All-fiber coherent laser image Lidar based on phase correction

Xiaojing Shi; Jianfeng Sun; Peng Jang; Peng Jang; Wei Lu; Qiqi Wang; Qi Wang

doi:10.1364/OE.27.026432

1. Introduction

Compared with the direct detection method, the use of a coherent lidar can provide higher sensitivity, can eliminate the influence of background light, and can obtain the echo signal intensity, range, or Doppler image by scanning. Coherent lidar can also analyze the correctness of the intensity images based on the speckle characteristics of the target. At present, most studies focus on the influence factors of coherent lidar ranging accuracy and on theoretical research regarding denoising methods for time domain signals [1,2]. However, for a non-cooperative target at a distance, the distance of the target as well as noise will affect the extraction of the target's intensity image. those noises are often consider that caused by local oscillator (LO) shot noise [3], instability of local oscillator power and detector. Yuen and Shapiro have proven that the local oscillator's quantum noise and other excessive noise can be eliminated through a splitter [4–7], so coherent lidar noise is mainly caused by instabilities of the local oscillator power and detector. In the case of the target echo signal and its inherent weakness, the instability of the local oscillator signal can exceed the amplitude of the echo signal so that the weak echo signal generated by the target is flooded, and it is difficult to extract the target’s intensity image.

Heyong Zhang has applied a signal segmentation cumulative averaging method and a spectrum averaging method to reduce the influence of noise on weak signals, thus, improve the signal-to-noise ratio of heterodyne signals (IF signals) [8]. Chen Li proposed a data denoising and signal extraction algorithm for a Mie lidar based on applying a particle filter and the Vernald method [9]. Although these methods can improve the signal-to-noise ratio of lidar echo signals, the location of the search heterodyne signal is still affected by noise, resulting in inaccurate location, so these methods are not sufficient to extract a coherent lidar intensity image under weak echo signals.

This study focuses on a method for phase correction and separation of echo signals to extract the relative intensity image of the target under the condition where the weak echo signal has been submerged. This method can more accurately determine the relative intensity value of each pixel of the target, and we analyze and verify this method by using false alarm rates, range, intensity accuracy, and speckle characteristics of the target. This study lays the foundation for a low-power laser heterodyne detection imaging system and an improved imaging range of coherent lidar systems. The rest of this paper is organized as follows: in Section 2, the phase correction of the coherent lidar and the theory of extracting relative intensity images are presented, and an introduction on how to verify the extracted intensity images is provided. Section 3 introduces the experimental coherent lidar system, and according to the theory presented in Section 2, we present and analyze the experimental results. Section 4 presents the conclusions.

2. Theoretical analysis

2.1. Heterodyne signal theory based on phase correction

At present, the position of the heterodyne signal in the time domain signal is mainly used to perform short-time Fourier transform, fast Fourier transform, and wavelet transform on the time domain signal, but these methods cannot accurately locate the position of the heterodyne signal. In this study, a phase correction method is proposed. First, after the initial positioning of the heterodyne signal is obtained by windowed Fourier transform, the phase correction method is used to compensate it. This method can obtain the precise position of the heterodyne signal of the coherent lidar. The heterodyne signal is generated by the echo signal and the local oscillator signal through the balance detector, and the echo signal can be expressed as

E_{S} (r, ϕ, t) = A_{s} (r, ϕ, t) \exp {i [w_{s} t + φ_{s} (r, ϕ, t)]} .

Here,

A_{s} (r, ϕ, t),

w_{s},

and

φ_{s}

represent the target echo signal light amplitude, angular frequency, and phase. The electric field strength of the local oscillator can be expressed as

E_{L} (r, ϕ, t) = A_{L} (r, ϕ, t) \exp {i [w_{L} t + φ_{l} (r, ϕ, t)]} .

A_{L} (r, ϕ, t),

w_{L},

and

φ_{L}

represent the local oscillator signal amplitude, angular frequency, and phase. The total electric field strength on the photosensitive surface is thus expressed as the sum of the two fields:

E (r, ϕ, t) = E_{s} (r, ϕ, t) + E_{L} (r, ϕ, t) .

