Theory of coherent active convolved illumination for superresolution enhancement

Abstract

Recently an optical amplification process called the plasmon injection scheme was introduced as an effective solution to overcoming losses in metamaterials. Implementations with near-field imaging applications have indicated substantial performance enhancements even in the presence of noise. This powerful and versatile compensation technique, which has since been renamed to a more generalized active convolved illumination, offers new possibilities of improving the performance of many previously conceived metamaterial-based devices and conventional imaging systems. In this work, we present, to the best of our knowledge, the first comprehensive mathematical breakdown of active convolved illumination for coherent imaging. Our analysis highlights the distinctive features of active convolved illumination, such as selective spectral amplification and correlations, and provides a rigorous understanding of the loss compensation process. These features are achieved by an auxiliary source coherently superimposed with the object field. The auxiliary source is designed to have three important properties. First, it is correlated with the object field. Second, it is defined over a finite spectral bandwidth. Third, it is amplified over that selected bandwidth. We derive the variance for the image spectrum and show that utilizing the auxiliary source with the above properties can significantly improve the spectral signal-to-noise ratio and resolution limit. Besides enhanced superresolution imaging, the theory can be potentially generalized to the compensation of information or photon loss in a wide variety of coherent and incoherent linear systems including those, for example, in atmospheric imaging, time-domain spectroscopy, P T symmetric non-Hermitian photonics, and even quantum computing.

Far field superlensing inside biological media through a nanorod lens using spatiotemporal information

“… 30 , it is discussed that if we manage to record the transient fields with a noise level lower than 1% (which is a reasonable assumption), the imaging procedure gives a super-resolved image of the object. It is noteworthy that recently introduced active convolved illumination techniques 48 based on optical amplification and using auxiliary sources can significantly improve the spectral signal-to-noise ratio and go beyond this noise threshold. Also, using filters in reconstruction algorithms, introduced in atmospheric imaging 49 in the presence of noise and scattering, could increase the robustness of our algorithm to the noise and lead to some level of additional detail in the obtained image.…”

Experimental realization of the active convolved illumination imaging technique for enhanced signal-to-noise ratio

“…This is true, however typically (e.g., for incoherent light), the magnitude of the transfer function for an imaging system with an unobstructed pupil decreases with increasing spatial frequency [1]. It follows that the spectral SNR then also decreases with increasing spatial frequency, since the shot noise variance is constant in the spatial frequency domain [2][3][4]. Consequently, adding up more photons blindly does not lead to much increase for the SNR of high spatial frequencies.…”

“…However, the photon losses hinder their further viability [28][29][30]. Inspiration from research in loss compensation for metamaterials and plasmonics employing 'virtual gain' [30][31][32][33] led us to propose a unique perspective on the noisy imaging problem [2,32,[34][35][36][37][38][39][40][41]. The fundamental resolution limit to superresolving lenses is not determined by the diffraction limit, but rather by a shot noise limit, i.e.…”

“…How to tackle this problem ideally has been an open question for decades [43][44][45][46][47][48]. The active convolved illumination (ACI) technique has recently been proposed theoretically as a ubiquitous noise and distortion mitigation scheme to improve the image signal-to-noise (SNR) ratio by systematically manipulating the image spectrum depending on the underlying stochastic behavior [2,32,37,[39][40][41]. Popular techniques to improve image resolution or SNR are structured illumination microscopy (SIM) [3,[49][50][51][52][53], stimulated emission depletion (STED) microscopy [49,54,55], stochastic optical reconstruction microscopy/photoactivated localization microscopy (STORM/PALM) [49,56,57], and computational methods [43][44][45][46][47][48][58][59][60] including machine learning [42,61,62].…”

“…It was hypothesized that the ACI could overcome the loss of information as depicted in Fig. 1(b) [2,32,37,39]. The light pattern which forms the object (black line) is superimposed with an auxiliary pattern (blue line) correlated with the object.…”