James S. Marsh

Diffraction patterns of simple apertures

The Fraunhofer diffraction patterns of the triangle, trapezoid, and hexagon are calculated and displayed in moire plots. The diffraction pattern of the general polygonal aperture with a finite number of vertices can be calculated in terms of elementary functions.

Optical factors in judgments of size through an aperture

An expression is derived relating retinal image size to object size when the object is seen through a pupil forming an aperture stop for the eye. The image size is related to object position, pupil position, and state of accommodation of the eye on the assumption that the chief ray determines the image of an out-of-focus object. Data obtained by Biersdorf and Baird agree with the expression. The expression is used as the basis of a quantitative discussion of Hennessys informal experiment and Roscoes zoom lens hypothesis.

Computer holograms with a desk‐top calculator

Computer‐generated holograms have been produced on the plotter of an HP 9100B desk‐top calculator. The use of simple stick objects allows us to calculate analytically the Fourier transform, the amplitude and relative phase of which are represented on the plot. Techniques for efficiency enhancement and saturation reduction are discussed.

Contour plots using a moiré technique

A simple method utilizing a moire technique for producing contour plots is described and applied to the rendering of calculated Fraunhofer diffraction patterns.

Light distribution near the focal point of a two‐dimensional lens

The distribution of light in the focal region of a lens in two dimensions is calculated in terms of the Fresnel integral. The result is a comparatively simple but very good analog for the focal region of a three‐dimensional lens discussed by Born and Wolf. In particular the cigar‐shaped channel through which the light penetrates the focal plane appears in the two‐dimensional as well as the three‐dimensional case.

Magnetic and electric fields of rotating charge distributions II.

A charge distribution with axial symmetry is allowed to rotate with constant angular velocity around the axis of symmetry. The magnetic field of the resultant current density is calculated in terms of the electrostatic field of the charge distribution. The relation is of greatest utility in the calculation of the magnetic field of a rotating spherically symmetric charge distribution in terms of its electrostatic potential.

Measurement of behind-armor debris using cylindrical holograms

Cylindrical holography has been utilized to capture 180 degree(s) field of view of high speed ballistic events. In this paper, we detail the methodology, design, and experimental results for a cylindrical hologram system that captures the fragment fields behind a penetrated armor plate. It is critical to use the wrap-around approach for proper test evaluation because of the possibility of large armor chunks blocking other fragments. An 18 ns pulse width, 3 Joule ruby laser is used as the illumination source for these 45.7 cm diameter holograms. For this application, the primary challenge has been the mitigation of the large flash caused by the projectile/target interaction. Several flash reduction techniques are discussed including narrow- band and neutral density filtering. Experimental results for this ongoing effort are presented.

Fragment volume determination in bullet/armor holograms

This report presents automatic data reduction techniques for determining bullet and fragment volumes, positions, and momenta from holograms of bullets penetrating armor. The holography technique and the computer data reduction methods are described. Initial results are shown and sources of error in the technique are described. 2D digital images of the hologram are computationally combined by running a backprojection algorithm to produce a 3D array that represents the space containing the bullet and fragments. Thresholding the numbers in this space from the backprojection algorithm produces a representation of the bullet and fragments. Methods of automatically counting the voxels (3D picture elements) that occur in separated fragments have been programmed. These programs also find the centroids and shapes of the fragments and determine velocity using timing information. Volume errors are 40% in current results. These errors could be reduced to less than 3% if the described error sources were eliminated. Future work to improve the algorithms and the holographic process is described.

Distortion compensation and elimination in holographic reconstruction.

We discuss the quantitative location of objects from holographic images when the reconstruction wavelength differs from the recording wavelength. The holographic image equations are interpreted in a way that clarifies the meaning of stereo pairs of holographic images and indicates how backprojection methods can be used in holography to locate objects. Alternative methods involving the production of distortion-free regions in the holographic image field during reconstruction, the use of self-calibrating objects in the object field during recording, and triangulation can be used to locate objects.

Lloyd's Mirror As An Optical Processor

This paper describes the use of Lloyds mirror in two optical processing applications. First it is shown that if the narrow slit in the usual Lloyds mirror set up is illuminated by polychromatic light, the interference pattern is the Fourier Cosine transform of the spectral intensity distribution of the light. Lloyds mirror may thus be used as the transforming element in a Fourier transform spectrometer of exceedingly simple and rugged design. An experimental realization of this process is displayed. Second it is shown that if the narrow slit in the Lloyds mirror set up is replaced by a wide slit or, more generally, by a one dimensional object illuminated by non-coherent monochromatic light, the interference pattern obtained is the Fourier transform of the intensity distribution of the object. Lloyds mirror may thus be used to produce Fourier holograms in non-coherent light of one dimensional objects. An experimental realization of this process is displayed. If the object is two dimensional the interference pattern is the Fourier transform of the intensity distribution of the object along one direction. If the transform of the object is obtained in several orientations of the object, the object may be recovered by the same process used in CAT SCAN.