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Reflector Synthesis of a LED Lighting Device for Office Lighting

Problem Description

The purpose of optical calculations is to obtain the required illuminance distribution on the working plane. The calculation is carried out for cylindrical symmetry.

Light Source

The light source is composed of three linear arrays of LEDs located along the sides of a pyramid with the cross-section of a equilateral triangle (Fig 1).

Fig. 1 Schematic representation of light sources

Each LED lamp has a luminous flux of 1700 lm and a luminous efficacy of 85 lm/W

The luminous intensity distribution curve (LIDC) is shown in Fig 2. LIDC’s shape is explained thatlinear arrays are mutually rotated by 120°. The LED luminous intensity distribution is assumed to be cosine.

Input ParameterValue
Type of light source Line
Light distribution type  I(α) – see Fig. 2
Type of the curve interpolationLinear

Luminous Intensity Distribution of the LED Source

Illuminated Area

The lluminance level at the working plane for office lighting is specified according to lighting regulations. The average illuminance level Eav must be not less than 500 lux if Emax/Emin is not more than 1.3.

For reflector synthesis the required illuminance distribution was specified (Fig 3)  A LED source is placed at a height of 2 m above the working plane 

Input ParameterValue
Direct light from the source  On
Type of light distribution Illuminance
Illuminance distribution E(x) – see Fig. 3
Distance to the working plane3 m
Boundary linear coordinates–3.3 m

Specified Illuminance Distribution on the Working Plane


Reflector dimensions are limited: 150 mm in width and 75 mm in length. Based on this the initial radius of the reflector shape is assumed to be 75 mm.

Input Parameter Value
Start angle285°
Final angle75°
Initial radius75 mm
Number of calculation points100 

Optical Scheme

Results of the Calculations

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. 6 represents the verifying illuminance curve, calculated by simulation routine. Fig. 7 represents the luminous intensity distribution curve of the lighting device.

Calculated Reflector ShapeIlluminance distribution on the working plane Red curve is the specified distribution Green curve is the distribution obtained by checking calcuation Luminous Intensity Distribution of the Lighting Device


The example presents an algorithm of optical design for a specific case. Type of the light source and illuminance distribution on the working plane were specified as input data for illumination problem.

The calculated reflector shape provided high luminaire efficiency (80%) and permitted use of fewer luminaires in the room in comparison with standard light sources (fluorescent light source). In addition LEDs have a long lifetime.

Fig. 8 and 9 represent the result of the lighting design of office lighting project using DIALux 4.10. Luminaires are represented as yellow contour lines.  The illuminance isolines are represented at the working plane level (Fig. 10).

Fig. 8 Room plan (DIALux)Fig. 9 Project visualization (DIALux)Fig.10 Illuminance distribution at the working plane level (DIALux)