# Speckle noise in optical fibre sensing

*A study using the Maximum Entropy method*
## L. Stergioulas, A. Vourdas and G.R. Jones

Department of Electrical Engineering and Electronics

University of Liverpool

P.O. Box 147

Liverpool L69 3BX

### Abstract

The spatial distribution of the intensity of light at the output of an
optical fibre can be useful in optical fibre sensing applications.
Noise however limits the use of the detailed shape of this
distribution for the development of highly sensitive sensors. In this
paper we use the maximum entropy method to obtain the most likely
spatial distribution consistent with the noisy data.
An image captured by a CCD camera at the output of an optical fibre
has been divided into many small regions. In each region we find
the first **N** moments and then calculate another
distribution that has the same first **N** moments but
also the maximum entropy. Noise reduction is thus associated with the
elimination of the detailed information in the higher moments of the
observed distribution. Results for various sizes of the regions and
various values of the number of moments **N** will be
presented.

A second approach has also been considered where many images have been
captured at different times providing a distribution of the intensity
at each pixel. We calculate the average **\mu_i** and
standard deviation **\sigma_i** of the intensity at the
pixel **i** and maximise the entropy with the constraint
that

is smaller than a certain value. Several examples will be presented.

The work applies the powerful maximum entropy technique in the context
of noise reduction in optical fibre systems and could play an
important role in increasing the sensitivity of these systems.

MaxEnt 94 Abstracts / mas@mrao.cam.ac.uk