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Geometrical theory of aberration for off-axis reflecting telescope and its applications

Geometrical theory of aberration for off-axis reflecting telescope and its applications. Seunghyuk Chang 2013.02.14. SSG13. On-Axis vs Off-Axis. On-Axis. Off-Axis. Secondary mirror blocks incoming rays. No obstruction. Clear aperture. On-Going Off-Axis Telescope Project.

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Geometrical theory of aberration for off-axis reflecting telescope and its applications

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  1. Geometrical theory of aberration for off-axis reflecting telescope and its applications Seunghyuk Chang 2013.02.14. SSG13

  2. On-Axis vs Off-Axis On-Axis Off-Axis Secondary mirror blocks incoming rays. No obstruction. Clear aperture.

  3. On-Going Off-Axis Telescope Project Advanced Technology Solar Telescope (ATST) 4-m aperture, largest solar telescope, off-axis Gregorian design

  4. On-Going Off-Axis Telescope Project Wide Field Infrared Survey Telescope (WFIRST) • Top-ranked large space mission in the New Worlds, New Horizon Decadal Survey of Astronomy and Astrophysics • Sky surveys, Exoplanet – Microlensing, Dark Energy • 1.3m aperture off-axis Three Mirror Anastigmat (TMA) design

  5. Basic Off-Axis Telescope Eccentric section of an on-axis parent system

  6. Confocal Plane-Symmetric Off-Axis Two-Mirror System The mirrors of a confocal system do not need to have a common axis for a perfect image at the system focus

  7. Vertex Equation for Off-Axis Portion of Conic Sections of Revolution • Vertex equation of conic sections of revolution : • A localized coordinate system is convenient to describe a mirror near a point (x0’, z0’)

  8. Expansion of Vertex Equation

  9. Optical Path Length (OPL) Astigmatism Coma • To compute the aberrations, the OPL for an arbitrary reflection point on the mirror is necessary • The OPL is constant in a perfect focusing mirror • The variance of the OPL yields aberrations

  10. Astigmatic Images The second order terms yields the two astigmatic image points Tangential Astigmatic Image: Sagittal Astigmatic Image:

  11. Tilted Astigmatic Image Planes Expanding the two astigmatic image distances to the first order of q yields the tangential and sagittal astigmatic image planes and linear astigmatism Tangential Astigmatic Image Plane Sagittal Astigmatic Image Plane Linear Astigmatism:

  12. IMAGE PLANES OF PARABOLOID On-Axis Off-Axis

  13. Coma and Third Order Astigmatism • The A2 term yields tangential coma aberration • Expanding the two astigmatic image points to second order on q yields third order astigmatism

  14. Aberrations of Classical Off-axis Two-mirror Telescopes • Aberrations of classical off-axis two-mirror telescopes can be obtained by cascading the aberrations of each mirror • Assume the aperture stop is located at the primary mirror

  15. Aperture Stop When aperture stop is displaced from the mirror surface, the reflection point of the chief ray depends on the field angle.

  16. Aperture Stop • A displaced aperture stop yields a new field angle q and a new chief ray incidence angle qs for the mirror

  17. Aperture Stop • A displaced aperture stop yields new astigmatism and coma aberration coefficient.

  18. Aberrations of Classical Off-Axis Two-mirror Telescopes Astigmatism Coma Rm Rs Rm (Rs) is the radius of curvature of the primary (secondary) parent mirror at its vertex.

  19. Linear Astigmatism of a Two-mirror Telescope

  20. Elimination of Linear Astigmatism and Third Order Coma • Linear astigmatism can be eliminated by enforcing • Third order coma is identical to an on-axis paraboloid

  21. Example • D=1000mm, f=2000mm • Satisfies zero-linear-astigmatism condition Astigmatism

  22. Spot Diagram Comparison Example On-Axis Paraboloid Spot diagrams of the two systems are identical as the presented theory predicted

  23. Off-axis On-axis Side View Spot Diagrams Example 1m f/8 classical Cassegrain

  24. Off-axis On-axis Side View Spot Diagrams Example 1m f/20 classical Gregorian

  25. Off-axis On-axis Side View Spot Diagrams Example 2.4m f/24 aplanatic Cassegrain

  26. Spot Diagrams Side View Example 10cm f/4 off-axis Schwarzschild flat-field anastigmat

  27. Off-axis Reflector Design forSPICA Channel 1 MIR Camera Camera Collimator • Both the collimator and the camera are off-axis reflecting telescopes with zero linear astigmatism.

  28. Off-axis Reflector Design forSPICA Channel 4 MIR Camera Camera Collimator • Both the collimator and the camera are off-axis reflecting telescopes with zero linear astigmatism.

  29. 6.5-m TAO Telescope • Mid-infrared re-imaging optics of 6.5m-TAO telescope has been developed based on linear-astigmatism theory.

  30. Off-axis Reflector Design forMcDonald 2.1-m Telescope Focal Reducer Camera Collimator • Both the collimator and the camera are off-axis reflecting telescopes with zero linear astigmatism. • Reduce the telescope focal ratio from f/13.6 to f/4.56

  31. Three-Mirror Off-Axis Telescope Two Mirror vs. Three Mirror R: removable, X:not removable

  32. Linear Astigmatism of Confocal Off-Axis N-Mirror System

  33. Image Planes of Kth mirror inConfocal Off-Axis N-Mirror System : Radius of curvature of the parent mirror at its vertex

  34. Image Planes of Confocal Off-AxisN-Mirror System Tangential image plane: Sagittal image plane:

  35. Elimination of Linear Astigmatism in Confocal Off-axis N-mirror System Two-mirror telescope : Three-mirror telescope :

  36. Advanced Technology Solar Telescope (ATST) • 4m-aperture off-axis Gregorian design • Off-axis section of an on-axis telescope • Gregorian focus does not satisfy linear-astigmatism-free condition • Linear astigmatism can be eliminated by adding M3

  37. Advanced Technology Solar Telescope (ATST) ATST ATST + M3

  38. WFIRST 1.3m-Aperture Off-Axis TMA Telescope

  39. WFIRST 1.3m-Aperture Off-Axis TMA Telescope Linear-astigmatism-free modification

  40. WFIRST 1.3m-Aperture Off-Axis TMA Telescope * : “Wide Field Infrared Survey Telescope [WFIRST]: telescope design and simulated performance,” Proc. SPIE 8442, Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, 84421U (September 21, 2012); doi:10.1117/12.927808

  41. References • S. Chang and A. Prata, Jr., "Geometrical theory of aberrations near the axis in classical off-axis reflecting telescopes," Journal of the Optical Society of America A 22, 2454-2464 (2005) • S. Chang, J. H. Lee, S. P. Kim, H. Kim, W. J. Kim, I. Song, and Y. Park, "Linear astigmatism of confocal off-axis reflective imaging systems and its elimination," Applied Optics 45, 484-488 (2006) • S. Chang, " Off-axis reflecting telescope with axially-symmetric optical property and its applications," Proc. SPIE, Vol. 6265, 626548 (2006) • S. Chang, “Elimination of linear astigmatism in N-confocal off-axis conic mirror imaging system,” in preparation

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