When designing light diffusing glasses to be used for the illuminating equipment it often occurs that the trigonometrical trace in a two-dimensional plane as used in designing ordinary optical lenses can not be applied and rays are to be traced in a tri-dimensional space on account of their asymmetricity with oahect to the optical axis.
As an example, a deflecting roundel for signal light is designed. Ordinary signal lights have spread angles of 1.5-3°. When located along the curved track a deflecting roundel is attached in order to spread the light beam horizontally as shown in Fig. 3. On the other hand, it is one of the effective means to reduce the so called “signal phantom” that the front surface of the roundel is direted downward as shown in Fig. 4. In this case, rays are traced in a tri-dimensional space shown in Figs. 5 and 6 by the formulae (1), (5)-(15). The result shows in this case that the light beam deflects not only horizontally but also vertically as shown in Figs. 7 and 8, a. The beam battern is bent as shown there and in order to correct it the flutes on the roundel are to be tilted to its vertical axis as shown in Fig. 9. Fig. 8, b shows the beam battern from the roundel with tilted flutes.
The light distribution is calculated by the formula (17). Fig. 10 shows the light distribution curve calculated in such a way from the roundel with the flutes the cross section of which is a single arc of a circle. Fig. 11 shows the required light distribution curves with the location of signal shown in Fig. 2 by the formula (19) which is derived from (18) assuming the validity of the Ricco's law to the visibility of signals. The required curves show under great deflecting angles generally smaller light intensity than the calculated curve. But with the greater deflecting angle the distance from the track to the signal reduces and hereby the Ricco's law will not apply. Then, as greater light intensity will be required than shown in Fig. 11, the curve in Fig. 10 will be considered to be practical with most location of signals. In order to fit the calculated light distribution to the required one the section of the flute is to be the combination of several arcs of circles having different radii or has the form of a curve satisfied with the differential equation f (r) =1/dr/dh.

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Measurement of the total luminous flux of linear light source by the integrating photometer rends to involve some errors due to unlike light distribution. The error of measurment can by discussed in terms of the coefficient of final illumination, K (θ, ψ) and relative sensitivity, Pm/Po. From the view point of proceeding coef f icinents, the author explains the following in this paper.
(1) It is possible to divide the error due to presence of the screen into two components, i. e. screen error and shadow error.
(2) The best position of the screen is 2/5 of radius from the spherical center.
(3) In the interest of the relative sensitivity, it is better to locate the linear source in parallel than at the right angle with the screen.
(4) The coefficient of relative sensitivity drops rapidly to about 80% of diameter, with more approaching to a spherical wall. Therefore, it is [desirable that the length of source is about 85% of diameter.
(5) As f ar as the linear source is measured within the limit of Pm/Po≅1, the substitution for the linear source and the point source can be measured at the same accuracy as for the susbtitution for the point and point source.
(6) It is certain that H. Korte's transmission screen is effective for avoiding the aforementioned screen error, but it is useful only in palliating the difference of the light distribution, the disposition of the source, etc.

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