Year: 2018
Type: article
Abstract: Driven by the development of freeform four-mirror solutions, we review and compare analytical methods to generate starting point designs with various states of correction, surface types, symmetry, and obscuration. The advantages and disadvantages of each are examined. We have combined several concepts and techniques from the literature to analytically generate unobscured freeform starting point designs that are corrected through the third-order image degrading aberrations. The surfaces in these starting point designs are described as base off-axis conics that image stigmatically for the central field point, also known as Cartesian reflectors, with an aspheric departure “cap” (quartic with the aperture) added to the Cartesian reflectors. Tilt angles are chosen to cancel field-asymmetric field-linear astigmatism and unobscure the system. Paraxial data from an equivalent on-axis system are used to solve a system of linear equations to determine the magnitude of the aspheric departure “caps” that are placed on top of the base Cartesian reflectors, in order to eliminate the remaining third-order image degrading aberrations. In this approach, each aspheric departure “cap” is centered about the intersection of the optical-axis-ray, also known as the base ray, with the base surface, rather than being centered about the axis of rotational invariance.
Source: Optical Engineering
Language: English
Subfield: Biomedical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Awards: I/UCRC: Collaborative Research: Center for Freeform Optics, FOUR-MIRROR FREEFORM REFLECTIVE IMAGING SYSTEMS CENTRAL OBJECTIVES: THE RESEARCH INVOLVES A REVELATION OF THE SOLUTION SPACE FOR REVOLUTIONARY FAMILIES OF FOUR-MIRROR FREEFORM REFLECTIVE IMAGING SYSTEMS. A FREEFORM OPTICAL SYSTEM IS ONE THAT LACKS ROTATIONAL SYMMETRY MEANING THERE IS NO CONSTRAINT ON THE SURFACE SHAPE OF THE MIRRORS. FREEFORM DESIGNS CAN MITIGATE THE DISADVANTAGES THAT PREVENT REFLECTIVE SYSTEMS FROM BEING USED IN LARGER FIELD OF VIEW APPLICATIONS BY YIELDING UNOBSCURED DESIGNS AND LEVERAGING THE ADDED FREEDOM OF SURFACE SHAPE TO BETTER CORRECT THE OPTICAL ABERRATIONS IN THE SYSTEM. FREEFORM DESIGNS ARE MADE UNOBSCURED BY BREAKING THE AXIS OF ROTATIONAL-SYMMETRY AND TILTING THE INDIVIDUAL ELEMENTS THEMSELVES. THEY DO NOT REQUIRE AN OFFSET APERTURE OR FIELD BIAS WHICH BRINGS A UNIQUE ADVANTAGE IN THE CORRECTION OF OPTICAL ABERRATIONS. BY GETTING THE MIRRORS OUT OF THEIR OWN WAY MORE SURFACES CAN BE INTRODUCED. WHEN COMPARED TO ALTERNATE SOLUTIONS WHETHER IT IS A ROTATIONALLY SYMMETRIC SYSTEM OR AN UNOBSCURED SYSTEM WITH THE SAME NUMBER OF ELEMENTS AN INCREASED DIFFRACTION-LIMITED FIELD OF VIEW HAS BEEN DEMONSTRATED IN OUR GROUP S