KEYWORDS: Metrology, Data acquisition, Time metrology, Sensors, Motion measurement, Mathematical modeling, LabVIEW, Freeform optics, Body temperature, Temperature metrology
As on-machine metrology for freeform optics becomes increasingly popular, error analysis and compensation techniques and probe path optimization must evolve in response. For this work, a four axis Moore Nanotech Universal Measuring Machine (based on a diamond turning machine design) is used with a Precitec chromatic confocal probe. The system is set up in a thermally controlled enclosure, and a LabVIEW data acquisition program is used to record probe data, time, and machine positioning data directly from the machine scales. Issues addressed include probe testing and calibration, thermal errors, data age, compensation methods, and probe path optimization for error reduction. The combined error reduction/compensation approach improves on-machine metrology for freeform optics.
The latest generation of optical sensing hardware comprises of optical surfaces without rotational symmetry, commonly known as freeform optics. Whether the goal is obtaining more information by using a larger aperture and/or field of view or to decrease the overall footprint of the system, freeform optics have demonstrated unique capabilities to enable these advancements. However, it is critical to use concurrent engineering practices between optical design, mechanical design, manufacture, and metrology to ensure that the final system meets the required optical design specs after applying manufacturing tolerances. Metrology of freeform optics and performance testing of the three-mirror telescope will incorporate multiple measurement technologies and methods. Measurement errors are reduced through machine error corrections using a mathematical machine model and tilt induced error correction in mid-spatial frequency measurements using a scanning white light interferometer (SWLI). The form measurement uncertainty will be evaluated using the machine model and the Monte Carlo method for simulating possible measurement results taking into consideration the uncertainty in the machine error measurements and probe measurement uncertainty. Form measurements include contact and non-contact instruments with different sampling strategies. SWLI and stylus measurements for surface roughness are utilized for both areal and profile measurements. Design for metrology" aims to inform the design and manufacturing process definition as part of the concurrent engineering goal. By considering metrology in the initial design and manufacturing through ease of mounting and appropriate fiducials it is possible to reduce wasted effort and manufacturing time.
When fringe projection profilometry is used for measuring rough/textured surfaces, the fidelity of the measurement is subject to the spatial frequency response. The instrument transfer function (ITF) is one appealing approach to characterize this property. The foundation of ITF analysis is based on the linear theory; only linear systems are appropriate for ITF analysis. A fringe projection system is intrinsically nonlinear, but it can be approximated as a linear system when certain conditions are met. Here we investigate the linear conditions of a custom fringe projection system designed for an additive manufacturing application. The applicability of ITF is discussed through mathematical analysis and simulations.
Mid-spatial frequency (MSF) texture on optical elements degrade their performance. A Zernike polynomial representation of the wavefront can be used to characterize the mid-spatial frequency and predict the optical performance. The ability to generate very large orders of Zernike polynomials enables fitting and describing optical wavefronts all the way from low order form errors to mid-spatial frequencies. Based on a filtering aspect of Zernike polynomials, we show how different fabrication signatures affect optical performance differently. We investigate the Strehl ratio and Modulation Transfer Function (MTF) as optical performance metrics for mid-spatial frequency. We then present how the orthogonality properties of Zernike polynomials along with linear systems theory of MTF can provide an effective tool in separating the optical performance degradation due to different mid-spatial frequency texture. We present an example of real mid-spatial frequency texture to examine the error in the approximation of MTF when using linear systems formulation.
Alternative techniques for measurement of misalignment in a segmented mirror are of interest to the telescope community in the limit of large misalignment that precludes interferometric tracking. A variation of phase measuring deflectometry can be used to determine 5 degrees of freedom (DOF) of the misalignment with knowledge of the remaining 1 DOF. A camera and screen are positioned near the center of curvature, and the camera collects images of the screen pattern reflected from the mirror. In this application, the form of each segmented mirror is assumed known, so the misalignment contribution to the measurement can be determined. The approach is based on a Zernike analysis of distorted fringe patterns and the sensitivity to misalignment. We discuss simulation results in this paper.
Mid-spatial frequency structure on freeform optical elements induces small-angle scatter and affects performance.
Fabrication techniques involved in making freeform surfaces leave tooling marks on the surface due to the sub-aperture
nature of the fabrication process. In recent years, there has been a growing need for specification and characterization of
the mid-spatial frequencies for freeform surfaces. There are a range of methods to consider for representing the midspatial
frequency content: the power spectral density (PSD), the structure function (SF) and a polynomial basis
representation such as Zernike and Forbes Q-polynomials, as examples. In this paper, we investigate a Zernike
polynomial representation for quantifying the mid-spatial frequency content in height maps. We will show fit
coefficients of synthesized and real data sets to Zernike polynomials from low orders to very large orders. We also
illustrate how this polynomial representation captures certain characteristics of the mid-spatial frequency error. The
results are analyzed and compared with Forbes gradient orthogonal polynomials. Finally, limits of Zernike polynomials
for representing mid-spatial frequency content of the surface are discussed.
