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Abstract
In ice thickness measurement (ICM) procedures based on Raman scattering, a key issue is the detection of ice–water interface using the slight difference between the Raman spectra of ice and water. To tackle this issue, we developed a new deep residual network (DRN) to cast this detection as an identification problem. Thus, the interface detection is converted to the prediction of the Raman spectra of ice and water. We enabled this process by designing a powerful DRN that was trained by a set of Raman spectral data, obtained in advance. In contrast to the state-of-the-art Gaussian fitting method (GFM), the proposed DRN enables ICM with a simple operation and low costs, as well as high accuracy and speed. Experimental results were collected to demonstrate the feasibility and effectiveness of the proposed DRN.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The polar regions have been receiving intense scientific and technological interest, due to global climate change and increasing industrial activity. In the polar regions, ice acts as an effective intermediary between the ocean and the atmosphere by modulating heat, mass, and momentum transfer [1]. As a result, ice studies help researchers to model, analyze, and forecast global climate change. As an important indicator, ice thickness measurements (ICMs) play an important role in ice studies. In addition, ICM can also be used to ensure safe voyages and explore resources [2–4].
Various ICM approaches have been developed, with varying degrees of accuracy, spatial and temporal resolution, capability, and cost. Drilling is the most common method and has the benefits of a simple procedure and accuracies on the scale of millimeters [5,6]. However, these benefits come at the cost of time, manpower, and requirement of working on the ice owing to its single-point measurement procedure. Thermistors can be employed in long-term range ICM; however, this method is seldom adopted in practice, as it requires massive manpower to recover equipment from the ice, and, in particular, it can only marginally distinguish the interface between melting ice and water, owing to the similar temperatures they share. Electro-magnetic sounding provides an excellent sampling rate [6]; however, its accuracy relies heavily upon ice salinity, porosity, and further calibrations. Upward-looking sonars are costly and commonly available for long-term measurements [7]. However, the ice velocity drift must also be obtained simultaneously to resolve the measurement correctly. Satellite remote sensing offers repeat data over large areas [8,9]. However, its accuracy is low and strongly influenced by weather conditions. Recently, a compact Raman LIDAR system with a spectrograph was developed to enable ICM [10,11]. The difference between the Raman spectra of ice and liquid water was used to identify the ice–water interface, while the elastic signal was employed to determine the air–ice interface. This system provides a simple implementation and does not require contact with the ice in its setup. Hence, it can be installed on an unmanned airplane or autonomous underwater vehicle. However, it requires sequential Raman data not only of the ice but also of the water to resolve the ice-water interface. This results in a high workload.
As one of the most attractive research fields in recent years, deep learning allows complex operations on raw datasets using multilayered artificial neural networks [12–14]. It has shown remarkable success in signal-extracting, feature-learning, and modelling complex relationships. However, deep learning for Raman studies remains a comparatively unexplored area. Liu et al. [15] proposed a unified solution to identify chemical species via deep learning, in which a convolutional neural network was trained to automatically identify substances according to their Raman spectrum, without preprocessing procedures. Krauß et al. [16] applied deep learning to the whole-image classifiers for Raman-microscopy-based cytopathology, thus resulting in a high accuracy. Fan et al. [17] proposed an approach titled “deep learning-based component identification for the Raman spectra of mixtures”. To the best of our knowledge, there is no existing work demonstrating deep learning approaches to deal with raw Raman spectra for ICM.
In this paper, we suggest an improved deep residual network (DRN) for ICM, using Raman scattering to facilitate a substantial performance enhancement. In our approach, the DRN is employed to extract the ice-water border from the Raman spectra. Experimental results demonstrate that, in contrast to [10,11], our approach not only greatly simplifies the work load at low costs, but also enables higher accuracy and faster operation times.
