So when the light source is illuminated to the target receiving plane perpendicular to the optical axis direction, the intensity distribution of the light source is [7]:
which I0 represents luminous intensity on the normal line, r is the distance between LED and the target reception plane, By Formula (4) that, the illuminance of LED at an arbitrary point P (x, y) in the Cartesian coordinate system on the x, y plane can be expressed as
which I represents light intensity of the surface light source, (X,Y) represents the coordinates of the surface light source in the x, y plane point.
In order to better study the LED array, we may study the light intensity distribution of two LEDs at a certain distance apart from each other. Because LED is a kind of incoherent light source,the total intensity of illumination at a certain area of the plane is the superposition of the two individual LEDs [8].