High-dimensional anticounterfeiting nanodiamonds authenticated with deep metric learning

doi:10.21203/rs.3.rs-3164142/v1

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High-dimensional anticounterfeiting nanodiamonds authenticated with deep metric learning

https://doi.org/10.21203/rs.3.rs-3164142/v1

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Physical unclonable function (PUF) labels have emerged as a promising candidate for achieving unbreakable anticounterfeiting. Despite their significant progress, two challenges for developing practical PUF systems remain, namely 1) fairly few high-dimensional encoded labels with excellent material properties, and 2) existing authentication methods with poor noise tolerance or inapplicability to untrained labels. Herein, we employ the linear polarization modulation of randomly distributed fluorescent nanodiamonds (FNDs) to demonstrate, for the first time, three-dimensional encoding for diamond-based labels. Briefly, our 3D encoding scheme provides digitized images with an encoding capacity of 10⁹⁷⁷¹ and high distinguishability under a short readout time of 7.5 s. The ultrahigh photostability and inertness of FNDs endow our labels with high reproducibility and long-term stability. To address the second challenge, we employ a deep metric learning algorithm to develop a novel authentication methodology that computes the similarity of deep features of digitized images, exhibiting a superior noise tolerance than the classical point-by-point comparison method. Meanwhile, it overcomes the key limitation of existing artificial intelligence (AI)-driven classification-based methods, i.e., inapplicability to untrained PUF labels. Considering the high performance of both FND PUF labels and deep metric learning authentication, our work paves the way for developing practical PUF anticounterfeiting systems.

Anticounterfeiting label

fluorescent nanodiamonds

artificial intelligence

Counterfeiting is a significant problem worldwide and is responsible for serious economic losses in a wide range of everyday transactions^{1, 2}. It can even be life-threatening when counterfeited goods such as fake medicines are passed off as genuine^{3, 4}. To tackle this critical issue, techniques such as water-marks or fluorescence labels have been developed, and such techniques are used on banknotes all over the world. However, these conventional approaches are now at risk of a resurgence of counterfeiting, due to the deterministic fabrication process which is prone to forgery⁵. To this end, the emerging physical unclonable function (PUF) systems, based on non-predictable responses of integrated circuits⁶ or random patterns of micro/nanostructures⁵, serve as an effective solution for unforgeable anticounterfeiting. Thanks to recent advancements in nanotechnology and optical cryptography techniques⁷, PUF labels have been successfully developed based on a large number of optical nanomaterials, including plasmonic nanoparticles^8–10, surface-enhanced Raman spectroscopy nanoparticles¹¹, quantum dots¹², Mie-resonant silicon nanoparticles¹³, upconverting nanoparticles¹⁴, and metasurfaces¹⁵. In general, these nanomaterials provide a variety of optical signals like photoluminescence, scattering and Raman signals, which can be tailored to carry authentic information for encryption/decryption.

To achieve unbreakable encryption for PUF labels, it is crucial to have a large enough encoding capacity which represents the theoretical maximum number of unique tags⁵. There are mainly two ways of enhancing encoding capacity⁵: 1) improving the pixel number of the encoded image, and/or 2) high-dimensional encoding. Compared with the former one, high-dimensional encoding requires a relatively short readout time and is thereby regarded as a promising solution. However, to date, there have been only a few attempts to create high-dimensional (≥ 3D) encoded PUF labels^{9, 11, 16, 17}. Particularly, the light has been intensively investigated to provide multi-dimensional encrypted information, owing to its abundant degrees of freedom such as polarization, phase, wavelength, and frequency ¹⁸. Among them, polarization has been explored extensively in various applications such as three-dimensional display technology¹⁹, optical communication²⁰, optical storage²¹, optical encryption²², super-resolution imaging^{23, 24}, and orientation measurements^{23, 24}. Among the different optical polarization-sensitive emitters (e.g., fluorescent molecules²⁵, plasmonic nanorods²⁶, upconverting nanorods²⁷, carbon nanotubes²⁸, defects in 2D materials²⁹), nitrogen-vacancy (NV) centers, a kind of photoluminescent defects hosted in diamond crystals, have been hailed as among the most promising candidates for anticounterfeiting labels due to their high contrast value in polarization modulation (~ 89% for single NV center³⁰), unlimited photostability^{31, 32}, and cost-effective mass production³³, not to mention the superior properties of diamond materials themselves^{34, 35}.

In a practical PUF anticounterfeiting system, the desired authentication method should have a low false-positive rate, low time consumption, and noise tolerance. However, to the best of our knowledge, prevailing techniques fall short of meeting these criteria. Firstly, due to broad applicability and a low false-positive rate⁵, the point-by-point comparison method (evaluated by the similarity index¹¹ or Hamming distance³⁶) is widely used^{11, 37–41}. However, this method shows poor noise tolerance, due to sensitivity to pixel level intensity information⁴² which is prone to being influenced by some common noise sources. Secondly, contemporary

artificial intelligence (AI)-driven methods^{9, 12, 16, 43} can achieve a low false-positive rate and be noise-resilient by learning robust feature representations with deep neural networks. Unfortunately, these approaches frame authentication as an image classification problem, which results in substantial time wastage in the training phase. Specifically, learning classifiers¹² typically requires the collection of numerous training samples for a single PUF label and necessitates the re-training of data from all PUF labels whenever a new PUF label is produced⁴³. Another AI-enhanced technique, known as deep metric learning⁴⁴, directly learns the optimal standard of comparison between data based on deep image features, enabling it not only to authenticate untrained objects⁴⁵ but also to be noise-robust⁴⁶. Therefore, metric learning is emerging as a promising candidate to solve the existing drawbacks of both the point-by-point comparison and classification methods.

