Several factors impact the light irradiance and relative illumination produced by a lens system at its image plane. In addition to the cosine-fourth-power radiometric law, image and pupil aberrations, and light vignetting also count. In this paper, we use an irradiance transport equation to derive a closed form solution that provides insight into how individual aberration terms affect the light irradiance and relative illumination. The theoretical results are in agreement with real ray tracing.

Several factors impact the light irradiance and relative illumination produced by a lens system at its image plane. In addition to cosine-fourth-power radiometric law, image and pupil aberrations and light vignetting also count. We use an irradiance transport equation to derive a closed form solution that provides insight into how individual aberration terms affect the light irradiance and relative illumination. The theoretical results are in agreement with real ray tracing. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)

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.

Many advances have occurred in the field of optical design during the past decade. Some of the newer topics and concepts associated with the design and use of optical systems are complex and require comprehensive understanding of theory, expertise in state-of-the-art technology, and extensive computer simulations. This dissertation focuses on development of practical methods and tools for successful lens design and evaluation of state-of-the-art imaging and illumination systems. The dissertation addresses several current topics in modern optical engineering and utilizes approaches to provide insights into the inner workings of optical systems. Examples of modern mobile camera lenses are provided to show how specific methods can help to better understand these lens designs and to expand the imaging capabilities of miniature camera systems. Two simple but effective real ray tracing methods for correcting chromatic aberrations in imaging systems are described. The proposed methods separate monochromatic and chromatic aberration correction into two independent problems. This two-step approach provides effective alternatives in correcting chromatic aberrations. A number of unique calculations have been performed and some novel and interesting theoretical results, including the fourth-order theory of irradiance changes in axially symmetric optical systems, are reported. The specific relationships between the irradiance distribution and wavefront aberration coefficients to fourth order are derived for the first time. The practical case of relative illumination at the image plane of an optical system is also discussed in some detail.

A detailed study of the aberrations of anamorphic optical systems is presented. This study has been developed with a theoretical structure similar to that of rotationally symmetric optical systems (RSOS) and can be considered a generalization.A general method of deriving the monochromatic primary aberration coefficient expressions for any anamorphic system types with double plane symmetry has been provided.The complete monochromatic primary aberration coefficient expressions for cylindrical anamorphic systems, toroidal anamorphic systems and general anamorphic systems with aspheric departure have been presented, in a form similar to the Seidel aberrations of RSOS.Some anamorphic image system design examples are provided that illustrate the use and value of the theory developed.

We pose that there is enough information left to reconstruct Petzval lens design approach, and answer the question of how Joseph Petzval design his famous portrait objective.