When symmetry is broken, the wave aberration function generalizes to have not just odd-orders, but also even-orders. Geometric interpretation of the lowest-order coefficients (i.e., second) and insights offered by consideration of these terms is presented.
As the number of smallsats and cubesats continues to increase , so does the interest in the space optics community to miniaturize reflective optical instrumentation for these smaller platforms. Applications of smallsats are typically for the Earth observing community, but recently opportunities for them are being made available for planetary science, heliophysics and astrophysics concepts . With the smaller satellite platforms come reduced instrument sizes that they accommodate, but the specifications such as field of view and working f/# imposed on the smaller optical systems are often the same, or even more challenging. To meet them, and to “fit in the box”, it is necessary to employ additional degrees of freedom to the optical design. An effective strategy to reduce package size is to remove rotational symmetry constraints on the system layout, allowing it to minimize the unused volume by applying rigid body tilts and decenters to mirrors. Requirements for faster systems and wider fields of view can be addressed by allowing optical surfaces to become “freeform” in shape, essentially removing rotational symmetry constraints on the mirrors themselves. This dual approach not only can reduce package size, but also can allow for increased fields of view with improved image quality. Tools were developed in the 1990s to compute low-order coefficients of the imaging properties of asymmetric tilted and decentered systems . That approach was then applied to reflective systems with plane symmetry, where the coefficients were used to create closed-form constraints to reduce the number of degrees of freedom of the design space confronting the designer . In this paper we describe the geometric interpretation of these coefficients for systems with a plane of symmetry, and discuss some insights that follow for the design of systems without closed-form constraints. We use a common three-mirror design form example to help illustrate these concepts, and incorporate freeform surfaces for each mirror shape. In section II, we evoke the typical form of the wave aberration function taught in most texts on geometrical optics, and then recast it into a general form that no longer assumes rotational symmetry. A freeform surface definition for mirrors is then defined, and the example three-mirror system used throughout this paper is introduced. In section III, the first-order coefficients of the plane symmetric system are discussed, and then the second-order in section IV. In both of these discussions, the example system is perturbed to present the explicit form of the aberration coefficient laid out in section II, and plots are presented using optical design software. Finally, some concluding remarks are given in section V.
The M-squared (M2) parameter for defining laser beam quality is a convenient metric to characterize the variation of the beam size and far field divergence of a “real” propagated optical beam, compared with that of an ideal Gaussian beam of the same wavelength. However, it can be problematic to use this parameter solely to characterize an input beam for propagation simulation software. Similar to RMS wavefront error or Strehl ratio, which can be used to define image quality, but do not characterize the shape of the wavefront, different factors can result in beams with identical M2 values, but very different propagation behavior. Beams that differ due to aberrations, non-Gaussian amplitude envelopes, and/or partial spatial coherence may have similar or identical M2 values, but very different far-field and/or near-field intensity and/or phase distributions. The situation is complicated further if the beam encounters non-ideal optics. In this paper, we investigate a number of beams that all have (approximately) the same M2. While M2 is invariant for propagation through an ideal optical system, we show that when an optical system introduces aberrations, it can alter different beams with the same, non-unity M2 in ways that differ significantly from one beam to another.
While system-level simulation can allow designers to assess optical system performance via measures such as signal
waveforms, spectra, eye diagrams, and BER calculations, component-level modeling can provide a more accurate
description of coupling into and out of individual devices, as well as their detailed signal propagation characteristics. In
particular, the system-level simulation of interface components used in optical systems, including splitters, combiners,
grating couplers, waveguides, spot-size converters, and lens assemblies, can benefit from more detailed component-level
modeling. Depending upon the nature of the device and the scale of the problem, simulation of optical transmission
through these components can be carried out using either electromagnetic device-level simulation, such as the beampropagation
method, or ray-based approaches. In either case, system-level simulation can interface to such componentlevel
modeling via a suitable exchange of optical signal data. This paper presents the use of a mixed-level simulation
flow in which both electromagnetic device-level and ray-based tools are integrated with a system-level simulation
environment in order to model the use of various interface components in optical systems for a range of purposes,
including, for example, coupling to and from optical transmission media such as single- and multimode optical fiber.
This approach enables case studies on the impact of physical and geometric component variations on system
performance, and the sensitivity of system behavior to misalignment between components.
Given a beam propagation algorithm, whether it is a commercial implementation or some other in-house or research
implementation, it is not trivial to determine whether it is suitable either for a wide range of applications or even for a
specific application. In this paper, we describe a range of tests with "known" results; these can be used to exercise beam
propagation algorithms and assess their robustness and accuracy. Three different categories of such tests are discussed.