This paper presents the first demonstration of high-dimensional (3D) encoding for diamond-based PUF labels, based on our previously reported linear polarization modulation (LPM) of NV centers in fluorescent nanodiamonds (FNDs)⁴⁷, as shown in Fig. 1a. Under the readout time of around 7.5s, we achieved an encoding capacity of 9^10×1024 (10⁹⁷⁷¹) for digitized images (pixel resolution of 32 × 32) with high distinguishability, reproducibility, and long-term stability proved by a point-by-point comparison method. Moreover, we propose a novel deep metric learning algorithm for robust authentication, based on comparing the similarity of abstracted deep features, as illustrated in Fig. 1b. Specifically, noise resilience evaluation demonstrates that our metric learning method effectively addresses the noise sensitivity issue inherent in the point-by-point comparison method, which is commonly encountered during an end user’s readout. In addition, when compared to the deep classification method during both training and testing processes, the metric learning method exhibits two clear benefits: 1) a reduced requirement for training data volume (only two sets of data are needed for a label), and 2) the capacity to effectively authenticate data from untrained labels, rather than necessitating retraining the whole system once a new label is added⁴³. These dual efficiencies significantly enhance the potential of our method for deployment in large-scale commercial settings.

1. LPM curves of FNDs providing feasibility for 3D anticounterfeiting

Diamond provides promising material properties for fabricating PUF labels, including ultrahigh photostability, long-term stability, and tolerance to physical stress. Specifically, both the Raman signal of diamond and the fluorescent signal of NV centers can be continuously emitted without blinking or bleaching^{31, 32, 38}, which provides the basis for maintaining the reproducibility of optical readout results. In addition, ultrahigh hardness³⁵ and inertness³⁴ make diamond-based labels tolerant to physical stress and long-term storage, respectively. However, despite the huge potential of existing diamond-based PUF labels^{38, 39, 48}, it has not yet been possible to achieve the much-desired high-dimensional (> 2D) encoding. We here propose a method to achieve a 3D encoded diamond-based PUF label, based on the linear polarization modulation (LPM)⁴⁷ curves of FNDs with random orientations.

Fabricated via an electrostatic absorption approach (See Methods for details), our PUF label is composed of FNDs with both high density and satisfactory dispersion on the cover glass (See SEM image in Fig. 2b). Due to the above two characteristics, there are 200–450 bright spots (BSs) over 30 µm × 30 µm area with a high probability close to diffraction-limited size, in fluorescent images of FND PUF labels. A typical example is given in Fig. 2a. As for the 3D anticounterfeiting information from FND PUF labels, the large number of BSs provides the basis for the distinguishability of encoded images (See Supplementary Notes 1 for detailed analysis), and diffraction-limited sizes of BSs are essential for sensitive optical readout (See latter content for details).

In the fluorescent images of our FND PUF labels, diffraction-limited BSs with LPM curves provide the foundation for obtaining three-dimensional anticounterfeiting information. Specifically, based on the optical polarization selective excitation phenomenon of NV centers³⁰, the LPM curves show the relationship between the polarization direction of linearly polarized excitation laser ($\beta$) and fluorescent intensity of FNDs (${I}_{\beta }$) (Fig. 1a). In actual measurement, when $\beta$ is changed at a constant speed through rotating a half wave plate with an electric rotation stage, wide-field fluorescent images are taken for a PUF label with a gap of $\beta$ as 6 degrees (See Methods for more details). To exactly extract the fluorescent signal corresponding to diffraction-limited BS (size is around 10 pixels × 10 pixels), ${I}_{\beta }$ is calculated via the total signal of 13 pixels × 13 pixels matched with the identified position. Experimental results show that the LPM curves of the identified diffraction-limited BSs can be well fitted (solid lines in Fig. 2c) via Eq. 1⁴⁷ with a coefficient of determination usually larger than 0.85.

$${I}_{\beta }={A}_{1}-{A}_{2}{cos}^{2}\left(\alpha -\beta \right) \left(1\right)$$

Where ${A}_{1}, {A}_{2}, \alpha$ are fitting parameters (${A}_{1}>0, {A}_{2}>0$), and ${I}_{\beta }$, $\beta$ are input parameters. Examples of six fitted LPM curves are shown in Fig. 2c. It should be noted that these LPM curves show different LPM contrast values ($\frac{{A}_{2}}{{A}_{1}}$) and LPM phase (the fitting result of $\alpha$), corresponding to different orientations of FNDs. Therefore, based on the fluorescent images under different $\beta$ values, it is possible to obtain the 3D encoded information, including LPM contrast values, LPM phases, and the positions of the diffraction-limited BSs.

