The light intensity curves for LEDs, regardless of whether they are collimated with a lens or reflectors, follow a bell shaped curve (often referred to as a “Lambertian” curve). The 50% intensity point for an LED with no optic (bare LED) is virtually always at approximately 120 degrees (60 degrees in each direction).
The 50% point (known as the “beam angle” or “viewing angle”) is a lesser number of degrees depending on the collimating specification used. The beam angle is the total angle in both plus and minus directions.
What is not commonly known by those not experienced in the physics of LED light emission and optics is that the Lambertian LED light intensity curves can be very misleading in terms of how much light is actually arriving at the receiving end.
The emitted light travels in a straight line whose length varies as the angle increases. A beam of LED light traveling at an angle of 45 degrees from straight ahead is at a diagonal, which is the hypotenuse of that 45-degree angle. That is, the light must travel 1.414 farther to reach its destination. For angles greater or less than 45 degrees, that diagonal distance is more or less.
Furthermore, it should be noted that light intensity (just like radio and sound waves) decreases inversely as the square of the distance. This characteristic is known as the “inverse square law.” That means that the light traveling diagonally, per a 45 degree shift to the left or right decreases by 1.0/1.4 x 1.4 or 1/1.96 = 1/2 if rounded off. The result is that the intensity of the LED beam of light, traveling at a 45-degree angle toward a wall, is reduced by 50% from what it would be if just traveling straight ahead at zero degrees.
Consequently, when one looks at a Lambertian LED intensity curve, or a “polar intensity plot” one must divide any value by the correction factor in order to know how much the light level is being attenuated before arriving at the target end.

Figure 4
shows a typical grow-light configuration, with the lighting place 2 feet above a 4×4 ft. growing area. It is well known that uneven light can adversely affect growth objects. Not only is inadequate light an issue, however; too much light can be an equal concern. In an ideal situation, the light would be perfectly even across the 16 sq. feet of growing area. Achieving such a perfectly “homogeneous” light level is next to impossible in grow light systems. Even near-homogeneity is difficult to achieve without substantial expense or attenuation of received light, as when substantial diffusion is used. While it is clear that high efficiency homogeneity is virtually unachievable, it is unnecessary to accept the severe light level variations resulting when LED optics are not carefully chosen with the “inverse square law” in mind.

Figure 5 shows what happens with typical grow light optics specified as “90 degree” and “60 degree” lenses or reflectors. Not only does the received light drop off faster; the optic for a 21 mm COB LED can result in the received light level received, instead of the expected 50% drop off at the prescribed beam angle, actually being far worse. Figure 4 shows that the typical COB optic causes a drop off in received light, down to only about 20% at 45 degrees in one direction, resulting in a 5:1 light variation across the grow area. In fact it is common to see variations up to 8:1 or more in a small area grow-light configuration where collimation is used.

The optimized EvenBeam lens has only dropped to 50% lens matching the emitted-light reduction of a so-called 90-degree optic. A similar reduction takes place for a 60-degree optic, where the 60-degree EvenBeam lens exhibits only half the drop-off. The EvenBeam lens, over a full 80 degrees has only a 40% drop meaning the light level across the 4×4′ area varies no more than approximately 1.4:1.
Part of the challenge has to do with the size of the COB. A typical lens for a 3mm LED might be only about 12mm in diameter to be able to collect all the light emitted up to 180 degrees and redirect it. That means a lens for a 21mm LED should ideally be at least 7 times larger, approximately 140-150 mm (close to 6 inches) in diameter. Instead of using such a far larger diameter, the EvenBeam lens is shape-optimized to minimize the sharp drop-off at the wider angles so there is not such a disparity of light levels across the growing areas.

What you don’t know about LED light intensity curves for grow light apps