier signal by Phase Modulation (PM). IF Transmitter sends the modulated signal into the calibration system to drive the Electro-Optic (EO) modulator. The time delay signal out from the calibration system is received by IF Receiver and demodulated by a Phase Demodulation circuit. The delay phase is calculated with
Results
We only chose two interference peaks with OPLs of 2ΔLM and 2ΔLM (t) + ΔLZ in Fig. 3 to calculate the change of ΔLZ with temperature from −20℃ to 60℃.
From Fig. 3 we can understand that the SMF is more sensitive to temperature change than the PSOF. The delay times at different temperatures can be measured by the distance between the two peaks of each interferometer signal in Fig. 3. The time delays of the two fibers versus temperature can be obtained by linear fitting, as shown in Fig. 4. The
Discussion
There are several error sources contributing to the final measurement error. First, the MODL is used to scan the time delay of the interferometer. Its time delay resolution contributes to the measurement error. For the MODL used in the system, the spatial accuracy of the stepper motor is 10um, so a temporal accuracy of 0.033 ps can be achieved (assuming n = 1). Second, by using the low coherence interferometry, the system resolution equals to coherence length of the light source [12]. The
Conclusion
In conclusion, we propose a high precision fiber based calibration system of range measurement system. To eliminate the temperature sensitivity of SMF, we use PSOF instead. We experimentally measure the thermal coefficients of delay of PSOF and SMF by using a low coherence interferometer. The results show that PSOF has lower temperature coefficient than SMF, by using the PSOF, the measurement precision can be increased by 4.15 times compared with the system using SMF, so PSOF has higher
Funding
This research received no external funding.
CRediT authorship contribution statement
Kang Wu: Conceptualization, Writing - original draft, Writing - review & editing. Yunqi Zhang: Investigation, Data curation. Haibin Jin: Methodology, Validation. Pan Pan: Formal analysis, Resources. Zhuo Meng: Conceptualization, Methodology, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (12)
- et al.
Determination of thermo-optic coefficient in liquids with fiber Bragg grating refractometer
Opt. Commun.
(2008) - TTC-A-04 - Issue 1, July...
- Amber Rader and Betty Lise Anderson, Demonstration of a linear optical true-time delay device by use of a...
- et al.
Phased-array beam steering using optical true time delay technique
Opt. Commun.
(2015) - Bousonville, Michael. K. Bock, M. Felber, Matthias. Ladwig, T. Lamb, Todd. Schlarb, H. Schulz, S. Sydlo, C. Kownacki,...
- et al.
Dual hollow core fiber-based Fabry-Perot interferometer for measuring the thermo-optic coefficients of liquids
Opt. Lett.
(2015)
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2023, Proceedings of SPIE - The International Society for Optical Engineering