The total current generated is expressed as

\begin{matrix} i (t) ~ I (t) = \frac{η e}{h v z} E (r, ϕ, t) * E^{*} (r, ϕ, t) = \\ \frac{η e}{h v z} [\begin{array}{l} 2 A_{s} (r, ϕ, t) A_{L} (r, ϕ, t) \cos [(w_{s} - w_{L}) t + φ_{s} (r, ϕ, t) - φ_{l} (r, ϕ, t)] + \\ A_{s}^{2} (r, ϕ, t) + A_{L}^{2} (r, ϕ, t) \end{array}] . \end{matrix}

Here, e is electronic charge, h is Planck's constant,

v

is the light frequency, and z is the impedance of the detector.

Because the dual path balancing detector can only respond to the intermediate-frequency (IF) signal, in which the DC component is not responded to, the IF signal from the balanced detector response is the first term in Eq. (4).

i_{I F} (t) ~ \frac{η e}{h v z} A_{s} (r, ϕ, t) A_{L} (r, ϕ, t) \cos [(w_{s} - w_{L}) t

When the coherent lidar uses the windowed Fourier transform to extract the position of the heterodyne signal from the time domain signal, there will be a certain degree of deviation due to the influence of noise, resulting in the inability to accurately locate the heterodyne signal. On this basis, according to the principle of balanced photodetectors, there is a phase difference of π between the intermediate frequency signal currents such that the IF signal power obtained by the device is the sum of the intermediate frequency powers of the two devices, where the noise and phases are random. After differential processing, they cancel each other out to greatly reduce the system noise. The Fourier transform of the heterodyne signal obtained from the initial positioning can be expressed as

F (f) = R (f) + i * I (f) .

I (f)

and

R (f)

are the imaginary and real parts of the Fourier transform of the IF signal in the window, respectively. According to Griffiths and deHaseth's work [10], the polar coordinate formula for the Fourier transform obtained by the Euler transform is

F (f) = | F (f) | * e^{j ϕ} .

Here,

| F (f) | = R^{2} (f) + I^{2} (f)

and

ϕ

is the phase of the extracted signal region [11,12]:

ϕ = a r c \tan {I (f) / R (f)} .

In the experiments conducted, the frequency of the IF signal is 30 MHz, and the resolution of the Fourier transform can be expressed as

Δ f = F_{S} / N,

where

F_{S}

is the sampling frequency and N is the sampling point. The lowest frequency resolution used in this signal processing process is 5 MHz, which allows the phase value to be accurately extracted. Subtracting

ϕ

from the π phase difference due to the photodetector, and then converting the phase to the time-domain difference yields

t_{2} = {\begin{cases} t_{1} + {| ϕ * \frac{180}{π} - 180 | / 360} * (1 / f^{'}) ϕ > 0 \\ t_{1} - {| ϕ * \frac{180}{π} + 180 | / 360} * (1 / f^{'}) ϕ < 0 \end{cases} .

Here,

t_{2}

is the time domain position of the heterodyne signal after phase correction,

t_{1}

is the time domain location of the initial positioning heterodyne signal, and

f^{'}

is the IF frequency. The position of the heterodyne signal is corrected in the time domain so that the corrected signals have the same phase. Finally, according to the position of the heterodyne signal after correcting the phase, the accuracy of the target’s position using the weak signal coherent lidar is improved, and a more accurate intensity image is obtained.

To verify the correctness of the proposed phase correction algorithm, a set of heterodyne time domain signals are simulated in our experiments, and the phase correction algorithm is used to achieve precise positioning. The representation of the simulated heterodyne signal according to the first term in Eq. (4) is given in Eq. (10).