For achieving a sensitive optical readout of the above 3D anticounterfeiting information, a sufficiently high LPM contrast value is required. We define the following criteria to determine a sufficiently high LPM contrast value: larger than 15%, which is 10 times the fluorescent intensity error (around 1.5%) in long-term detection (Figure S1). Experimental results show that diffraction-limited BSs own LPM contrast values usually larger than 15%, but the LPM contrast values of bigger BSs have a high probability of less than 15% (Figure S2). Therefore, the crucial point to obtain a sufficiently high LPM contrast value is the high probability of finding diffraction-limited BSs. Our PUF label is well matched with this crucial point (see the previous description of Fig. 2a), which causes a high ratio of obtaining high enough contrast values. A typical example is given in Fig. 2d: 215 of 306 identified BSs own LPM contrast values larger than 15%.

2. Anticounterfeiting performance of 3D encoded images

Then, based on the above mentioned 3D anticounterfeiting information, we proposed a 3D encoding scheme to obtain digitized images. With the classical and widely used authentication method called point-by-point comparison⁵, the anticounterfeiting performances of digitized images were tested for distinguishability, reproducibility, and long-term stability.

Digitized results were obtained based on the optical images of FND PUF labels under different $\beta$ values with pixel resolution of 32 × 32. (See Methods for details) To effectively show the information in the two dimensions including LPM contrast value and LPM phase, a feasible method is to utilize the relative change of ${I}_{\beta }$ corresponding to different $\beta$. To reflect this relative change, we convert the photon number to contrast values in the image pixels via Eq. 2:

$${contrast}_{\beta =n}=\frac{{counts}_{\beta =n}-{counts}_{\beta =0}}{{counts}_{\beta =0}} \left(2\right)$$

Where ${contrast}_{\beta =n}$ and ${counts}_{\beta =n}$ mean the contrast values and photon number in image pixels, respectively, with the condition of $\beta =n$. In the digitization process, 9 contrast levels are set according to Table S2, which is designed based on the precision and range of the contrast value. An example of the digitized images is given in Fig. 3a: there are three encoding dimensions, including contrast levels, polarization angles, and pixel position. Calculated via the inserted formula^{5, 11} in Fig. 3a, the encoding capacity of our PUF label can arrive at 9^10×1024 (10⁹⁷⁷¹), which is much larger than the commonly suggested minimum encoding capacity (10³⁰⁰)⁵. In addition, the readout time corresponding to these digitized images is just 7.5 s. Therefore, we achieved a sufficiently large encoding capacity as the basis for unbreakable encryption, within a relatively short readout time.

To demonstrate the feasibility of the above encoding method in distinguishing different PUF labels, we applied the broadly used authentication method called point-by-point-comparison⁵. Specifically, when two groups of digitized images are compared pixel-by-pixel, the ratio of the same pixels is recorded as the similarity index¹¹. If there exists an evident gap between the similarity indexes of the same labels and different labels, a threshold value within the gap can be chosen to correctly distinguish the different PUF labels. In our authentication process, the similarity indexes are calculated among the two groups of digitized images for 100 PUF labels. Calculation results are shown in Fig. 3b: the similarity indexes of the same labels are always higher than 76%, and the similarity indexes of the different labels are always less than 69%. Therefore, we can choose the threshold value as 75% (within the gap of 69–76%) to successfully distinguish all the 100 PUF labels.

Moreover, based on the above threshold value, we evaluated the reproducibility and long-term stability of the digitized readout results for our PUF label. First, for reproducibility, we calculated the similarity indexes among 10 groups of digitized images for the same PUF label. All the authentication results for 20 PUF labels show satisfactory reproducibility in Fig. 3c: the similarity indexes are always significantly higher than the threshold value (75%) (See Figure S3 for specific examples of the reproducibility of a specific label). Then, long-term stability was tested based on repeated readout results of one PUF label for a period of around 150 days. For each readout date, corresponding similarity indexes are calculated between the digitized readout results on this date and the digitized readout results on the first day. The authentication result confirmed satisfactory long-term stability: the similarity indexes are always stable at around 84%, much higher than the threshold value (75%) (Fig. 3d).

3. Deep metric learning for authenticating noise-affected digitized images

In terms of practical authentication for anticounterfeiting labels, the system’s tolerance to common noise sources is crucial. Specifically, in the practical authentication process, manufacturers provide images taken under ideal laboratory conditions, but end users may employ images taken in environments saturated with various additional noise sources. Even if the optical signal from a PUF label is stable, these noise sources influence the readout process, which might prevent the authentication algorithms (i.e., point-by-point comparison) from working⁴².

To this end, simulating the actual authentication process, we conduct a noise resilience evaluation for point-by-point comparison method with FND PUF label. In the noise resilience evaluation, images of PUF labels taken under two different optical readout conditions are used for authentication based on the similarity index, as shown in the left panel of Fig. 4a. Specifically, our experiment mirrors the image capture process by both the manufacturer and the end users, where an optical readout of 50 PUF labels was conducted under ideal laboratory conditions and laboratory conditions contaminated with three kinds of noise sources, respectively (refer to Supplementary Notes 3 for details). These noise sources include background light, sample drift, and out-of-focus, all of which are common noise sources for the readout process. Digitized images corresponding to the above two optical readout conditions show evident differences, with a typical example in the right panel of Fig. 4a. As shown in Fig. 4b, experimental results show that there is an overlap between the distributions of the similarity index for intra-digitized images and inter-digitized images. This implies that it is impossible to find an appropriate threshold to distinguish PUF labels. In noise resilience evaluation results for other PUF labels based on point-by-point comparison⁴², negative results have also been found and were attributed to the widespread limitation of the point-by-point comparison method, i.e., sensitive to some noise sources. Therefore, this highlights the need for a more robust authentication algorithm.

