Fundamental Limits on Subwavelength Range Resolution
- URL: http://arxiv.org/abs/2308.06252v1
- Date: Fri, 11 Aug 2023 17:38:10 GMT
- Title: Fundamental Limits on Subwavelength Range Resolution
- Authors: Andrew N. Jordan and John C. Howell
- Abstract summary: We establish fundamental bounds on subwavelength resolution for the radar ranging problem, super radar''
For the minimal separation distance, both the direct field method and photon counting method show that the discriminability vanishes quadratically as the target separation goes to zero.
We discuss the application of maximum likelihood estimation to improve the range precision with optimal performance.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We establish fundamental bounds on subwavelength resolution for the radar
ranging problem, ``super radar''. Information theoretical metrics are applied
to probe the resolution limits for the case of both direct electric field
measurement and photon-counting measurements. To establish fundamental limits,
we begin with the simplest case of range resolution of two point targets from a
metrology perspective. These information-based metrics establish fundamental
bounds on both the minimal discrimination distance of two targets as well as
the precision on the separation of two subwavelength resolved targets. For the
minimal separation distance, both the direct field method and photon counting
method show that the discriminability vanishes quadratically as the target
separation goes to zero, and is proportional to the variance of the second
derivative of the electromagnetic field profile. Nevertheless, robust
subwavelength estimation is possible. Several different band-limited function
classes are introduced to optimize discrimination. We discuss the application
of maximum likelihood estimation to improve the range precision with optimal
performance. The general theory of multi-parameter estimation is analyzed, and
a simple example of estimating both the separation and relative strength of the
two point reflectors is presented.
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