Inverse-square law?

November 4, 2014

The first thing that comes to mind and the same question arises when I “tackle” a new topic: “What does it have to do with cameras - optical and thermal?” Well, I am glad you ask, as this is one of the most important aspects you have to know, when you can call yourself a camera supplier/installer or a CCTV expert. To be bold, and by virtue of asking my piers if they do know about the above, an astonishing high percentage of business owners, design engineers, sales managers and staff, project managers and technicians, they did not have a clue what it is about and even more so, what it mean within their world of expertise.

 

Let me try and explain, if you do not know the effect of the above when installing an optical camera with illuminators or a thermal camera, you will not understand why the system does not work as expected. The same old question will arise, I cannot see the person or even I can see the person but it does not detect. (Needless to say and to keep in mind, I do not include mist or the influence of the four categories thereof, or even atmospheric attenuation as examples.)

 

We are looking at the effect of distance on radiation from source in best conditions. In more scientific words, it means that when you double the distance you reduce the illumination/radiation to one quarter, or similarly, to halve the illumination/radiation you have to increase the distance with a factor of 1.4 (square root of 2), or similarly, to double the illumination/radiation you have to reduce the distance with a factor of 0.7 (square root of ½).

 

 

Can you see the light fade over distance?

 

Why is that?

 

When you have a source of sort, you will have flux (flow of a physical property in space) emanating from this source into space. In the CCTV world it means an IR illuminator or light with an optical camera or a person/heat source in front of a thermal camera. The amount of flux or the amount of flux lines/radiation is very much dependent on the strength of the source. The amount of flux lines/radiation stays constant with the increase of distance. The more flux lines/radiation or the greater the density of flux lines you have at source, the stronger the field will be. Now we will get this important statement, and please try and follow this……The density of flux lines (or to use different words, the amount of radiation power/energy) at this point away from the source, is inversely proportional to the square of the distance from the source.

 

Why, why, why…..because the surface area of the source/sphere will increase with the square of the radius. If you are with me still, then you will understand that the strength of the field is inversely proportional to the square of the distance from this source.

 

I know, this is a mouthful, a picture is always better!

 

I believe that the above makes the understanding much more clear.

 

So, what does the CCTV industry do to combat this, the use more focussed light sources, which travels at a frequency which is beyond eye response (>850nm) and they reach towards laser light sources (which has its own danger areas to consider like safety, power etc.) as well.

 

In general, when you do your design with optical camera and illuminators, and even when you do your design with relation to thermal camera and object distances, please over-engineer your design. Remember that you will lose energy away from the source, illuminator or heat source, double the distance will equate to one quarter of the amount of energy.

 

Yes, integrators think that being cheaper, use less equipment – go further – save on the equipment amount is best, but unfortunately science is fixed and to comply too science in ensuring a perfect working system, it will come at a price. Cheaper is not always better, but achieving the correct solution on behalf of the customer, is best.

 

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