To develop a more robust algorithm tolerant of noise, our key inspiration was that it was hard, using the naked eye, to differentiate digitized images of a PUF label in the presence of noise (such as Fig. 4a). However, it is possible for us to recognize natural images with the naked eye, even when they are mixed with noise⁴⁹. The reason is that most of the noise in our daily life affects information at the pixel level, while we have seen many natural images and have been “trained” to recognize them based on high-level semantic information⁵⁰. Thus, to solve the challenge in noise resilience evaluation, the critical factor is to show our machine as many PUF labels as possible at an early stage (i.e., prior information), and teach them to differentiate different PUF labels based on patch-level information.

Given the profound capacity of deep learning^51–53 to learn prior information and the ability of a convolutional neural network to extract deep patch-level features from images, we propose to exploit these features for our authentication system. In particular, we propose the use of deep metric learning⁴⁴ to conduct anticounterfeiting authentication. Specifically, metric learning excels at identifying essential differences between data instances, making it well-suited for authentication tasks. By learning a distance metric that reflects intrinsic similarities and dissimilarities among instances, metric learning has demonstrated effectiveness in actual applications such as robust face verification in the wild⁵⁴, variation-tolerant face recognition^{46, 55}, and person re-identification⁵⁶.

The core concept of metric learning, as shown in Fig. 5a, is to enable the accurate clustering of images based on their content, even when subjected to noise or distortions. In the original image space depicted on the left side of Fig. 5a, we have an image ${I}_{X}$, which becomes more distant from its original position when affected by noise, resulting in the image ${I}_{{X}^{{\prime }}}$. Consequently, if we measure the distance with the point-by-point comparison, Image ${I}_{X}$ becomes closer to another image ${I}_{Y}$, which could cause a wrong matching. To tackle this issue, our metric learning framework utilizes a neural network trained to extract noise-resistant features, allowing images with similar content to be accurately categorized together, as depicted on the right side of Fig. 5a. In other words, high-level information of the digitized image is extracted and represented like a deep key in the metric space. In this way, we can compare digitized images’ similarity by calculating a similarity score (see method) in the metric space, instead of a point-by-point comparison in the original image space.

To achieve this goal, the key innovation of metric learning lies in its unique training strategy. As shown in Fig. 5b, a deep neural network is trained to bring features (i.e., ${F}_{X}$ and ${F}_{{X}^{{\prime }}}$) belonging to the same PUF label closer together while pushing features (i.e., ${F}_{Y}$ and ${F}_{{X}^{{\prime }}}$) from different PUF labels further apart. Before training, features from the same label might be far apart in the metric space (or too close to a different label), which is contrary to our desired outcome. In such cases, the loss function penalizes the network, forcing it to adjust its parameters in the appropriate direction via back-propagation. After several iterations, our network learns how to extract the key information from images, resulting in a metric space where features of the same label are close together, and features of different labels are farther apart. Compared to similarity indices based on point-by-point comparison, neural networks typically extract patch-level structural features, which are more resilient to noise.

We demonstrate the robustness of our method against a variety of noise sources commonly encountered during the readout process. Especially, during training, we do not assume prior knowledge about the noise that may present in practical use and apply PUF data from the ideal condition for training. This avoids introducing biased evaluation results. For validation, we use the same 50 pairs of PUF images employed in Fig. 4b. As depicted in Fig. 5c,d, even under challenging conditions, our method accurately distinguishes between different pairs of PUF labels and identical pairs of PUF labels with 100% precision. It can be seen that there is a significant gap (approximately 27% − 38%) between the similarity score distributions of intra-pair PUF labels and inter-pair PUF labels. By contrast, authentication with point-by-point comparison reveals a tendency to confusion (see Fig. 4b,c). These results demonstrate that our algorithm can recognize PUF labels better than the point-by-point comparison method in the presence of the investigated noise sources. Additionally, we provide validation results of our method under ideal conditions in Figure S4, highlighting even more distinct decision boundaries. This further proves the robustness and reliability of our metric learning-based approach for accurate PUF label authentication, whether under ideal conditions or in real-life noise environments.

4. Characteristics of metric learning method relative to classification method.

Some previous studies^{9, 12, 16, 43} have explored the use of AI methods for random pattern image authentication, and their methods are mainly based on classification. Here, we analyzed the difference between our metric learning-based authentication method and classification-based authentication methods in the training and testing stages.