2. Principle
2.1 Experimental setup
Figure 1 shows the experimental setup, the sample is excited by an argon-ion laser at 514 nm. The output beam is collimated and expanded by a beam expander BE, then converged by an objective lens (OL) with a focal length of 180 mm, to illuminate the remote sample. The beam scattered from the sample is collected by OL again and then guided via a beam splitter BS to converge onto a spectrometer (AvaSpec-HS1024*122TEC with resolution of 1.5 nm and spectral range of 200–1160 nm) via a collection lens CL. An ice cube was formed from tap water in a laboratory refrigerator, it had a good optical quality with a few defects such as bubbles, brines, and cracks inside. The ice sample was then put into a jar, where it floated on top of tap water. During the measurement process, we varied the lens-to-sample distance and detected signals from different laser beam waist positions. In this scenario, the focal length of OL should be greater than the ice thickness but as small as possible to optimize the spatial resolution. Thus, we affix the lens OL onto a micro-motional scanning stage, to search the air–ice interface and the ice–water interface, respectively. The air–ice interface can be estimated at the maximum value of the elastic signal, whose position is set to zero in the following analysis. However, as pointed out by [10], the identification of the ice–water interface is a key issue, in which the Raman OH-band profiles need to be calculated. In [11], the profile was fitted with a Gaussian fitting method (GFM), by plotting the corresponding curve centers as functions of the lens-to-sample distance. However, this method required a series of Raman spectra from ice and water, resulting in an extremely complex measuring process with low speed. To simplify the process and ensure high speed at high accuracies, we develop an improved DRN to recognize the Raman signal. To investigate the generalization of the improved DRN in spectral recognition, we carry out the following steps to obtain datasets, and conduct classification experiments. First, after an ice cube is inserted into the water jar, multiple Raman signals are acquired along the optical axis from ice to water using the apparatus shown in Fig. 1. To make the data more representative, we repeat the data acquisition in random positions with different sizes of ice cubes. As a result, we obtain a large number of Raman signals for both floating ice and water. Second, the Raman signals are divided into two types according to the position of the laser focal point. In such cases, the one hot code [18] is employed to represent the Raman spectra of ice and water, with (0, 1) as ice and (1, 0) as water, in which the ratio between them is about 1:1. Third, after collecting signals of multiple ice cubes, we obtain 2290 Raman datasets. Finally, we assess the model through the classic train-validation-test approach. During the assessment process, the aforementioned Raman datasets are randomly separated into two subsets, with a ratio of 85:15 for training and validation, respectively, while other different Raman datasets are used for testing. To relieve the effect of the differences of the spectral peak intensities on the measuring accuracy, and to speed up the learning convergence, all the Raman spectra data used in the experiments are normalized.
Fig. 1. Experimental setup for ICM: M1 and M2 represent the mirrors; BE the beam expander; BS the beam splitter; OL the objective lens; and CL the collection lens.
2.2 Improved DRN
Deep learning has been shown to be effective for a variety of recognition, classification, and segmentation tasks [19–26]. Normally, deep learning models share convolution kernels to exploit the local features of data and then, extract global training features. In the traditional convolutional neural network (CNN) [20–23], as the number of network layers deepens, the problem of gradient disappearance/explosion arises, resulting in a decrease in accuracy. DRNs [27–29] were proposed to solve this issue. In DRNs, the input information is directly connected to the output, to protect the integrity of the information. Unlike traditional networks, which are the DRNs used for image classification, we develop an improved DRN for one-dimensional (1D) Raman spectral recognition.
The basic architecture of the improved DRN is shown in Fig. 2. There are several functional layers, including residual convolutional layer, pooling layer, fully connected layer, and output layer. Assuming that for the k-th convolutional layer, the number of the convolution kernel is K(k), and the convolution result is cjk (j = 1, 2, …, K(k)). The convolutional layer in each block can be described as
Fig. 2. Basic architecture of the improved DRN. In each layer, a residual convolutional layer and a max pooling are involved, in which “×3” on the top of “Block” indicates repeating the block three times. “FC1” and “FC2” denote fully connected layers, “Dropout” represents the dropout layer. In the Feature Extraction, the kernel size and depth are demonstrated at the bottom of each layer, in which “depth_n” (n = 1, 2, …, 7) means 32, 32, 64, 64, 128, 128, and 256, respectively. In the Regression, the input Raman signals are predicted with a response, denoting the estimated position of the ice–water interface.
