RESUMO
We demonstrate a new way to analyze stable, multipass optical cavities (Herriott cells), using the linear canonical transform formalism, showing that re-entrant designs reproduce an arbitrary input field at the output, resulting in useful symmetries. We use this analysis to predict the stability of cavities used in interferometric delay lines for temporal pulse addition.
RESUMO
Sensory inputs conveying information about the environment are often noisy and incomplete, yet the brain can achieve remarkable consistency in recognizing objects. Presumably, transforming the varying input patterns into invariant object representations is pivotal for this cognitive robustness. In the classic hierarchical representation framework, early stages of sensory processing utilize independent components of environmental stimuli to ensure efficient information transmission. Representations in subsequent stages are based on increasingly complex receptive fields along a hierarchical network. This framework accurately captures the input structures; however, it is challenging to achieve invariance in representing different appearances of objects. Here we assess theoretical and experimental inconsistencies of the current framework. In its place, we propose that individual neurons encode objects by following the principle of maximal dependence capturing (MDC), which compels each neuron to capture the structural components that contain maximal information about specific objects. We implement the proposition in a computational framework incorporating dimension expansion and sparse coding, which achieves consistent representations of object identities under occlusion, corruption, or high noise conditions. The framework neither requires learning the corrupted forms nor comprises deep network layers. Moreover, it explains various receptive field properties of neurons. Thus, MDC provides a unifying principle for sensory processing.