Imaging in laser spectroscopy by a single-pixel camera based on speckle patterns

Compressed sensing (CS) is a branch of computational optics able to reconstruct an image (or any other information) from a reduced number of measurements – thus significantly saving measurement time. It relies on encoding the detected information by a random pattern and consequent mathematical reconstruction. CS can be the enabling step to carry out imaging in many time-consuming measurements. The critical step in CS experiments is the method to invoke encoding by a random mask. Complex devices and relay optics are commonly used for the purpose. We present a new approach of creating the random mask by using laser speckles from coherent laser light passing through a diffusor. This concept is especially powerful in laser spectroscopy, where it does not require any complicated modification of the current techniques. The main advantage consist in the unmatched simplicity of the random pattern generation and a versatility of the pattern resolution. Unlike in the case of commonly used random masks, here the pattern fineness can be adjusted by changing the laser spot size being diffused. We demonstrate the pattern tuning together with the connected changes in the pattern statistics. In particular, the issue of patterns orthogonality, which is important for the CS applications, is discussed. Finally, we demonstrate on a set of 200 acquired speckle patterns that the concept can be successfully employed for single-pixel camera imaging. We discuss requirements on detector noise for the image reconstruction.