E = A_{s} A_{l} \cos (Δ w t + Δ φ) = \cos (1.2 π t - π)

The signal-to-noise ratio (SNR) of this signal is 0.01, the IF frequency is 0.6 Hz, and the phase difference is $π .$ The number of pre-collected signals is set to 40, sampling frequency is 10 Hz, and signal width is 10 s. Figure 1 shows the simulation of a heterodyne time domain signal with white Gaussian noise. The wavelet denoising technique is used to denoise the time domain signal, and the peak value of the spectrum peak is obtained by windowed Fourier transform, as shown in Fig. 1(b), thereby demonstrating the search process for the actual position of the heterodyne signal. It can be seen from Fig. 1(b) that the peak value of the spectral peak curve obtained by the windowed Fourier transform (red box) exhibits jitter because of the presence of noise. The position of the maximum value is the 47th point, and the position of the actual signal is the 41st point, indicating that the peak extraction caused a deviation.

Fig. 1 (a) Simulated heterodyne time domain signal; (b) windowed Fourier transform plot showing the peak curve.

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Using Eq. (8) at the frequency domain peak of the window where the 47th point is located, the phase ( $ϕ = 5.4035$ ) of the initial positioning heterodyne signal is obtained. According to Eq. (9), the obtained phase is converted into a time domain difference represented by $Δ t =$ 0.6 and $t_{1} = 47$ for a sampling interval of 0.1 s, resulting in $t_{2} = 41$ , which represents the actual (true) position. To further verify the feasibility of the algorithm, the experiment was repeated 1000 times, and the deviation value curves obtained by simply searching for the heterodyne signal using wavelet denoising before windowed Fourier transform and the position obtained by repositioning the heterodyne signal by phase correction were obtained. The comparison of the values obtained is shown in Fig. 2.

Fig. 2 (a) Deviation curve of the heterodyne signal position by window Fourier transform; (b) deviation value curve of the position of the heterodyne signal obtained after phase correction.

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It can be seen from Fig. 2 that the number of outliers in the positioning heterodyne signal position after phase correction is obviously lower than that without phase correction. In Fig. 2(a), the absolute value of the deviation of the position of the heterodyne signal for 1000 tests is 4.177, while the absolute value of the heterodyne signal deviation obtained after phase correction is 2.09 (Fig. 2(b)). Based on these results, it can be concluded that applying phase correction can reduce the probability of the deviation of the positioning heterodyne signal significantly, which indicates that the algorithm is effective for improving the positioning accuracy of the heterodyne signal.

2.2. Weak signal coherent lidar intensity image extraction

After the above-mentioned accurate position of the heterodyne signal is obtained by the phase correction compensation method, the echo signal is extracted from the heterodyne signal, and the relative intensity image of the signal can be obtained. When the echo signal is extremely weak, the instability of the local oscillator causes the intensity value of the echo signal to be submerged. The method proposed in this study mainly focuses on the problem where the weak echo signal strength change is extracted from the heterodyne signal, so it is not affected by the instability of the local oscillator signal. Based on Eq. (4), the electric field intensity of the heterodyne signal is expressed as

\begin{array}{l} E_{I F} = A_{s} * A_{l} * \cos (Δ w t + Δ φ) . \\ Δ w = w_{s} - w_{l} \\ Δ φ = φ_{s} - φ_{l} \end{array}

Equation (11) indicates the case wherein because of the weak signal light in the heterodyne signal, the light intensity change of the echo signal is submerged in the heterodyne signal when the laser hits different positions of the target. Therefore, we propose to extract the amplitude

A_{s}

of the target echo signal in the heterodyne signal to synthesize the intensity image. Suppose the IF signal at each sample point on the target is expressed as

\begin{array}{l} E_{I F 1} = A_{s 1} * A_{l 1} * \cos (Δ w t + Δ φ) = A_{s 1} * (A_{l} + n_{1}) * \cos (Δ w t + Δ φ) \\ E_{I F 2} = A_{s 2} * A_{l 2} * \cos (Δ w t + Δ φ) = A_{s 2} * (A_{l} + n_{2}) * \cos (Δ w t + Δ φ) \\ E_{I F 3} = A_{s 3} * A_{l 3} * \cos (Δ w t + Δ φ) = A_{s 3} * (A_{l} + n_{3}) * \cos (Δ w t + Δ φ) . \\ ...... \\ E_{I F n} = A_{s n} * A_{\ln} * \cos (Δ w t + Δ φ) = A_{s n} * (A_{l} + n_{n}) * \cos (Δ w t + Δ φ) \end{array}

