Hubble Space Telescope · 1990s

Image sharpness

The PSF figure of merit that sets point-source signal-to-noise.

Definition

S = Σ P², the sum of the squared normalised PSF over pixels

Meaning

1/S is the effective number of pixels contributing background noise

Typical values

≈ 0.11 for the WFPC2 Wide Field Camera, ≈ 0.06 for the Planetary Camera

Written up in

Brown & Burrows 1990 (Icarus 87, 484); WFPC2 Instrument Handbook (1994); Appendix D, “Sharpness”, in Bely (ed.), The Design and Construction of Large Optical Telescopes (Springer 2003), pp. 433–435

Adopted by

Kasdin & Braems (Princeton MAE), Bayesian hypothesis testing for planet detection

Chris defined sharpness as the integral of the square of the normalised point-spread function, sampled on the detector's pixels. For a background-limited point source it is the quantity that matters: the signal-to-noise ratio of an optimal PSF fit scales as the square root of the sharpness, so 1/S acts as the effective number of noise pixels.

He introduced it in the WFPC2 Instrument Handbook, which he wrote, where tables give sharpness by camera, wavelength and the star's position within a pixel, and observers still use it to estimate exposure times. The term already appears in Brown and Burrows (1990), on detecting extrasolar planets with Hubble, and his note on it became an appendix, “Sharpness”, in Pierre Bely's book The Design and Construction of Large Optical Telescopes (Springer, 2003), for which he is also listed among the contributors and reviewers, for image quality.

Jeremy Kasdin of Princeton's Mechanical and Aerospace Engineering department later carried it into the planet-detection literature. His work with Isabelle Braems on planet-detection algorithms for the Terrestrial Planet Finder (preprint 2004; ApJ 646, 1260, 2006) attributes the term to Brown and Burrows (1990), as the ratio of PSF area to pixel area in the signal-to-noise expression. Mighell (2005) used the same definition for discrete-PSF photometry.

Papers

• 2003
  Sharpness (Appendix), in The Design and Construction of Large Optical Telescopes, P. Y. Bely (ed.), pp. 433–435

  Burrows, C. J.

  Springer-Verlag, New York

  DOI (book)
• 1990
  On the feasibility of detecting extrasolar planets by reflected starlight using the Hubble Space Telescope

  Brown, R. A.; Burrows, C. J.

  Icarus 87, 484

  DOI
• 1994
  Wide Field and Planetary Camera 2 Instrument Handbook, Version 2.0 (May 1994)

  Burrows, C. J. (Ed.), with Griffiths, R. E.; Krist, J.; MacKenty, J. W.; et al.

  STScI

  PDF
• 2004
  Bayesian hypothesis testing for planet detection (published as Kasdin & Braems, Linear and Bayesian planet detection algorithms for the Terrestrial Planet Finder, ApJ 646, 1260, 2006)

  Braems, I.; Kasdin, N. J.

  arXiv astro-ph/0404220

  arXivApJ 2006
• 2005
  Stellar photometry and astrometry with discrete point spread functions

  Mighell, K. J.

  MNRAS 361, 861

  ArticlearXiv