1. Introduction

Wavelength-stabilized single-frequency lasers have many applications in various fields such as quantum technologies and metrology. Prime examples include atom-based quantum computers and clocks where lasers are used for cooling of atoms and spin-state manipulation [1,2]. They are also a key component in laser trackers [3] for interferometric distance measurements. Some gas lasers exhibit an intrinsic absolute wavelength accuracy due to the used gain medium. A famous example is the Helium-Neon laser emitting at 633 nm, with a long-term frequency stability of typically 10$^{-8}$, which refers to the relative statistical uncertainty of the measured frequency at averaging times of several months or even years [4,5]. Gas lasers, however, have some fundamental drawbacks. For example, the available wavelengths are limited, the lasers are not tunable, and the output power is relatively low. These drawbacks can be overcome by diode lasers.

An absolute wavelength accuracy with diode lasers can be achieved by locking the laser to an atomic or molecular reference, using techniques such as side-of-fringe or top-of-fringe stabilization to the transmission signal through a spectroscopy cell. In general, the full stabilization process consists of the following steps: First, the laser frequency is scanned over several absorption lines. Second, the target line (corresponding to the desired laser frequency) is identified and the operating point of the laser (e.g. the diode current or temperature) is set accordingly. Finally, an electronic feedback loop is closed to actively stabilize the laser frequency. For applications that require an absolute accuracy, it is crucial that the system is locked to the same absorption line every time this process is executed. In typical setups, the task of identifying the line in the spectrum is performed by a human. However, in many situations, a fully automatic locking procedure without any user interaction is desired. In addition, this locking procedure must work reliably even for changing ambient conditions (e.g. thermal or mechanical stress) and over the full lifetime of the system (typically more than 20,000 operating hours for industry applications) in which degradation of the diode and other components may occur. These effects can lead to a change in the detected spectroscopic signals and will in general deteriorate the reliability of the locking procedure.

Automatic locking procedures based on threshold detection of photodiode signals [6] and cross-correlations [7] have been demonstrated. These approaches, however, have the aforementioned drawback of being susceptible to environmental changes and degradation of components. A recent publication [8] demonstrates automatic locking to an alkaline transition using pattern recognition based on a support vector machine. Here, we present a machine learning approach to automatic frequency locking of lasers based on artificial neural networks. A tunable single-frequency laser at 633 nm is locked to an absorption line of molecular iodine. We show that this approach is very reliable by testing it over a wide range of operating conditions.

2. Experimental setup

To stabilize a diode laser to an iodine absorption line, we use the setup shown in Fig. 1. The used laser system is a distributed-Bragg-reflector (DBR) laser with an emission wavelength of approximately 633 nm [9]. The laser has a linewidth of < 1 MHz and an output power of up to 10 mW. Part of the light passes through an iodine cell and is detected by a photodiode, while another part is directed to a second photodiode to normalize the spectroscopy signal. The temperature of the iodine cell can be controlled between 40 and 80$^{\circ }$C. The laser is controlled using a digital laser controller (TOPTICA DLC pro), which includes analog-digital converters to read the photodiode signals, and PID controllers for stabilizing the laser.

 

Fig. 1. Setup for frequency stabilization. A fraction of the light is split off using a beam splitter (BS) and is measured by a wavelength meter (WM). Part of the light used for stabilization is directed to a photodiode (PD), which is used for normalization, while the other part passes an iodine cell before being directed to another photodiode, which records the spectroscopy signal. The laser is controlled by a digital laser controller (DLC), which is also used to read the photodiode signals.

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To stabilize the laser to the target line, it is first scanned over a wide range of frequencies by tuning the diode temperature while both photodiode signals are recorded. Then, the target line is identified in the resulting normalized spectrum using a neural network. After identification of the target line, the diode is set to the corresponding temperature and the laser frequency is stabilized by closing an electronic feedback loop.

