Are the optical properties of lighting fixtures with the same beam angle the same?

Through detailed analysis, this paper clarifies that luminaires with the same beam angle may not have the same optical performance, and even have great differences. Clarified people's fuzzy understanding of the beam angle of the lamp, which is more reasonable and scientific in the lighting design.

1 Introduction

The beam angle is one of the most important technical parameters of the luminaire. It refers to the angle between the two directions of the light intensity equal to 50% of the maximum light intensity on one plane of the beam center line. (The definition of the beam angle is adopted by the International Commission on Illumination CIE. Instead of the North American Lighting Engineering Association IESNA's "10% Maximum Light Intensity" definition). According to the size of its value, it is usually divided into three types: narrow beam, medium beam and wide beam.

They can be visually distinguished by a light distribution curve. However, there is a potential problem here: Is the optical performance of the luminaire with the same beam angle the same? The purpose of this paper is to solve this problem through detailed analysis, which will help lighting designers to design lighting more rationally and scientifically.

2, the mathematical expression of the light distribution curve

In [3], the intensity of the axisymmetric light distribution luminaire in a certain direction is expressed as the following formula:

I(θ)=I0(cosθ)m (1)

For the convenience of discussion, and without loss of generality, this paper takes the 30° beam angle as an example. In order to simplify the problem, only the symmetrical lamps with axial symmetry are discussed here.

It can be seen from the literature [3] that for the beam angle 2β=30°, β=15°, the index m:


Set the lamp efficiency η=72%, then the center light intensity:


Therefore, the light intensity expression:

I(θ)=2405.7(cosθ)19.9937 (2)

The corresponding Cartesian coordinates and polar coordinate distribution curves are shown in Figure 1:

Are the optical properties of lighting fixtures with the same beam angle the same?

Figure 1 30 ° beam angle lamp light distribution curve

In some cases, the formula (1) can well fit the light intensity Iθ at the direction angle θ.

However, this formula does not cover all possible light distribution shapes.

Here, we discuss the following four typical light distribution curve shapes. For comparison, their beam angles are unified to 30°, and the power of all four lamps is 10W, and the lamp efficiency is 72%, that is, when the initial luminous flux is 1000LM, the luminous flux output is 720LM.

With the "Microsoft Mathematics" software, we fit each of the light distribution curves into a mathematical expression in order to give a precise conclusion.

For each light intensity expression of each luminaire, check whether the beam angle is 30°, and accurately calculate the luminous flux output by the following formula (3). The derivation process of formula (3) and the symbolic meaning are shown in [3].

Φ=2π0°90°Iθsinθdθ (3)

22MM Metal Switches

22Mm Metal Switches

22Mm Metal Switches is a larger size in the Metal Switches serious. It is designed vary from people and regions and the design of larger operation button face is for increasing the convenience and comfort when operating.

In order to create more function and save more space for this , Waterproof Metal Switch, we adopt single and dual control design, so our one switch could have multiple purposes. This Stainless Steel Switch are widely used in human interface panel, it has P67 dust-proof and waterproof function, IK10 stainless steel material damage resistance level, advanced mechanical life.

Anti Vandal Switches

In addition, in order to meet customer requirements, our larger Anti Vandal Switches has passed the EU green environmental protection RoHS certification, the US UL testing certification, IP67 certification and TUV certification.

Moreover, customers can choose the metal button with LED light indication according to their own product requirements. The LED lamp beads are all from international brand suppliers to ensure the high life of LED lamp beads and the long-term work without discoloration effect.

Waterproof Push Button Switch

22Mm Metal Switches,22Mm Waterproof Metal Switch,22Mm Stainless Steel Switch,22Mm Metal Flush Push Button Switch