Here,

n_{k}

indicates the amplitude jitter due to the instability of the local oscillator signal (i.e., the vibration amplitude

n_{k}

is greater than the target echo signal light variation), and the phase difference of the IF signal at each point after phase correction is assumed constant. At this time, the heterodyne signal of each pixel in the time domain is divided by the heterodyne signal of the time domain whose intensity is closest to the mean value of all the pixel points, per Eq. (13):

\begin{array}{l} \frac{E_{I F 1}}{E_{I F m}} = \frac{A_{s 1} * (A_{l} + n_{1}) * \cos (Δ w t + Δ φ)}{A_{s m} * (A_{l} + n_{m}) * \cos (Δ w t + Δ φ)} = \frac{A_{s 1}}{A_{s m}} * [1 + \frac{(n_{m} - n_{1})}{(A_{l} + n_{m})}] \\ ...... \\ \frac{E_{I F n}}{E_{I F m}} = \frac{A_{s n} * (A_{l} + n_{2}) * \cos (Δ w t + Δ φ)}{A_{s m} * (A_{l} + n_{m}) * \cos (Δ w t + Δ φ)} = \frac{A_{s n}}{A_{s m}} * [1 + \frac{(n_{m} - n_{1})}{(A_{l} + n_{m})}] . \end{array}

In Eq. (13), m is the pixel closest to the mean of the spectral peaks of all pixel heterodyne signals. The variation of the local oscillator signal intensity (n_m – n₁) is small relative to the amplitude of the local oscillator, so

[1 + \frac{(n_{m} - n_{1})}{(A_{l} + n_{1})}] \approx 1.

The intensity value of each point in the obtained result is equivalent to the signal light relative intensity E in the point difference frequency signal. As shown in Eq. (13), the maximum value of E is the relative intensity value having the minimum impact on the local signal jitter, which allows us to extract the intensity image as

E \approx \frac{A_{s n}}{A_{s m}} .

2.3. Intensity image verification

In this study, the correctness of the extracted intensity image is verified based on the statistical distribution of the target intensity. As most targets are optically rough surfaces, the diffuse scattered light from the coherent lidar is reflected when it reaches the target, and although a target may produce one or more micro-mirror scintillation reflections, the signal returned by the target generally exhibits speckle. Therefore, the target echo signal strength of a coherent lidar with weak signal-to-noise ratio should be subject to speckle distribution, and the probability density function of the gray value of the echo signal strength caused by speckle is given by Eq. (15). If the incident light energy is a speckle field with M degrees of freedom, the probability density function $P (I)$ can be well approximated as $Γ (M)$ by the probability density function with parameter M [13,14].

P (I) = \int_{I}^{\infty} p_{I} (τ) d τ = {(\frac{M}{< I >})}^{M} \times \frac{I^{M - 1} \times e x p [- M \frac{I}{< I >}]}{Γ (M)}

In Eq. (15), <I> denotes the mean value of the grayscale values of the echo signal strength and I represents the normalized echo signal strength value. For a normalized distribution (<I> = 1), the intensity image can be verified according to the target intensity image conforming to the speckle distribution characteristics.

3. Experiments and results

3.1. Experimental system

The coherent lidar system includes a coherent lidar transmitting part, an optical system part, and a receiving/processing part. The coherent lidar emitting part consists of a generator, an acousto-optic modulator, and a pulse amplifier. The optical system part includes a scanning galvanometer and an optical transceiver system. The receiving/processing section is composed of a coupler and a detector, an amplifier, and a subsequent processing unit.

