KEYWORDS: Modulation transfer functions, Data modeling, Wavefronts, Tolerancing, Image quality, Lenses, Point spread functions, Monte Carlo methods, Imaging systems
Ruda designs high performance imaging systems to meet difficult mission requirements, but these nearly diffraction limited systems often have small margins between the image quality of the nominal design and the required performance of the as-built system. Due to this we may spend significant resources designing and operating specialized test setups to ensure that results of MTF and Ensquared Energy (EE) measurements are well-calibrated and accurate. Alternatively, wavefront measurements – like those captured by wavefront sensors and interferometers – can be taken of the system to characterize the quality of the as-built system. Wavefront measurements are typically higher resolution, faster to setup, and quicker to measure than image quality metrics, making them particularly attractive for use when validating as-built system quality. Since the wavefront is related to the point spread function, and thereby the image quality, different wavefront measurements can contain information about the system MTF and EE. Thus, if the relationship between the wavefront and image quality metrics of interest can be established for an as-built system, it is possible to supplement or fully validate MTF and EE requirements from wavefront measurements. To investigate this relationship, we used Zemax OpticStudio to generate toleranced Monte Carlo trials of two nearly diffraction limited imaging systems designed by Ruda. The Monte Carlo models were then analyzed to form large data sets for statistical analysis. For wavefront data, the simulation produces single pass and double pass wavefront Zernike decompositions as well as wavefront root mean squared error over a range of object fields and visible wavelengths. For image quality data, the MTF at three spatial frequencies and the EE at two integration lengths are computed for the same fields and wavelengths as the wavefront data. These data sets are then processed to demonstrate that high degrees of correlation can exist between wavefront data and image quality metrics in toleranced high performance imaging systems, even when there is a difference in wavelength between the metrics. Sources of noise in these correlations are identified, and paths for supplementing or validating image quality requirement with correlated wavefront measurement data through machine learning are discussed.
Threaded mounts are one of the most common interfaces between optical systems and commercial-off-the-shelf cameras. Popular examples include the established C-mount, as well as the newer TFL-mount which accommodates for larger sensor formats such as the APS-C detector. In all cases, the thread is used to adjust for focus by clocking the optical system with respect to a fixed camera assembly or vice versa. For this reason, the alignment between the datum axis of the optical system and the array detector plane inside the camera depends on both the allowances and tolerances of the thread interface, and on the manufacturing tolerances of the mount components. To highlight how the stack up of these tolerances can affect image quality of an optical system, we first perform an inverse sensitivity analysis to determine the detector alignment specification as a function of system F/#, field of view, and chief ray angle. We then calculate the misalignment contributions of the thread between the optical system and the lock ring that sets the camera axial position for best focus. This optomechanical analysis allows us to determine if thread mounts are appropriate for the specifications of the optical system under consideration and to specify the tolerances of the thread interface when this is the case.
Passively athermalized optical systems produce high quality images over a large thermal range without actively adjusting focus. This athermalization is achieved through careful selection of the glass for each lens and metal for each mount. For drop-in systems, the material combination for best optical performance often leads to a lens stack with an overall coefficient of thermal expansion (CTE) that is different from the CTE of the barrel that holds it together. Since bulk glass and metal are relatively stiff, this CTE mismatch results in large variations of the preload force retaining the lens stack in compression over the optical system’s survival thermal range. For this reason, compliant spacers are commonly added to the lens stack in an effort to attenuate these preload force variations. However, the effect of these compliant spacers on the athermalization of optical systems is seldom analyzed. We perform a first-order calculation of the effective CTE of compliant spacers to assess their impact on optical performance and introduce an optomechanical design approach to reduce the amount of compliance needed by matching the overall CTE of the lens stack to the CTE of the barrel.
Optical systems are often athermalized over large temperature ranges through the proper choice of glasses and mounting materials. However, variations in the coefficients of thermal expansion (CTE) and thermo-optical coefficients that govern thermal behavior are seldom included in the tolerance analysis. Manufacturers rarely provide these material tolerances and we can only account for their effects through custom macros in lens design software. We demonstrate that a first-order sensitivity analysis on the change in focus position at each environmental condition accurately predicts the degradation of the system performance. We verified this correlation by creating a custom catalog of identical glasses with perturbed thermal parameters and evaluating the RMS wavefront error for each material substitution.
