# Selected Publications on Dimensional Metrology

**Other Calibrations**

**On The Measurement of Thread Measuring Wires**, Norden, B. Nelson, NBS Report **10-987**, 19 p. (January 24, 1973).

**Abstract:** In view of the future NBS three-dimensional facility, we have sought to review some of our current calibration procedures and, where appropriate, evaluate the feasibility of transfer to the new facility. In cases where it is not feasible to transfer, to upgrade our former procedures, this report is the first in a series which will be referred to as calibration procedure reports. In many cases the facts which will be presented in this series of documents are widely known but their collection into concise reports will, it is hoped, serve the purposes of: (1) acquainting other individuals in our section with the nomenclature of calibrations now, being performed, (2) serving as a focal point for discussion as to how we may either transfer or upgrade procedures, (3) permitting us to standardize many of our procedures so we may analyze our mechanical measurements to view the relative indexes of precision and, where appropriate, define new ones. Some procedures are always in a state of flux; therefore, only current calibration procedures will be emphasized. During recent months, with the installation of a computer time-sharing facility, we have adopted more automated procedures of data processing wherever possible. The advantages of this type of operation are self-evident. The methods of accomplishing this processing are varied, but a few appropriate ways will be discussed at some later date. In the specific case of the calibration of reference thread measuring wires, a version of the measurement assurance program has been adopted to assist in achieving the stated goals.

**Measurements of Cylindrical Standards**, Veale, Ralph C., NBS Internal Report **73-136**, 22 p. (March 14, 1973).

**Abstract:** Cylinders are widely used in industry and standards labs as a form of length transfer. The measurement algorithm used by the dimensional metrology section to determine the diameters of master cylinders is given in detail. It has been found that a mechanical transfer from interferometrically measured gage blocks is the most satisfactory method.

**Gage Block Flatness and Parallelism Measurement**, Beers, John S., Tucker, Clyde D., NBS Internal Report **73-239**, 8 p. (August 1973).

**Abstract:** Geometric properties of gage blocks are important in many length measurement applications. Methods are described for measuring the flatness of gaging faces and the parallelism between opposing gaging faces. These methods, used for many years, employ interferometers and electro-mechanical gage block comparators.

**On the Compression of a Cylinder in Contact with a Plane Surface**, Norden, B. Nelson, NBS Internal Report **73-243**, 67 p. (July 19, 1973).

**Abstract:** The measurement of a diameter of a cylinder has widespread application in the metrology field and industrial sector. Since the cylinder is usually placed between two flat parallel anvils, one needs to be able to apply corrections, to account for the finite measuring force used, for the most accurate determination of a diameter of the cylinder. An extensive literature search was conducted to assemble the equations which have been developed for deformation of a cylinder to plane contact case. There are a number of formulae depending upon the assumptions made in the development. It was immediately evident hat this subject has been unexplored in depth by the metrology community, and thus no coherent treatise for practical usage has been developed.

This report is an attempt to analyze the majority of these equations and to compare their results within the force range normally encountered in the metrology field. Graphs have been developed to facilitate easy computation of the maximum compressive stress encountered in the steel cylinder-steel plane contact case and the actual deformation involved.

Since the ultimate usefulness of any formula depends upon experimental verification, we have compiled results of pertinent experiments and various empirical formulae. A complete bibliography has been included for the cylinder-plane contact case for the interested reader.

**On Characterizing Master Involute Profiles**, Erber, Edgar G., Norden, Nelson B., NBS Internal Report **73-272**, 29 p. (August 28, 1973).

**Abstract:** The involute profile plays an important role in gear metrology. It is necessary to quantify that profile on involute masters so that an accurate for gear teeth may be transferred from the master profile. The procedures for calibration of a master involute profile on a two coordinate axis measuring machine is the function of this paper.

**A Method of Calibrating Two-dimensional Reference Plates**, Reeve, Charles P., NBS Internal Report **74-532**, 25 p. (July 26, 1974).

**Abstract:** With the acquisition of a three coordinate measuring machine the Dimensional Technology Section began investigating the problem of precisely measuring two-dimensional reference plates. The algorithm which was developed for this measurement process is highly redundant and incorporates a nonlinear mathematical model. Both the mean and standard deviation of the relative (x,y) coordinates of the points on the reference plates are estimated.

The long term goal of the investigation is to use this algorithm as a tool in developing a measurement process which is under statistical control. On the way to that goal certain problems and pitfalls associated with two-dimensional measurements are sure to arise and will be examined. It is hoped that some light will be shed on areas such as long term stability of measuring performance, measuring machine characterization, temperature problems, and the stability of two-dimensional standards.

**The Calibration of a Roundness Standard**, Reeve, Charles P., NBS Internal Report **79-1758**, 21 p. (June 1979).

**Abstract:** For the past decade the National Bureau of Standards has been making high precision roundness measurements using an algorithm which allows the spindle out-of-roundness to be separated from the true profile of the workpiece. The algorithm requires multiple traces on a roundness measuring instrument, and the resulting redundancy provides an estimate of the measurement precision. The primary purpose of this paper is to describe in detail the mathematical model used for this measurement process. Some related topics are discussed briefly and an example is given.

**The Calibration of Indexing Tables by Subdivision**, Reeve, Charles P., NBS Internal Report **75-750**, 38 p. (July 1975).

