Understanding measurement uncertainty is critical for qualifying an instrument for a specific task and for improving the instrument’s performance. Specifying that uncertainty requires a precise definition of the particular quantity being measured and the conditions under which it is measured. These should both be relevant to the end user’s application. In this paper I re-examine and summarize some of the definitions and test methods that have been used to characterize Fizeau interferometers and attempt to encourage a discussion about how to best specify the performance of Fizeau interferometers for today’s demanding applications.
Conventional optical spectrometers that are based on bulk optical components tend to be relatively large and expensive
compared to the other components used in systems designed for detecting chemical/biological agents. Microspectrometers
based on focusing waveguide gratings incorporate both spectral dispersion and focusing functions into a
single component that can be fabricated hundreds at a time at the wafer level using nano-imprint lithography techniques.
These types of spectrometers are ideal for integration into micro-fluidic systems because the signals can be directly
coupled into the planar waveguide. We present preliminary data from a prototype system and explore potential
applications for these devices.
Waveguide grating couplers (WGC) are used for input and output coupling in many planar waveguide
based sensors. By using a chirped grating, guided light can be decoupled and focused to a desired location. The
location and spot size of focused beam depends upon the size and chirp of the grating as well as the wavelength of
the light. The locus of the focused beams for different wavelengths lies along a curve. In many applications a planar
detector array is used to capture spectral data. Wherever the planar detector array does not intersect this focal curve,
images of a point source will be defocused. We develop a theoretical model to calculate the image location and
geometric spot size for a given set of grating parameters.
In order to experimentally verify the model, chirped waveguide grating couplers were fabricated on
HfO2/Quartz planar waveguides using e-beam lithography. The spot size, intensity, and location of diffracted beam
was measured at several wavelengths and compared with the theoretical results.
KEYWORDS: Line edge roughness, Data modeling, Ellipsometry, Mueller matrices, Spectroscopy, Line width roughness, Silicon, Numerical modeling, Process control, Optics manufacturing
We used azimuthally-resolved spectroscopic Mueller matrix ellipsometry to study a periodic silicon line structure with
and without artificially-generated line edge roughness (LER). The unperturbed, reference grating profile was determined
from multiple azimuthal configurations using a generalized ellipsometer, focusing the incident beam into a 60 μm spot.
We used rigorous numerical modeling, taking into account the finite numerical aperture, introducing significant
depolarization effects, and determining the profile shape using a four trapezoid model for the line profile. Data obtained
from the artificially perturbed grating were then fit using the same model, and the resulting root-mean-square error
(RMSE) values for both targets were compared. The comparison shows an increase in RMSE values for the perturbed
grating that can be attributed to the effects of LER.
Line width roughness (LWR) has been identified as a potential source of uncertainty in scatterometry measurements, and
characterizing its effect is required to improve the method's accuracy and to make measurements traceable. In this work,
we extend previous work by using rigorous coupled wave (RCW) analysis on two-dimensionally periodic structures to
examine the effects of LWR. We compare the results with simpler models relying upon a number of effective medium
approximations. We find that the effective medium approximations yield an approximate order of magnitude indicator of
the effect, but that the quantitative agreement may not be good enough to include in scatterometry models.
Optical scattering techniques can provide rapid, non-destructive measurements of nanometer-scale structures for micro-fabrication
process control. In general, these techniques compare measured optical characteristics of a sample to results
generated from a theoretical model. The models can be computationally expensive, especially when used with iterative
methods to obtain a solution to the inverse problem. However, the structures of interest are normally restricted to small
changes from some nominal structure. Perturbation theories have been used to efficiently calculate the effects of small
changes on the performance of photonic crystals. In this paper, we apply these perturbation techniques to the optical
scatterometry problem and demonstrate a calculation of the change in the scattered signal due to edge roughness from an
array of holes in a dielectric.
Micro-refractive lenses are an important example of components and subsystems that are being used increasingly in optical sensors, communications, data storage, and other diverse applications. These lenses have a continuous relief surface such that details of their dimensional shape, refractive index, and homogeneity all influence performance. Measurement capabilities for micro-refractives fall short of current and future needs and are complicated by the need to fabricate non-spherical refractive surfaces. To control the fabrication process, the target measurement uncertainties are approximately 3 parts in 10-4 for radius and on the nanometer scale for figure measurements. Carrying out metrology at this level is very challenging and especially so for micro-scale components. Micro-interferometry is the most promising tool and can be used to measure radius of curvature, focal length, dimensional surface errors, and transmitted wavefront. Common practice is to calibrate with a single high quality artifact for measurements of a range of different radii, and we see that this is only approximately valid. Figure measurement calibration, for example, will be improved if the radius of the calibration artifact closely matches the radii of the test lenses, but acquiring such a range of artifacts is not practical. We have demonstrated the application of a self-calibration procedure for figure measurement and transmitted wavefront measurement calibration, called the random ball test. Radius measurements on the micro-scale are also challenging. Our research focuses on measurement advances for refractive components and new data analysis strategies to optimize the impact of measurement results.
