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English Afrikaans Albanian Arabic Armenian Azerbaijani Basque Belarusian Bulgarian Catalan Chinese (Simplified) Croatian Czech Danish Dutch Filipino Finnish French German Greek Hebrew Hindi Hungarian Icelandic Indonesian Irish Italian Japanese Korean Latvian Lithuanian Macedonian Malay Maltese Norwegian Persian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swahili Swedish Thai Turkish Ukrainian Urdu Vietnamese

CaliBall Papers

A Model for Cavity Induced Errors with Wavefront Slope in High Accuracy Spherical Fizeau Metrology (ABSTRACT)

A paper by Sykora of Zygo showing that the Random Ball Test (RBT) works less and less precisely as the numerical aperture of the transmission sphere becomes smaller. In other words, the RBT works best for fast transmission spheres and another means of calibration should be used for slow test optics.

A Practical Implementation of the Random Ball Test (ABSTRACT)

ABSTRACT: A note describing the Random Ball Test (RBT) for calibrating interferometer transmission spheres by averaging a number of interferograms taken of different, randomly positioned, patches of a precision silicon nitride ball.

A Simple Ball Averager for Reference Sphere Calibrations (ABSTRACT)

ABSTRACT: A paper by authors at NIST about simulations and experiments done with the Random Ball Test (RBT) giving criteria for establishing the precision of transmission sphere calibration using the RBT.

Absolute Measurement of Surface Roughness (ABSTRACT)

ABSTRACT: A paper by Creath and Wyant explaining the method of calibration of surface roughness interferometers. This same method is used in the Random Ball Test (RBT) except that the random surface over which interferograms are averaged is not a plane but a sphere.

Calibration of Interferometer Transmission Spheres (ABSTRACT)

ABSTRACT: A readable copy of the original paper on the Random Ball Test (RBT) authored at NIST that was published in a non-archival meeting journal. Even here the figures are not legible. For better example figures see "A practical implementation of the random ball test".

Calibration of Spherical Reference Surfaces for Fizeau Interferometry (ABSTRACT)

ABSTRACT: A study by Burke and Wu of CSIRO comparing several methods of transmission sphere calibration that concludes the Random Ball Test (RBT) has the highest precision of all the methods tried though it is tedious to perform for highest precision if the RBT is not automated.

Fabrication and Testing of a High-Precision Concave Spherical Mirror (ABSTRACT)

ABSTRACT: Slides by Burke and Wu of CSIRO about Random Ball Test (RBT) calibration of a transmission sphere prior to its use in the test of a high precision hemisphere.

Interferometer Calibration using the Random Ball Test (ABSTRACT)

ABSTRACT: Paper by W. Cai, et. al., comparing experimental results in the Random Ball Test (RBT) between using a clean ball and systematic measurement versus a somewhat dirty ball and casual measurement.  The results gave identical precision within reasonable statistical limits.

Limits for Interferometer Calibration Using the Random Ball Test (ABSTRACT)

ABSTRACT: A paper by P. Zhou examining the precision with which the Random Ball Test (RBT) can be done as a function of the spatial frequency of the errors in the transmission sphere, the radius of curvature of the ball used and diffration at the edge of the aperture. The conclusion is that the RBT works most precisely for fast transmission spheres.

Self-Referencing Calibration Method for Transmission Spheres in Fizeau Interferometry (ABSTRACT)

ABSTRACT: Another paper by Burke and Wu at CSIRO that says the Random Ball Test (RBT) is the most precise method for calibrating fast transmission spheres but that it is tedious for highest precision unless automated.

Bibliography: Papers on the random ball test, aka as CaliBall

Certification, self–calibration and uncertainty in optical surface testing.”, Evans, C. J., & Davies, A. D. (2013), testing. International Journal of Precision Technology, 3(4), 388-402. Shows that the RBT along with an uncertainty analysis and a known wavelength source gives "traceability that satisfy the requirements of ISO 17015".