First, our method is more data-efficient during the training phase. Specifically, learning a classifier requires a lot of data for each category, as it aims to predict the probability for each category given an input. If there is not enough data for a category, the model is prone to overfitting the training data and performs poorly during testing⁵⁷. Metric learning, on the other hand, focuses on learning a similarity measurement to evaluate whether a given pair of readout results are similar or not, specifically, predicting a similarity score for a pair of readout results. This task can be accomplished with pairs or triplets of samples (a reference sample, a positive sample from the same category, and a negative sample from a different category), and therefore does not require a large amount of sample data for each category⁵⁷. A striking example of this data efficiency in the training stage is shown in Fig. 6a. For each PUF label, to enable robust recognition, many (tens to thousands) readout results under various conditions should be collected to train the classification method⁵⁷, while our method requires only two readout results. In sum, our method needs much less training data, thereby saving a lot of time that would otherwise be consumed in the repeated readout of PUF labels.

Second, our method can effectively authenticate novel PUF labels unseen during training (Fig. 5c,d), a capability that classification-based methods lack^{9, 12, 43}. As shown in Fig. 6b, classification methods fix the number of categories (e.g., ten) during the training phase. In this case, the model predicts the probabilities of ten categories and utilizes the highest one to determine the class to which a PUF label belongs. Consequently, if a provider manufactures a new 11th PUF label, the network will still only predict probabilities of ten categories. Under these circumstances, the method would either predict all ten probability values to be low, thereby deeming the label to be false, or one probability might be high, leading to an incorrect classification of the label. By contrast, our method compares whether two readout results of PUF labels are similar and the learned similarity metric can be applied for novel PUF labels. Consequently, even if we only use digitized images of certain PUF labels (such as PUF1-PUF10) during the training stage, we can still compare two new readout results (for instance, from PUF11 and PUF12). Our approach achieves 100% authentication performance on novel PUF labels, as shown in Fig. 5c,d and Figure S4. We emphasize that we use novel PUF labels for all our experimental evaluations. Therefore, our method is well-suited for use in real-world business situations where new PUF labels are continually being created, while the classification technique’s requirement for retraining makes it inconvenient to use in such conditions.

Combining the advantages of both FNDs sample and our 3D encoding scheme, LPM of FND is a promising candidate to achieve a useful PUF label, which can satisfy most common requirements in both the aspects of commercial and anticounterfeiting performances. Specifically, common commercial requirements⁵ contain 1) low-cost and scalable fabrication and 2) convenient and fast readout. As for our FND PUF label, the estimated cost of a working label is considerably lower than 0.19 USD (Table S1). Its simple fabrication method using a mature commercial sample (See Methods for details) offers the opportunity for scalable fabrication, and the strong optical signal of FNDs (Figure S5) provides the basis for fast optical readout (in our scheme, integration time for an image is 50 ms, and total readout time is 7.5 s). In addition, some common requirements for anticounterfeiting performances of PUF labels are listed as 1) high encoding capacity for achieving unbreakable encryption⁵, 2) reproducible authentication results¹¹, and 3) labels available for precise authentication within a long time. Authentication results (Fig. 3) prove that our FND PUF label is well able to meet these requirements: encoding capacity as high as 10⁹⁷⁷¹ under pixel resolution of 32 × 32 with satisfactory distinguishability, reproducible authentication for 10 times of readout results of the same label, and stable anticounterfeiting information for a period of around 150 days.

Building on the similarity score extracted from the deep features of two sets of digitized results, we propose a novel metric learning authentication method. This method amply satisfies practical application requirements, including robust authentication in noisy environments, high data efficiency during the training phase, adaptability to untrained PUF labels and sufficient authentication speed for practical usage. Specifically, unlike the previous classification method¹² that uses the same artificially created ‘noise’ or disruptions during both the training and testing phases, our CNN network is trained via data readout under ideal laboratory conditions, but demonstrates robust noise tolerance in evaluations (refer to Fig. 5b,c). This proves that our method potentially has a better capability to handle data readout in a variety of real-world scenarios. In addition, in contrast to the classification approach^{9, 12, 43}, in which a large amount of training data for each PUF label is needed and repeated training is required when new labels are introduced, our method requires only two sets of readout results for each PUF label and obviates the need for re-training in the event of encountering new objects, thereby saving a lot of time. Moreover, in our authentication method, the time of comparing digitized images with one set of stored objects is 1.38ms, which is sufficiently rapid for practical use with a well-matched design of the authentication process (See Supplementary Notes 4 for detailed analysis).

Experimental apparatus

All fluorescent images for the FND PUF labels were taken by a customized wide-field fluorescence microscope. In the excitation optical path, the linear polarization direction of a continuous 532 nm laser is changed via a half-wave plate (WPH10M-532, Thorlabs) mounted on the electrical rotation stage (PT-GD62, PDV). The excitation laser is then focused on the back-focal plane of an oil immersion objective (NA 1.45, UPLXAPO100XO, Olympus) to illuminate the sample. The sample position can be finely adjusted via a nanopositioning stage (P561.3CD, Physik Instrumente). In the detection optical path, filtered with a long pass filter (FELH0650, Thorlabs), the fluorescence signal is detected via a water-cooled EMCCD (iXon Ultra 897, Andor) with a field of view of around 30 µm × 30 µm.

