Diffraction analysis of pupil mapping systems for planet finding

Robert J. Vanderbei

Research output: Contribution to journalConference articlepeer-review


Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from starlight, can be mapped into a non-uniformly illuminated exit pupil, such that the image formed from this pupil will have suppressed sidelobes, many orders of magnitude weaker than classical Airy ring intensities. Pupil mapping is therefore a candidate technique for coronagraphic imaging of extrasolar planets around nearby stars. Pupil mapping is lossless and preserves the full angular resolution of the collecting telescope. Prior analyses based on pupil-to-pupil ray-tracing indicate that a planet fainter than 10 -10 times its parent star, and as close as about 2 λ/D, could be detectable. In this paper, we describe the results of careful diffraction analysis of pupil mapping systems. These results reveal a serious unresolved issue. Namely, high-contrast pupil mappings distribute light from very near the edge of the first pupil to a broad area of the second pupil thereby dramatically amplifying diffraction-based edge effects resulting in a limiting attainable contrast of about 10 -5. We provide two hybrid designs that provide partial solutions to this problem but a complete resolution remains open.

Original languageEnglish (US)
Article number590517
Pages (from-to)1-12
Number of pages12
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2005
Externally publishedYes
EventTechniques and Instrumentation for Detection of Exoplanets II - San Diego, CA, United States
Duration: Aug 2 2005Aug 4 2005

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Computer Science Applications


  • Apodization
  • Coronagraphy
  • Diffraction analysis
  • Extrasolar planets
  • Fresnel propagation
  • PIAA
  • Point spread function
  • Pupil mapping


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