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Reflector Synthesis of a LED Lighting Device for Hay Bay Lighting

Problem Description

Optical calculations are carried out for problems where desired luminous intensity distribution of lighting devices must be provided. This is the illumination of rooms (for example, warehouses) with luminaires suspended at a great height for concentrated luminous intensity distribution (Fig. 1). The calculation is carried out for rotational symmetry.

Fig. 1 Types of luminous intensity distribution

Light Source

CREE MC-E high-luminance light-emitting diode is chosen as a light source (Fig. 2)

Fig. 2 LED light source

The LED light source luminous efficacy is more than 80 lm/W and luminous flux is 430 lm. The LED luminous intensity distribution is cosine (Fig. 3).

Input ParameterValue
Type of light source Point
Type of light distributionI(α) – see Fig. 3
Type of the curve interpolation Linear

Fig.3 Luminous intensity distribution of LED source

Illuminated Area

The required level of average illuminance Eav for shelving storage warehouses is 200 lux. The ratio of  Emax/Emin should be not more than 1.5.

To calculate the reflector shape (synthesis problem), the luminous intensity distribution curve recommended for illumination problem of this type (Fig. 4).

Input Parameter Value
Direct light flux from the sourceOn
Type of light distributionLuminous intensity distribution curve
Luminous intensity distribution I(α) – see Fig.4
Boundary angular coordinates0,30°


For more effective luminous flux conversion, reflector for each LED was calculated. Thus, the initial data for reflector calculations are specified by the LEDs location and number (Fig. 4).

Fig.4 Variations of a luminaire construction

Input ParameterValue
Reflectance  0.8
Start angle40°
Final angle90°
Initial radius50 mm
Number of calculation points100

Calculation Results

As a result of the calculations, the full accordance with the illuminance requirements is obtained. Fig. 5 represents the calculated reflector shape and the ray-tracing.

Fig. 5 Calculated rotationally symmetric shape


This example shows how to design the reflector shape of specified dimensions on the basis of the required luminous intensity distribution of the lighting device. Calculated reflector shape provides high light output ratio of the lighting device (80%).

Fig. 6 and 7 represent the results of the lighting design of warehouse lighting project using DIALux 4.10. Luminaires are represented as yellow contour lines. The isolux curves are represented at the working plane (floor) level (Fig. 8).

Fig. 6 Room plan (DIALux)Fig. 7 Project visualization (DIALux)Fig. 8 Illuminance distribution on the floor (DIALux)