Mid-spatial frequency structure on an optical surface induces small-angle scatter in the transmitted wavefront. Freeform
surfaces are particularly susceptible to mid-spatial frequency errors due to the sub-aperture nature of the fabrication
processes. Several surface metrology methods that work for freeform surfaces use an indirect principle, reconstructing
the surface shape from measured surface slope data. The integration process in the presence of measurement noise adds a
spatial correlation to the dataset, leading to spurious spatial frequency structure. In this paper, we use the autocorrelation
function to characterize and evaluate this artificial mid-spatial frequency structure on optical surfaces that are
reconstructed by zonal integration methods.
The structure function (SF) represents the average height difference squared as a function of separation. The linear SF
has been used in astronomy and captures data of all spatial frequencies. However, it does not capture anisotropy on the
surface. The one-quadrant area SF has been introduced to represent surface roughness information, but it is inadequate
when surfaces are rotationally varying, as is frequently the case for optical surfaces. The recently introduced twoquadrant
representation of the area SF can be calculated for any aperture shape, for all spatial content and isotropies.
This paper describes the physical interpretation of the two-quadrant area SF and the comparison to area power spectral
density (PSD) and area autocorrelation function (ACF) for a range of optical surfaces.
Many different approaches may be taken in the certification of reference flats used for acceptance testing of optical
quality surfaces. Measurement services offered by national measurement institutes cover a limited size range and the
uncertainties associated with the transfer of a calibration must be considered when data from any testing service is used
in quality assurance. In-situ self-calibration using a full area variant of the 3-flat test enables the lowest possible
uncertainty. The first part of this paper shows the options for external calibration and certification as a function of flat
size, and orientation. Next the conditions that must be met to achieve traceability, according to the requirements of ISO
17025, will be discussed. Finally hardware and procedures will be described, and data presented, showing traceable
measurement of a 450 mm aperture flat with nm level uncertainties.
Peak-to-valley departure (PV) is entrenched in optics design and manufacture as a characterization of an optical figure; modern interferometers commonly use 1k×1k detectors, the output of which may not be well represented by two points. PVr is a newly proposed robust amplitude parameter that combines the PV of a 36-term Zernike fit and the root mean square of the residual. This provides automatic filtering, is insensitive to system resolution, and relates directly to imaging performance via the Marechal criterion. Use of PVr in place of PV is recommended.
Two specially-designed visible-wavelength interferometers meet demanding performance requirements in the mid-spatial frequency regime for current and next generation free-form x-ray and EUV optics. A Fizeau phase shifting interferometer measures waviness in the spatial frequency range from 0.5 to 10 mm-1 and an interferometric microscope measures finer-scale deviations from 1 to 1000 mm-1. Uncertainty analysis and experimental work demonstrate <1-nm system error after calibration and 0.05-nm repeatability for both instruments working in a clean-room environment.
The use of diamonds to generate precision patterns and precision surfaces on a micrometer or nanometer scale has a history that dates back centuries. Uses of diamond in semi-automated machinery can be traced to ruling machines, pantographs, and ornamental turning with "diamond turning" dating back about a century. Poor behavior in machining more common materials (e.g. ferrous alloys) has limited diamond use in traditional industrial machining. The niche of
the single crystal diamond is its edge sharpness and the ability to produce near-optical finish in materials such as aluminum, copper and their alloys; however, due to machine limitations, diamond machining remained a novelty until relatively recently. A convergence of machine technologies developed for both weapons and commercial applications led to modern diamond turning. Current turnkey machines can produce contoured surfaces with surface finish in the range of 5 nm Ra and long range accuracy of micrometers or less. Macroscopic scale, three axis, diamond machining is a well-developed technology; machining of features on a micrometer and submicrometer scale is a new and rapidly developing application of single crystal diamond machining. The role of this technology in micro-optics replication has
yet to be fully defined.
The radius of curvature of spherical surfaces may be determined using the well-known radius, or optical, bench. In this method, a figure measuring interferometer is employed to identify the null positions at the center of curvature (confocal) and surface (cat's eye) of the test optic. A linear slide provides motion between these positions and one or more displacement transducers is used to record the displacement between the cat's eye and confocal positions and, hence, the radius of curvature. Measurements of a polished Zerodur sphere have been completed on the X-ray Optics Calibration Interferometer (XCALIBIR) using both Twyman-Green and Fizeau configurations. Mechanical measurements of the spherical artifact have also been completed using a coordinate measuring machine (CMM). Recorded disagreement between the individual transmission sphere measurements and CMM measurements under well-controlled environmental conditions is larger than the limits predicted from a traditional uncertainty analysis based on a geometric measurement model. Additional uncertainty sources for the geometric model, as well as a physical optics model of the propagation of light, are therefore suggested. The expanded uncertainty analysis is described.
Conventional interferometric testing of the flatness of photomask substrates is rendered difficult by the long coherence length of the HeNe laser sources typically used in commercially available phase measuring interferometers appropriate for flatness testing. The Ritchey-Common configuration allows testing of flats in a spherical wavefront; this paper shows that, under appropriate conditions, high resolution surface flatness maps of photomask substrates may be obtained using instrumentation currently available in many optical shops.
