The top of the so-called non-hemispherical packaging is still the hemisphere, however there is a piece of cylinder below, shown as figure 7, this shape is close to the real subject. At this time, the emergent light can be divided into two parts, one part is sent out from the top hemisphere, the other part is sent out from the cylinder. We assume that the cylinder height is half the semi diameter of the sphere (h= r /2), but the maximum incidence angle of the cylindrical part is arctg (1/2) (=26.50). It is easy to get the incidence angle of the cylindrical part. For the hemispherical part, based on sine theorem, △ABO is shown as figure 7:

Figure 7 non-hemispherical packaging sketch maps

We can work out the incidence angle of the cylindrical part. The refractive index of the packaging material is 1.5, the total refraction angle is 420, but the LED incidence angle of this kind of packaging shape doesn’t exceed this value. According to the refraction theorem and angle calculation, we can get the angle of the emergent ray relative to the symmetry axis, namely the attitude angle.

According to 2.1, we can get the light intensity distribution curve between 0-90 degrees, as well as the attitude angle and the relatively light intensity value Wp, Ws of the corresponding p,s component. Work out the incidence angle i and emergence angle i2, as well as the average light intensity value Tp, Ts of p, s component. Work out the average value of the two and calculate the relative quantity, get the relatively light intensity distribution curve between 0-90 degrees, as shown in figure 8

Figure 8 non-hemispherical LED relatively light intensity distribution curve

The joint of the cylinder and the hemisphere causes the rough of the relatively light intensity distribution curve. According to the calculation result, when the cylinder height is half the semi diameter of the sphere, the beam angle is 90, therefore, we only need to consider the top efficiency. After calculation, the top emergence light is about 88% of the LED chip total emergence light. The interval is 0.1, the cylinder height is respectively 0.5-1.3 the semi diameter of the sphere, the efficiency of the same refractive index and different height, as shown in the following table:

Figure 9 the influence of the ratio of the cylinder height and sphere semi diameter on the efficiency

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