Diffractive Deep Neural Network
It opens up fundamentally new opportunities to use an artificial intelligence-based passive device to instantaneously analyze data, images, and classify objects.
Introduction
D2NN[1] has demonstrated its importance in performing various all-optical machine learning tasks, e.g., classification, segmentation.
This optical artificial neural network device is intuitively modeled on how the brain processes information. It could be scaled up to enable new camera designs and unique optical components that work passively in medical technologies, robotics, security or any application where image and video data are essential.
Theory
Optical Computing
Optical computing (also known as optoelectronic computing and photonic computing) is a computation paradigm that uses photons (small packets of light energy) produced by laser/diodes for digital computation. Photons have proved to give us a higher bandwidth than the electrons we use in conventional computer systems. The optical computers would give us a higher performance and hence be faster than the electronic ones.
Deep Learning
It is an artificial intelligence (AI) function that imitates the workings of the human brain in processing data and creating patterns for use in decision making. Deep learning is a subset of machine learning in artificial intelligence that has networks capable of learning unsupervised from data that is unstructured or unlabeled. Also known as deep neural learning or deep neural network.
Mathematical Analysis
D2NN bases on phase modulations originated by the multiple layer diffractive surfaces and diffraction propagations between the layers[2]. So, in a D2NN system, there exist only two operations: phase modulation and propagation.
According to the angular spectrum theory, the propagation of an optical field in free space can be described as
where E(kx, ky) is the angular spectrum of the optical field before propagation, and Ez(kx, ky) for the angular spectrum after propagation of a distance z. The propagation operator 𝑃 can be defined as
where 𝐹 is the operator for 2D-Fourier transform, correspondingly, 𝐹-1 represents the inverse 2D-Fourier transform. k is the angular wavenumber of the fields.
Several laws are found for the Diffractive Deep Neural Networks (D2NN).
They reveal the inner product of any two light fields in D2NN is invariant and the D2NN act as a unitary transformation for optical fields. If the output intensities of the two inputs are separated spatially, the input fields must be orthogonal. These laws imply that the D2NN is not only suitable for the classification of general objects but also more suitable for applications aim to the optical orthogonal modes. Therefore, researchers believe that the D2NN is not only applicable to the classification of general objects but more applicable for the optical orthogonal modes. Simulations show D2NN performs well in mode conversion, mode multiplexer/de-multiplexer and optical mode recognition.
D2NN is a powerful tool for manipulation of optical orthogonal modes, which have the potential applications in many fields, especially in modal characterization and optical communication.
Advantages
- Scalable: It can easily be scaled up using numerous high-throughput and large-area 3D fabrication methods, such as soft-lithography, additive manufacturing, and wide-field optical components and detection systems.
- Easily reconfigurable: D2NN can be easily improved by additional 3D printed layers or replacing some of the existing layers with newly trained ones.
- Lightening speed: Once the device is trained, it works at the speed of light.
- Efficient: No energy is consumed to run the device.
- Cost-effective: The device can be reproduced for less than $50, making it very cost-effective.
Future Work
Residual D2NNs (Res-D2NN)
Deeper D2NNs that provide higher inference complexity are more difficult to train due to the problem of gradient vanishing. Then the residual D2NNs (Res-D2NN)[3] are introduced, which enables us to train substantially deeper diffractive networks by constructing diffractive residual learning blocks to learn the residual mapping functions. Unlike the existing plain D2NNs, Res-D2NNs contribute to the design of a learnable light shortcut to directly connect the input and output between optical layers. Such a shortcut offers a direct path for gradient back propagation in training, which is an effective way to alleviate the gradient vanishing issue on very deep diffractive neural networks. Experimental results on image classification and pixel super-resolution demonstrate the superiority of Res-D2NNs over the existing plainD2NN architectures.
Fourier-space Diffractive Deep Neural Network
The Fourier-space diffractive deep neural network (F-D^{2}NN)[4] for all-optical image processing performs advanced computer vision tasks at the speed of light. The F-D^{2}NN is achieved by placing the extremely compact diffractive modulation layers at the Fourier plane or both Fourier and imaging planes of an optical system, where the optical nonlinearity is introduced from ferroelectric thin films. We demonstrated that F-D^{2}NN can be trained with deep learning algorithms for all-optical saliency detection and high-accuracy object classification.
References
- ↑ Lin, Xing; Rivenson, Yair; Yardimci, Nezih T.; Veli, Muhammed; Luo, Yi; Jarrahi, Mona; Ozcan, Aydogan (2018). "All-optical machine learning using diffractive deep neural networks". Science. 361 (6406): 1004–1008. arXiv:1804.08711. Bibcode:2018Sci...361.1004L. doi:10.1126/science.aat8084. PMID 30049787.
- ↑ Zheng, Shuiqin; Zeng, Xuanke; Zha, Lang; Shangguan, Huancheng; Xu, Shixiang; Fan, Dianyuan (2018). "Orthogonality of Diffractive Deep Neural Networks". arXiv:1811.03370 [physics.optics].
- ↑ Dou, Hongkun; Deng, Yue; Yan, Tao; Wu, Huaqiang; Lin, Xing; Dai, Qionghai (2020). "Residual D2NN: Training diffractive deep neural networks via learnable light shortcuts". Optics Letters. 45 (10): 2688–2691. Bibcode:2020OptL...45.2688D. doi:10.1364/OL.389696. PMID 32412442 Check
|pmid=value (help). - ↑ Yan, T.; Wu, J.; Zhou, T.; Xie, H.; Xu, F.; Fan, J.; Fang, L.; Lin, X.; Dai, Q. (2019). "Fourier-space Diffractive Deep Neural Network". Physical Review Letters. 123 (2): 023901. Bibcode:2019PhRvL.123b3901Y. doi:10.1103/PhysRevLett.123.023901. PMID 31386516.
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