We describe a novel, IR phase shifting Haidinger fringe interferometer for measuring the thickness, total thickness variation (TTV) and bow of silicon wafers. We show that by taking 3 interferograms of the wafer in different positions in the cavity it is possible to separate thickness, TTV and bow. We also show that bow has an effect on the measurement of TTV.
The basic goal of the Advanced Optics Metrology program in NIST's Manufacturing Engineering Laboratory is to help industry ensure that their measurement results of optical figure and wavefront are traceable. This paper underscores the importance of traceability and reviews the facilities and projects dedicated to achieving that objective.
The NIST (National Institute of Standards and Technology) virtual/physical surface roughness calibration standard consists of physical specimens whose surfaces are manufactured by a numerically controlled diamond-turning process using digitized profiles. These standards are designed for checking the characteristics and algorithms of surface measuring systems, and for sensing the amount of distortion of the surface information flow though different measuring systems. The digitized profiles can also be used for remote instrument calibration and surface measurement unification. The design, manufacture, test results, and potential uses of the NIST prototype specimens are discussed.
The rapidly renewable lap is based on the simple concept of generating the figure needed in a lap substrate and then replicating it into a thin film slumped over the substrate. Based on this concept, we describe how efficient laps can be constructed for the lapping and polishing of crystalline, amorphous, and metallic surfaces.
A number of 150 mm apertures in 250 mm diameter plano- concave with departures from the nominal figure of a few nm were carefully tested using phase measuring interferometry and the data reduced using pixel based absolute testing techniques. We discuss some of the data reduction techniques used as well as the precautions taken to verify the accuracy of the result. After accounting for systematic errors introduced by interferometer imaging, we show that the surfaces can be characterized to a few nm peak-to-valley over spatial scales form the measurement aperture to a few mm.
The microstructure of sapphire modulus of rupture bars has been examined before and after a high-temperature anneal using a variety of characterization methods, collectively described as 'advanced diagnostics'. These methods include the localized techniques of transmission electron microscopy, Raman spectroscopy and high magnification polarized light microscopy, as well as the global techniques of x-ray diffraction topography, polariscope and wave font analysis. Comparison of data before and after annealing indicate that no change has occurred in the long-range strain distribution or subgrain structure. However, changes in microstructure consistent with the motion of dislocations within approximately 100 nm of the surface were observed.
A new optical alignment artifact under development at NIST is described. This artifact, referred to as a stepped microcone, is designed to assist users and manufacturers of overlay metrology tools in the reduction of tool-induced measurement errors. We outline the design criteria and diamond turning lathe techniques used for manufacturing this structure. The alignment methods using this artifact allow the separation of error components associated with the optical system or the mechanical positioning systems as encountered when performing measurements in different focal planes.Although some difficulties have been encountered when performing measurements in different focal planes. Although some difficulties have been encountered in the actual diamond turning process,the data presented show some improvements with the more recent prototypes which indicate that this method of fabrication will be useful. Photometer scan data and CCD image acquisition hardware show a significant optical response at the step edges from these structures. Initial analysis of the optical response of these edges shows sensitivity to the material used and the details of the manufacturing processes.
Textured laps can be created by 'slumping' uniform thin films of appropriate materials over textured substrates that have been generated to the required figure. The film can easily be replaced and the lap shape is invariant since the lap substrate never contacts the workpiece nor the polishing compound. Thus extremely repeatable lapping and polishing processes are obtained. This paper introduces this approach to lap construction and presents preliminary results.
In response to the needs of the emerging field of normal incidence soft x-ray optics, a field with applications ranging from extreme ultraviolet (XUV) solar imaging to x-ray lithography, the National Institute of Standards and Technology (NIST) has initiated an XUV multilayer and optical substrate characterization program. In this paper, we give an overview of the present capabilities of the NIST facility and discuss some of the proposed improvements, concentrating on the new soft x-ray reflectometry facility being built at SURF.
Even unusual care in polishing leads to optics with somewhat damaged working faces. The question is to what degree? the physical nature of this damage depeids on the ductility or plasticity of the constniction material. Glassy materials (glass brittle metals and semiconductors) fracture while ductile materials work harden. Beryffium suffers from both modes. To physically model damage we oversimplify and picture a surface layer with two features a depth and an intensity of the IvjIk property changes. A statistical alternative to intensity is the visible flaw density. We use a variety of analytical mathods but mainly x-ray diffraction metallography and instrumented microindentation and frequently use them in combination. Our problem is to develop a general hasis and means of characterizing subsurface damage. To illustrate the diversity difficulty and our progress with the problem we will report experiences with a variety of examples. The talk will consider damage in ductile regimeN ground classically polished fused silica BK-7 pyrex optics esuperu polished BK-i precision ground silicon nitride and aluminaceramics and precision CBN turned beryllium.
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