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Simulating image coaddition with the Nancy Grace Roman Space Telescope: II. Analysis of the simulated images and implications for weak lensing

Masaya Yamamoto, Katherine Laliotis, Emily Macbeth, Tianqing Zhang, Christopher M. Hirata, M. A. Troxel, Kaili Cao, Ami Choi, Jahmour Givans, Katrin Heitmann, Mustapha Ishak, Mike Jarvis, Eve Kovacs, Heyang Long, Rachel Mandelbaum, Andy Park, Anna Porredon, Christopher W. Walter, W. Michael Wood-Vasey

Abstract

One challenge for applying current weak lensing analysis tools to the Nancy Grace Roman Space Telescope is that individual images will be undersampled. Our companion paper presented an initial application of Imcom - an algorithm that builds an optimal mapping from input to output pixels to reconstruct a fully sampled combined image - on the Roman image simulations. In this paper, we measure the output noise power spectra, identify the sources of the major features in the power spectra, and show that simple analytic models that ignore sampling effects underestimate the power spectra of the coadded noise images. We compute the moments of both idealized injected stars and fully simulated stars in the coadded images, and their 1- and 2-point statistics. We show that the idealized injected stars have root-mean-square ellipticity errors (1 - 6) x 10-4 per component depending on the band; the correlation functions are >= 2 orders of magnitude below requirements, indicating that the image combination step itself is using a small fraction of the overall Roman 2nd moment error budget, although the 4th moments are larger and warrant further investigation. The stars in the simulated sky images, which include blending and chromaticity effects, have correlation functions near the requirement level (and below the requirement level in a wide-band image constructed by stacking all 4 filters). We evaluate the noise-induced biases in the ellipticities of injected stars, and explain the resulting trends with an analytical model. We conclude by enumerating the next steps in developing an image coaddition pipeline for Roman.

Simulating image coaddition with the Nancy Grace Roman Space Telescope: II. Analysis of the simulated images and implications for weak lensing

Abstract

One challenge for applying current weak lensing analysis tools to the Nancy Grace Roman Space Telescope is that individual images will be undersampled. Our companion paper presented an initial application of Imcom - an algorithm that builds an optimal mapping from input to output pixels to reconstruct a fully sampled combined image - on the Roman image simulations. In this paper, we measure the output noise power spectra, identify the sources of the major features in the power spectra, and show that simple analytic models that ignore sampling effects underestimate the power spectra of the coadded noise images. We compute the moments of both idealized injected stars and fully simulated stars in the coadded images, and their 1- and 2-point statistics. We show that the idealized injected stars have root-mean-square ellipticity errors (1 - 6) x 10-4 per component depending on the band; the correlation functions are >= 2 orders of magnitude below requirements, indicating that the image combination step itself is using a small fraction of the overall Roman 2nd moment error budget, although the 4th moments are larger and warrant further investigation. The stars in the simulated sky images, which include blending and chromaticity effects, have correlation functions near the requirement level (and below the requirement level in a wide-band image constructed by stacking all 4 filters). We evaluate the noise-induced biases in the ellipticities of injected stars, and explain the resulting trends with an analytical model. We conclude by enumerating the next steps in developing an image coaddition pipeline for Roman.
Paper Structure (21 sections, 71 equations, 20 figures, 1 table)

This paper contains 21 sections, 71 equations, 20 figures, 1 table.

Table of Contents

  1. Introduction
  2. Simulated Data
  3. Measurement of noise correlations
  4. Overview
  5. 2D noise power spectra
  6. Azimuthally averaged power spectra
  7. Moments Analysis of the coadded images
  8. Moments of the injected sources
  9. Measurement of stars in the simulated images
  10. Correlation functions of stars in various outputs
  11. Correlations of fourth moments
  12. Estimation of additive noise bias
  13. Synthetic wide band images
  14. Summary and Discussion
  15. Models for the output noise power spectra in the absence of sampling effects
  16. ...and 6 more sections

Figures (20)

  • Figure 1: Coadded injected GalSim stars (left), white noise (center) and $1/f$ noise (right) realizations, displayed as 3-color F184 (red)/J129 (green)/Y106 (blue) combinations. Each image shows a $700\times 700$ output pixel ($17.5\times 17.5$ arcsec) region of the coadded images, from the gsstar14, whitenoise1, and 1fnoise2 layers, respectively. The color scale is a fourth-root stretch (0 to 0.2 input flux per input pixel) in the injected star image (left); and for the noise realizations it is linear, spanning $\pm 1.25$ (center) or $\pm 4$ (right) in input units. Note that the input white noise layer leads to output noise correlated on the scale of the input pixels, whereas the $1/f$ noise layer shows the characteristic striping at each of the 2 input rolls. These rolls are at different angles in each filter, hence the color pattern. The region shown is $270\le x<970$, $301\le y<1001$ of block (2,30).
  • Figure 2: 2D averaged power spectrum of the white noise field of each band, plotted on a logarithmic color scale. The horizontal and vertical axes show wave vector components ($u$ and $v$ respectively) ranging from $-20$ to $+20$ cycles arcsec$^{-1}$. The color scale shows the power $P(u, v)$ in units of arcsec$^2$ (Eq. \ref{['eq:P2D']}). The minimum and maximum values of each power spectrum are as follows: $6.6 \times 10^{-8}$ to $6.7 \times 10^{-3}$ for Y106; $3.4 \times 10^{-8}$ to $3.5 \times 10^{-3}$ for J129; $5.9 \times 10^{-8}$ to $3.2 \times 10^{-3}$ for H158; and $2.0 \times 10^{-8}$ to $4.8 \times 10^{-3}$ for F184.
  • Figure 3: The 2D averaged power spectrum of the coadded $1/f$ noise field of each band, plotted on a logarithmic color scale. The horizontal and vertical axes show wave vector components ($u$ and $v$ respectively) ranging from $-20$ to $+20$ cycles arcsec$^{-1}$. The color scale shows the power $P(u, v)$ in units of arcsec$^2$ (Eq. \ref{['eq:P2D']}). The minimum and maximum values of each power spectrum are as follows: $1.8 \times 10^{-6}$ to $5.4 \times 10^1$ for Y106; $8.5 \times 10^{-7}$ to $4.6 \times 10^1$ for J129; $6.9 \times 10^{-7}$ to $4.8 \times 10^1$ for H158; and $2.1 \times 10^{-7}$ to $5.6 \times 10^1$ for F184. The X-shape, $+$ sign, spots (in H158 and F184), and vertical fringes (in J129) are discussed in the main text.
  • Figure 4: Top row: 1D power spectra for the output white noise fields in each filter. Bottom row: 1D power spectra for the output $1/f$ noise fields in each filter. Each filter's spectra are divided into five even-width bins of mean coverage ("mc" in short), and plotted against the analytical expectation for noise power spectra for combining 5 exposures in the absence of sampling issues (see Appendix \ref{['app:out-noise']} for derivations).
  • Figure 5: Zoomed in image of the central features in the input white noise power spectra. By stretching the color scale we can see more clearly that the zero-wavenumber modes do not contribute the most to power in the output noise, particularly in Y106.
  • ...and 15 more figures