"Interferometer calibration using the random ball test." Cai, W., Kim, D. W., Zhou, P., Parks, R. E., & Burge, J. H. (2010, June). In Optical Fabrication and Testing (p. OMA7). Optical Society of America. Compares experimental results of the RBT between a clean ball and systematic measurement versus a dirty ball and casual measurement. The results are nearly the same.

"A practical implementation of the random ball test." Parks, R. E. (2006, October). In Optical Fabrication and Testing (p. OFMC12). Optical Society of America. Describes a practical implementation the RBT using a CaliBall™ for calibrating interferometer transmission spheres by averaging interferograms of various, randomly positioned, patches of a precision SiN ball.

"Absolute measurement of surface roughness." Creath, K., & Wyant, J. C. (1990). Applied optics, 29(26), 3823-3827. Explains the method of calibration of surface roughness interferometers. The same method is used in the RBT except that the random surface is a precise ball.

"Calibration of interferometer transmission spheres." Parks, R. E., Evans, C. J., & Shao, L. (1998, June). In Optical fabrication and testing workshop, OSA Technical digest series (Vol. 12, pp. 80-83). The original paper describing the Random Ball Test (RBT) by authors at OPG and NIST that was published in a non-archival meeting journal.

"Limits for interferometer calibration using the random ball test." Zhou, P., & Burge, J. H. (2009, August). In SPIE Optical Engineering+ Applications (pp. 74260U-74260U). International Society for Optics and Photonics. Shows that RBT precision is adversely influenced if the transmission sphere is not nulled to the ball, and that the results degrade the slower the transmission sphere.

"A simple ball averager for reference sphere calibrations." Griesmann, U., Wang, Q., Soons, J., & Carakos, R. (2005, August). In Optics & Photonics 2005 (pp. 58690S-58690S). International Society for Optics and Photonics. Simulations and experiments done with the RBT giving criteria for establishing the precision of transmission sphere calibration using the RBT.

"A model for cavity induced errors with wavefront slope in high accuracy spherical Fizeau metrology." Sykora, D. M. (2008, October). In Optical Fabrication and Testing (p. OWB7). Optical Society of America. Shows the RBT works less precisely as the numerical aperture of the transmission sphere becomes smaller, therefore the RBT works best for fast transmission spheres.

"Self-referencing calibration method for transmission spheres in Fizeau interferometry." Burke, J., & Wu, D. S. (2010, August). In SPIE Optical Engineering+ Applications (pp. 77900F-77900F). International Society for Optics and Photonics. Good discussion of how many averages are needed to reach a certain level of precision. Points out that environmental noise should be based on the distance the test object is from the TS, not how far the ball is.

"Application of the random ball test for calibrating slope-dependent errors in profilometry measurements." Zhou, Y., Ghim, Y. S., Fard, A., & Davies, A. (2013). Applied optics, 52(24), 5925-5931. Shows that OPD errors are greatest where the slope of the calibration ball is the greatest at the edges of the field of view of SWLI and confocal microscopes.

"Self calibration for slope-dependent errors in optical profilometry by using the random ball test." Zhou, Y., Ghim, Y. S., & Davies, A. (2012, September). In SPIE Optical Engineering+ Applications (pp. 84930H-84930H). International Society for Optics and Photonics. Paper shows that OPD errors are greatest at the edges of the field of view of SWLI and confocal microscopes where the slope of the calibration ball is the greatest.

"Self-calibration for microrefractive lens measurements." Gardner, N., & Davies, A. (2006). Optical Engineering, 45(3), 033603-033603. Discusses use of very small balls in the RBT to calibrate a micro-interferometer for testing the form of lenses in microlens arrays.

"Retrace error evaluation on a figure-measuring interferometer." Gardner, N., & Davies, A. (2005, August). In Optics & Photonics 2005 (pp. 58690V-58690V). International Society for Optics and Photonics. Shows that retrace errors can have a significant impact on the precision of the RBT when using very small diameter balls as part of the RBT.

