The contour integration formula,
E=
L/2∫
s cos
δ·
dω for calculating the illuminance of a flat surface source is composed of cos
δ and d
ω, which are not easy to solve. Based on analysis of a three dimensional model, the above formula was modified into the following formulae:
(1) When the surface source is parallel to the illuminated plane:
E'=
L/2∫
ban/
l2)
dx(2) When the surface source is inclined to the illuminated plane by ∠
β:
(
E')=
L/2cos
β∫
ban/
l2dx(3) When the surface source is perpendicular to the illuminated plane:
((
E'))=-
L/2z∫
ba1/
l2dxwhere
E'=the illuminance component of the interval A to B on the boundary of the flat surface source,
n=the length of an intercept on the
y axis by the tangent to the boundary,
l=the distance between the illuminated point and the minute segment AB on the boundary of the flat surface source. Since
n and
l2 in these formulae can easily be obtained from
x,
y and
z, all calculations of the illuminance of a flat surface source of an arbitrary shape that can be expressed by
x and
y can easily be obtained from the sum of the illuminance components
E'.
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