ABSTRACT WANNA, NADIM GEORGE. Design of Reflective Optical Systems. (Under the direction of Thomas A. Dow). The primary objective of this research is to develop optical and opto-mechanical design procedures for reflective optical systems. Challenges in fabrication and testing have limited the choice of surfaces used in the design of reflective optical systems to rotationally symmetric surfaces. Freeform surfaces or non-rotationally symmetric surfaces are necessary to meet challenging performance and packaging requirements. To gain familiarity with optical and opto-mechanical design techniques, two systems were considered: a two mirror Ritchey-Chrétien telescope and a Three Mirror Anastigmat. The two mirror Ritchey-Chrétien optical system using rotationally symmetric hyperbolic surfaces is designed. The opto-mechanical design incorporates the use of radial and axial fiducial surfaces to locate the two mirrors onto a tube relating the optical surfaces to each other and to the detector through a spacer plate. Optical performance improvement over the two mirror telescope is achieved with the addition of a third mirror. The Three Mirror Anastigmat (TMA) optical design uses off- axis conic sections of a rotationally symmetric system. Further improvement to the optical performance is achieved with a freeform TMA optical system and optical surface fabrication feedback to the designer. Opto-mechanical design of the TMA incorporates the use of a telescope frame to constrain each mirror in six degrees of freedom and relate the optical surfaces to each other and to the detector. The mirrors are held in place through independent mounting clamps to sustain high gravitational acceleration with minimum optical surface distortion. The two mirror telescope optical performance is limited by optical aberrations especially at high field angles. Locating the mirrors on a tube over-constrains the components and distorts the optical surfaces. Multiple assembly configurations or non-repeatability is due to symmetry of mounting screws. Impressive optical performance, 58 times wavefront error improvement over the two mirror system, is achieved with an unobstructed TMA optical system using freeform surfaces. A snap-together repeatable assembly without adjustments is designed using conventional fiducial techniques and independent mounting clamps minimizing optical surface distortion. DESIGN OF REFLECTIVE OPTICAL SYSTEMS by NADIM G. WANNA A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science MECHANICAL AND AEROSPACE ENGINEERING NORTH CAROLINA STATE UNIVERSITY Raleigh, NC 2006 APPROVED BY: Dr. Ron Scattergood Dr. Jeffrey Eischen Dr. Thomas Dow BIOGRAPHY Nadim Wanna was born and raised in Beirut, Lebanon. He graduated from Saint Joseph School in 2000 and then entered the American University of Beirut before transferring to the Department of Mechanical and Aerospace Engineering at North Carolina State University in Raleigh, NC. While an undergraduate at North Carolina State University, Nadim participated in research on object transportation theory in the Precision Engineering Center under the direction of Dr. Ro for six months. Nadim also interned at Lebanon Chemicals Company in Beirut, Lebanon during the summer of 2004. After completing his Bachelor of Science in Mechanical Engineering with High Distinction in 2004, Nadim pursued his Masters in the spring of 2004 at North Carolina State University. ii ACKNOWLEDGEMENTS I would like to express my sincere gratitude to the invaluable experience gained with pursuing my Masters. I would like to individually thank: • Dr. Dow, my advisor for his great knowledge, constant pursue of excellent, and his support and guidance. • Dr. Eischen and Dr. Scattergood, my committee members, for being part of this research. • Alex Sohn and Ken Garrard, for all the help, support, and knowledge. • Lucas Lamonds and Rob Woodside, for making this project a wonderful experience. • Lara Masters, Roxie Gold, and Donna Irwin, for answering all the questions. • The rest of the students at the PEC, Brett, Nathan, Kara, Dave, Yanbo, Tim, Quenyi, and Arun. • Tarek Salloum and Nabil Attallah for all the support throughout the years. • To my parents, George and Amal Wanna, and my brother Bassam for always being there for me and their endless support. Thank you for everything. iii TABLE OF CONTENTS LIST OF FIGURES ........................................................................................................ vii LIST OF TABLES ............................................................................................................ x 1 INTRODUCTION..................................................................................................... 1 1.1 BACKGROUND...................................................................................................... 1 1.1.1 Two Mirror Optical Designs........................................................................... 2 1.1.2 Three Mirror Optical Designs ........................................................................ 2 1.2 PREVIOUS RESEARCH........................................................................................... 3 1.2.1 Freeform Optics.............................................................................................. 3 1.2.2 Freeform Fabrication ..................................................................................... 4 1.2.3 Freeform Metrology........................................................................................ 5 1.2.4 Opto-Mechanical Design................................................................................ 6 1.3 PROBLEM STATEMENT ......................................................................................... 8 2 OPTICAL DESIGN OF TWO MIRROR TELESCOPE...................................... 9 2.1 INTRODUCTION .................................................................................................... 9 2.2 CONFIGURATION ................................................................................................ 10 2.2.1 Size and Shape .............................................................................................. 10 2.2.2 Detector......................................................................................................... 12 2.2.3 Optimization.................................................................................................. 13 2.3 THEORETICAL PERFORMANCE............................................................................ 17 2.3.1 Aberrations ................................................................................................... 18 2.3.1.1 Astigmatism .......................................................................................... 18 2.3.1.2 Coma..................................................................................................... 19 2.3.1.3 Spherical Aberration ............................................................................. 22 2.3.2 Wavefront Analysis ....................................................................................... 23 2.3.3 Modulation Transfer Function...................................................................... 26 2.3.4 Spot Diagram................................................................................................ 28 2.4 SENSITIVITY ANALYSIS...................................................................................... 29 3 OPTOMECHANICAL DESIGN OF TWO MIRROR TELESCOPE .............. 32 3.1 INTRODUCTION .................................................................................................. 32 3.2 MATERIAL ......................................................................................................... 32 3.3 STRUCTURE........................................................................................................ 32 3.3.1 Telescope Support......................................................................................... 33 3.3.2 Camera Support............................................................................................ 37 3.3.3 Manufacturing Feasibility ............................................................................ 38 3.4 TWO MIRROR DESIGN CONCLUSION .................................................................. 39 3.4.1 Dual Pass Measurements.............................................................................. 39 3.4.2 Aspect Ratio .................................................................................................. 42 3.4.3 Primary Mirror Structure ............................................................................. 43 3.4.4 Secondary Mirror Structure.......................................................................... 47 iv 4 OPTICAL DESIGN OF TMA ............................................................................... 49 4.1 INTRODUCTION .................................................................................................. 49 4.2 CONFIGURATION ................................................................................................ 50 4.2.1 TMA using Conic Surfaces............................................................................ 50 4.2.1.1 Size and Shape of Conic Surfaces ........................................................ 50 4.2.1.2 Detector................................................................................................. 51 4.2.1.3 Optimization of Conic Surfaces...........................................................