**Abstract:** The indexing table plays a vital role in the calibration of angle standards at the National Bureau of Standards. It is often useful to know the values of several different intervals on the table as precisely as possible. The usual measurement designs call for a complete intercomparison of two tables which are being calibrated simultaneously. Two new types of measurement designs have been developed which call for only a fraction of this effort. One type of design subdivides the entire circle on each table into equal segments, and the other design subdivides these into smaller segments. Together the designs form a flexible system for calibrating any desired intervals on the two tables. Formulae are given for the propagation of random errors through all levels of subdivision. An example is included.

**The Calibration of a Pentaprism**, Reeve, Charles P., Veale, Ralph C., NBS Internal Report **76-993**, 30 p. (January 1976).

**Abstract:** A pentaprism, or optical square, is one of a class of objects known as “constant deviation prisms” whose purpose is to bend a beam of light exactly 90° regardless of the angle of incidence of the light. It is used in many optical measurements where the line of sight or beam of light must be turned at a right angle. The calibration process which is described is fairly simple and requires two mirrors, two autocollimators, and a surface plate. Consideration is given to the effects of small angular errors in both the internal geometry of the pentaprism and the positioning of the pentaprism relative to an autocollimator. An example of the calibration of the important pentaprism parameters is given. A simple statistical test is employed for testing whether the measurement system is in control.

**The Calibration of Angle Blocks by Intercomparison**, Reeve, Charles P., NBS Internal Report **80-1967**, 24 p. (April 1980).

**Abstract:** One service performed by the National Bureau of Standards is the calibration of angle blocks. Test blocks normally come in sets of 15 nominal sizes from 1" to 45°. Their angular values are calibrated by intercomparison with NBS master angle blocks and other test blocks of the same nominal size. Each test block is also measured for its maximum out-of-flatness and out-of-squareness. Statistical tests are performed in order to maintain control over the short-term and long-term variability of the measurement process.

A complete description of the measurement process is given with special attention paid to the mathematical model for the measurements and the least squares estimation of the angular values. The method for determining the standard deviations of the short-term and long-term errors is also given.

**A Survey of the Temporal Stability of Angle Blocks**, Veale, Ralph C., Reeve, Charles P., NBS Internal Report **74-601**, 21 p. (November 1974).

**Abstract:** The National Bureau of Standards is often asked how frequently a set of angle blocks should be calibrated. In order to provide a basis for answering that question, a survey was made of the long-term stability of several sets of angle blocks over a ten-year period. Data is given concerning the short-term and long-term variability of the measurement process as well as the observed long-term slope of the computed values. The conclusion is that a significant long-term variation in the measurement system does exist, but the long-term slope of the blocks which were surveyed is not significantly different from zero.

**The Calibration of an Optical Flat by Interferometric Comparison to a Master Optical Flat**, Reeve, Charles P., NBS Internal Report **75-975**, 39 p. (December 1975).

**Abstract:** Optical flats are normally calibrated by one of two methods at the National Bureau of Standards. The most frequently used method involves a direct interferometric comparison of a test flat to a master flat. The purpose of this paper is to present a detailed description of this measurement process. Some of the topics discussed are methods of supporting the flats, effects of gravitational bending, measurement of interference fringes, formulation and solution of the linear least squares model, analysis of errors, choice of profile reference line, and display of profiles. An example is worked out in a step-by-step fashion in order to illustrate the process, and a statistical test is incorporated to check whether the process is in control.

**A Survey of the Stability of Optical Flats**, Reeve, Charles P., Veale, Ralph C., NBS Internal Report **73-232** 25 p. (June 1973).

**Abstract:** Some optical flat owners are concerned about the long term stability of their optical flats. To examine this problem, a survey was made of several optical flats which where calibrated by the National Bureau of Standards at least three times during the period from 1959 to 1972. The measured profiles of these flats are presented graphically so that the different calibrations can be compared. The conclusion of this survey is that optical flats are quite stable over a period of several years, but since the individual requirements for precision may vary greatly, it should be left up to the owner to weigh the appropriate factors in determining how frequently he needs his optical flat calibrated.

**On Characterizing Measuring Machine Geometry**, Hocken, Robert J.; Borchardt, Bruce R., NBS Internal Report **79-1752**, 22 p. (June 1979).

**Abstract:** We present a simple method for removing axis nonorthogonality and checking for length dependent scale errors in two-dimensional measurements. Use of this method requires that a two-dimensional master gage (ball or grid plate, for example) be measured in two positions which differ by a rotation of the plate 90° with respect to the measuring machine axis. The method is similar to that proposed by Reeve, but requires only linear least squares fitting on a small computer.

**Length Metrology of Complementary Small Plastic Rulers**, Doiron, Daniel T.; Doiron, Theodore D. Dr., Proceedings of the Measurement Science Conference, Pasadena, California, 7 p. (January 1994).

**Abstract:** The national measurement system concerns the relationships between individual measurements and the specific units of measure. In some cases, gage blocks for example, there are standards, a large body of scientific research, and considerable effort taken to trace the accuracy of blocks used in manufacturing back to the unit of length. The international trend to laboratory accreditation (NVLAP, NAMAS, etc.) is a formalization of the idea of assuring measurement accuracy by assessment of laboratory practice and evaluation of a measurement system’s relation to the unit of length.