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Utilization Factor and Illuminance Uniformity Estimation for Optical System

This example is available in a professional edition.

This example is valid for the reflector simulation problem.

In this example various optical systems are estimated for different geometrical parameters of lighting area. The illuminance distribution of optical system and its uniformity are set as maintained parameters of light distribution quality.

Input data:

Input parameterValue
Type of the problemReflector simulation
The system symmetryRotational
Type of light distributionIlluminance Distribution
The parameters of the illuminated area 
Start Coordinate, m10
Filnal Coordinate, m0
The light source’s parameters 
Type of SourceEllipse
TransparentOff
Luminance15000
Geometry 
1st semiaxis, mm61
2nd semiaxis, mm97.15
The reflector’s parameters 
Reflectance0,8
Type of presentationRay-tracing function
ProfileSpecial

Geometric parameters of illuminated area differ in each lighting project. These parameters are size of illuminated area and mounting height of light fixture. Thus there should use optimal light fixture with optical system which forms satisfactory light distribution in each case. Accept illuminance distribution and its uniformity as maintained parameters of light distribution quality. Various optical systems will have different light distributions therefore different efficiency for concrete light project. When quality parameter posses needed value, used optical system is the optimal solution.

In this example three optical systems are compared for various geometrical parameters of illuminated area. The light source is ellipsoid sodium high-pressure lamp (NAV). On Fig. 1 there is general view of optical system to be simulated. Profile’s parameter and luminous intensity distribution type (Fig. 2) of compared optical systems are in table below.

LID typeReflector’s Initial Radius, mmOptical system factor, %
Narrow335.62336384
Cosine274.33942382
Wide257.01904875

Fig. 1 The optical system

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

Fig. 2 The luminous intensity distribution curves of compared optical systems: red curve - narrow LID, cyan curve - cosine LID, magenta curve - wide curve

Note. Light distributions are normalized to the same value of light flux for the ease of comparison.

Efficiency of the optical systems (UF) is defined as product of utilization factor and factor of optical system. Utilization factor is ratio of incident light flux on illuminated area to full light flux of optical system. Also it needed to calculate illuminance uniformity (IU) for more detailed comparing as said above. Uniformity is ratio of minimum illuminance value to maximum illuminance value on the illuminated area.

Mounting height and area width (Fig. 3) used in calculating are shown in table below:

Geometry parameter for calculationValue
Mounting height, m6, 10, 14
Area width, m2.5, 6, 10, 20

Fig. 3 Illuminated area

Illuminance distribution is calculated for three different optical systems with various luminous intensity distributions (Fig. 2): narrow, cosine and wide. There are general views of optical systems and illuminance distribution on area width of 20 m on the Fig. 4 - 9. It is clear from the Fig. 4, 6, 8 that bright region of illuminated area enlarges when luminous intensity distribution of the optical system becomes wider.

Fig. 4 Optical system with narrow luminous intensity distribution and its illuminance distribution for mounting heihgt 6 mFig. 5 The illuminance distribution curves of compared optical systems for mounting height 6 m: yellow curve - direct light curve, red curve - illuminance of system with narrow LID, cyan curve - illuminance of system with cosine LID, magenta curve - illuminance of system with wide LID

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

Fig. 6 Optical system with cosine luminous intensity distribution and its illuminance distribution for mounting heihgt 6 mFig. 7 The illuminance distribution curves of compared optical systems for mounting height 10 m: yellow curve - direct light curve, red curve - illuminance of system with narrow LID, cyan curve - illuminance of system with cosine LID, magenta curve - illuminance of system with wide LIDFig. 8 Optical system with wide luminous intensity distribution and its illuminance distribution for mounting heihgt 6 mFig. 9 The illuminance distribution curves of compared optical systems for mounting height 14 m: yellow curve - direct light curve, red curve - illuminance of system with narrow LID, cyan curve - illuminance of system with cosine LID, magenta curve - illuminance of system with wide LID

Result of optical system calculating is set of UF and IU values for given geometric parameters. On Fig. 10 - 12 there are graphs showed like efficiency of optical system depends on area width and mounting height. The following rules ensue from the graphs:

  1. IU increases and UF decreases when area width is fixed and mounting height enlarges;
  2. UF increases and IU decreases when area width enlarges and mounting height is fixed;

For each of compared optical systems UF and IU rate of change differ. So it can be found from graphs which optical system is optimal for concrete case.

Fig. 10 Utilization factor (UF) and illuminance uniformity (IU) curvesFig. 11 Utilization factor (UF) and illuminance uniformity (IU) curvesFig. 12 Utilization factor (UF) and illuminance uniformity (IU) curvesFig. 9 The illuminance distribution curves of compared optical systems for mounting height 14 m: yellow curve - direct light curve, red curve - illuminance of system with narrow LID, cyan curve - illuminance of system with cosine LID, magenta curve - illuminance of system with wide LID

On graphs (Fig. 10 - 12) is marked point with area width value for IU = 1:2.5 for each optical system. Optimal systems for given geometry parameters and IU ≥ 1:2.5 are in the table below:

Area width, mMounting height, m
61014
2.5NarrowNarrowNarrow
6Narrow / CosineNarrowNarrow
10Cosine / WideNarrow / CosineNarrow
20WideCosine / Wide

Conclusion

When choosing of light fixtures it needs to take into consideration specific parameters of illuminating area. Light fixture efficiency is determined by the factor of optical system. When certain light project is calculated, utilization factor of optical system is needed too. Together with illuminance distribution and its uniformity it is possible to determine optimal light fixture from set of existing one.

In this example were determined geometric parameters of illuminated area for each compared optical systems when concerned optical system is optimal. So optical system with narrow LID is prefer for illuminating of small areas (5 - 78 m2) and high mounting height (10 - 14 m). Optical system with cosine LID is prefer for illuminating of small areas (28 - 78 m2) and low mounting height (6 - 10 m). At last optical system with wide LID is prefer for illuminating of big areas (78 - 314 m2) and high mounting height (10 - 14 m).