Iodine allows for room-temperature spectroscopy of approximately 60,000 absorption lines in the spectral range from 500 nm to the near-infrared [10]. We select the transition ($J^{\prime \prime } = 73$; $\nu ^{\prime \prime } = 4$) $\rightarrow$ ($J^{\prime } = 73$; $\nu ^{\prime } = 8$) at a frequency of 473138.8 GHz as the target line. Depending on the operating conditions of the laser and the environment, the recorded spectrum changes. For example, change of the alignment alters the signal-to-noise ratio, while changing laser power and cell temperature can lead to different lineshapes and saturation effects. Figure 2 shows measured spectra including the target line under different conditions. The lines are Doppler-broadened with a typical width of 1 GHz.

 

Fig. 2. Measured transmission spectra of iodine with the target line at the center under normal conditions, with an increased cell temperature and with misaligned photo diodes. Unless otherwise stated, the spectra are measured with a diode current of 140 mA and a cell temperature of 40$^{\circ }$C. The scan range of 1 K corresponds to about 35 GHz.

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3. Neural network design and training

3.1 Design

The task of identifying a particular line in a wide spectrum is similar to the task of keyword spotting in the processing of audio data where a few particular words in a continuous stream of audio data need to be identified, e.g. to spot when a user tries to activate a smart assistant using a spoken command. Such an activation command must be recognized from conversations even in the presence of a wide range of background noises. When locating a spectral line, we also need to recognize a certain pattern from long one-dimensional data. Similar to keyword spotting, it is crucial to avoid false-positives. Due to these similarities, we use a convolutional neural network structure which has been applied successfully in keyword spotting applications [11]. Figure 3 schematically shows the structure of the neural network used here.

 

Fig. 3. Line identification process. First, a wide input spectrum is recorded by sweeping the laser diode temperature. This spectrum is then divided into overlapping segments with a fixed width, the so-called windows. Second, each of these windows is classified by a neural network consisting of two convolutional layers and a dense layer. For details of the individuals layers see Table 1. The output is the likelihood of this window containing the target line. Third, the individual likelihoods are combined and the target temperature is identified.

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We aim to identify a particular line in a given input spectrum. In general, this spectrum can be of variable width and resolution, and hence can have variable number of data points. The desired output is the diode temperature corresponding to the target line. However, this format of input with a variable number of data points is not suitable as neural networks typically map a fixed number of input values to a fixed number of output values. We therefore use the sliding window method [12]. This method slides a "window" of fixed width over the input spectrum, yielding overlapping fixed-width subsections of the spectrum with the number of subsections depending on the width of the full spectrum. For each of these subsections, the neural network individually assesses the likelihood of this subsection containing the target line at its center. Using these likelihoods, we determine if and where the target line is located in the spectrum.

Table 1. Layers of the neural network. Input is a single window containing 500 data points, corresponding to approximately 35 GHz. Output is the likelihood of the target line being at the center of the window. For a more detailed explanation of the individual layers, see e.g. [13].

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The chosen neural network consists of an input and output layer with six hidden layers in between: a convolutional layer and a pooling layer, a second convolution layer and a second pooling layer, a dense layer and a normalization layer. An overview of the layers and their respective shapes is given in Table 1. The one-dimensional input layer has a width corresponding to 1 K temperature change of the laser diode (about 35 GHz) as this is sufficient for a human to unambiguously recognize a particular line within the full investigated spectral range of 700 GHz. We found that 500 points in the input layer are a good trade-off between spectral resolution and computational expense. We therefore always generate a fixed number of 500 datapoints by linear interpolation. This number corresponds to a spectral resolution of about 70 MHz, which is much smaller than the linewidth of the individual absorption lines.

