Inverse Square Law

Whenever I explore a new topic, one question always comes to mind: “What does this have to do with cameras optical or thermal?”

I’m glad you asked, because this principle is one of the most important foundations every true camera supplier, installer, or CCTV expert should understand.

To be bold, and somewhat disappointed, when I ask my peers in the industry about the inverse-square law, an astonishingly high percentage of business owners, design engineers, sales managers, project managers, and even technicians have no idea what it means or how it applies within their world of so-called expertise.

Let me explain.If you do not understand this effect when installing an optical camera with illuminators or a thermal camera, you will never understand why your system underperforms. You’ll find yourself asking the same old questions:

• “Why can’t I see the person?”

• “Why can I see the person, but the system doesn’t detect?”

  
  

(Naturally, for this discussion, we are excluding the effects of mist, the four main atmospheric categories, and attenuation phenomena.)

Understanding the Principle

We are looking at the effect of distance on radiation from a source, under ideal conditions. In scientific terms:

• When you double the distance, you reduce the illumination or radiation to one quarter.

• To halve the illumination or radiation, you must increase the distance by a factor of 1.4 (the square root of 2).

• Conversely, to double the illumination or radiation, you must reduce the distance by a factor of 0.7 (the square root of ½).

Can you see the light fading over distance?

Why Does This Happen?

Every source emits flux, a flow of physical energy into space.In the CCTV world, this might be:

• An IR illuminator for an optical camera, or

• A person or heat source observed by a thermal camera.

  
  

The total amount of flux (or radiation) remains constant regardless of distance.However, as distance increases, that same amount of energy spreads across a larger surface area.

Here’s the key principle:

The intensity (or density) of the radiation field is inversely proportional to the square of the distance from the source.

Why? Because the surface area of a sphere increases with the square of its radius.Therefore, the strength of the field or the power per unit area decreases with the square of the distance from the source.

In simple terms:

Double the distance → one-quarter the energy.

Visualising the Concept

A picture is indeed worth a thousand words. The diagram below (not included here) illustrates how radiation or illumination spreads, showing the geometric expansion of energy fields over distance. Once you visualize it, the concept becomes crystal clear.

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

Practical Application in CCTV Design

To overcome this physical limitation, the CCTV industry increasingly uses focused light sources operating at infrared wavelengths beyond human vision (>850 nm), and even laser-based illuminators. These technologies improve range and intensity but introduce other challenges, such as safety concerns and power management.

When designing systems whether with optical cameras and illuminators, or thermal cameras and object detection distances,

always over-engineer your design or under promise and over deliver!

Remember:

Doubling the distance equals one-quarter of the energy at the target.

Cutting corners by using fewer illuminators or underpowered lenses might save costs upfront, but science is non-negotiable. Reliable, effective systems must comply with the laws of physics, even if it means higher investment.

As I often say:

Cheaper is not always better. Delivering the correct solution on behalf of the customer, always is.

By Tinus Diedericks

CEO of Timeless Technologies