Light from an LED has a Lambertian radiation pattern, and the radiation pattern depends on the Lambertian order. And Lambert's mode number depends on the semi-angle of the LED. I have a clear understanding of the semi-angle of LED. But I am not able to understand the significance of Lambert's mode number and can't figure out that why we need this factor. Please anyone clarify.
Definitely, Lambert's mode number or the Lambertian order depends on the half-power angle of the LED. Also, it affects the radiation intensity. The Lambertian order is a measure of how focused the LED light is. You can plot the received intensities on a plane perpendicular to the LED's axis and by changing the Lambertian order, the spatial intensity distribution changes. So LED's with different half-power angles and Lambertian order have different spreading of light.
Kapila W. S. Palitharathna Thank you so much for this great explanation.
Dear Mohd IMRAN Khan ,
Kapila W. S. Palitharathna explains the function of the Lambert mode number m. Simply you need to draw curves for cos^m phi with m increases an integer say 1,2,3 and so on. You will see theta the radiation pattern becomes more concentrated near the angle phi =0.
Therefore m represents the directivity of the radiation of the light source in space.
Best wishes
Lambertian order m indicates the half-power angle of the LED. This semi-angle is a measure of how large is the area illuminated by the LED radiation pattern. A small m (around m=1) means the LED illuminates a wide region, and a high m is for LEDs with highly focused light. Also m indicates how concentrated is the LED light is in the direction that points the LED. Nevertheless, LEDs come in many varieties and forms, and the angular distribution of the intensity profile may be quite different from the Lambertian model. A more realistic model for the radiant intensity pattern may be found in:
I. Moreno and C-C Sun, "Modeling the radiation pattern of LEDs," Opt. Express 16, 1808 (2008).
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