Abstract

The distribution of light in a searchlight beam is computed by determining the image formation at a point on the mirror or lens, then from this elemental image the image from a zone is derived. These zonal images are in turn summed graphically to find the beam from the complete searchlight. Some of the more important characteristics of a projected beam, such as angular width and the region in which the inverse square rule may be used to compute illumination, are outlined, and some attention is paid to the short range region that must often be used in testing. Lenses are discussed, largely to bring out their limitations, and some of the characteristics of the ellipsoid and hyperboloid are outlined. Test data on a mirror made of a combination of these two basic curves are presented to show how the filament images can be suppressed.

© 1945 Optical Society of America

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Figures (10)

Fig. 1
Fig. 1

Fresnel’s solution for excessive weight and cost of glass was to replace the original curve of a thick lens with a series of steps of limited height as shown above.

Fig. 2
Fig. 2

The inside step construction gives a Fresnel type that is easily kept clean, but the loss of light on the risers puts a sharp limit to the speed of the lens.

Fig. 3
Fig. 3

This is the simplest of the Fresnel lenses, but it is not economical of light, and its actual f speed is low.

Fig. 4
Fig. 4

The inverse square law is ordinarily used to compute illuminations in a searchlight beam. The shaded areas show the regions where this is a valid procedure.

Fig. 5
Fig. 5

The theory of beam formations given in the text is based on elemental images of the source that vary in size and shape as here shown for each point on a meridian line on the surface of the mirror.

Fig. 6
Fig. 6

The combination of all the elemental images in a zone into a zonal image is here illustrated, the elemental image being below the horizontal axis, and the zonal image above.

Fig. 7
Fig. 7

A graphical summation of zonal images into the total image, or beam, from a complete reflector is here carried out. Curve A is for an acceptance angle of 60°, B for 90°, and C for 120°, a common focal length being used for all three.

Fig. 8
Fig. 8

In the text these three mirrors of equal diameters but variable focal lengths and acceptance angles are used to illustrate how these variables are related to beam lumens, beam width, beam outline, and central intensity.

Fig. 9
Fig. 9

An ellipsoid and a hyperboloid having a common acceptance angle b will give beams identical in all parts when the product of their eccentricities is equal to unity.

Fig. 10
Fig. 10

This photograph of a curtain illuminated by a floodlight beam some 45° in diameter illustrates how the filament images ordinarily seen may be suppressed by attention to certain design details.

Equations (6)

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L 0 = y 2 100 r sin a meters ,
L 0 = 2 F 2 tan ( a / 2 ) sec 2 ( a / 2 ) 100 r cos a meters ,
W = 2 tan - 1 ( r / F ) degrees .
I = 4 π I 0 K F 2 tan 2 ( a / 2 ) ,
I = I 0 K ( R 2 / R 1 ) 2 candles ,
e e e h = 1 ,