Radius of curvature is a critical parameter to measure in the manufacturing of micro-refractive elements. It defines the power of the surface and provides important information about the stability and uniformity of the manufacturing process. The radius of curvature of an optical surface can be measured using an interferometer and radius slide where the distance is measured as the surface is moved between the confocal and cat’s eye positions. However, the radius of curvature for micro-refractive elements can be on the order of a few hundred microns and the uncertainty in the measurement due to stage error motions can become a significant portion of the tolerance. Typically the radius slide is calibrated using an artifact, but the radius of the artifact must be traceable to the base unit of length and the calibration is subject to misalignment errors. Alternatively, the stage error motions can be measured with standard machine tool metrology techniques and used to correct the errors in the radius of curvature measurement. This paper details the implementation of a directly traceable radius of curvature measurement on a micro-interferometer, including alignment procedures, measurement of stage error motions, displacement gauge calibration, and data analysis strategies.
Micro-optic components and subsystems are becoming increasingly important in optical sensors, communications, data storage, and many other diverse applications. In order to adequately predict the performance of the final system, it is important to understand how the optical elements affect the wavefront as it is transmitted through the system. The wavefront can be measured using interferometric means, however, both random and systematic errors contribute to the uncertainty of the measurement. If an artifact is used to calibrate the system it must itself be traceable to some external standard. Self-calibration techniques exploit symmetries of the measurement to separate the systematic errors of the instrument from the errors in the test piece. If the transmitted wavefront of a ball lens is measured in a number of random orientations and the measurements are averaged, the only remaining deviations from a perfect wavefront will be due to spherical aberration contributions from the ball lens and the systematic errors of the interferometer. If the radius, aperture, and focal length of the ball lens are known, the spherical aberration contributions can be calculated and subtracted, leaving only the systematic errors of the interferometer. This paper develops the theory behind the technique and describes the calibration of a micro-interferometer used to measure the transmitted wavefront error of micro-refractive lenses.
Metrology is one of the critical enabling technologies for realizing the full market potential for micro-optical systems. Measurement capabilities are currently far behind present and future needs. Much of today’s test equipment was developed for the micro-electronics industry and is not optimized for micro-optic materials and geometries. Metrology capabilities currently limit the components that can be realized, in many cases. Improved testing will be come increasingly important as the technology moves to integration where it will become important to “test early and test often” to achieve high yields. In this paper, we focus on micro-refractive components in particular, and describe measurement challenges for this class of components and current and future needs. We also describe a new micro-optics metrology research program at UNC Charlotte under the Center for Precision Metrology and the new Center for Optoelectronics and Optical Communications to address these needs.
We have focused on measurement needs for micro-refractive lenses and have developed a flexible and compact micro-interferometer that can be used to measure lens radius of curvature and form errors. Transmitted wavefront and back focal length measurements can be easily added to the instrument. This instrument addresses measurement needs for micro refractive lenses. The interferometer is based on a Mitutoyo metallurgical microscope and operates with a 633 nm helium neon source. The radius of curvature measurement is directly traceable, meaning an external artifact is not required for calibration. This requires a careful mechanical design, a detailed alignment procedure with estimates of alignment uncertainties, and stage error motion characterization with estimates of uncertainties. The instrument can also be used to measure some diffractive components and mold form errors. We describe the instrument in this paper and discuss design goals and measurement specifications.
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.
High-resolution measurement of the free spectral range (FSR) for an etalon is becoming more important as greater amounts of information are multiplexed through a single fiber. A method to test the FSR of etalons or etalon based optical components used at telecommunication frequencies is discussed. Slope at a specific point of the etalon response curve is utilized as a means measurement of FSR. The theory that describes how slope, varying as a function of differing etalon signal peaks, can be utilized for the measurement of FSR is developed. This technique has been shown to measure FSR with a resolution of approximately one part in 2000.
A non-contact (i.e., optical) technique is required to measure the deformation of a free oil surface under the influence of a localized thermal load. This deformation is caused by surface tension driven thermal convective flow inside the fluid, and can be as large as 250 micrometers . Therefore, conventional interferometry is not possible. Instead, a Ronchi technique is proposed for contour mapping the oil surface. This paper presents a design concept for a two channel Ronchi instrument and some preliminary results from a feasibility study using a single channel Ronchi instrument.
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