Objective In recent years, on-chip spectroscopy has garnered considerable interests across multiple applications, primarily owing to its exceptional integration capabilities. Benefiting from mature image sensors with millions of pixels, wavelength-dependent image coding technology has emerged as a promising integrated spectroscopy method. However, achieving accurate decoding of spectral information in the images typically requires objective lenses and larger working distances, thereby increasing both the complexity of the optical system and the overall size of the inspection system. This limits its use in portable platforms such as mobiles. The aim of this work is to develop a lens-free image encoding method for on-chip spectroscopy and to address how to extract accurate spectral information from encoded images with high correlation.

Methods A lens-free speckle image encoding method was developed for on-chip spectroscopy, where a PVP film embedded with Au nanorods was intimately integrated on an image sensor with a mm³ scale (Fig.1). The speckle of each signal wavelength was recorded to construct a responsive matrix for image encoding in advance. Although the image correlation is high in such a compact configuration (Fig.3), a convolutional neural network algorithm was applied to decode the image-spectrum relation by classifying the images with multilayer perceptron to extract high-level features (Fig.2). Once the calibration of image encoding is finished, the real-time spectral reconstruction takes only 1 s.

Results and Discussions Spectral information was encoded in the speckle patterns generated by the Au nanorods. Conventional compressive sensing algorithm failed to reconstruct the original spectra due to the large image correlation in such a compact configuration (Fig.4). A convolution neutral network algorithm was developed to extract spectral features from low-contrast images and demonstrated accurate spectral reconstruction. For monochromatic light at 610 nm, 630 nm, 650 nm, 670 nm, and 690 nm, the deviation of the peak wavelength is consistently less than 1 nm in all cases (Fig.4(a)). Similar results were observed in the cases of single-layer frosted glass, double-layer frosted glass and triple-layer annealed gold particles, which shows the robustness of this method. The transmission spectra of three bandpass filters with varying filter ranges, as well as the emission spectra of a single LED were presented (Fig.5). And in every instance, the system predicts a wavelength peak deviation of less than 1 nm, with the spectral shape also demonstrating good agreement, indicating the applicability of the technology.

Conclusions The work shows the possibility to develop an advanced image decoding algorithm based on convolution neutral network to compensate the limited hardware for on-chip spectroscopy based on image encoding. Such a ultracompact configuration together with decent spectroscopy performance enables potential applications in on-site inspection and distributed sensor network.