Freeform surfaces offer many advantages in the design of optical systems. To perform STOP analyses[1] of systems containing freeform surfaces, the nominal surface geometry must be accurately represented. Forbes polynomials[2] (sometimes called Q2D polynomials) are often used to represent freeform surfaces in optical design codes. This paper discusses the use of Q2D polynomial surfaces in STOP analysis. Topics include comparison to standard Zernike polynomials and passing finite element results to optics analysis software.
The ultimate design goal of an imaging optical system subjected to thermal and dynamic loads is to minimize system level wavefront error (WFE). System WFE is impossible to predict from finite element random response results due to the loss of phase information. In the past, the use of system WFE was limited by the difficulty of obtaining a linear optics model (LOM). In this paper, an automated method for determining system level WFE using a linear optics model is presented. The technique is applied to a simple telescope using structural optimization to automatically handle the conflicting design requirements of thermal and random response loads. The technique is demonstrated by example with SigFit, a commercially available tool integrating mechanical analysis with optical analysis.
In conducting a STOP analysis, it is often required to convert laser fluence maps or voxel maps from an optical analysis into finite element heat loads for thermal and thermoelastic analyses. These fluence maps are usually represented as a rectangular array at optical surfaces. A technique has been developed to convert these maps into surface and volumetric loads on arbitrary 2D and 3D finite element (FE) meshes. For lenses, any number of intermediate maps through the lens thickness are allowed when more resolution is required. Another output format used by optics codes is three dimensional cubes called voxels. Voxel data can also be converted to FE loads. As data checks, the total heat absorbed is reported for each surface and each lens volume and compared to the FE load created. The technique is available in SigFit, a commercially available tool integrating mechanical analysis with optical analysis.
The employment of actively controlled segmented mirror architectures has become increasingly common in the development of current astronomical telescopes. Optomechanical analysis of such hardware presents unique issues compared to that of monolithic mirror designs. The work presented here is a review of current capabilities and improvements in the methodology of the analysis of mechanically induced surface deformation of such systems. The recent improvements include capability to differentiate surface deformation at the array and segment level. This differentiation allowing surface deformation analysis at each individual segment level offers useful insight into the mechanical behavior of the segments that is unavailable by analysis solely at the parent array level. In addition, capability to characterize the full displacement vector deformation of collections of points allows analysis of mechanical disturbance predictions of assembly interfaces relative to other assembly interfaces. This capability, called racking analysis, allows engineers to develop designs for segment-to-segment phasing performance in assembly integration, 0g release, and thermal stability of operation. The performance predicted by racking has the advantage of being comparable to the measurements used in assembly of hardware. Approaches to all of the above issues are presented and demonstrated by example with SigFit, a commercially available tool integrating mechanical analysis with optical analysis.
KEYWORDS: Mirrors, James Webb Space Telescope, Optical alignment, Space telescopes, Optical components, Space telescopes, Optical telescopes, Adaptive optics, Data modeling, Telescopes, Shape memory alloys
The optical telescope element (OTE) of the James Webb Space Telescope has now been integrated and aligned. The OTE comprises the flight mirrors and the structure that supports them – 18 primary mirror segments, the secondary mirror, and the tertiary and fine steering mirrors (both housed in the aft optics subsystem). The primary mirror segments and the secondary mirror have actuators to actively control their positions during operations. This allows the requirements for aligning the OTE subsystems to be in the range of microns rather than nanometers. During OTE integration, the alignment of the major subsystems of the OTE structure and optics were controlled to ensure that, when the telescope is on orbit and at cryogenic temperatures, the active mirrors will be within the adjustment range of the actuators. Though the alignment of this flagship mission was complex and intricate, the key to a successful integration process turned out to be very basic: a clear, concise series of steps employing advanced planning, backup measurements, and cross checks that this multi-organizational team executed with a careful and methodical approach. This approach was not only critical to our own success but has implications for future space observatories.
Mechanical tolerances within an optical system can consist of a wide array of variables including machining tolerances,
variability in material properties, uncertainty in applied loads, and discrete resolution of actuation hardware. This paper
discusses methods to use integrated modeling and Monte Carlo techniques to determine the effect of such tolerances on
optical performance so that the allocation of such tolerances is based upon optical performance metrics. With many
random variables involved, statistical approaches provide a useful means to study performance metrics. Examples
include the effect of mount flatness on surface RMS and Zernike coefficients and the effect of actuator resolution on the
performance of an adaptively corrected deformable mirror. Coefficient of thermal expansion and thermal control
tolerances impacting both line-of-sight errors and surface RMS errors are also addressed.
The development of the optimum locations of actuators for an adaptive optic has in the past been a manually iterative process. Such a manual process becomes fruitless when multiple disturbance cases (e.g., gravity and thermoelastic deformations) need to be considered in the development of a single actuator layout. A more automated yet efficient method is desired to quickly develop an optimum actuator layout and the associated optical performance. A genetic design optimization algorithm is developed and implemented in software. The method is then demonstrated on an example adaptive optic design to show how it can be used to develop optimum actuator layouts for a fixed number of actuators or to conduct design trades in choosing the number of actuators.
The accuracy of optical modeling techniques to represent finite element derived surface displacements is evaluated using commercial software tools. Optical modeling methods compared include the Zernike polynomial surface definition, surface interferogram files, and uniform arrays of data in representing rigid-body and elastic surface errors. Methods to create surface normal displacements and sag displacements from FEA displacement data are compared. Optical performance evaluations are performed as a function of surface curvature (f/#). Advantages and disadvantages of each approach are discussed.
By linking predictive methods from multiple engineering disciplines, engineers are able to compute more meaningful predictions of a product's performance. By coupling mechanical and optical predictive techniques mechanical design can be performed to optimize optical performance. This paper demonstrates how mechanical design optimization using system level optical performance can be used in the development of the design of a high precision adaptive optical telescope. While mechanical design parameters are treated as the design variables, the objective function is taken to be the adaptively corrected optical imaging performance of an orbiting two-mirror telescope.
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