For each window, the classifier outputs the likelihood whether it contains the target line at the center. These values are then processed further: First, a moving average over the individual likelihoods is calculated to suppress possible noise in the results. If this moving average exceeds a certain threshold, we consider this a successful identification of the target line. Typically, the output only exceeds the threshold for a narrow range surrounding the target line and we locate the target line at the maximum output value. However, if the threshold is exceeded in several unconnected areas, this means that the neural network has identified the target line at multiple locations in the spectrum. There are two possible reasons for this: Either a false positive detection by the neural network or a mode-hop in the laser’s frequency scan. However, as the DBR laser has a large modehop-free tuning range, we do not expect modehops to occur in our application. Therefore we treat multiple identifications of the target line within one spectrum as if the neural network had not identified a line to reduce possible false-positives.

In the convolutional layers, several filters of a fixed width are slid over the input data and multiplied with it, corresponding to a (discrete) convolution of filter and input. This means that the layer can only recognize features that have approximately the size of the filters. The convolutional layers are followed by pooling layers which discard unnecessary information by selecting the maximum value of neighbouring data points. As the previous convolutional layer has identified larger features, a reduced number of datapoints is now sufficient. The combination of a convolutional layer and a pooling layer is repeated to identify smaller features in the first step and larger features in the second step. The next layer is a dense layer, meant to determine whether the features identified in the previous layers are the target line. For this purpose, all data points of the previous layer are connected to two neurons (target line and other). Then, the output is normalized in the last layer using the softmax function, providing two probability values with a sum of 1: the probability of the input being the target line and the probability of the input being anything else.

During the training process, the dropout method [14] is used: A fixed fraction of the neurons is disabled. In general, this technique makes the neural network robust as it cannot rely on individual neurons anymore if random neurons are disabled during training and therefore needs to combine multiple features. After training, dropout is disabled to achieve the highest possible accuracy. The neural network described here is implemented in Tensorflow [15] and all processing is done on a standard desktop computer using an i7-2600@3.40 GHz processor with four cores available.

3.2 Generation of training data

The quality of the training data used for optimizing the neural network’s parameters is crucial for the success of machine learning. In general, two conditions must be fulfilled. Firstly, the training data needs to be sufficiently similar to the data in the real application. Otherwise, the learned patterns will not translate to the real application. Secondly, the training data set needs to be sufficiently large so the neural network can learn to recognize general patterns. If the training data set is too small, no general patterns will be learnt and the algorithm instead overfits to the provided training data.

In general, both measured or simulated data can be used for training. Creating a large enough data set from measured data, however, would be extremely cumbersome: Many spectra would need to be recorded in a wide range of operating conditions. In addition, the data would have to be labeled manually. The method developed here should be versatile enough to work for other lines in the iodine spectrum, therefore it would be a large disadvantage if the training data needed to be re-labelled every time a new target line is chosen. Therefore, we use only simulated data for training.

First, we simulate an iodine spectrum over the full wavelength tuning range of the laser using the software IodineSpec [16]. This software is based on molecular potentials for the two electronic states involved. The Doppler-broadened spectrum is simulated by summing the Voigt profiles of the hyperfine lines [9]. The width of the individual lines is given by the intrinsic linewidth, and collisional and Doppler broadening. In our situation, Doppler broadening is the dominating effect and hence the line profiles are approximately Gaussian. The cell temperature is set to 55$^{\circ }$C and only the isotope $^{127}$I is taken into account. This spectrum is copied multiple times and different distortions are applied to simulate different conditions that may occur in practice. In addition, the data is prepared to match the intended input format of the neural network. In the following, these steps will be described in more detail.

3.3 Generation of validation and test data

There are many choices to make for the hyperparameters of the neural network, which are not optimized during the training process, e.g. the strength of distortions in the training set and the network architecture. To make these choices, we train multiple neural networks with different hyperparameters and evaluate them with regards to the validation set. Then, the best-performing network is chosen and its performance is measured using a new, independent data set, the test set. This avoids overfitting to the validation data.

