Abstract
Although the surface-integration method is fundamental way to calculate the illuminance by a flat surface source, its application to a complex source has been considered to be difficult,
It, however, turned out that this problem can be solved by the perspective figure of the flat surface source on a horizontal picture plane in the height of v from illuminated plane is obtained by the via-perspective method.
Then, the illuminance obtained from elementary area t·dtde of the perspective figure in polar-system is calculated by the surface-integration method, as shown in the following equations.
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Where E=the illuminance at calculating point, L=the luminance of the source, t=the radius vector to the elementary area, p=the radius vector to the contour, θ= the radious vector angle from the y axis, n=the intercept on the y axis, l= the distance between the elementary area and the calculating point.
The above second intermediate equation obtained from the double-definite-integration when solved for t is transformable to the modiffied-cotour-integration formula, as shown in the third equation.
Since this modiffied-contour-integration formula is applicable to all forms of the flat surface source, the application range of surface-integration method can extend even to all types of complex fiat surface source.
