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CaliBall I & II

CaliBall, a calibration artifact and mount for use in the Random Ball Test

Interferometric optical test precision is primarily limited by the interferometer transmission sphere quality. The CaliBall is a means of in-house transmission sphere calibration using the Random Ball Test.

The CaliBall is designed so that it can be used immediately before or after a critical test of an optic without changing anything in the test setup other than inserting or removing the CaliBall itself.

Transmission spheres are factory calibrated, but shipping, handling, thermal and other environmental effects degrade the factory calibration precision.

The CaliBall eliminates these uncertainties by calibrating the transmission sphere in the test set up, an assurance that the interferometric test results are precise.



The CaliBall uses averaging of random patches of the CaliBall to calibrate transmission spheres exactly the same way surface roughness interferometers are calibrated by averaging random patches of a plane surface.

Simple CaliBall Instructions

CaliBallTM is a 25.4 mm diameter, silicon nitride ball and kinematic mount used to calibrate phase-measuring interferometers by determining the errors in the transmission sphere reference surface.

The CaliBallTM is located with its center at the focus of the interferometer transmission sphere and aligned to better than one fringe.

A measurement of the ball is taken, the ball picked up, arbitrarily rotated and replaced in its mount.

The center of the ball will return to its original position due to the kinematic mount. Another measurement of the ball is then taken.

This process is repeated about a dozen times and the interferograms averaged.

The average represents the errors in the transmission sphere and interferometer because the ball is extremely round and the small, uncorrelated imperfections of the ball average to zero.

The calibration can be done in as little as 10 minutes and the results are difficult to dispute.



Calibration Procedure

The calibration procedure is simple and the precision of the results are easily calculated. 

See "A Practical Implementation of the Random Ball Test"

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Other Papers

 Papers about the Random Ball Test and the use of the CaliBall are listed under “Technical Library”.

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CaliBall Instructions

Detailed Instructions for CaliBallTM

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Both CaliBall models are available directly from Optical Perspectives Group.


CALIBALL™ I is for either horizontal or vertical interferometer set ups but it requires an x-y-z stage to position the CaliBall center at the transmission sphere focus.



CALIBALL™ II is for horizontal set ups which bayonet mounts into a typical Zygo or ESDI 4″ mount.


Scroll down to bottom for a bibliography of archival CaliBall papers.

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Caliball Users

CaliBall users include OptiMax, Edmund Optics, IOM, Fisba Optik, Zeeko, Goddard Space Flight Center, The Aerospace Corporation and others.

logos caliball 2cropped

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

  • How small can the PSM be used for centering on a cylindrical axis?

    The PSM is an ideal tool for finding the center of curvature of a ball or the axis of a cylinder. The question is for how small a ball or cylinder can the PSM do this?

    The smallest article that was readily available was a piece of monofilament 8 pound test fishing line that was 290 μm in diameter. There was no problem finding the axis of the fishline, and separating the Cat’s eye reflection from the surface from the confocal reflection of the axis. The experiment was done with a 5x objective, and the result would have been even more definitive using a 10x objective.

  • 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.

OPG Customers