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.