While the neural network is trained using only simulated data, we use measured data with manually generated labels as validation and test data to get a more realistic measure of its performance. The spectra are recorded under different conditions, including changes in the environment temperature, the temperature of the iodine cell, the diode current, the feedforward signal (linear increase of the diode current with the diode temperature) and the scanning speed of the diode temperature when recording the spectra.

The validation set contains spectra that are very challenging to classify for a human, including multimode spectra and spectra with high noise as well as a wide range of operating conditions with environment temperatures between 0 and 40$^{\circ }$C, cell temperatures between 40 and 80$^{\circ }$C and diode currents between 120 and 160 mA. These conditions are chosen to test the limits of the neural network. The extreme cases are not to be expected to occur in practice and correspond to the worst-case scenario.

To test the final network, we apply it to another laser system under changing conditions. These include environmental temperatures between 0 and 50$^{\circ }$C, cell temperatures between 50 and 70$^{\circ }$C and diode currents between 100 and 125 mA, corresponding to a change in optical power of up to a factor of two. To get a realistic prediction of how the neural network will perform in real-world applications, the operating conditions are strongly varied, however, we avoided unrealistic conditions, e.g. strong deliberate misalignment of the system. If the diode temperature predicted by the neural network is within 0.02 K, corresponding to 700 MHz, of the manual label, we consider the target line to be identified correctly as this is within the slope of an absorption line.

4. Results

We first evaluate how the choice of hyperparameters influences the quality of the trained neural network. We take a set of hyperparameters that produces good results and then vary individual hyperparameters in the training process to observe their influence on the loss (Tensorflows’s sparse softmax cross entropy) of the trained network in training and validation data. Loss is a suitable metric to choose a set of hyperparameters as it makes the results independent of the choice of threshold above which a line is classified as the target line. The neural network trained with the chosen hyperparameters is then applied to all full spectra of the validation data and then the number of true positives and negatives and false positives and negatives is determined, as this metric is most relevant for the final application. Finally, the neural network is applied to a test data set to assess its real-world performance.

 

Fig. 4. Simulated training data. Left column: Windows with the target line at the center. Right column: Windows not containing the target line.

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The runtime of the whole line-identification process is about 80 s on a standard desktop computer, which consists of pre-processing the spectrum (87%), classification (8%) and post-processing (5%).

4.1 Influence of hyperparameters

We evaluate the effect of all distortions described earlier on the overall loss. A strong reduction in loss (more than one order of magnitude after 30,000 steps) can be observed when introducing saturation and additional negatives containing modified versions of the target line. Minor reductions in loss can be observed when introducing Gaussian noise, baselines and intensity variations. When adding additional negatives containing randomly generated spectra and multimode spectra, we actually see a slight increase in loss in the validation data set. Despite this, we include a small number of these spectra in the training set in order to make the trained neural network more robust.

4.2 Validation data

Next, we train a neural network using the hyperparameters optimized for minimum loss on individual validation set windows. This trained neural network is then applied to the full validation spectra with a threshold of 0.91 for classifying the target line. This threshold is empirically chosen for a low number of false negatives, while safeguarding against any false positives in the validation data set. In total, the validation set contains 2641 spectra. 502 of them do not contain the target line and the neural network does recognize that in all cases (true negative). Of the 2139 spectra containing the target line, the target line is correctly identified in 97% of the cases (true positive). In the remaining 3%, the neural network cannot identify the target line at all (false negatives). Most importantly, there are no false positives. The corresponding confusion matrix is shown in Table 2(a).

Table 2. Confusion matrices for the validation (a) and test data (b). In the validation set, the target line is correctly identified in 98% of all spectra. The remaining 2% are spectra containing the target line, which was not detected by the neural network (false negatives). In the test data, the target line is always identified correctly. The superior performance in the test set is due to the fact that the validation data corresponds to worst-case scenarios, while the test data set contains typical spectra which occur in real world conditions.