After each application of the ReLU, the intermediate data is divided equally and then, added to enable information fusion, which helps to enhance the extraction capacity of the underlying characterization. The combination of convolution and fusion is the essential building block of our network and is repeated three times. To ease the training of networks and gain accuracy on the feature extraction of the spectral peak, a shortcut flow is introduced to complete the residual convolutional layer. This shortcut flow is marked by the blue line [27–29]. We define the input data as x and the output data as y. The residual is F(x), and the residual module can then be written as
Then the residual convolutional layer is followed by a maximum pooling layer [18,22] to down-sample the feature map but retain the main features as much as possible, the schematic for the maximum pooling is shown in Fig. 3. As shown in Fig. 3, we employ the maximum value as the representation over a small region. This operation greatly reduces the spatial dimension of the representation and the number of parameters, subsequently reducing the computation cost. It could also help the network to prevent over-fitting. The residual convolution and maximum pooling form a complex layer which is repeated seven times, thus resulting in the final feature extraction module, as shown in Fig. 2. This module is employed to identify the implicit features of the Raman spectra.Thereafter, the extracted feature information is sent into the fully connected layer (FCL) [18]. To avoid over-fitting while increasing the learning speed, a dropout layer [31] is introduced to guard the network. Through each training iteration, the individual nodes are either retained (with a probability of p) or cast away from the network (with a probability of 1−p), thereby yielding a compressed network [31]. The combination of the FCL and dropout layer is grouped as the regression module for regression analysis, which is repeated twice. Finally, the output layer gives a predicted response.
To train the network, we need a substantial number of Raman signals, including those of ice and water. Thereafter, we assign the real code as the response to each Raman signal, as shown in Section 2.1. Suppose y is the estimated output and yr is the corresponding real code. In such a case, the one-hot code of yr indicates the probability distribution under ideal conditions, in which (1, 0) represents water, and (0, 1) represents ice. As a result, each neuron array in the output layer becomes a 1 × 2 array. The network training is completed by minimizing the loss function. In general, the loss function L(·) [32] for each sample is a multi-class cross entropy loss function, which can be described as follows:
3. Results
To demonstrate the feasibility of the proposed DRN, we froze tap water in a laboratory refrigerator to form different sizes of ice cubes. The system shown in Fig. 1 was employed to collect Raman data. For comparison, the Raman spectra of water and ice were separately collected before the ice cube was inserted into the water jar, and the results are shown in Fig. 4(a). It is clear that there is a difference between the Raman spectra of water and ice before the insertion, which agrees well with the results obtained in [10] and [33]. Afterwards, the spectra collections were performed after the ice cube had been inserted into the water jar, and the results are shown in Fig. 4(b). It is notably difficult to distinguish the spectral differences between ice and water near the ice-water interface through manual classification alone. To search for an optimal method of performing data classification, we trained the proposed DRN to predict the two types of aforementioned samples. Meanwhile, we employed the one-hot code to identify the Raman spectra of ice and water.
Fig. 4. Typical Raman spectra of water and floating ice. (a) before ice insertion, (b) after ice insertion, in which “+” indicates the ice spectrum obtained above the ice-water interface, and “−“ indicates the water spectrum obtained beneath the ice-water interface.
After acquiring 2290 Raman data with a ratio of 1:1 for ice and water, we randomly divided the data into two subsets, with a ratio of 85:15 for training and validation, respectively. The DRN is trained using the Adam optimizer [22], which is a form of gradient descent method. In this case, the learning rate was empirically set to 10−6 and allowed to decay with a rate of 0.99 at each training iteration. To solve the issues of (i) memory constraints and (ii) stagnation in local minima during optimization, at each iteration a single mini-batch [18,22] of 20 from the whole training data was sent into the network for training, instead of the entire set of Raman data. All the weights are initialized using truncated normalization with a standard deviation of 0.1, and the biases were initialized with a constant value of 0. In each mini-batch training step, one iteration of the optimization was conducted, and the parameters of the network were updated. The dropout probability was fixed at 0.5 during training, while in validation and testing it was set as 1. This enabled 50% of the nodes to be randomly selected and intentionally invalidated in training, to reduce over-fitting. The training environment was an Intel(R) Core(TM) i3–8100 CPU @3.60 GHz, with 8 GB memory.