Fabrication of FND PUF label

The PUF label is fabricated by FND-COOH containing ensemble NV centers (BR100, FND Biotech, Inc.) through electrostatic absorption. Specifically, cover slides are activated by plasma for 10 min (200 W), and then immersed into the 3-aminopropyltriethoxysilane (APTES, Sigma) solution in ethanol (v/v,5%). After reaction for 24h at room temperature, the cover slides are taken out and washed with ethanol and water, respectively. After that, 0.02 mg/mL FND solution is drop-casted on the obtained positive-charged cover glass and incubated in the refrigerator for 3 hours. Next, the obtained samples are washed with DI water and dried in air. Finally, a PDMS film is coated onto the cover glass as a protection layer.

Particle location code

We use the peak location function (pkfind()) and spatial bandpass filter function (bpass()) in MATLAB particle location code from Daniel Blair and Eric Dufresne (https://site.physics.georgetown.edu/matlab/index.html). The spatial bandpass filter function is used to filter the noise from wide-field fluorescent images. The peak location function is then used to identify and locate the BSs. Without special instruction, the wide-field fluorescent images described in formal content and supporting information have been processed via spatial bandpass filter.

Measurement of LPM curves

First, wide-field fluorescent images of FND PUF label are taken with 6 degrees gap of linear polarization direction of the excitation laser, 50 ms integration time, and around 10 mW laser power. Then, with the peak location function, we identify and locate BSs with threshold value as 3000 counts and spot size as 10 pixels. Next, the total signals of the 13 pixels × 13 pixels matched with the location of identified BSs are calculated as fluorescent intensity. Finally, the LPM curve is recorded as the relationship between fluorescent intensity and the linear polarization direction of the excitation laser. The recorded LPM curve is fitted via the curve fitting function (fit()) in MATLAB based on Eq. 1.

Optical readout and digitization

First, with parameters of 512 × 512 pixel resolution, 50 ms integration time, and around 10 mW laser power, wide-field fluorescent images of FND PUF label are taken under polarization directions of excitation laser as 0, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144 degrees. Next, by accumulating the total signal of 16 pixels × 16 pixels into a new pixel, we change the pixel resolution to 32 × 32. Then, contrast values for each pixel are calculated via Eq. 2. Finally, contrast values are digitized as shown in Table S2.

Training of metric learning

For our experiments, we produced 100 pairs of readout results from 100 distinct PUF labels, which were randomly divided into 80 pairs for training and 20 pairs for testing. As shown in Figure S9, the network used is a Siamese network, a type of convolutional neural network (CNN) that processes two inputs concurrently and extracts their deep features. When provided with two digitized images X and X', the Siamese network extracts their corresponding features as follows:

$$F=CNN\left(X\right), {F}^{{\prime }}=CNN\left({X}^{{\prime }}\right).$$

Within our metric learning framework, the objective is to maximize the cosine similarity between F and F' if X and X' belong to the same PUF label, and to minimize the similarity if they belong to different PUF labels. To achieve this, the CNN needs to extract the most notable characteristics of a PUF label that differentiate it from other labels. These features are often patch-level, preserve robust structural information, and exhibit greater resilience to noise. To train the network, we calculate the cosine similarity of feature maps and use the Focal loss to update the CNN. The model employs the Adam⁵⁸ optimizer with an initial learning rate of 0.0001. It is trained with a batch size of 32 for up to 10,000 iterations. Further details regarding the network architecture, cosine similarity calculation, and loss function can be found in Supplementary Notes 5.

Author Contribution

Z.Q.C. and X.J.Q. conceived the idea and supervised the project. L.Z.W. performed the optical measurements and analyzed data. X.Y. designed the metric learning algorithm, and conducted the experiments and evaluation. Y.H. fabricated the nanodiamonds-based anticounterfeiting label. L.Z.W., and X.Y. wrote the manuscript with input from all authors. T.T.Z. and D.Y.L. discussed the results and commented on the manuscript.

Acknowledgements

Z.Q.C. acknowledges the financial support from the HKSAR Research Grants Council (RGC) Research Matching Grant Scheme (RMGS, No. 207300313); HKU Seed Fund; and the Health@InnoHK program of the Innovation and Technology Commission of the Hong Kong SAR Government. X.J.Q. acknowledges the financial support from the HKSAR RGC Early Career Scheme (No. 27209621), General Research Fund (No. 17202422), and Research Matching Grant Scheme. D.Y.L. acknowledges the financial support of the Innovation and Technology Commission of Hong Kong through the Guangdong-Hong Kong Technology Cooperation Funding Scheme (Reference no. GHP/026/19GD).

