A Caltech Library Service

How to COAAD Images. II. A Coaddition Image that is Optimal for Any Purpose in the Background-dominated Noise Limit

Zackay, Barak and Ofek, Eran O. (2017) How to COAAD Images. II. A Coaddition Image that is Optimal for Any Purpose in the Background-dominated Noise Limit. Astrophysical Journal, 836 (2). Art. No. 188. ISSN 1538-4357.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


Image coaddition is one of the most basic operations that astronomers perform. In Paper I, we presented the optimal ways to coadd images in order to detect faint sources and to perform flux measurements under the assumption that the noise is approximately Gaussian. Here, we build on these results and derive from first principles a coaddition technique that is optimal for any hypothesis testing and measurement (e.g., source detection, flux or shape measurements, and star/galaxy separation), in the background-noise-dominated case. This method has several important properties. The pixels of the resulting coadded image are uncorrelated. This image preserves all the information (from the original individual images) on all spatial frequencies. Any hypothesis testing or measurement that can be done on all the individual images simultaneously, can be done on the coadded image without any loss of information. The PSF of this image is typically as narrow, or narrower than the PSF of the best image in the ensemble. Moreover, this image is practically indistinguishable from a regular single image, meaning that any code that measures any property on a regular astronomical image can be applied to it unchanged. In particular, the optimal source detection statistic derived in Paper I is reproduced by matched filtering this image with its own PSF. This coaddition process, which we call proper coaddition, can be understood as the maximum signal-to-noise ratio measurement of the Fourier transform of the image, weighted in such a way that the noise in the entire Fourier domain is of equal variance. This method has important implications for multi-epoch seeing-limited deep surveys, weak lensing galaxy shape measurements, and diffraction-limited imaging via speckle observations. The last topic will be covered in depth in future papers. We provide an implementation of this algorithm in MATLAB.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Ofek, Eran O.0000-0002-6786-8774
Additional Information:© 2017 The American Astronomical Society. Received 2015 December 6; revised 2016 October 21; accepted 2016 December 28; published 2017 February 21. We thank Avishay Gal-Yam, Guy Nir, Ora Zackay, Maayane Soumagnac, Adam Rubin, Frank Masci, Dovi Poznanski, and Assaf Horesh for their comments and suggestions. We thank Guy Nir and Ilan Manulis for help with obtaining the speckle images presented here. B.Z. is grateful for receiving the Clore fellowship. E.O.O. is incumbent of the Arye Dissentshik career development chair and is grateful for support by grants from the Willner Family Leadership Institute Ilan Gluzman (Secaucus, NJ), Israel Science Foundation, Minerva, Weizmann-UK, and the I-Core program by the Israeli Committee for Planning and Budgeting and the Israel Science Foundation (ISF).
Group:Palomar Transient Factory
Funding AgencyGrant Number
Weizmann Institute of ScienceUNSPECIFIED
Willner Family Leadership Institute Ilan GluzmanUNSPECIFIED
Israel Science FoundationUNSPECIFIED
I-CORE Program of the Planning and Budgeting CommitteeUNSPECIFIED
Subject Keywords:gravitational lensing: weak – instrumentation: high angular resolution – methods: data analysis – methods: statistical – techniques: image processing – techniques: photometric
Issue or Number:2
Record Number:CaltechAUTHORS:20190529-074656999
Persistent URL:
Official Citation:Barak Zackay and Eran O. Ofek 2017 ApJ 836 188
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95840
Deposited By: Tony Diaz
Deposited On:30 May 2019 22:30
Last Modified:03 Oct 2019 21:17

Repository Staff Only: item control page