Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Cramer–Rao bounds for intensity interferometry measurements

Not Accessible

Your library or personal account may give you access

Abstract

The question of signal-to-noise ratio (SNR) in intensity interferometry has been revisited in recent years, as researchers have realized that various innovations can offer significant improvements in SNR. These innovations include improved signal processing. Two such innovations, the use of positivity and the use of knowledge of the general shape of the object, have been proposed. This paper investigates the potential gains offered by these two approaches using Cramer–Rao lower bounds (CRLBs). The CRLB on the variance of the positivity-constrained maximum likelihood (ML) estimate is at best 1/4 of the variance of the unconstrained estimator. This is compared to the positivity-constrained ML estimator, which delivers a best-case variance reduction of only (11/π)/2=34.1%. The gains offered by prior knowledge depend on the quality of such information, as might be expected from optimal weighting of such data with the measured data. Furthermore, biases are induced by the application of constraints, and these biases can eliminate some or all of the advantage of lower variances, as found when considering the total root-mean-square error. A form of CRLB for variance is presented that properly incorporates prior information.

© 2013 Optical Society of America

Full Article  |  PDF Article
More Like This
Cramér-Rao bounds on mensuration errors

R. A. Gonsalves
Appl. Opt. 15(5) 1270-1275 (1976)

Biased Cramér-Rao lower bound calculations for inequality-constrained estimators

Charles L. Matson and Alim Haji
J. Opt. Soc. Am. A 23(11) 2702-2713 (2006)

Theoretical range precision obtained by maximum likelihood estimation in laser radar compared with the Cramer–Rao bound

Zhiyong Gu, Jiancheng Lai, Chunyong Wang, Wei Yan, Yunjing Ji, and Zhenhua Li
Appl. Opt. 57(34) 9951-9957 (2018)

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (6)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (51)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved