Optical fabrication and testing spans an enormous range of manufacturing procedures and optical test configurations.
The manufacture of a conventional spherical lens typically begins with the generation of the optic's rough shape by grinding a glass blank. This can be done, for example, with ring tools. Next, the lens surface is polished to its final form. Typically this is done by lapping—rotating and rubbing the rough lens surface against a tool with the desired surface shape, with a mixture of abrasives and fluid in between.
Typically a carved pitch tool is used to polish the surface of a lens. The mixture of abrasive is called slurry and it is typically made from cerium or zirconium oxide in water with lubricants added to facilitate pitch tool movement without sticking to the lens. The particle size in the slurry is adjusted to get the desired shape and finish.
During polishing, the lens may be tested to confirm that the desired shape is being produced, and to ensure that the final shape has the correct form to within the allowed precision. The deviation of an optical surface from the correct shape is typically expressed in fractions of a wavelength, for some convenient wavelength of light (perhaps the wavelength at which the lens is to be used, or a visible wavelength for which a source is available). Inexpensive lenses may have deviations of form as large as several wavelengths (λ, 2λ, etc.). More typical industrial lenses would have deviations no larger than a quarter wavelength (λ/4). Precision lenses for use in applications such as lasers, interferometers, and holography have surfaces with a tenth of a wavelength (λ/10) tolerance or better. In addition to surface profile, a lens must meet requirements for surface quality (scratches, pits, specks, etc.) and accuracy of dimensions.
In scientific inquiry and academic research, fabrication is the intentional misrepresentation of research results by making up data, such as that reported in a journal article. As with other forms of scientific misconduct, it is the intent to deceive that marks fabrication as highly unethical and different from scientists deceiving themselves. In some jurisdictions, fabrication may be illegal.
Examples of activities that constitute fabrication include:
Outright synthesis of experimental data; reporting experiments that were never conducted. Sometimes referred to as "drylabbing".
"Fudging", "massaging", or outright manufacture of experimental data.
Some forms of unintentional academic incompetence or malpractice can be difficult to distinguish from intentional fabrication. Examples of this include the failure to account for measurement error, or the failure to adequately control experiments for any parameters being measured.
Fabrication can also occur in the context of undergraduate or graduate studies wherein a student fabricates a laboratory or homework assignment. Such cheating, when discovered, is usually handled within the institution, and does not become a scandal within the larger academic community (as cheating by students seldom has any academic significance).
Precision is the authorized march of Royal Military College of Canada. The RMC band performs Precision on parades for march pasts, on Ex Cadet Weekends for the parade to the Memorial Arch, and on the return, the Cadet Wing sings Tom Gelley’s words to welcome the Ex Cadets to the Parade Square.
Precision was composed in 1932 by Denise Chabot, wife of Major C. A. Chabot, a Royal Canadian Artillery officer on staff as professor of French at the College at the time. She earned the degree of Associate of the Royal Conservatory of Music and was the president of the Kingston Music Club.
Precision was inspired by "Madelon", one of the popular marching songs sung and whistled by the cadets marching on their way to the Riding School, and the favourite song of the Class of 1932. Mme Chabot improvised a variation on the song, to represent the cadence of the cadets on the march. The composition starts, “We are the gentlemen cadets of RMC We have sworn to love and serve Her Majesty…”
In statistics, the dual term variability is preferred to the use of precision. Variability is the amount of imprecision.
There can be differences in usage of the term for particular statistical models but, in common statistical usage, the precision is defined to be the reciprocal of the variance, while the precision matrix is the matrix inverse of the covariance matrix.
One particular use of the precision matrix is in the context of Bayesian analysis of the multivariate normal distribution: for example, Bernardo & Smith prefer to parameterise the multivariate normal distribution in terms of the precision matrix rather than the covariance matrix because of certain simplifications that then arise.
The term precision in this sense (“mensura praecisionis observationum”) first appeared in the works of Gauss (1809) “Theoria motus corporum coelestium in sectionibus conicis solem ambientium” (page 212). Gauss’s definition differs from the modern one by a factor of . He writes, for the density function of a normal random variable with precision h,