multimode fiber schematic

A speckle pattern from an image transmitted through a multimode fiber passes through a deep neural network and is reproduced as the number 3. [Image: Demetri Psaltis / Swiss Federal Institute of Technology Lausanne]

Researchers from Switzerland, led by OSA Fellow Demetri Psaltis, applied a deep neural network (DNN)—a kind of machine-learning algorithm—to identify and reconstruct the image of a number from the speckle pattern it created while traveling through a multimode fiber (MMF) (Optica: doi: 10.1364/OPTICA.5.000960). The team trained the DNN with a database of 16,000 handwritten numbers so that the algorithm could associate a particular speckle pattern at the far end of the MMF with a specific number that serves as the original input image at the beginning of the MMF.

The machine-learning approach, say the researchers, is simpler than current methods of image reconstruction from speckle that require holographic measurement of the output signal. Moreover, because MMFs offer multiple parallel channels, they can carry several streams of information at once, and they are not susceptible to environmental instabilities like changes in temperature or movement. Ultimately, the Swiss team believes its optical application will benefit a variety of fields, including telecommunications and endoscopy for medical diagnosis.

Repetition is the mother of all learning

Teaching a DNN to recognize an object is similar to teaching a human: Repetition, repetition, repetition. For Psaltis and his colleagues, this meant training their DNN to recognize images of numerals 0 to 9 from a database of 16,000 hand-written examples. Simply put, the more 9s the DNN “sees” during training, the easier it is for the DNN to identify a 9 when it is tested with images outside the training database.

However, the DNN wasn’t trained to identify actual images of the numerals. It was trained to identify numbers based on the speckle patterns they created when light from an illuminated number at the start of the MMF reached a camera at the output end.

With testing, the researchers were able to demonstrate that their machine-learning algorithm could achieve 97 percent accuracy for images of numerals sent through a short, 0.1-m-long MMF, and 90 percent accuracy for a 1.0-km-long MMF.

Understanding the speckle pattern

MMFs can carry more information than standard optical fibers because they have several channels (spatial modes) that can transmit several streams of data at the same time. However, by the time these data streams reach the end of the MMF, they are read by the human eye as speckle patterns, not as the image that appeared at the MMF’s origin. Psaltis and his team made MMFs more practical for transmitting complex signals like images by using a DNN to associate a speckle pattern with a number shape.

While being able to identify and reproduce a number from a speckle pattern delivered across a kilometer of MMF is impressive, the researchers have bigger dreams for their machine-learning technique. MMFs, which are thinner than traditional optical fibers, seem ideal for use in endoscopy probes to unobtrusively collect and transfer information about what is going on inside the body. The DNN technique could allow such applications for MMF without the need for a holographic recorder, and is also robust against noise and distortions caused, for example, by small movements such as the patient’s breathing.

Similarly, the DNN technique could improve the prospects of MMFs for carrying telecommunications signals. Such signals must run for several kilometers, and are susceptible to distortions caused by changes in temperature or wind. The use of DNNs could help correct some of those problems, as the network “learns” and statistically cancels out background noise as well.