In this blog the measurement of steep spheres and aspheres with a Fizeau interferometer is discussed.
Steep Convex Spheres – Stitching
A limitation of Fizeau interferometry is the inability to measure steep convex spheres with f#’s beyond the reference surface f#. This is a severe limitation for spot polishing machines that require data across the entire surface to apply the necessary corrections. The solution is a stitching system that acquires sub-apertures across the partially covered surface and mathematically combines them into a complete surface. Stitching includes matching overlapping areas for tips and tilts, and sometimes distortions and rotations and is not a simple image stitch. Several manufacturers now offer these systems.
Stitching can introduce errors. Stitching errors are found in the lowest spatial frequencies, particularly power. A simple test for errors in power is the measurement of radius of curvature. Measure a part’s radius of curvature across the vertex sub-aperture and compare this value to the radius of curvature measured across the entire stitched surface. The difference of these two includes the stitching errors, plus the reproducibility of the two radius of curvature measurements. Measuring radius of curvature is challenging and careful metrology practice must be followed to confirm this test. To assess surface irregularity accuracy compare a surface measured with a f/0.75 Transmission Sphere (Fizeau reference) and the same surface area stitched with a
n f/3.3 Transmission Sphere. Best is subtracting the two measurements from each other to highlight the stitching errors, though this is not always easy to implemented due to differing data set sizes. Stitching systems by leading manufacturers appear to have solved these problems, yet understanding potential limitations is important.
The major limitations now seem to be cost and speed of measurement.
Asphere Metrology
Aspheres are difficult to measure with Fizeau interferometers. A Fizeau operates best when the surface is a nulled sphere to minimize ray-trace errors, and aspheres can greatly deviate from a sphere. Further the high slopes of aspheres can exceed the slope limit of the imaging system causing the measurement to fail. Multiple approaches to overcome these limitations are used.
Asphere Stitching
Just like spheres an asphere stitching system builds up the surface by measuring sub-apertures. This is more difficult than measuring a sphere as the ray-trace errors will exist in each sub-aperture which must be minimized, or calculated and removed. With steep aspheres even the sub-apertures exhibit slopes exceeding the imaging limit of the interferometer. Complicated compensation techniques (such as rotating wedges) are used to minimize measured slopes, requiring mathematically correction for ray-trace errors, and induced distortions of the variable compensating wedges. Measurement time (>30 minutes) and cost tend to be the major concerns for these systems.
Measurable aspheres are limited to near axially symmetric surfaces with nominally monotonically increasing curvature. Reversed curvature (gull wing) aspheres are not measurable with these systems.
Asphere Scanning Fizeau
Scanning Fizeau is similar to stitching systems, but scan only in Z, along the parts optical axis. Rings of data paired with the caustic zone Z is compared to the expected Z position and surface surface shape. Since data is acquired at the null of each ring, ray tracing errors are minimized, for low measurement uncertainty. These systems have been used with picometer measurement uncertainty for semiconductor lithography optics asphere manufacture. Limitations due to the reference sphere f# and surface curvatures exist limiting its application to specific lens types. Since a full ring of data is measured these systems tend to measure an entire surface in <5 minutes.
Scanning Fizeau systems promise high accuracy with fast data acquisition. Yet measurable aspheres are limited to near axially symmetric surfaces with nominally monotonically increasing curvature. Reversed curvature (gull wing) aspheres are not measurable with these systems.
Asphere Sub-Nyquist Fizeau
Sub-Nyquist has existed since the 1980’s but only recently introduced commercially. This system pinhole masks the detector allowing fringes beyond the nyquist limit to be detected and thus acquired.
Sub-nyquist fringes by nature are highly tilted, introducing errors that vary from measured part to measured part. These ray-trace errors are calculated and removed mathematically considering both the interferometer optical design AND the part under test. Mathematical ray-trace error removal demands full knowledge of the interferometer optical design, as manufactured, and its sensitivity to varying environmental influences. For this reason sub-nyquist accuracy can be considered limited to commercial grade parts. Sub-nyquist promises fast measurement (<3 minutes) on a limited set of surfaces with limited accuracy.
