Some Important Photometry Concepts.

1. In the International System of Units (SI), Illuminance is measured in Lux (Lx).  Luminous Flux is measured in Lumens (Lm).

2. Relation of Illuminance and Luminous Flux.

If the light stream from a light source is perpendicular to area being uniformly illuminated by this light sources, then:

                       1 Lux = 1 Lumen/Square Meter.    (1)

This means that 1 Lux of Illuminance corresponds to 1 Lumen of Luminous Flux if the uniformly illuminated surface is 1 square meter in area.  For example, if the Luminous Flux is equal to 1000 Lumens and the uniformly illuminated surface is 1 square meter in area, then the Illuminance of that area is equal to 1000 Lux.  If the Luminous Flux remains the same (1000 Lm), but the illuminated area increases to 10 square meters then the illuminance will decrease tenfold and will be equal to 100 Lux.

Thus, in order to measure the Luminous Flux in a uniformly illuminated area of 1 square meter, it is enough to place a Lux meter anywhere in the illuminated area.  In this case the Illuminance in Lux and the Luminous Flux in Lumens will be of equal value.

                          Flashlights based on LED’s.

Some companies producing light sources (flashlights) based on powerful light emitting diodes claim values of Luminous Flux that at times are higher than the maximum value that can be emitted by the light emitting diode in all directions.  These “results” first of all have to do with not taking into account the uniformity of illuminance of the illuminated area where the measurements were taken.

An example to illustrate the above said.

Two flashlights were chosen for the measurements (Fig. 1 and Fig. 2)

The two flashlights above have identical electrical specifications but use different optical schematics.

The ND HB F5 on Fig. 1 utilizes a patented optical schematic that allows for concentrated light emission with uniform Luminous Flux throughout the light stream and a +/-2.5° angle of dispersion relative to the optical axis.

The ND HB VIGOUR on Fig. 2 one focusing output lens uses.

The illuminated fields “a” and “b” on Fig. 3 belong to the HB VIGOUR and the HB F5 respectively and are 1.12 meters in diameter.  It is clear that the area of each field is 1 square meter.

                                                       Fig.4.

a) – the illuminated area of 1 square meter, illuminated by the flashlight on Fig. 2, the distance from the flashlight to the screen – 5 meters.

b) – the illuminated area of 1 square meter, illuminated by the flashlight on Fig. 1, the distance from the flashlight to the screen – 10.5 meters.

The distribution of Illuminance throughout the illuminated fields a) and b) on Fig. 4 is given by the formula (1) in units of Luminous Flux and is illustrated by Diagram 1.      

Distance From the Center of the Field in Centimeters.  

                                                                Diagram 1

Illuminance Distribution Depending on Luminous Flux.

A – distribution of illuminance in a 1-square meter field for the regular flashlight.  The maximum luminous flux is 135 Lm.

B – distribution of illuminance in a 1-square meter field for the flashlight with the special optics.  The luminous flux is uniform throughout 95% - 80Lm.

C – Maximum luminous flux of the light emitting diode used in both flashlights – 107 Lm.

From the analysis of the curves in Diagram 1 it is clear that:

1. The area S1 under the curve A is smaller than the area S2 under the curve B.  The area S2 is equal to 112x80 = 8960 units while S1 is equal to a certain integral of the function:

                                                                           2

                                              Y = 1/ √2תּ exp (-x /2), т. е.,

We now calculate S1:

                                                                          56                        2

                                          S1 = ∫ [1/ √2תּ exp (-x /2)]dx = 7795;                                                                        

                                                -56

Thus, S1/S2 = 0.87 and since both curves share the same X-axis, the luminous flux of curve “A” is equal to 87% of 80 Lm which is 70 Lm (but not 135 Lm as some manufacturers of regular flashlights would desire).

2. It is clear that the uniformly distributed Luminous Flux cannot exceed the value of 107 lumens because this value is the maximum output of the light emitting diode used in both flashlights.

For even better understanding, here is another photo, where both flashlights are illuminating screens from the same distance – 5 meters:

The diameter of field a) remains the same 1.12 meters, but the diameter of field b) is 0.5 meters and its area 0.2 square meters.  The Illuminance of field b) is 150 Lux but we will not rename it into 150 Lm under any circumstances.

Matvey Shpizel , PhD.