Hardy, J. Estimating the global economic and social impacts of counterfeiting and piracy. World Trademark Review https://www.worldtrademarkreview.com/global-guide/anti-counterfeiting-and-online-brand-enforcement/2017/article/estimating-the-global-economic-and-social-impacts-of-counterfeiting-and-piracy (2017).
Organization for Economic Cooperation and Development (OECD)/European Union Intellectual Property Office. Trade in counterfeit and pirated goods: Mapping the economic impact. (OECD Publishing, 2016).
Aldhous, P. Murder by medicine. Nature 434, 132–134 (2005).
Mackey, T. K. & Nayyar, G. A review of existing and emerging digital technologies to combat the global trade in fake medicines. Expert Opin. Drug Saf. 16, 587–602 (2017).
Arppe, R. & Sørensen, T. J. Physical unclonable functions generated through chemical methods for anti-counterfeiting. Nat. Rev. Chem. 1, 0031 (2017).
Suh, G. E. & Devadas, S. Physical unclonable functions for device authentication and secret key generation. In Proc. 44th ACM Annual Design Automation Conference 9–14 (ACM, 2007).
Fighting counterfeiting at the nanoscale. Nat. Nanotechnol. 14, 497 (2019).
Smith, A. F., Patton, P. & Skrabalak, S. E. Plasmonic nanoparticles as a physically unclonable function for responsive anti-counterfeit nanofingerprints. Adv. Funct. Mater. 26, 1315–1321 (2016).
Smith, J. D. et al. Plasmonic anticounterfeit tags with high encoding capacity rapidly authenticated with deep machine learning. ACS Nano 15, 2901–2910 (2021).
Lu, Y. et al. Dynamic cryptography through plasmon-enhanced fluorescence blinking. Adv. Funct. Mater. 32, 2201372 (2022).
Gu, Y. et al. Gap-enhanced raman tags for physically unclonable anticounterfeiting labels. Nat. Commun. 11, 516 (2020).
Liu, Y. et al. Inkjet-printed unclonable quantum dot fluorescent anti-counterfeiting labels with artificial intelligence authentication. Nat. Commun. 10, 2409 (2019).
Kustov, P. et al. Mie-resonant silicon nanoparticles for physically unclonable anti-counterfeiting labels. ACS Appl. Nano Mater. 5, 10548–10559 (2022).
Carro-Temboury, M. R., Arppe, R., Vosch, T. & Sørensen, T. J. An optical authentication system based on imaging of excitation-selected lanthanide luminescence. Sci. Adv. 4, e1701384 (2018).
Chen, F. et al. Unclonable fluorescence behaviors of perovskite quantum dots/chaotic metasurfaces hybrid nanostructures for versatile security primitive. Chem. Eng. J. 411, 128350 (2021).
Wang, J. et al. Triple-layer unclonable anti-counterfeiting enabled by huge-encoding capacity algorithm and artificial intelligence authentication. Nano Today 41, (2021).
Li, J., He, C., Qu, H., Shen, F. & Ye, J. Five-dimensional unclonable anticounterfeiting orthogonal raman labels. J. Mater. Chem. C 10, 7273–7282 (2022).
Liu, S., Liu, X., Yuan, J. & Bao, J. Multidimensional information encryption and storage: When the input is light. Research 2021, 7897849 (2021).
Geng, J. Three-dimensional display technologies. Adv. Opt. Photonics 5, 456–535 (2013).
Han, Y. & Li, G. Coherent optical communication using polarization multiple-input-multiple-output. Opt. Express 13, 7527–7534 (2005).
Gu, M., Li, X. & Cao, Y. Optical storage arrays: a perspective for future big data storage. Light: Sci. Appl. 3, e177 (2014).
Li, X., Lan, T. H., Tien, C. H. & Gu, M. Three-dimensional orientation-unlimited polarization encryption by a single optically configured vectorial beam. Nat. Commun. 3, 998 (2012).
Backlund, M. P., Lew, M. D., Backer, A. S., Sahl, S. J. & Moerner, W. E. The role of molecular dipole orientation in single-molecule fluorescence microscopy and implications for super-resolution imaging. ChemPhysChem 15, 587–599 (2014).
Zhang, O. et al. Six-dimensional single-molecule imaging with isotropic resolution using a multi-view reflector microscope. Nat. Photonics 17, 179–186 (2023).
Forkey, J. N., Quinlan, M. E., Alexander Shaw, M., Corrie, J. E. T. & Goldman, Y. E. Three-dimensional structural dynamics of myosin v by single-molecule fluorescence polarization. Nature 422, 399–404 (2003).
Chen, K. et al. Characteristic rotational behaviors of rod-shaped cargo revealed by automated five-dimensional single particle tracking. Nat. Commun. 8, 887 (2017).
Kim, J. et al. Monitoring the orientation of rare-earth-doped nanorods for flow shear tomography. Nat. Nanotechnol. 12, 914–919 (2017).
Lu, W., Wang, D. & Chen, L. Near-static dielectric polarization of individual carbon nanotubes. Nano Lett. 7, 2729–2733 (2007).
Tran, T. T., Bray, K., Ford, M. J., Toth, M. & Aharonovich, I. Quantum emission from hexagonal boron nitride monolayers. Nat. Nanotechnol. 11, 37–41 (2016).
Alegre, T. P. M., Santori, C., Medeiros-Ribeiro, G. & Beausoleil, R. G. Polarization-selective excitation of nitrogen vacancy centers in diamond. Phys. Rev. B 76, 165205 (2007).
Kurtsiefer, C., Mayer, S., Zarda, P. & Weinfurter, H. Stable solid-state source of single photons. Phys. Rev. Lett. 85, 290–293 (2000).