RESEARCH. METHODS/TECHNIQUES: THE EXPLORATION OF THE SOLUTION SPACE WILL BE ACCOMPLISHED BY EXPANDING UPON THE WORK OF ANDREW RAKICH WHO DERIVED THE ANALYTICAL SOLUTION SPACE FOR FOUR-MIRROR ANASTIGMAT TELESCOPES. THE SYSTEMS THAT ARE YIELDED FROM HIS METHOD HAVE SPHERICAL SURFACES AND AN AXIS OF ROTATIONAL SYMMETRY. THESE DESIGNS WILL BE USED AS STARTING POINTS FOR SUBSEQUENT FREEFORM DESIGNS. LENS DESIGN SOFTWARE WILL BE USED TO OPTIMIZE THE DESIGN AS THE ELEMENTS ARE TILTED. WHEN TILTING ELEMENTS VERY STRONG ASTIGMATISM IS INTRODUCED. THEREFORE TOROIDAL BASE MIRRORS FOR THE FREEFORM SURFACES ARE NEEDED FOR CORRECTION. ZERNIKE POLYNOMIALS ARE THEN INTRODUCED TO THE TOROIDAL BASE SHAPES TO FURTHER CORRECT THE SYSTEM. THE RESEARCH AIMS TO EXPLORE A VARIETY OF TARGETED RESEARCH QUESTIONS THAT AIM TO ADDRESS SPACE TECHNOLOGY CHALLENGES. THE SENSITIVITY OF THE DESIGNS FROM THE SOLUTION SPACE TO COMMON TOLERANCES WILL BE STUDIED USING FULL-FIELD DISPLAYS THAT ISOLATE EACH ABERRATION AND SHOW ITS DEPENDENCE OVER THE FIELD COMBINED WITH NODAL ABERRATION THEORY THAT PUTS TOLERANCES IN LINEAR SPACE MAKING THE SENSITIVITY CALCULATION EFFICIENT AND COMPLETE. SPECIAL ATTENTION WILL BE PAID TO GEOMETRIES THAT MAY BE MORE CONDUCIVE TO STRAY LIGHT REDUCTION THROUGH THE USE OF BAFFLES. SIMILARLY OTHER GEOMETRIES MAY BE MORE CONDUCIVE TO RADIATION SHIELDING BY USING THE MIRROR SUBSTRATES THEMSELVES AS PART OF THE SHIELDING. THE ADDED FLEXIBILITY OF FOLDING GEOMETRY ALLOWS FOR THE DESIGN TO BE TAILORED TO SYSTEM ENGINEERING CONSTRAINTS THAT COULD NOT BE ADDRESSED WITH ROTATIONALLY SYMMETRIC SYSTEMS OR UNOBSCURED NON-FREEFORM SYSTEMS. DESIGN APPROACHES TO ACHIEVE THESE CHARACTERISTICS WILL BE DEVELOPED. SIGNIFICANCE: THIS RESEARCH WILL ADDRESS NASA INTERESTS AS PER THE JULY 2015 TECHNOLOGY ROADMAP ITEM TA 8.2.1.3. A KEY DRIVING ASPECT OF THIS WORK WILL BE TO FOCUS ON REVEALING KEY FLAT FIELD LARGE LOW COST LIGHTWEIGHT PRECISION MONOLITHIC MIRRORS THAT PROVIDE A HIGH DEGREE OF THERMAL AND DYNAMIC STABILITY AND WAVEFRONT SENSING AND CONTROL FOR ULTRA-STABLE LARGE-APERTURE UV/VISIBLE/NEAR-IR TELESCOPES. THIS RESEARCH IS DIRECTLY RELEVANT TO THE OBSERVATORIES LEVEL 2 TABS ELEMENT 8.2. MORE SPECIFICALLY IT IS RELEVANT TO THE LEVEL 3 TABS ELEMENT MIRROR SYSTEMS. THE SIGNIFICANCE OF THIS WORK IS TO PROVIDE IMAGING SYSTEM DESIGNS WITH LARGER DIFFRACTIONLIMITED ETENDUES THAN THE STATE-OF-THE-ART (MEANING LARGER APERTURES AND FIELDS OF VIEW) WHICH WILL MAKE THE MOST OF LIMITED PACKAGE SIZES AND MASS CONSTRAINTS. THIS WILL ADVANCE THE OPTICAL INSTRUMENTATION ON SPACE PROBES AS WELL AS OBSERVATORIES ON THE GROUND TOWARDS NEW SPACE DISCOVERIES AND KNOWLEDGE, I/UCRC: Collaborative Research: Center for Freeform Optics
OpenAlex ID: W2809783833