As an advanced fiber-optic sensing technology, optical frequency domain reflection (OFDR) has attracted increasing attention from researchers since its first proposal in the 1980s, owing to its advantages of high spatial resolution, high sensitivity, and high precision range. However, as the detection accuracy improves, errors and noise in some signal-processing processes can affect OFDR detection. Harmonic noise is common in analog signal processing and analog-to-digital converters. Operational amplifiers, transistors, and analog-to-digital converter chips, which are commonly used in analog signal processing, introduce harmonic noise. Because harmonic noise is generally separated from the measured signal in the frequency domain, traditional filters can eliminate it. However, this does not apply to OFDR signals. When harmonic noise appears in a signal’s frequency domain, it may interfere with the OFDR detection or sensing results, causing sensing errors or erroneous judgment results.

In this study, we design a real-time short-term frequency variable-coefficient finite-length impulse response (STF-VCFIR) filter system. We use a field-programmable gate array (FPGA) as the real-time processing unit of the system and design a real-time computing method based on the pipeline characteristics of FPGA processing.

In this study, we analyzed the impact of harmonic noise on the OFDR and theoretically calculated the location of harmonic-noise occurrences. Through analysis, we know that the position of harmonics in the spectrum changes with the number of harmonics and may not necessarily be greater than the signal position. However, when the harmonic frequency is lower than the signal frequency, the harmonics overlap with the signal and are difficult to remove. This implies that harmonic signals must be filtered out before resampling. We drew a time-frequency graph of the OFDR signal and compared it with those of traditional filters. Thus, we know that the fixed cut-off frequency of traditional filters cannot completely eliminate harmonic noise.

In summary, we proposed an ideal filter model that can filter harmonic noise. A real-time short-term frequency variable-coefficient finite-length impulse response (STF-VCFIR) filter system was designed based on an ideal filter model. The system used an FPGA as the real-time processing platform and obtained the short-term frequency by zero-crossing counting the auxiliary interferometer signal. It then selected filter coefficients based on the short-term frequency to obtain a dynamic cut-off frequency and avoid excessive storage-space consumption.

To verify the effectiveness and performance of the STF-VCFIR filtering system in practical applications, we construct an OFDR experimental platform. The TSL-710 frequency-scanning laser has a scanning range of 1549.5?1550.5 nm (specific range is 1 nm), a scanning speed of 40 nm/s, and a theoretical spatial resolution of about 0.8 mm. The Newport 1811 photodetector has a conversion bandwidth of 0?125 MHz. The arm-length difference of the auxiliary interferometer is 150.0001 m and the maximum theoretical detection distance is 75 m.

Data are collected, analyzed and processed separately using filtering-free, fixed-coefficient filtering and STF-VCFIR filtering. The fixed-coefficient FIR filter adopts a 63^rd-order FIR filter with a 6 MHz cut-off frequency. The Hamming-window function-design method is used. The processing clock is synchronized with the sampling clock. The STF-VCFIR filter adopts a 63^rd-order FIR filter with a segmentation coefficient of 32 segments and a cut-off frequancy range of 0.1 MHz?6 MHz, and all designs adopt Hamming-window functions.

Both filter types are implemented in the FPGA using fixed-point calculations. A single coefficient has a bit width of 16 bits and a total bit width of 512 bits (16×64/2). The coefficient-pool address has a bit width of 5 bits, occupying 2 kB of space. Owing to the use of FPGA calculations, the operation time of the filtering system is synchronized with the sampling time, with a difference of only three clock beats, enabling real-time processing.

In the experiment, we compare the complete waveform and detailed images processed using the three algorithms. By observing the complete waveform, we know that the filtering algorithm has a minimal impact on the signal within the passband and the relative maximum error of the test results is 0.025%. By observing the details, we know that the traditional fixed-coefficient FIR filter can reduce the harmonic peaks; however, its effect is limited. The STF-VCFIR filtering algorithm can significantly suppress harmonic noise.

The experimental results show that the system can eliminate harmonic noise in real time with a maximum elimination ability of over 8 dB. At this point, the intensity of the harmonic noise is smaller than the noise fluctuation range, thus reducing the probability of a sensing error or misjudging the harmonic noise as a reflection point.

However, this study still has fundamental limitations. The measurement of the short-term frequency lags behind the frequency of the measured signal because the zero-crossing counter outputs the previous cycle, which can lead to an error between the cut-off and current frequencies. However, because the OFDR frequency signal does not exhibit sudden changes, a fixed-frequency offset can be used to solve the problem. In addition, directly replacing the filter coefficients in this study to achieve a dynamic cut-off frequency can smooth the filter transition and further approximate an ideal filter. These points will be further discussed in the future.