David S. Grey

Fourier Treatment of Optical Processes

Many optical processes of image formation, image transfer, and image analysis may be represented as one, or a succession of several, linear operations. A linear operation upon a flux distribution function of an n-dimensional argument is defined as one which replaces the value of the function at a point by a linear, weighted average taken over a neighborhood of that point. While such an operation is completely determined by the weighting function used, it is also determined by a “wave-number” spectrum which is a function of an n-dimensional wave-number vector. This wave-number spectrum is the complex conjugate of the n-dimensional Fourier transform of the weighting function. The wave-number spectrum of the flux distribution modified by any number of successive linear operations is the product of the wave-number spectrum of the original distribution, and the wave-number spectra of the several linear operations. An analysis thus performed in wave-number space replaces successive integrations by successive multiplications.This method of analysis is an extension of the usual method of treating filters in electronic circuits, and may be used to solve problems analogous to those treated in circuit theory. These are: (1) to evaluate the performance of a system; (2) to design a process to search an image for a configuration; (3) to reproduce a picture, with discrimination in favor of a configuration desired, and against others; and (4) to equalize a picture, i.e., to remove image degradation.

Infra-Red Microspectroscopy*

A discussion of the performance characteristics of an infra-red microspectrometer is given in terms of the cross-sectional area and minimum volume, V, which can be observed with satisfactory signal-to-noise ratio. Methods of increasing the ratio of measured absorption to spectrometer noise are discussed and five ways are enumerated. It is pointed out that for a microscope objective of numerical aperture NAm associated with a spectrometer of numerical aperture NAs, the useful magnification is (NAm)/(NAs). The design of reflecting-type infra-red microscope objectives having numerical apertures up to 1.5 is described.A description of an experimental infra-red microspectrometer is given. Use is made of a commercial spectrometer and conversion from a micro to a macro instrument can be made in a few minutes. In the experimental arrangement no changes were introduced that affected the operation of the spectrometer as a macro instrument. Calculations indicate that by making use of other components now available, such as a hotter source and a smaller, more sensitive thermal detector, it will be possible to obtain infra-red spectral measurements of specimens whose linear dimensions approximate those set by diffraction.Examples of infra-red spectra of crystals, fibers, and tissues of microscopic area are shown. Comparisons of spectral data with those obtained for macro samples are made and an indication of the experimental limitations of the technique is given.

A New Series of Microscope Objectives: I. Catadioptric Newtonian Systems*

The problem of computing a microscope objective corrected for visible light and for ultraviolet light is reviewed. As it does not seem possible to achieve freedom from chromatic aberrations over this interval with purely refractive objectives of large numerical apertures, a study of catadioptric objectives limited to spherical surfaces is initiated. Catadioptric objectives containing two mirror surfaces may be described as deriving from either the Newtonian or the Schwarzschild telescope objective. Construction data are given for Newtonian objectives which have numerical aperture 1.0 and which are corrected from 220 mμ through the visible spectrum. These modified Newtonian objectives have one serious defect: a large central portion of the aperture is obscured.

A New Series of Microscope Objectives: II. Preliminary Investigation of Catadioptric Schwarzschild Systems*

This paper presents a preliminary study of combining the Schwarzschild pair of mirrors with lenses of fused quartz and fluorite to obtain an ultraviolet microscope objective. It is found that the catadioptric Schwarzschild objective is superior to the catadioptric Newtonian objectives described in Paper I.An objective using spherical surfaces and corrected from 220 mμ into the near infra-red is described. The obscuring ratio of this objective is 7 percent in area at NA 1.1.

A New Series of Microscope Objectives.* III. Ultraviolet Objectives of Intermediate Numerical Aperture†

Paper II of this series demonstrates that spherical lens elements combined with spherical mirrors may provide well-corrected and achromatized ultraviolet microscope objectives. The present paper presents a further study of several types of catadioptric Schwarzschild systems which provide microscope objectives relatively easy to construct, convenient to use, and for which ultraviolet and visual range performance characteristics are not compromised. Several modifications with numerical apertures within the range 0.4 to 1.0 are presented.

Athermalization of optical systems.

Equations are given for the condition that the focal surface of a lens system remain at a predetermined position for a range of ambient temperatures. Simple methods of satisfying these equations for lens systems composed predominantly or entirely of plastic components are described.

Computed Aberrations of Spherical Schwarzschild Reflecting Microscope Objectives

A microscope objective with (small) central obstruction of aperture and small wave-front deformation has a loss of amplitude at the center of the Airy disk which may be expressed in terms of losses due to spherical aberration, coma, and central obstruction. These losses are essentially independent; the net loss is the sum of the separate losses. Data are presented from which these losses for Schwarzschild spherical mirror systems of high initial magnification may be computed. It is shown that for visible or ultraviolet light and for numerical apertures greater than about 0.5, the net loss of central amplitude becomes excessive unless the object field is restricted to an extraordinarily small diameter. The numerical aperture at which such restriction of the field is necessary may be increased if the initial magnification is made small, e.g., about 8×, as is possible and convenient for infrared microspectroscopy.

Orthogonal Polynomials As Lens-Aberration Coefficients

Circular polynomials orthogonal over an elliptical exit pupil and their use in lens design and tolerancing are described.

New Class of Wide-Range Logarithmic Circuit for a Light-Intensity Meter

A new wide-range logarithmic circuit for a light-intensity meter is described. The circuit, consisting only of photoconductors and constant resistors, takes advantage of the inverse power law that the photoconductors obey. The indicator (microammeter) used is of simple linear type: the deflection is proportional to the current. Accordingly, the over-all response is logarithmic in light intensity. An experimental unit covering more than four decades of intensity is described. The same principle may be applied to nuclear radiation meters.