The system uses a 1.06 μm pumping source as the generator with a line width of 5 MHz, a 1.06 μm laser diode as the seed source, and the emitted beam is divided into two beams: one is the local oscillator, and the other is the signal light, which is shifted by an acousto-optic modulator (AOM) with a frequency shift rate of 30 MHz. The AOM externally triggers the modulated signal with a pulse width of 200 ns at a frequency of 10 KHz. The signal light with a pulse energy of 5 μJ is transmitted to a galvanometer through a circulator and emission collimating mirror, and the oscillations of the galvanometer are controlled by the upper computer (PC) to obtain the scanning range. The galvanometer supply voltage is ± 0.25V, the galvanometer x-axis direction voltage follows a sinusoidal distribution, and the y-axis direction voltage is stepped. The received echo is input into the balance detection system through the other end of the circulator and is coupled with the local oscillator light through the coupler, forming an heterodyne signal between the echo light and the local oscillator light. The AD is used to collect signals for subsequent processing on the PC. During an experiment, the signal is transmitted and is then collected under an external trigger so that the acquisition is synchronized with the trigger signal. An image of the test equipment and a schematic of the test system are shown in Fig. 3 and Fig. 4, respectively.

Fig. 3 Image of the test equipment.

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Fig. 4 Schematic of the test system.

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On this basis, we conducted two experiments, first performing intensity image extraction experiments. Then, according to the characteristics of the speckle distribution based on the target intensity value proposed in Chapter 2, the extracted intensity image is subjected to verification experiments.

The target position and the single pixel signal collected by the acquisition card are shown in Fig. 5. Figure 5(a) shows the target used in the experimental system, where the wall is located 47.6 meters away from the equipment (other than the lidar). The target is a whiteboard that is 85 cm wide and 78 cm long. The target whiteboard moves backward in increments of 1 m, starting 30 m – and ending 33 m away from the lidar. The coherent lidar acquisition signal is collected at the falling edge of the trigger signal after a time delay signal of 480 ns. The single pixel signal collected by the acquisition card is shown in Fig. 5(b).

Fig. 5 (a) Whiteboard target used in the experiments; (b) a single pixel signal collected by the acquisition card.

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In Fig. 5(b), the first part of the signal is the time delay signal, the second part is the heterodyne signal of the optical surface (the heterodyne signal reflected by the optical lens), and the third part is the heterodyne signal of the target, at this point we only consider the heterodyne signal of the target. It can be seen that the heterodyne signal of target has been completely submerged and macroscopically invisible. Finding the position of the heterodyne signal of the target from the time domain signal takes place after the window Fourier transformation, the distance of the target when ranging is equal to the speed of light in the medium c (refractive index of the atmospheric medium n = 1) times the round trip time $Δ t$ divided by 2. The distance of the target is calculated from $L = c Δ t / 2.$

Owing to the influence of noise, the extracted heterodyne signal of the target is unstable, so first, wavelet denoising is performed on the time domain signal, and then windowed Fourier transform is applied to the result. The end of each signal from the optical surface is the starting position, the laser pulse width (200 ns) is used as the length of the window, the step size is the unit acquisition time (2 ns), the Fourier transform is performed on the signals in each window in turn, and then the peaks are extracted. Because some peaks may be generated by noise, a peak value that is not at the IF frequency in each window is assigned as 0; thus, the position of the window where the maximum value of all the peaks (at the IF frequency) is found is the true position of the heterodyne signal of the target. When one target is set, the spectrum is broadened owing to the influence of noise on the signal, and the measured peak of the spectrum is unstable, so the width of the added window is the pulse width. Because the system line width is 5K Hz and the coherence time is 0.2 ms, the delay of the echo relative to the local oscillator is less than the coherence length, so the intermediate frequency signal can be extracted.

3.2. Experiment results and analysis of Intensity image extraction

Following the traditional target intensity image extraction method after wavelet denoising of the time domain signal, the intensity image of each pixel is obtained by finding the peak envelope of the signal. In this way, the intensity at target distances of 30 m and 33 m are extracted, as shown in Fig. 6.

Fig. 6 Intensity images for a target distance of (a) 30 m and (b) 33 m from the lidar.

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It can be seen from Figs. 6(a) and 6(b) that the target intensity change has been almost submerged, because the jitter of the local oscillator signal has exceeded the amplitude of the target echo signal, so the intensity is poorly displayed. Thus, this method is not suitable for the extraction of the intensity image using a coherent lidar with low SNR.