Yu, S. J., Kang, M. W., Chang, H. C., Chen, K. M. & Yu, Y. C. Bright fluorescent nanodiamonds: no photobleaching and low cytotoxicity. J. Am. Chem. Soc. 127, 17604–17605 (2005).
Chang, Y. R. et al. Mass production and dynamic imaging of fluorescent nanodiamonds. Nat. Nanotechnol. 3, 284–288 (2008).
Chipaux, M. et al. Nanodiamonds and their applications in cells. Small 14, e1704263 (2018).
Blank, V. et al. Ultrahard and superhard phases of fullerite C₆₀: Comparison with diamond on hardness and wear. Diamond Relat. Mater. 7, 427–431 (1998).
Maiti, A., Gunreddy, V. & Schaumont, P. A systematic method to evaluate and compare the performance of physical unclonable functions. In Embedded Systems Design with FPGAs 245–267 (Springer, 2013).
Leem, J. W. et al. Edible unclonable functions. Nat. Commun. 11, 328 (2020).
Hu, Y. W. et al. Flexible and biocompatible physical unclonable function anti-counterfeiting label. Adv. Funct. Mater. 31, 2102108 (2021).
Zhang, T. et al. Multimodal dynamic and unclonable anti-counterfeiting using robust diamond microparticles on heterogeneous substrate. Nat. Commun. 14, 2507 (2023).
Kim, J. H. et al. Nanoscale physical unclonable function labels based on block copolymer self-assembly. Nat. Electron. 5, 433–442 (2022).
Zhang, J. et al. An all-in-one nanoprinting approach for the synthesis of a nanofilm library for unclonable anti-counterfeiting applications. Nat. Nanotechnol. (2023). https://doi.org/10.1038/s41565-023-01405-3
Arenas, M., Demirci, H. & Lenzini, G. Cholesteric spherical reflectors as physical unclonable identifiers in anti-counterfeiting. In The 16th International Conference on Availability, Reliability and Security 1–11 (ACM, 2021).
Sun, N. et al. Random fractal-enabled physical unclonable functions with dynamic ai authentication. Nat. Commun. 14, 2185 (2023).
Hoffer, E. & Ailon, N. Deep metric learning using triplet network. In Similarity-Based Pattern Recognition 84–92 (Springer, 2015).
Zhai, A. & Wu, H.Y. Classification is a strong baseline for deep metric learning. Preprint at https://arxiv.org/abs/1811.12649 (2019).
Schroff, F., Kalenichenko, D. & Philbin, J. FaceNet: a unified embedding for face recognition and clustering. In Proc. IEEE Conference on Computer Vision and Pattern Recognition 815–823 (IEEE, 2015).
Wang, L. et al. All-optical modulation of single defects in nanodiamonds: revealing rotational and translational motions in cell traction force fields. Nano Lett. 22, 7714–7723 (2022).
Kehayias, P., Bussmann, E., Lu, T. M. & Mounce, A. M. A physically unclonable function using NV diamond magnetometry and micromagnet arrays. J. Appl. Phys. 127, 203904 (2020).
Pinto, N., DiCarlo, J. J. & Cox, D. D. How far can you get with a modern face recognition test set using only simple features? In Proc. IEEE Conference on Computer Vision and Pattern Recognition 2591–2598 (IEEE, 2009).
Oliva, A. & Torralba, A. Modeling the shape of the scene: a holistic representation of the spatial envelope. Int. J. Comput. Vis. 42, 145–175 (2001).
LeCun, Y. et al. Backpropagation applied to handwritten zip code recognition. Neural Comput. 1, 541–551 (1989).
Krizhevsky, A., Sutskever, I. & Hinton, G. E. Imagenet classification with deep convolutional neural networks. Commun. ACM 60, 84–90 (2017).
Simonyan, K. & Zisserman, A. Very deep convolutional networks for large-scale image recognition. Preprint at http://arXiv.org/abs/1409.1556 (2014).
Hu, J., Lu, J. & Tan, Y. P. Discriminative deep metric learning for face verification in the wild. In Proc. IEEE Conference on Computer Vision and Pattern Recognition 1875–1882 (IEEE, 2014).
Liu, W. et al. SphereFace: deep hypersphere embedding for face recognition. In Proc. IEEE Conference on Computer Vision and Pattern Recognition 212–220 (IEEE, 2017).
Yang, X., Wang, M. & Tao, D. Person re-identification with metric learning using privileged information. IEEE Trans. Image Process. 27, 791–805 (2019).
Song, H. O., Xiang, Y., Jegelka, S. & Savarese, S. Deep metric learning via lifted structured feature embedding. In Proc. IEEE Conference on Computer Vision and Pattern Recognition 4004–4012 (IEEE, 2016).
Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. Preprint at https://arxiv.org/abs/1412.6980 (2014).

Competing interests: The authors declare no competing interests.

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High-dimensional anticounterfeiting nanodiamonds authenticated with deep metric learning

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Abstract

Figures

Introduction

Results

1. LPM curves of FNDs providing feasibility for 3D anticounterfeiting

2. Anticounterfeiting performance of 3D encoded images

3. Deep metric learning for authenticating noise-affected digitized images

Discussion

Methods

Experimental apparatus

Fabrication of FND PUF label

Particle location code

Measurement of LPM curves

Optical readout and digitization

Training of metric learning

Declarations

Author Contribution

Acknowledgements

References

Additional Declarations

Supplementary Files

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