Richard E. Swing

Ambiguity of the Transfer Function with Partially Coherent Illumination

The one-dimensional case of the image of a sinusoidal transmittance distribution in partially coherent illumination (with the quasimonochromatic approximation) is described analytically, and shown generally to bear a nonlinear relation to the object. It is shown that the significant parameter is the ratio of coherence interval to the diameter of the Airy disk (or diffraction spot) of the imaging lens. It is further shown that since the spatial frequency of the object is related to coherence interval, typical nonlinear effects can take place at low frequencies. Since the transfer function is defined only for the incoherent limit without ambiguity, an apparent transfer function, dealing only with the image component which existed in the object, is used for comparison. The harmonics generated by the nonlinear behavior are ignored, and the variation of transfer function is observed to be a function of coherence and input modulation. It becomes apparent that the transfer function, as currently defined and measured, is inadequate to describe optical-system performance under all conditions of illumination.

Conditions for Microdensitometer Linearity

A simple microdensitometer system is analyzed using the principles and analytical techniques of the theory of partial coherence. A specification of the physical conditions under which the instrument is linear is obtained, for incoherent illumination. The illuminating mutual intensity is then generalized, by the Van Cittert–Zernike theorem, and conditions on the partial coherence of the preslit illumination necessary for effective incoherence are determined. The new conditions determine a mode of linear operation for the microdensitometer for which an optical transfer function may be unambiguously defined.

General Transfer Function for the Pinhole Camera

The theory of partial coherence is applied to the classical pinhole camera. This study extends the previous work of Reynolds and Ward, and derives the general transfer function for the pinhole camera. System performance is covered for all field conditions, from Fresnel to Fraunhofer, in closed solution. From initial considerations of the one-dimensional case, a technique for generating low-frequency, controlled-modulation sinusoidal irradiance distributions is established; its transfer function is determined. Experimental evidence is introduced to support the theoretical contentions; agreement is obtained.

Microdensitometer Optical Performance: Scalar Theory and Experiment

The scalar theory of microdensitometer performance developed in previous papers is revised and expanded to include coherent illumination. The central ideas of scalar microdensitometry are combined from several basic sources and summarized ; this paper serves as a convenient single source of microdensitometer theory. Eight distinct variations of instrument configuration and operation are identified, and the image characteristics and conditions for linear microdensitometry are developed for each. The concept of effective incoherence is summarized and discussed. Further consideration of the problems associated with aperture sizes, determination of the sampling aperture size and image vs sample scanning are presented. An experimental test program, carried out with the Mann-Data Microanalyzer, by experienced operators, under closely controlled conditions to test the theory, is reported. Among the conclusions is that the instrument manifests its best performance with overfilled optics and sample scanning, and that an increased reduction factor on the influx side would be useful with image scanning. Several fundamental problems surface during the course of the investigation. These are discussed and the need for further study in certain areas is emphasized.

The Optics of Microdensitometry

A review of the current developments in microdensitometry is made, with emphasis on the investigations leading to the current level of understanding of optical performance. The classical microdensitometer is then analyzed according to the principles of the theory of partial coherence. Conditions for the insuring of linear operation are derived, and the idea of effective incoherence at the source aperture is presented with a discussion of the implications. The various microdensitometer configurations are subjected to analysis, and the four possible variations (viz., overfilling, underfilling, with two possible locations for the sampling aperture) are thoroughly evaluated. The new concept of linear microdensitometry is discussed and summarized briefly. The current concerns of microdensitometry are then presented and considered. The restrictions on maximum sample frequency as a result of the partial coherence in the illumination is a major concern of this paper, and tables are presented for typical microdensitometer configurations that delineate the kinds of limitations that can be expected.

Comparison Of Linewidth Measurements On An Sem/Interferometer System And An Optical Linewidth-Measuring Microscope

In the current linewidth-measurement program at the National Bureau of Standards, the primary measurement of micrometer-wide lines on black-chromium artifacts is made with an interferometer located in a scanning electron microscope (SEM). The data output consists of a line-image profile from the electron detector and a fringe pattern from the interferometer. A correlation between edge location and fringe location is made for both line edges to give the linewidth in units of the wavelength of a He-Ne laser. A model has been developed to describe the interaction of the electrons with the material line and thereby relate a threshold value on the SEM image profile to a selected point on the material line. An optical linewidth-measuring microscope is used to transfer the primary measurements to secondary measurement artifacts; these artifacts will be used to transfer the linewidth measurements to the integrated-circuit industry. Linewidth measurements from the SEM/interferometer system and the optical linewidth-measuring microscope are compared, and the level of measurement uncertainty for each system is discussed.