The second processing method is to extract the intensity image after extracting the position of the heterodyne signal of the target by windowed Fourier transformation. The time domain matrix of the heterodyne signal of the target at each pixel point is divided by the time domain matrix of the IF signal of the target at the pixel point of mean intensity to obtain a set of data, and the maximum value found is the relative strength value of the pixel point. Figure 7 shows the intensity images for target distances of 30, 31, 32, and 33 m using this approach.

Fig. 7 (a) – (d): Non-phase compensated relative intensity images for target distances of 30, 31, 32, and 33 m, respectively.

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From the intensity image extraction algorithm proposed in this study, the target contour can be seen clearly; the relative intensity of the weak target echo signal is not affected by the instability of the local oscillator laser power. The intensity shown is the strength of the speckle of the signal light at different locations on the target. It can be seen in Fig. 7 that there is more noise in the graphs. This is because the position of the heterodyne signal of the target is inaccurate owing to the influence of noise on the windowed Fourier transform.

The third method is to perform the phase correction on the heterodyne signal of the target position after applying the windowed Fourier transform to the time domain signal, and then applying the intensity image extraction algorithm given by Eq. (11) to extract the relative intensity of the target echo signals to obtain the corrected intensity image, as shown in Fig. 8.

Fig. 8 (a) – (d) Phase compensated relative intensity images for target distances of 30, 31, 32, and 33 m, respectively.

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Figure 8 shows that the intensity images after phase correction reflect the actual target contours; the target outline is sharper and the images contain less noise. The relative intensity value in the intensity image is normalized and the value obtained is greater than 1 if a point is a target point, and is less than 1 if it is a background point. At this time, the relative intensity value of the pixel whose value is greater than 1, but is not a target point, is set as the false alarm point. The calculated false-insurance rates of the target distances of 30, 31, 32, and 33 meters without phase correction are 0.0618, 0.0714, 0.0907, and 0.1223, and the intensity-like false alarm rates after phase correction are 0.0481, 0.0495, 0.0549, and 0.0426, respectively. The results demonstrate that the false alarm rate of the relative intensity image after phase correction is lower than that of the intensity image without phase correction, and the farther the target distance is, the weaker the echo intensity. The more obvious the algorithm's capability to correct the intensity image of the coherent lidar is, the better the relative recovery of the intensity image. The target is a whiteboard with uniform roughness. From the mean strength of the target position, when the target is 30, 31,32, and 33 m away from the equipment, the mean relative strength of the target intensity without phase correction is calculated to be 1.9316, 1.8560, 1.6788, and 1.6073, respectively, while the mean strength of the target intensity after phase correction is 2.5193, 2.3833, 2.3720, and 2.1703. Thus, without phase correction, the heterodyne signal of the target in the time domain signal echo positioning leads to higher noise that affects the influence factors of the pixels’ relative strength values, which in turn reduces the relative strength of the point values and leads to an inaccurate position estimate. Thus, the phase correction algorithm can be applied to improve the positioning precision of the heterodyne signal of the target by improving the strength of the echo signal intensity.

To evaluate the influence of the phase correction algorithm on the accuracy of the target range, Fig. 9 shows distance images without phase correction and with phase correction when the target is 30 m away from the coherent lidar.

Fig. 9 (a) Distance image before phase correction; (b) distance image after phase correction.

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It can be seen from Fig. 9(b) that the distance value at the target after phase correction is closer to 30 m than the value without phase correction. The confidence interval in which the confidence of the distance value at the target whiteboard without phase correction is 95% is calculated as 32.7–33.2), while the confidence interval with phase correction is 29.8–30.7), which indicates that the accuracy of the target range can be improved after phase correction. To further prove the validity of the corrected intensity image, statistical distributions of the intensity images according to the target echo intensity values are examined through the speckle distribution in the following section.

3.3. Intensity image verification experiment

Put the normalized target image obtained by Eq. (14) into Eq. (15), the relative intensity probability density curve of the target subject to speckle distribution can be obtained, as shown in Fig. 10, and the nature of the distribution provides high contrast with the gray values, E₁ is the normalized value by the relative intensity E.