"Ray-trace simulation of the random ball test to improve microlens metrology." Gardner, N. W., & Davies, A. D. (2006, August). In SPIE Optics+ Photonics (pp. 629204-629204). International Society for Optics and Photonics. Ray trace simulation of the RBT using a model ball based on spherical harmonics, but only shows initial results for a perfect ball and 1/2 wave of spherical aberration.

"New methods for calibrating systematic errors in interferometric measurements." O’Donohue, S., Devries, G., Murphy, P., Forbes, G., & Dumas, P. (2005, August). In Proc. SPIE (Vol. 5869, p. 58690T). Shows that transmission sphere errors determined by RBT or other means must be removed from subaperture test data before stitching subapertures together.

"Micro-optic reflection and transmission interferometer for complete microlens characterization." Gomez, V., Ghim, Y. S., Ottevaere, H., Gardner, N., Bergner, B., Medicus, K., & Thienpont, H. (2009). Measurement Science and Technology, 20(2), 025901. Describes an interferometer specifically designed to test microlenses in both reflection and transmission that was calibrated by means of the RBT.

"Estimating the root mean square of a wave front and its uncertainty." Davies, A., & Levenson, M. S. (2001). Applied optics, 40(34), 6203-6209. Estimating the rms error of an optical surface using the RBT as an example of the process, and shows that without some correction the rms estimate is conservative.

"Absolute calibration of a spherical reference surface for a Fizeau interferometer with the shift-rotation method of iterative algorithm." Song, W., Wu, F., Hou, X., Wu, G., Liu, B., & Wan, Y. (2013). Optical Engineering, 52(3), 033601-033601. Demonstrates that a complex method of Zernike decomposition and shearing gives virtually identical calibration results for a transmission sphere as the RBT.

"Calibration of spherical reference surfaces for Fizeau interferometry: a comparative study of methods." Burke, J., & Wu, D. S. (2010). Applied Optics, 49(31), 6014-6023. Compares several methods of calibrating interferometer transmission spheres and concludes the RBT is the most precise but lengthy if ultimate precision is needed.

"Transmission sphere calibration and its current limits." Yang, P., Xu, J., Zhu, J., & Hippler, S. (2011, May). In SPIE Optical Metrology (pp. 80822L-80822L). International Society for Optics and Photonics. After pointing out many possible sources of error in the RBT the paper gives an example of calibrating a f/3/3 transmission sphere to 3.8 nm rms.

"Calculation of the reference surface error by analyzing a multiple set of sub-measurements." Maurer, R., Schneider, F., Wünsche, C., & Rascher, R. (2013, September). In SPIE Optical Engineering+ Applications (pp. 88380E-88380E). International Society for Optics and Photonics. Calculation of a reference surface by a complex explicit calculation based on the location and orientation of subapertures rather than a random average as in the RBT.

"Analysis and experiment of random ball test." Lu, L., Wu, F., Hou, X., & Zhang, C. (2012, October). In 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT 2012) (pp. 84170X-84170X). International Society for Optics and Photonics. Another verification that the precision of the RBT improves as the square root of the number of averages, this time using air floatation to rotate the ball.

"Using the random ball test to calibrate slope dependent errors in optical profilometry." Zhou, Y., Troutman, J., Evans, C. J., & Davies, A. D. (2014, June). In Optical Fabrication and Testing (pp. OW4B-2). Optical Society of America. Demonstrates using a ball as a means of varying the slopes presented to an optical profilometer in order to calibrate OPD errors dependent on the slope of the measurand.

Case Studies & Testimonials

Why is proper alignment so important?

Here is a case of a very happy customer due to better optics.

A few days ago an astronomer friend of mine commented that he had gotten the optics of his telescope improved and the improvement reduced the time it took to get data by a factor of 3. For an astronomer this is a dramatic improvement since observing time on large telescopes can cost thousands of dollars an hour.

My friend did not say how the optics had been improved, but the important point is that better optics, whether due to figure errors, mounting or alignment mean more productive optics. I generally think of better optics as a better product leaving the manufacturing facility without thinking about how much the better optics mean to the productivity of the customer.