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Calculating Profile with Limited Dimensions

This example is available in a professional edition.

This example is valid for the reflector synthesis problem.

The example is reflector’s profile calculation under specified illuminance distribution. Reflector synthesis is provided for different reflector's initial parameters to choose the optical system with specified dimensions and high efficiency.

Input data:

Input parameterValue
Type of the problemReflector synthesis
The system symmetryRotational
Type of light distributionIlluminance Distribution
The light source’s parameters 
Type of SourceEllipse
1st semiaxis, mm61
2nd semiaxis, mm97.15
The reflector’s parameters 
Final Angle, deg55
The parameters of the illuminated area 
Start Coordinate, m0
Start Coordinate, m-10.5
Height, m10

Optical system of mirror reflector and ellipsoid lamp is used often. For example, it is suitable for industrial lighting, and the system consisting of aluminum mirror reflector and sodium high-pressure lamp (NAV) is used (fig. 1).

Fig. 1 Typical optical system for industrial lighting

Such light fixture forms needed illuminance distribution on illuminated area for specified mounting height. For profile calculation it needs to know initial parameters which may mean dimensions of reflector. Standard dimensions for such lighting problem are in ranges 280-300 mm for height and 450-500 mm for diameter. Height (B) and diameter (A) are shown on Fig. 4. These values are limit dimensions of calculating profile in this example. The example is reflector’s profile calculation under specified illuminance distribution (Fig. 2) – reflector synthesis. There are several calculations characterized with different reflector's initial parameters. Initial parameters are initial radius and start angle of reflector which define curve of profile and thus dimensions.

The optical system’s factor is needed to calculate too. The factor is calculated as ratio of optical system’s output luminous flux to lamp’s luminous flux. Its value must be over 70 %. The luminous intensity distribution of the light source is shown on Fig. 3.

Fig. 2 The illuminance distribution curveFig. 3 The luminous intensity of the light source

There are results of calculations in the table below:

ProfileThe reflector’s parametersDimensions (Fig. 4)Factor of optical system, %
Initial Radius, mmStart angle, degA, mmB, mm


Fig. 4 The dimensions of reflectorFig. 3 The luminous intensity of the light source

The general view of calculated optical system is shown on Fig. 5. The calculated profile curves with different reflector’s initial parameters are shown on Fig. 6. The illuminance distribution curves of calculated optical systems are shown oh Fig. 7.

It is clear from the table above that all three calculated profiles form needed illuminance distribution and have factor over 70 %. However the task was to calculate the reflector which has dimensions limited with 280-300 mm for height and 450-500 mm for diameter. And this is third reflector with height B=294 mm and diameter A=473 mm (Fig. 4), and its factor equals 80 %.

Fig. 5 Optical system in 3D-viewFig. 3 The luminous intensity of the light source

Note. There is luminous surface of real lamp shown on the figure above.

Fig. 6 The light source and compared profiles: blue curve - first profile, pirple curve - second profile, red curve - third profileFig. 7 The illuminance distribution curves of compared optical systems: yellow curve - direct light curve, green curve - verifying curve, red curve - specified curve

Note. Light distributions are normalized to the same value of axial illuminance for the ease of comparison.


When the reflector is calculated it is needed to account practicable limitations on dimensions. Variations in reflector’s initial parameters give set of various profiles differing in dimensions. Such method of solution allows choosing the proper reflector from set of various calculated reflectors. In this example the reflector’s initial radius and start angle are varied to calculate three different profiles. All three calculated reflectors are form specified illuminance distribution and have factor over 70 %. However, only one of them has appropriate dimensions which are limited in specified range.