MISALIGNMENT INDUCED NODAL ABERRATION FIELDS AND THEIR USE IN THE ALIGNMENT ...

291 Pages·2010·12.45 MB·English

by  Tobias Schmid

MISALIGNMENT INDUCED NODAL ABERRATION FIELDS AND THEIR USE IN THE
ALIGNMENT OF ASTRONOMICAL TELESCOPES

by

TOBIAS SCHMID
Dipl. Ing. University of Applied Sciences, Regensburg, Germany, 2004
M.S. University of Central Florida, USA, 2006

A dissertation submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy
in the College of Optics and Photonics
at the University of Central Florida
Orlando, Florida

Summer Term
2010

Major Professor: Jannick P. Rolland
© 2010 Tobias Schmid

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ABSTRACT
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-Chrétien (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.
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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
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astronomical telescopes, the methods and algorithms developed in this work can be equally
applied to any imaging system.

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To my wife Noel and son Carsten.

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ACKNOWLEDGMENTS
I would like to thank Dr. Roland Schiek, a former professor during my studies in electrical
engineering, who motivated and supervised my first research projects in optics, together with Dr.
George Stegeman.
I started my graduate degree in optics at CREOL – The College of Optics and Photonics
in 2005 and after initial work in the development of sources for EUV – Lithography I focused
my dissertation research on the aberration theory of optical systems without symmetry.
Many thanks to Optical Research Associates, Pasadena, California, for providing a
student license for CODE V and LightTools, and also for an opportunity to do an internship in
the engineering group in Fall 2008. Special thanks for numerous discussions, especially with Dr.
John Tamkin, Dr. John Rogers, John Isenberg, Matthew Rimmer, Dr. Mary Kate Crawford, and
Dave Hasenauer for engineering work. I also would like to thank Brian McGrath, Aaron
Kruglyak, Dr. Mike Hayford, Dr. Bill Cassarly, Mike Zollers for valuable discussions
concerning software testing.
Special thanks to my advisor Prof. Jannick Rolland who motivated and enabled my
research and helped me improve my writing skills and to Dr. Kevin Thompson (Optical Research
Associates) for the extensive theoretical and historical input. I also would like to extend special
thanks to Dr. Andrew Rakich for numerous discussions on telescope alignment, and specifically
on many discussions involving practical considerations. Much thank also to Dr. Jacques Sebag,
William Gressler, and Douglas Neill from LSST Corporation/NOAO for the joint work on an
alignment strategy for the Large Synoptic Survey Telescope.
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I also would like to thank my current and previous labmates/officemates: Dr. Ozan
Cakmakci, Florian Fournier, Kyle Fuerschbach, Sophie Vo, Dr. Kye-Sung Lee, Panomsak
Meemon, Dr. Supraja Murali, Ilhan Kaya, Bob Gray , and Cristina Canavesi.

