Information geometry, Pythagorean-theorem extension, and Euclidean distance behind optical sensing via spectral analysis Academic Article uri icon

abstract

  • Abstract We present an information-geometric perspective on a generic spectral-analysis task pertaining to a vast class of optical measurements in which a parameter needs to be evaluated from -dependent spectral features in a measurable optical readout. We show that the spectral shift and line broadening driven by small variations can be isolated as orthogonal components in a Pythagorean-theorem extension for a Euclidean distance in the space of probability distributions, representing the -induced information gain, expressible via the relative entropy and the pertinent Fisher information. This result offers important insights into the limits of optical signal analysis, as well as into the ultimate spectral resolution and the limiting sensitivity of a vast class of optical measurements. As one example, we derive a physically transparent closed-form analytical solution for the information-theory bound on the precision of all-optical temperature sensors based on color centers in diamond.

published proceedings

  • LASER PHYSICS LETTERS

author list (cited authors)

  • Zheltikov, A. M.

citation count

  • 0

complete list of authors

  • Zheltikov, AM

publication date

  • June 2022