TAOS Photometry with the Expectation-Maximization Algorithm

Matthew J. Lehner

Harvard-Smithsonian Center for Astrophysics

University of Pennsylvania

The TAOS Collaboration:

C. Alcock (CfA)

T. Axelrod (Arizona)

F. Bianco (UPenn)

Y.-I. Byun (Yonsei)

W.-P. Chen (NCU)

K. Cook (LLNL)

R. Dave (UPenn)

J. Giammarco (Upenn)

D.-W. Kim (Yonsei)

S.-K. King (ASIAA)

T. Lee (ASIAA)

M. Lehner (CfA/UPenn)

J. Lissauer (NASA Ames)

S. L. Marshall (KIPAC/SLAC)

T. Nihei (UPenn)

I. de Pater (UC Berkeley)

J. Rice (UC Berkeley)

M. Schwamb (UPenn)

A. Wang (ASIAA)

S.-Y. Wang (ASIAA)

C.-Y. Wen (ASIAA)

Z.-W. Zhang (NCU)

Plan of the talk:

Background, Motivation

EM Algorithm and Stellar Photometry

Current Status

Future Plans

TAOS:

Discover small/distant KBOs by searching for occultations of distant stars

Event durations ~200 ms, sample at 5 Hz

Events extremely rare, monitor 1000's of stars

Limit false positives, use multiple (4) telescopes

TAOS:

Reduce data in real time for follow-up

4 telescopes  3000 stars  5 Hz = 60,000 photometric reductions/second, 100 GB/night

Read out all stars in 64  2048 subimage, extremely crowded

Low bandwidth network, low power budget

Rare events, weak signature: accuracy important

fl depends on all other parameters

→ Non-linear system of npN* eqn's, npN* unknowns

Not a problem if field is sparse:

Crowded field becomes “sparse”

nj

z1j

z2j

z3j

Expectation-Maximization Algorithm

Some “unobservable data” which simplifies problem

Calculate “complete log-likelihood” function assuming unobservable data known

Assume we have CCD which gives number of photons in each pixel from each star, zij.

EM Algorithm

2) Calculate

1) Initial guesses

4) Repeat until convergence

3) Maximize

Current Status

Algorithm works on simulated test images

Code meets speed requirements (60,000 PSFs/sec)

Initialization nearly ready for testing

Currently working on tracking issues to reduce initialization overhead

Future applications

Fitting galaxies (weak lensing)

Overlapping galaxies, point sources

Model galaxies with “shapelet” expansion

Use EM algorithm for blended fits

Funded by NASA AISR program

Shapelet Expansion

Eigenfunctions of 2-D quantum harmonic quantum oscillator

Shapelet Expansion

Refregier, Chang and Bacon (2002)

My name is Charles Alcock. I am a professor in the Department of Physics and Astronomy here at the University of Pennsylvania.

Matthew Lehner

2004-02-02T16:50:32