# Refined Test and Evaluation Method of Side Viewing Angle of LED Display Module
## 2 Methods  
### LED Luminous Intensity and Distribution  
The luminescence intensity of an LED represents how strongly or weakly it emits light in a certain direction. The different light intensity at different spatial angles directly affects the minimum viewing angle of the LED display device. If the light intensity distribution of the LED super-large color display is inconsistent, the audience facing the display at a large angle will see a color cast image. Luminescence intensity is an important parameter to characterize light-emitting devices. The unit of luminous intensity is candela (cd), which represents the luminous flux (in lumens) emitted by the light source within a unit solid angle of a given direction [10]. The angular distribution of the luminous intensity \(I(\theta)\) describes the luminous intensity distribution of the LED light-emitting device in all directions in space. The relative luminescence intensity along the normal direction is defined as 1, and the larger the angle away from the normal direction, the smaller the relative luminescence intensity is [11]. Assuming that all LED devices on the LED module are point light sources with the same luminous intensity distribution and luminous flux, the approximate Lambertian light source, that is, the luminous intensity distribution of the LED device can be expressed by the power function of the viewing angle cosine [12], which is given by Equation (1):  
\[I(\theta)=I_{0}\cos^{m}(\theta) \tag{1}\]  
Luminance refers to the ratio of the luminous intensity of the illuminant to the area of the light source, that is, the luminous intensity per unit projected area. The human eye can intuitively feel the luminance, so this paper judges the viewing angle characteristics by collecting the luminance. Then, the luminance \(L\) (cd/m\({}^{2}\)) of a point P on the target plane at a distance from the LED light source \(r\) is as follows:  
\[L(r,\theta)=\frac{I_{0}\cos^{m}(\theta)}{r^{2}} \tag{2}\]  
Among them, \(I_{0}\) is the normal luminous intensity of the LED, \(\theta\) is the luminous angle of the LED and \(m\) is the light distribution curve of the LED light-emitting chip, which is related to the packaging material of the LED package [13]. In the practical engineering application of Mini LED flip-chip LED display, the light-emitting chip needs to be fixed on a substrate, through a process called \"bonding\", and in this process, the optical axes of all LED light-emitting chips are required to be parallel [14], but due to differences in technology, the optical axis of one or some LED light-emitting chips is offset, as shown in Figure 1.  
The bonding causes the optical axis to shift, resulting in a change in the maximum luminous intensity at the angle. Let the spatial horizontal angle offset be \(\Delta\theta\) (the vertical angle is not common in engineering, so this article only studies the horizontal angle), then the luminance changes to  
\[L(r,\theta+\Delta\theta)=\frac{I_{0}\cos^{m}(\theta+\Delta\theta)}{r^{2}} \tag{3}\]  
Since the distance \(r\) of the optical axis offset of the light-emitting chip relative to a certain point in space is extremely small, it is considered that \(r\) does not change. Divide Equation (3) by Equation (2) to get the change ratio of the luminance after the optical axis shift:  
\[\frac{L(r,\theta+\Delta\theta)}{L(r,\theta)}=(cos\Delta\theta-tan\theta sin \Delta\theta)^{m} \tag{4}\]  
After the bonding is finished, the light-emitting chip needs to be encapsulated to protect the light-emitting chip. During this process, the particulate matter and thickness of the adhesive layer will affect the light-emitting viewing angle and light-emitting intensity of the light-emitting chip.