Sub-nyquist Fizeau promises fast data acquisition with the ability to measure non-axially symmetric surfaces with nominally monotonically increasing curvature. Reversed curvature (gull wing) aspheres are not measurable with these systems.
Tilted Wave Interferometer for Asphere Measurement
A new entrant into asphere metrology is the tilted wave interferometer. In development for the last 10 years the tilted wave promises high speed metrology of asphere surfaces. By moving the source position multiple areas of an aspheric surface can be acquired and then analyzed. The tilted wave can be thought of as a stitching interferometer (without the motion) and yet requires a sub-nyquist type of calibration for every point in the measurement VOLUME.
Each point in the measurement volume must be calibrated for each transmission element. These calibrations can be temperature dependent and a function of the manufacturing tolerances. Calibration of the actual system is required and most likely on a repeated basis. This type of system seems close to commercialization and it will be interesting to learn of its measurement uncertainty, correlation to other technologies, speed of measurement (one of it proposed benefits) and cost.
Fizeau Interferometer Limited to Near Axially Symmetric and Monotonically Curved Aspheres
In all cases applying Fizeau interferometers to aspheric surfaces extends its capabilities to perform outside its “sweet spot”. Mathematical combinatorial techniques along with extensive “calibrations” achieve acceptable measurement uncertainty.
Even with these impressive innovations non-monotonically varying slopes and non-axially symmetric surfaces are a major limitation for Fizeau interferometers, especially if the surface reverses curvature relative to the base sphere. In these cases the reflected light does not enter the interferometer and the surface is not measurable. This is especially true for gull-wing and sombrero lenses and free form surfaces which cannot be measured with Fizeau interferometers. This is not to say that modified Fizeau interferometers don’t have their place regarding aspheres. The main benefit, when they are applicable is higher spatial resolution in an acceptable time period compared to stylus profilers. For general purpose measurement of the wide range of potential surface shapes is needed and when a high resolution or 3D image of the surface is not required, contact stylus and optical stylus systems are favored for asphere metrology.
Final Word
Though not generally considered an interferometer, the Luphos optical probe is a single point, multi-wavelength Fizeau interferometer.
It has the same limitations as all Fizeau interferometer with two benefits: Absolute position sensing and single point. The absolute positioning allows the probe to sense a position in space to nanometers within a few millimeters. Thus if the probe “falls off” a part it can regain position, depending on the stability of the metrology frame. Being single point, if the metrology frame and positioning system support the motions the probe can follow non-rotationally symmetric surfaces and potentially reversing curvature (gull-wing) parts. Thus it is more general purpose, and like any other stitching system can measure steep surfaces. Just like any Fizeau, deviations from measuring off the surface normal produce two errors: The signal can be lost if no light returns and ray-tracing errors occur in the probe degrading performance. These errors are accommodated by adding a B axis to an XYZ positioning system. The more complex motion of a B axis requires careful calibration to achieve 50 nm level performance.
Next post: Thin plates measurement
1 A. Kulawiec, “Extended Aspheric Measurement Capability with Subaperture Stitching Interferometry”, http://www.photonics.com/Article.aspx?AID=34816
2 M Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces”, Proc. of SPIE Vol. 7389 738916-1
3J. Greivenkamp ; A. Lowman and R. Palum”Sub‐Nyquist interferometry: implementation and measurement capability”, Opt. Eng. 35(10), 2962-2969 (Oct 01, 1996)
4 E. Garbusi, C. Pruss, J. Liesener, W. Osten, “New technique for flexible and rapid measurement of precision aspheres”, Proc. of SPIE Vol. 6616, 661629, (2007)
5 G.Berger, J. Petter “Non-contact metrology of aspheric surfaces based on MWLI technology”, Proc. SPIE 8884, Optifab 2013, 88840V (September 6, 2013)