The Theoretical Basis Of A New Optical Method For The Accurate Measurement Of Small Line-Widths

As part of the effort conducted at NBS to solve some of the fundamental problems associated with width measurement of very small (l-5-µm) lines and spaces, the performance of an optical microscope with coherent illumination is investigated. From these studies, the theoretical basis for a new method of accurate width measurements is developed and explored. The new method, in effect, produces an optical transformation in which the image no longer resembles the original line but in which the location of the line-edges is marked by two narrow, dark lines within a bright surround. The correct line-width is then given by the distance between these two lines, a measurement that eliminates the orientation problems normally associated with filar eyepieces and sidesteps the coherence problem that affects shearing eyepieces. Suggestions are made about implementing the technique. Available microscope objectives are not suitable for such a system, and a redesign is recommended.

The Case For The Pupil Function

In 1968, those of us at NBS concerned with classical optics, felt it important to resume the testing of optical systems and components and decided to develop a method that was in keeping with the advances being made in lens design and manufacture. The technique previously used at NBS1 was limited to about 200 cycles/mm by considerations of partial coherence, and could measure phase shifts only with great difficulty and low precision. The forthcoming high-quality optics indicated by activity in the design community were clearly beyond the capability of this testing system. Further, the increasing use of microscope optics in such devices as microdensitometers, reduction cameras and other specialized equipment showed the need for an accurate testing technique that would include these kinds of optical components. Our intent was to concentrate on the test and evaluation of high-quality optics such as might be used in microdensitometry, microelectric circuit applications, and high resolution aerial cameras, to develop an inexpensive and accurate measurement technique, and to provide a modest NBS measurement service that would be used by commerical firms and other government agencies when it was necessary (for contractual reasons) to have the NBS imprimatur on the results or when it was impractical for the requestor to have his own test equipment.

Adjustment and practical calibration of microdensitometers

The calibration of densitometers and microdensitometers is discussed in terms of the physical standards necessary to accomplish it. The need for calibration of these instruments is briefly considered, particularly for those forensic investigators looking at evidential photographic materials with a microdensitometer. The calibration process is reviewed for both instruments to prepare for a new procedure to follow. Since a great deal of microdensitometer work is carried out on materials about whose characteristics nothing is known, the problem of obtaining data in terms of diffuse (visual) density is almost impossible. However, a bootstrap calibration, based on the scan of a standard step tablet and scans of selected portions of the specimen is shown to be feasible. It requires a calibrated densitometer to quantify the results and has reasonable accuracy within the necessary assumptions. An example is given.

The Sampling Aperture For Linear Microdensitometry

In the development of modern linear microdensitometry, the trend of optical system design has been towards the condition of underfilling the efflux optics, with total collection of light after it passes through the sample. The system transfer function is therefore attributable to the influx optics, and the sampling aperture is the light distribution impinging on the sample, reduced from an illuminated slit or circular aperture through the influx optical system. The maximum frequency response of the system is obtained when the sample is illuminated with the impulse response of the influx optics. However, the theoretical impulse response can only be realized by imaging a delta-function and this is photometrically impossible. Similarly, because the system images an illuminated aperture onto the sample, scanning with a pure, geometrically-characterized slit or spot is not possible due to lens response and diffraction. These two problems are investigated, for both coherent and incoherent illumination. For both impulse response and slit image, the MTF is investigated, and its deviation from the ideal is calculated. The results are characterized in terms of RMS-MTF differences over the spectrum for 10, 5, 2 and 1% levels. The controlling parameter is the ratio N/R, where R is the reduction factor employed for the influx optics, and N is the number of resolution elements contained within the nominal object slit width. The study shows that there are significant differences in these values for the same RMS difference level, with coherent and incoherent illumination, and that there are compromises to be made with both kinds of illumination. The results of this study facilitate calculation of system response for any configuration of object slit and influx optics (within the linear microdensitometer system), and defines limits on slit sizes for operation with impulse response and geometrically characterized slit images for the sampling aperture. The effects expected with the linear polarization associated with laser illuminat