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Figure 5 shows a typical spectrum with the corresponding output of the neural network. The output for the target line is 0.98, well above the threshold of 0.91, thus the target line is identified correctly. The second-highest local maximum of the output is only 0.04, well below the threshold. This small peak makes sense, as the respective line actually looks similar to the target line.

 

Fig. 5. A typical normalized iodine spectrum (blue) recorded by sweeping the diode temperature from 0 to 20$^{\circ }$C. The output of the neural network (red) shows a clear peak at the target line at 13.79$^{\circ }$C, reaching a maximum of 0.98, well above the threshold for line identification (dashed pink, 0.91). A second, much smaller peak with a value of 0.04 is visible at a diode temperature of 6.6$^{\circ }$C, where a similar looking line is located. For all other areas of the spectrum, the output is below 0.002.

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The false negatives occur under three conditions: Very noisy spectra, multimode spectra and highly non-linear baselines. An example is shown in Fig. 6, where a multimode region is located right next to the target line. In this case, there is a local maximum around the target line, but it lies below the threshold, therefore no line is identified. Similar results can be observed for extremely noisy spectra and spectra with highly non-linear baselines. The high-noise and multimode spectra are also very difficult to recognize for a human.

 

Fig. 6. Example of a false negative due to a multi-mode spectrum. In this particular case, the laser is in multi-mode operation for diode temperatures below approximately 13$^{\circ }$C, changing the appearance of the spectrum in the left half of the window. Such multi-mode spectra are also difficult to classify for humans.

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4.3 Test data

Next, the neural network is applied to another laser system, acting as the test system. The laser is operated under realistic operating conditions (see Section 3.3). Spectra are recorded for the respective laser settings while the environment temperature is varied and the target line is identified during operation. When comparing the lines identified by the neural network with labels created by a human, we find that it detects 922 true positives and 12 true negatives, while there are no errors at all (see Table 2b). This shows that the chosen model can be applied to another laser system without any adjustments. The results are even better than in the validation set, which is due to the fact that the validation data corresponds to worst-case scenarios, while the test data set contains typical spectra which occur in real world conditions.

As an additional test, we perform the scan and identification process in combination with a subsequent lock of the laser to the identified absorption line using a top-of-fringe lock without any human interaction. For this test, the ambient temperature is varied between 0 to 40$^{\circ }$. Under these conditions, we first perform a frequency scan of the laser, then identify the target line using the neural network and stabilize the laser to the respective line. When the laser is locked, its frequency is measured using a wavelength meter and compared to the target frequency. The laser is then turned off after each lock to simulate a cold start of the system before recording a new spectrum. As shown in Fig. 7, the laser is always stabilized to the correct line. We attribute the slight offset between the target frequency and the measured frequency to an inaccurate calibration of the wavelength meter.

 

Fig. 7. The laser is stabilized to the absorption line identified by the neural network. Frequency deviations of the stabilized laser with respect to the the target line (solid line) are shown in blue. The neighboring absorption lines are shown with dashed lines. The laser is clearly stabilized to the target line in all cases.

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5. Conclusion

We have shown that an individual absorption line can be recognized from an iodine absorption spectrum using a neural network. The neural network reliably identifies the target line under a wide range of operating conditions, including changing power levels and environment temperatures as well as low-signal-to-noise ratios and multi-mode operation close to the target frequency. No false positives were detected during the extensive test campaign. Our method allows for reliable fully automatic stabilization of a laser to a target line, which is in particular crucial in applications where user interaction is not possible or not desired. Our system can therefore enable future hands-off industrial laser applications in harsh environments.

The number of false negatives could be further reduced by including non-linear baselines into the training data. The process can be sped up by reducing the pre-processing time, by more efficient data handling. For further integration, our demonstration can be implemented on a microcontroller, by exploiting the TensorFlow Lite library [17]. Also, this method can be straightforwardly extended to other molecular or atomic spectrum and thereby to other wavelength ranges.