aberration theory, astronomical instrumentation, alignment


Following the foundation of aberration theory for rotationally symmetric optical systems established by Seidel, Schwarzschild, Burch, Conrady, Buchdahl, and in its most useful form H.H. Hopkins, Shack, Buchroeder, Thompson, and Rogers developed a vectorial form of the wave aberration theory that enables addressing optical systems without symmetry. In this research, a vectorial theory is utilized and extended for the alignment of two- and three-mirror astronomical telescopes, including the effects of pointing changes and astigmatic figure errors. Importantly, it is demonstrated that the vectorial form of aberration theory, also referred to as nodal aberration theory, not only provides valuable insights but also facilitates a quantitative description of the aberrations in optical systems without symmetry. Specifically, nodal aberration theory has been utilized to establish key insights into the aberration field response of astronomical telescopes to misalignments. Important nodal properties have been derived and discussed and the theoretical predictions have been validated with optical design software. It has been demonstrated that the removal of on-axis coma in some of the most common astronomical telescopes in use today directly leads to a constraint for one of the nodes for astigmatism to be located at the field center, which is exactly true for Cassegrain or Gregorian telescopes, and approximately true for Ritchey-Chretien (or aplanatic Gregorian) telescopes. These observations led to important conclusions concerning the alignment of astronomical telescopes. First, the correction of these telescopes on-axis for zero coma removes all misalignment induced aberrations only on-axis. Secondly, given that the image quality at the field center remains stigmatic in the presence of misalignments, for these telescopes non-zero astigmatism measured at the field-center directly reveals astigmatic mirror figure errors. Importantly, the effects of misalignments and astigmatic figure error can be clearly distinguished if present in combination, even in the presence of significant boresight errors. Having the possibility to clearly distinguish between misalignment and astigmatic mirror figure error provides an important prerequisite for the optimal operation of active/adaptive optics systems that are becoming standard in observatory class telescopes. Subsequent work on TMA telescopes revealed that even though TMAs are limited by fifth order aberrations in their nominal alignment state, third order nodal aberration theory provides accurate image quality predictions for misalignments and astigmatic figure (third order) effects in these optical systems. It has been demonstrated for the first time that analytical expressions can be devised that describe the characteristic misalignment induced aberration fields of any TMA telescope, leading to two main image quality degrading aberrations, field-constant coma and field-linear, field-asymmetric astigmatism. These new insights can be strategically leveraged in the development of alignment strategies for TMAs. The final part of this work analyzed how third and fifth order nodal aberration fields can be utilized in the alignment of wide-angle telescopes, with the specific example of the Large Synoptic Survey Telescope (LSST). In cooperation with the National Optical Astronomy Observatory (NOAO) an alignment strategy has been developed for the LSST (without camera) to expedite the commissioning of the telescope, providing for the first time analytical expressions for the computation of misalignment parameters in three-mirror telescopes, taking into account fabrication tolerances for the alignment of the tertiary mirror on the primary mirror substrate. Even though the discussion has been focused primarily on alignment strategies of astronomical telescopes, the methods and algorithms developed in this work can be equally applied to any imaging system.


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Graduation Date



Rolland, Jannick


Doctor of Philosophy (Ph.D.)


College of Optics and Photonics


Optics and Photonics

Degree Program









Release Date

August 2010

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)