One category is tests of self-consistency. Such tests often rely on symmetry to make guarantees about some aspect of
the resulting field. While passing such tests does not guarantee correct results in detail, they can nonetheless point
towards problems with an algorithm when they fail, and build confidence when they pass. Another category of tests
compares the complex field to values that have been experimentally measured. While the experimental data is not
always known in precisely, and the experimental setup might not always be accessible, these tests can provide
reasonable quantitative comparisons that can also point towards problems with the algorithm. The final category of tests
discussed is those for which the propagated complex field can be computed independently. The test systems for this
category tend to be relatively simple, such as diffraction through apertures in free space or in the pupil of an ideal
imaging system. Despite their relative simplicity, there are a number of advantages to these tests. For example, they can
provide quantitative measures of accuracy. These tests also allow one to develop an understanding of how the execution
time (or similarly, memory usage) scales as the region-of-interest over which one desires the field is changed.
Design methods are described for unobstructed, plane-symmetric, anamorphic systems
composed of three mirrors. Low order imaging constraints are used to reduce the dimensionality of the
configuration space. Examples are presented from a specific class of systems with fixed packaging
There are a variety of aspects of interferometers that can be well-modeled by using rays. For example, ray-based models
allow predictions to be made regarding the changes to a measurement when aberrations are introduced into the input
wavefront. However, there are other aspects that are more difficult (or impossible) to model well with ray-based
approaches. For instance, when a surface under test is not conjugate to the detector, the effects due to diffraction from
the edge of the surface cannot be modeled with ray-based approaches. Modern lens design software generally includes
tools for modeling beam propagation. These tools can be used to go beyond conventional ray-based modeling of
interferometers. In this paper, we demonstrate the utility of these beam propagation tools by modeling various aspects of
a point-diffraction interferometer that go beyond solely ray-based approaches.
Design methods are described for unobstructed, plane-symmetric systems composed of three conic mirrors. Low order imaging constraints (including the requirement of nonanamorphism) are used to reduce the dimensionality of the configuration space. Examples are presented.
Conventional ray tracing cannot always adequately model propagation of optical beams. We compare three approaches for modeling diffraction effects throughout an optical system: (1) FFT-based, (2) Gaussian beam decomposition, and (3) the SAFE method of Forbes and Alonso. The basic idea behind each method is described and some simple examples are given that highlight the main features of each method.
We investigate unobstructed plane-symmetric imaging systems of two spherical mirrors having three- or four-reflections. Geometry constraints are used to ensure that the odd numbered reflections occur on one spherical mirror, and that even numbered reflections occur on a separate spherical mirror. Imaging constraints are used to ensure appropriate first-order behavior. These geometry and imaging constraints eliminate degrees of freedom from the configuration space, thereby simplifying the design process. For the three-reflection systems, the available degrees of freedom are reduced to four, and for four-reflection systems, they are reduced to five. An alternate method using pickup constraints is discussed. Global optimization using simulated annealing is performed, and example systems are presented.
Full acceptance of 157nm technology for next generation lithography requires that critical optical components and systems be characterized at this wavelength. Some of the challenges inherent in the 157nm test regime include purged beam paths, a partially coherent and astigmatic light source, limitations in reflective and transmissive optical components, and immature CCD detector technology. A Twyman-Green interferometer specially devised for testing lithographic objective lenses and systems at 157nm that addresses these challenges is presented. A description of the design and components used is provided along with test results obtained with the interferometer.
The process for designing optomechanical devices usually involves independent design optimization within each discipline. For instance, an optics engineer would optimize the optics of the device for image quality using Computer Aided Engineering (CAE) tools such as CODE V and OSLO. The structural engineer would then optimize the design to minimize deformation using CAE tools such as SDRC I-DEAS and MSC/NASTRAN. That is, the optics and structure are typically optimized independent of each other. In this paper, two additional methods for optimizing optomechanical devices are investigated. One method involves sequential design optimization. The other method involves the simultaneous design optimization of both the optics and structure of an optomechanical device. Two example problems are used to ex;lore the types of problems that each method is most suitable for. The first example involves an optomechanical device under thermal and gravity load, while the second example involves two thin lenses resting on a cantilevered beam.
It is impossible for a zoom lens to image perfectly throughout its zoom range. That is, regardless of how complex a zoom system is made, there are necessarily residual aberrations. The principles of Hamiltonian optics can be used to determine the smallest level of such residual aberrations for a specific set of design requirements: zoom range, field of view, speed, etc. The best imagery that can be achieved by a zoom system, in the geometric limit, is referred to as the fundamental limit. The nature of the residual aberrations at the fundamental limit is investigated for a particular class of zoom system. It is found that the coefficients of the wave aberration function associated with each of the lens groups is not unique at the fundamental limit. As an example, the fundamental limit for a particular zoom system is determined, and the possibility of using this information in design is discussed.