NATIONAL BUREAU OF STANDARDS The National Bureau of Standards1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Institute for Computer Sciences and Technology, the Office for Information Programs, and the Office of Experimental Technology Incentives Program. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of the Office of Measurement Services, and the following center and divisions: Mechanics Heat Cryogenics2 Optical Physics - Center for Radiation Research — LabElectromagnetics - Time and Frequency'. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized materials needed by industry, commerce, educational institutions, and Government; provides advisory and research services to other Government agencies; and develops, produces, and distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials, the Office of Air and Water Measurement, and the following divisions: Analytical Chemistry Polymers Metallurgy Inorganic Materials — Reactor Radiation — Physical Chemistry. THE INSTITUTE FOR APPLIED TECHNOLOGY provides technical services developing and promoting the use of available technology; cooperates with public and private organizations in developing technological standards, codes, and test methods; and provides technical advice services, and information to Government agencies and the public. The Institute consists of the following divisions and centers: Standards Application and Analysis Electronic Technology Center for Consumer Product Technology: Product Systems Analysis; Product Engineering - Center for Building Technology: Structures, Materials, and Safety; Building Environment; Technical Evaluation and Application Center for Fire Research: Fire Science; Fire Safety Engineering. THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition, and effective utilization of automatic data processing equipment; and serves as the principal focus wthin the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer languages. The Institute consist of the following divisions: Computer Services Systems and Software - Computer Systems Engineering - Information Technology. THE OFFICE OF EXPERIMENTAL TECHNOLOGY INCENTIVES PROGRAM seeks to affect public policy and process to facilitate technological change in the private sector by examining and experimenting with Government policies and practices in order to identify and remove Government-related barriers and to correct inherent market imperfections that impede the innovation process. THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS; promotes the development of the National Standard Reference Data System and a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum accessibility to the scientific information of the world. The Office consists of the following organizational units: Office of Standard Reference Data — Office of Information Activities Office of Technical Publications 1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234. 2 Located at Boulder, Colorado 80302. Library Semiconductor Measurement Technology: U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary Dr. Sidney Harman, Under Secretary Jordan J. Baruch, Assistant Secretary for Science and Technology NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director APPENDIX C directly; the remainder of the harmonics may be calculated by using a simple recurrence relation for the cosine function. The use of a periodic object greatly simplifies the calculation of the intensity distribution in partially coherent imaging. In general, the calculation of the image intensity requires three separate integrations: (1) the integration over the source as given by eq (C-8) to determine the performance of the optical system; (2) the integration over the tject spectrum as given by eq (C-7) to determine the intensity spectrum; and (3) the integra tion over the intensity spectrum as given by eq (C-3b) (the inverse Fourier transform) to obtain the intensity distribution itself. In practical calculations, these integrations ca be intolerably tedious. The above analysis shows that with a one-dimensional periodic ctject, two of the three integrations, eqs (C-3b) and (C-7), reduce to discrete summations, eqs (C-13) and (C-14), thus eliminating the problems of convergence associated with numercal integration. Although infinite limits are specified for the summations in eqs (C-13 and (C-14), the function T(1;52) vanishes for large values of the arguments, due to the f. nite extent of the pupil function and the source function. Therefore, the summations in e: (C-13) and (C-14) may be truncated at predetermined limits without loss of accuracy. So great are the advantages of using a periodic object that it is worthwhile to express eve a non-periodic object in terms of a periodic model. This is readily accomplished if a lar period is chosen so that the object is effectively isolated and does not interfere with its periodic neighbors. The periodic model may be compared directly with the non-periodic ctject to verify the accuracy of the approximation. It should be emphasized that this per. ic approximation, which is so easily checked, is, in fact, the only approximation in the is aging calculation; all the other steps of the calculation are exact. In practice, the image plane is sampled by a scanning slit, which must be convolved with thy intensity distribution to obtain the distribution recorded by the scanning system. Since convolution in the image plane corresponds to multiplication in the pupil plane, it is c.venient to multiply the intensity spectrum in eq (C-13) by the Fourier transform of the s Thus, the intensity spectrum actually observed is where w is the full width of the scanning slit in dimensionless coordinates. Therefore, the complete calculation for the partially coherent imaging process is chara: ized by the equation A periodic rectangular waveform as shown in figure C-1, which characterizes a periodic object, is given by a Fourier series, eq (C-11), with coefficients < 0.1, each line is effectively isolated and behaves as a single line object. The Then w t uantities t and 단 t tò may, of course, be complex to model a line object with phase variation. lthough the procedures described above simplify the calculation of the image intensity disribution in partially coherent imaging, the integration for the function T describing the ptical system, eq (C-8) or eq (C-10), remains a formidable problem. It will be noted that his integration represents a generalized convolution of the source function J with the obective pupil function K. Where the source and objective apertures are circular and the obective pupil includes aberrations, this convolution has no simple solution and implies an Extremely tedious numerical integration. To avoid this, two alternative compromises are _vailable. irst, where the source aperture is small (less than the objective aperture), it is possible o reduce the integration to one dimension rather than two, in which case numerical integraion becomes feasible. It is thus possible to test the effects of aberrations such as deocusing and spherical aberration. As the source size approaches the size of the objective perture, this model becomes less reliable. econd, if all variations in the source aperture and objective pupil are suppressed (i.e., o aberrations), then the two-dimensional integration corresponds to the generalized convoluion of three uniform circles; that is, the problem reduces to finding the area of the mutu1 intersection of the source aperture and the shifted objective pupils (see fig. C-2 and ef. [C-4]). This is a fairly strenuous exercise in logic and geometry, but it yields an eficient algorithm for the optical performance function T. he above method may be extended to systems with annular sources (see fig. C-3). First, he function To is computed for a system including a source with radius equal to the outer adius of the annulus. Second, the function T is computed for a source with radius equal o the inner radius of the annulus. Then the difference between To and TI yields the value |