OCCULAR OCCUltation Limovie Analysis Routine Presented by: Bob Anderson and Tony George (IOTA) A program to easily detect and time occultations and standardize data reduction from LiMovie files

Motivation for OCCULAR: how to deal with noise… Above is a plot from a LiMovie processed occultation event. One would like to: Locate a likely occultation event that is obscured by noise Calculate D and R in a standardized manner Use statistics to gain confidence that the event is not noise

The good news is that the troublesome noise is gaussian (normal distribution) Because the noise is gaussian, we are on solid ground to use… Standard least-squares estimates of event parameters Standard statistical confidence measures

Another piece of good news…. In the absence of noise, we expect our observations to look like one of the idealized data traces shown below … …and since we know the expected shape of our event, we can use standard techniques from signal processing theory to locate where in the data our event is positioned.

Occular nomenclature and conventions wing transition event b a wing= 17 readings event = 4 readings transition = 2 readings is how the above shape would be specified The values for b (baseline) and a (asteroid) are output values determined by least-squares fit event (FWHM) = 7 readings This alternative way of setting shape width is also available Note: D, R, and duration are reported at FWHM If that is not appropriate, the user will have to manually calculate these numbers from the available data. Note: D, R, and duration are reported at FWHM If that is not appropriate, the user will have to manually calculate these numbers from the available data.

The OCCULAR algorithm pseudo-code Accept user input to define a range of ideal signal shapes (min max for event width and transition, and wing size) for each (signal) { position signal at the left edge of the input data set max FOM found to zero do { calculate a figure of merit (FOM) for how well signal matches data calculate least-squares value for the event parameters calculate statistical measures of the fit (Tstat) keep track of the max FOM found so far (and associated information) slide the signal one step to the right } until (signal is at right edge of input data) add the data found at max FOM to the maxFOM list } Look through the maxFOM list and highlight the list entry that contains the max maxFOM value. This is the found event. Display a plot of the results.

FOM (figure of merit) calculation // Calculate the normalized correlation coefficient. double xySum = 0.0; double yySum = 0.0; double xxSum = 0.0; for (i = leftIndex; i <= rightIndex; i++) { xySum += data[i] * signal[i]; yySum += data[i] * data[i]; xxSum += signal[i] * signal[i]; } fom = xySum / (Sqrt(xxSum) * Sqrt(yySum)); if (fom < 0) fom = 0.0; This is a standard technique used to locate the position of a known signal (x) in a noisy data stream (y) Note: the data[i] and signal[i] have been adjusted to have a mean of zero before the following code is executed. leftIndex and rightIndex deal with the occasions where some part of the signal lies outside the input data.

Our main statistical measure (Students – t) n 1 = number of readings in wings n 2 = number of readings at the bottom of the event S 2 x = variance of X (the b value of our signal) S 2 y = variance of Y (the a value of our signal) df = degrees of freedom Note: we do NOT include readings in the transition zone in the calculation of T

A visual to give substance to the earlier discussion…

Tstat Position of event Width of event (1 to 250) Cancri Tstat surface (perspective view)

Position of event Width of event (1 to 250) A view of Cancri Tstat surface from above

In a moment, Tony George is going to demonstrate OCCULAR. He will begin by showing the program at work on the Hiraoka data. Unlike the Cancri event, which was clearly detected, the Hiraoka data is an example where one must spend more time answering the question Did we really observe an occultation event, or was that just noise? The following two slides illustrate the issue.

Width of event Position of event FOM Hiraoka FOM surface This shows an event that is similar to noise FOM may be somewhat ambiguous, but Tstat tells a different story…

Tstat Position of event Width of event (1 to 100) This event is now more clearly distinguished Hiraoka Tstat surface

And now Tony will demonstrate the program in action on real data….