In the design of optical assemblies, emphasis is placed on tolerancing the surface irregularity, which is a driving factor in price and manufacturing prices and time during polishing. Quite often, the default irregularity tolerance in modeling software is assumed to be a 50:50 split between astigmatism and 3rd order spherical aberration (i.e. symmetric zonal errors). In this paper, we reviewed the irregularity of over 1,000 custom fabrication optical surfaces. We looked at the relationship between the spherical and astigmatism aberrations and found generally that a surface will be either astigmatic or spherical, but rarely a mixture of the two. We also looked at the PV and rms of the surfaces and how that compares to the model and the general knowledge. One striking result of our analysis came from a closer analysis of how the optical modeling software package handles ‘power’ errors in the irregularity tolerance. It is possible that there is a mismatch between the model and the optical manufacturer.
Optical designs for phased-array imaging telescopes, and for interferometers with sparsely filled apertures, using simple two-mirror subtelescopes are discussed. Limitations to the field of view caused by Petzval curvature and distortion are discussed. Methods for reducing or correcting Petzval curvature in these systems by the use of off-axis paraboloidal mirrors are presented and design examples are given. It is shown that a 2.4 times increase in the field of view is possible for 10m diameter arrays, but that residual distortion precludes application of the method to the 50m diameter interferometers considered.
This paper concerns a new, machine mounted aspheric metrology device designed to measure a broad range of figures without the use of auxiliary optics. A prototype device, based on the classical Hartmann test, called a Hartmann Optical Surface Tester (HOST) was evaluated on a single point diamond turning machine. Design, initial testing, and validation data from reference spheres, and two types of aspheres are discussed. Results of a simulation model for estimating acceptable alignment errors for the HOST on the diamond turning machine also are presented. Peak-to-valley measurement uncertainty on the test optics was found to be better than 0.08 micrometers .
Recent advances in axial gradient material fabrication via the diffusion of glass plates has opened the door to a wide variety of optical design applications incorporating entire lenses of gradient index material. A proprietary software-driven process developed at LightPath Technologies Inc. creates gradient index glass by fusing together a stack of discrete glass plates, where each constituent plate has a distinctive composition and desired optical properties. LightPath's ability to prescribe large optical index changes (up to 0.47) throughout a glass substrate of virtually any diameter and thickness (macro gradient), invokes an interesting question: what are the properties of a solid gradient index lens and how can these properties be used most efficiently and effectively? This paper reports on a parametric study of third order spherical aberration vs. shape factor, for a macro gradient F/3 singlet lens whose index varies by +/- 0.4 in linear, quadratic and cubic profiles.
Designs for phased-array imaging telescopes covering a wide field of view (0.25 degrees) with satisfaction of all optical phasing conditions have been developed. Important concerns regarding the implementation of these telescopes include misalignment types and tolerances, and the complexity of active alignment systems needed to correct the misalignments. In this paper a phased-array telescope point design is briefly described. Possible misalignments in the array configuration are defined, and functional forms are given. A technique is introduced for including array misalignments in the wavefront aberration polynomial used to describe image quality in the final array focal plane. This polynomial is then used to show to what extent the misalignment-induced subtelescope aberrations defocus and coma may be corrected using only adjustments in the array configuration. Application to the point design shows that defocus and coma may be corrected, by the addition of piston and tilt terms, by factors equal to the ratio between the Seidel aberration coefficient and the corresponding Zernike polynomial coefficient. It is shown that correction possibilities result in looser subtelescope alignment tolerances and in the simplification of active alignment systems for individual subtelescopes.
The design for a telescope is presented which calls for small optical components in an all-reflective wide-field-of-view phased-array configuration. Attention is given to the geometric phasing conditions and other phasing requirements for the phased-array design, and analytical expressions are set forth for the paraxial relations and distortion. The design of the subtelescopes is based on a three-mirror design, and particular attention is given to the problem of subtelescope field curvature. It is shown that several configurations provide the required corrections for the field curvature and the stigmatic aberrations. Subtelescope aberrations such as coma can affect optical phasing, which indicates that a tolerance analysis conducted aberration-by-aberration is necessary for developing the all-reflective configuration.
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