Decoding wavelengths from compressed speckle patterns with deep learning

Recovering the wavelengths from disordered speckle patterns has emerged as an exciting prospect as a wavelength measurement method due to its combination of high resolution and straightforward design. In previous studies, panel cameras were commonly utilized as the speckle image receiver. However, high cost (especially in a near-infrared range), bulky size, and low speed have limited its application in optical communications, metrology, and optical sensing. In this work, we effectively compressed speckle patterns into four intensities by using a quadrant detector (QD), bypassing the need for millions of pixels as in conventional cameras. Remarkably, wavelengths can still be recovered through only these four pixels. A new CNN based demodulation algorithm, shallow residual network (SRN), was proposed to recognize the wavelengths from the highly compressed speckle images. Finally, a wavelength precision of 4 fm (∼ 0.5 MHz) with an updating speed of ∼ 1 kHz was achieved in the demonstrations. In addition, the SRN shows a broad measurement range and good noise robustness. Compared with a camera-based system, the QD detection scheme associated with the CNN algorithm provides a compact, high-speed, and low-cost method to examine the speckle patterns, which opens new routes in many other fields.