Figure 5 shows the losses during the training process, in which the loss was recorded every fifteen iterations. It is clear that the proposed DRN converges gradually, since the loss descends along the course of training. After training for 7365 steps, the loss approached the order of 0.4. This accords with our expectation that the network is continuously updating its parameters and studying representative features of the Raman signals, resulting in a satisfactory training speed.
After training and validation of the DRN, a series of new Raman spectra, which had not appeared before, were fed into the network for testing. In this case, the Raman signals were acquired from different positions by varying the lens-to-sample distance with an increment of 1 mm. During testing, we not only ran the proposed network, but also compared it with the GFM. The results are illustrated in Fig. 6. To obtain a better comparison, the results are demonstrated side by side. For the GFM [10,11], the Raman OH-band profile was fitted by a Gaussian function, and the resulting curve centers were plotted as a function of the lens-to-sample distance. In this case, the center of the confidence band was taken as a quantitative indicator for the identification of the ice-water interface. The result is shown in Fig. 6(a). However, a group of Raman data near the ice-water interface (indicated by the green arrow line in Fig. 6(a)) required fitting with linear regression, thereby resulting in an extremely heavy measurement burden, and further limiting the measurement speed. Meanwhile, the measurement accuracy was determined by the confidence band interval around the inflection point. Therefore, apart from the micro-motional scanning stage, GFM also requires a high precision spectrometer, i.e., a spectrograph (Spectra Physics, MS127i with a resolution of 0.1 nm and spectral range of 500–750 nm), combined with a gated detector (ICCD, Andor iStar), to ensure measurement accuracy. However, in contrast to the GFM, the proposed DRN needs only a few data from near the ice-water interface (indicated by the green arrow line in Fig. 6(b)) and can immediately identify the ice-water interface once the water spectrum is determined. In other words, the proposed DRN requires neither the high precision spectrometer, nor a set of Raman data for the water from below the ice-water interface. After identifying the ice-water interface, the ICM can be completed by computing the distance between the air–ice interface and the ice–water interface. Thus, in contrast to the GFM, the proposed network can perform the ICM using a simple operation and at a low cost, whilst maintaining high accuracy and speed.
To further evaluate the performance, we compared the measured results of the GFM and proposed DRN using different thicknesses of ice, in which the nominal thickness of the ice is supplied by a Vernier caliper. The results are shown in Table 1, in which both absolute errors and relative errors have been calculated. It is obvious that in contrast to the GFM, the proposed DRN has a lower error. This further proves that the proposed DRN can provide high accuracy. It is noted that owing to the limitations imposed upon us by our ordinary laboratory conditions, such as the low laser power and small travel range of the scanning stage, the samples used for this study are less than 100.0 mm. To measure realistic samples (i.e., very thick samples), a Raman LIDAR with high power pulse laser [10,11] should be employed, as this would simultaneously measure the Raman spectra at multiple distances [34], or work in a single-photon counting and time-of-light measurement mode [35]. This will be a part of future study.
Table 1. Comparison of the measurement error between DRN and GFM
4. Conclusion
In conclusion, we report an improved DRN to enable ICM based on Raman scattering. Unlike the conventional GFM, we consider the detection of the ice–water interface as an identification problem in which the DRN is employed to predict the Raman spectra of ice and water. The experimental results demonstrate that DRN can perform ICM with ease of operability and low cost, whilst maintaining high accuracy and speeds. We hope that the proposed method can be found to be practical in ICM applications.
Funding
National Natural Science Foundation of China (61775046); Natural Science Foundation of Heilongjiang Province (LC2018027).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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