Experimental setup
The QD is usually applied in light spot detection due to its high sensitivity to lateral movements. It splits the detection area into 4 independent parts, each taking one quadrant of the circular light receiving area, so named as quadrant detector. In our demonstration, a QD (HAMAMASTU G6849, spectral response range from 0.9 to 1.7 µm, cutoff frequency = 30 MHz) was used as the speckle detector. A 50 cm long RCF (NA = 0.15, outer diameter = 125 µm, core = 100 × 25 µm) was utilized as the diffusing media. And a polarization maintaining fiber (PMF) was connected to the RCF to avoid polarization disturbance. In order to eliminate noise produced from ambient light and environmental vibrations, the detector and the RCF were fixed together using a funnel-shaped mold. The schematic diagram and wavelength reconstruction algorithm of the proposed system are shown in Fig. 1(a) and (b). Four low-noise high-precision operational amplifiers were used to amplify the output currents and to convert them into analog signals. Then, the signals were sampled by a data acquisition card (DAQ, National Instrument USB-6251, acquisition depth = 16 bit). Benefiting from higher acquisition depth, the QD can detect more subtle intensity changes compared with panel cameras which are only of 8 ~ 12 bit.
As shown in Fig. 1 (a), a speckle image was compressed to 2 × 2 by the QD. When tuning the wavelength of the input light, the intensity distribution of the speckle pattern varies due to the mode interference in the multimode fiber and the QD data is consequently changed. Figure 1 (c) shows the recorded intensity variations of the QD and the corresponding speckle patterns in the range of 1550.000 nm -1550.500 nm with a step of 5 pm. It can be seen that the compressed speckle patterns show a strong wavelength dependent. In order to demonstrate the wavelength precision of the proposed measurement system via these QD data, an ultra-high resolution laser frequency tuning system was built. The details of the system refer to our previous work [7].
Measurement accuracy of the setup
The measurement results of this proposed setup can be obtained by a trained deep learning network (explained in methods section). The accuracy was examined by using selected test images (24 pieces per wavelength). The results are displayed in a confusion chart, as shown in Fig. 2 (a). The chart can be regarded as a matrix, where the rows and the columns represent the predicted wavelengths and the true wavelengths respectively. Diagonal elements correspond to correctly classified wavelengths while off-diagonal elements correspond to incorrectly classified wavelengths. The values of the diagonal element denote the number of correctly classified pieces for each tested wavelength. All the test results show that the wavelength precision is better than 0.5 MHz (~ 4 fm). For comparison, the wavelength precision based on cameras was also examined. Firstly, we sampled the speckle patterns with a resolution of 0.5 MHz to build the dataset. The network and the training options were same as the QD solution, but the network input layers were changed to 256×256. After training, the validation accuracy can easily achieve to 100%, as shown in Fig. 2 (b). However, limited by the pixel readout mechanism and the camera exposure time, the commonly used InGaAs camera only has a sample rate of 60–100 Hz. Table 1 shows the comparison of performance between the QD and the InGaAs camera The QD can not only get the same wavelength precision as the camera, but also has the advantages of higher speed, smaller size, and lower cost.
Table 1
The comparison between QD and InGaAs camera
| Quadrant detector | InGaAs camera |
Precision | 0.5 MHz | 0.5 MHz |
Speed | ~ kHz | < 50 Hz |
Volumn | 1 cm3 | 375 cm3 |
Cost | < 0.2 k $ | > 16 k $ |
Response range | 900–1700 nm | 900–1700 nm |
The broadband range
Meanwhile, the measurement range of this device is also an important indicator for wavelengths recovery. In this case, the range is determined by the uniqueness of upsampled speckle patterns and network feature extraction capability. A technique called t-Distributed Stochastic Neighbor Embedding (t-SNE) was introduced according to [8]. This method is a visual tool that can project speckle patterns’ feature extracted by trained network into a lower dimension (generally the coordinates of the Cartesian coordinate system). In this study, the tool was used to verify whether the untrained upsampled speckle images are correctly classified by the trained CNN. The speckle patterns produced from laser with wavelengths around 1530 and 1560 nm were recorded in verification experiments. For each wavelength, its central wavelength was tuned by increments (Δλ) of 4, 8, 12, 16, 18, and 24 fm. Fifty upsampled speckle patterns were recorded for each tuning step. Then these untrained speckle patterns were inputted to the trained SRN. The output of the network’s fully connected layers is the features of upsampled speckle patterns. These features were used as the input of the t-SNE tool. As shown in the Fig. 3, upsampled speckle patterns with wavelength difference of only 0.5 MHz were clearly clustered by the t-SNE tool. It means that unsampled speckle patterns can be classified in the given range precisely. Most importantly, the results show that a wider band of measurement can be obtained [8].