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TABLE OF CONTENTS
LIST OF FIGURES ........................................................................................................................... XII
LIST OF TABLES ............................................................................................................................. XX
CHAPTER 1: INTRODUCTION .................................................................................................. 1
1.1. Historical Perspective of Reflective Astronomical Telescopes ...................................... 1
1.2. Alignment Methods for Astronomical Telescopes ......................................................... 9
1.3. Motivation ..................................................................................................................... 11
1.4. Research Summary ....................................................................................................... 14
1.5. Dissertation Outline ...................................................................................................... 17
CHAPTER 2: NODAL ABERRATION THEORY FOR OPTICAL SYSTEMS WITHOUT
SYMMETRY ........................................................................................................ 19
2.1 Concepts and Definitions .............................................................................................. 19
2.2 Local Coordinate System Paraxial Raytrace................................................................. 23
2.2.1 Definition of Surface Local Object/Image and Entrance/Exit-Pupil Planes ............. 24
2.2.2 Definition of an Equivalent Tilt Parameter for a Spherical Surface: β# ................ 25
0
2.2.3 Locating the Centers of the Local Objects/Images (Q, Q’) and Entrance/
Exit-Pupils (E,E’) ..................................................................................................... 26
2.2.4 Parameterizing the OAR ........................................................................................... 29
2.3 The Vector that Locates the Center of the Aberration Field Symmetry for a Tilted
and Decentered Surface ................................................................................................ 31
2.3.1 Shifted Aberration Field Center Associated with the Spherical Base Curve σ(sph) . 31
2.3.2 Shifted Aberration Field Center Associated with the Aspheric Departure from the
Spherical Base Curve σ(asph) .................................................................................... 33
2.4 Real-Ray Equivalent Approach to Find Individual Surface Aberration Field Centers 34
2.5 Nodal Properties of Third Order Aberrations ............................................................... 36
2.5.1 Concept of Shifted Aberration Field Centers and Effective Field Height ................ 37
2.5.2 Third Order Spherical Aberration in Optical Systems Without Symmetry .............. 40
2.5.3 Third Order Coma in Optical Systems Without Symmetry ...................................... 41
2.5.4 Third Order Astigmatism in Optical Systems Without Symmetry ........................... 47
2.5.5 Third Order Medial Focal Surface in Optical Systems Without Symmetry ............. 53
CHAPTER 3: MISALIGNMENT ABERRATION FIELDS IN ASTRONOMICAL
TELESCOPES ...................................................................................................... 57
3.1 Definition of Structural and Systems Parameters ......................................................... 58
3.2 Wave Aberration Coefficients for Two-Mirror Telescopes .......................................... 61
3.3 Effects Induced By Transverse Misalignments ............................................................ 65
3.3.1 Misalignment Induced First Order Effects/Boresight Error ..................................... 66
3.3.2 Locating the Aberration Field Centers in Misaligned Two-Mirror Telescopes ....... 68
3.3.3 Third Order Nodal Aberrations in Misaligned Two-Mirror Telescopes and
Computation of Misalignment Parameters ............................................................... 79
3.4 Pivot Points in Two-Mirror Telescopes ........................................................................ 90
3.4.1 Rotations of a Mirror about its Center of Curvature ................................................. 90
3.4.2 Rotations of a Mirror about the Coma-Free Pivot Point ........................................... 93
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3.5 A Unique Astigmatic Nodal Property in Misaligned Cassegrain, Gregorian, and
Ritchey-Chrétien Telescopes With Misalignment Coma Removed ........................... 103
3.5.1 Nodal Constraints of a Coma-Aligned Cassegrain or Gregorian Telescope
with the Aperture Stop Located on the Primary Mirror .......................................... 106
3.5.2 Nodal Constraints of a Coma-Aligned Ritchey-Chrétien or Aplanatic Gregorian
Telescope Assuming the Aperture Stop is Located on the Primary Mirror ............ 110
CHAPTER 4: MISALIGNMENT ABERRATION FIELDS IN THREE-MIRROR
ANASTIGMATIC ASTRONOMICAL TELESCOPES .................................... 118
4.1 Abberation Fields of Telescope Configurations Throughout the 20th Century .......... 118
4.2 Application of Nodal Aberration Theory to Derive the Dominant Characteristic
Response of any TMA Telescope to Misalignments .................................................. 121
4.3 Interpretation of the Dominant, Characteristic Misaligned TMA Aberration Field
Response Functions .................................................................................................... 127
4.4 Application – James-Webb-like Space Telescope ...................................................... 129
4.4.1 Utilizing Full-Field-Displays to Explore the Effects of Misalignments on the
Aberration Fields .................................................................................................... 130
4.4.2 Developing Expressions for Misalignment Parameters based on Nodal Aberration
Theory ..................................................................................................................... 147
CHAPTER 5: ABERRATION FIELD RE-CONSTRUCTION BASED ON SPARSE
WAVEFRONT MEASUREMENTS .................................................................. 154
5.1 Prediction of Point Spread Functions for Misaligned Astronomical Telescopes ....... 154
5.2 Discussion of the Minimum Field Sampling to Fully Re-Construct the Aberration
Fields ........................................................................................................................... 160
5.2.1 Third Order Spherical Aberration ........................................................................... 161
5.2.2 Third Order Coma ................................................................................................... 162
5.2.3 Third Order Astigmatism ........................................................................................ 165
5.3 Effects of Uncertainties in the Wavefront Measurement on the Accuracy in the
Prediction of Misalignment Parameters ...................................................................... 170
CHAPTER 6: DISTINGUISHING PRIMARY MIRROR FIGURE ERROR FROM
MISALIGNMENT INDUCED ASTIGMATISM IN ASTRONOMICAL
TELESCOPES .................................................................................................... 173
6.1 Consequences of Actively Controlled Primary Mirrors in the Context of Telescope
Alignment ................................................................................................................... 174
6.2 Formulating Nodal Aberration Theory of a Misaligned Ritchey-Chrétien Telescope
with Astigmatic Figure Error on the Primary Mirror.................................................. 176
6.3 Binodal Response of the Astigmatic Field Dependence of a Ritchey-Chrétien
Telescope with Primary Mirror Astigmatic Figure Error ........................................... 183
6.4 Binodal Response of the Astigmatic Field Dependence of a Ritchey-Chrétien
Telescope with Misalignments and Astigmatic Figure Error ..................................... 184
6.4.1 Conditions Imposed as a Result of Aligning a Ritchey-Chrétien Telescope to
Remove Field-Constant Coma ................................................................................ 185
6.4.2 Conditions Resulting from Primary Mirror Astigmatic Figure Error and
Misalignments in a Ritchey-Chrétien Telescope .................................................... 186
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