Fig. 10 Probability density function of intensity values under the speckle mechanism (Normalized negative exponential distribution).

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Based on Eq. (14), the relative intensity of target echo signal $E$ is obtained, and normalization of the extracted target relative intensity image, statistical distribution scatter plots were constructed and compared with the probability density function obtained by the speckle theory, and the correlation indices were obtained. The results are shown in Fig. 11.

Fig. 11 (a) – (d) Statistical distributions of the relative intensity for target distances of 30, 31, 32, and 33 m without phase correction, respectively.

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Figures 11(a)–11(d) show the intensity images for target distances of 30, 31, 32, and 33 m where the intensity image grayscale values extracted without phase compensation are normalized to provide the statistical distributions. The results obtained when applying phase compensation are shown in Fig. 12.

Fig. 12 (a) – (d) Statistical distributions of the relative intensity for target distances of 30, 31, 32, and 33 m after phase correction, respectively.

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Figures 12(a)–12(d) show the intensity images after phase compensation for target distances of 30, 31, 32, and 33 m. From the results of Figs. 11 and 12, the target intensity image obtained by the intensity image extraction method proposed in this study (Fig. 12) conforms more closely to the speckle theoretical distribution, which confirms the validity of the method.

In Fig. 11, the correlation indices of the target intensity image and the speckle probability density curve without phase correction are 0.2719, 0.5530, 0.5969, and 0.5412, while after phase correction (Fig. 12), the correlation indices are 0.8317, 0.7359, 0.8061, and 0.7335. The statistical distribution of the relative intensity image without phase correction deviates greatly from the speckle density function, while the statistical distribution of the target intensity values after phase correction are more consistent with the distributions of the speckle probability density curves, which further supports the correctness of extracting the intensity image by phase correction.

4. Conclusions

In this study, a new model is proposed for imaging of a weak signal all-fiber coherent lidar when the signal is submerged in noise. In this case, the traditional intensity image extraction algorithm is not applicable to a coherent lidar with weak SNR detecting a distant target. After using the windowed Fourier transform to initially locate the heterodyne signal position, the position of the heterodyne signal extracted from the time domain signal is unstable because of noise. Based on the balanced detector principle, phase correction of the position of the initially located heterodyne signal is applied to improve its positioning accuracy. Because of the instability of the local oscillator, a useful intensity image of the target cannot be extracted; therefore, this study proposes extracting the target echo signal from the heterodyne signal of the target to obtain the change of the relative intensity of the target echo signal. Compared with the traditional imaging method, it is found that the intensity image of a weak echo signal processed by the method proposed in this study more closely approximates the actual target, indicating that this method is suitable for coherent lidar with a weak signal-to-noise ratio. Comparing false alarm rates for the intensity accuracy and range, the relative strength image false alarm rate after phase correction is lower and the relative strength is stronger, indicating that the proposed method is less affected by noise and produces a more accurate target distance. To further verify the correctness of the intensity image after phase correction, the speckle characteristics of the target echo signal were compared with the target intensity gray values (normalized values) through statistical distributions (the gray value distributions were compared to the theoretical speckle probability density function distribution). The statistical distributions of the target intensity values after phase correction more closely fit the speckle probability density distribution, thus verifying the feasibility of the method. The target echo signals associated with long-range coherent lidar imaging are weak, and the method proposed in this study provides significant improvements to all-fiber coherent lidar long-range target imaging systems.

Acknowledgments

The authors are grateful to the anonymous reviewers for their constructive comments.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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All-fiber coherent laser image Lidar based on phase correction

Abstract

1. Introduction

2. Theoretical analysis

2.1. Heterodyne signal theory based on phase correction

2.2. Weak signal coherent lidar intensity image extraction

2.3. Intensity image verification

3. Experiments and results

3.1. Experimental system

3.2. Experiment results and analysis of Intensity image extraction

3.3. Intensity image verification experiment

4. Conclusions

Acknowledgments

Disclosures

References

Cited By

Figures (12)

Equations (15)

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