*Andrew Baker, Sales Director North Europe, Flir Systems Ltd, explains the issue of using a thermal imaging camera to measure temperatures over different distances.*

Maybe you have bought a thermal imaging camera but are unsure of how it can be used over distance. Or you could be about to buy a camera but need guidance on which model will accurately measure the temperature of your application without breaking the budget. To make that assessment, thermographers need to consider several factors including:

- Resolution
- Instantaneous field of view
- Lenses
- The size of the object

You can compare it to an eye test. When you look at the eye chart from the optician's chair, you may be able to see that there are letters on the smallest line – but at what distance can you still read the letters (akin to 'measuring' them)? If you have 20/20 vision, you can define the smallest letters at greater distances. In this case, 20/20 vision would be equivalent to a high-resolution thermal imaging camera. If your vision is not perfect, you can improve it with glasses (equating to adding a magnifying glass to the camera) or getting closer to the eye chart (ie reducing the distance to the target).

### Spot-size ratio

Understanding spot-size ratio is especially important. Spot-size ratio is a number that tells you how far you can be from a target of a given size and still get an accurate temperature measurement.

For the most accurate temperature measurement, you want to get as many pixels from your camera's detector as possible onto your target; this will give you more detail in your thermal image. As you move farther and farther away from the object you want to measure, you lose the ability to measure temperature accurately. The higher the resolution your camera has, the more likely you are to get more pixels on a target from farther away with accurate results. Digital zoom does not improve accuracy, so higher resolution or narrow field of view (FOV) is key here.

Let us say you are looking to get an accurate temperature measurement of a 20mm target from 15m away with your thermal camera. How do you figure out whether your camera can do this? You will need to check the specification of your camera and know both the field of view and the resolution. For this example, letus say your camera's resolution is 320 x 240 pixels and your lens has a 24-degree horizontal field of view.

You first need to calculate IFOV in milliradians (mrad) with this formula:

IFOV = (FOV/number of pixels*) x [(3.14/180)(1000)]

*Use the number of pixels that matches the direction (horizontal/vertical) of your FOV.

Since your lens has a 24-degree horizontal FOV, you will divide 24 by the camera's horizontal pixel resolution — in this case, 320. Then you will multiply that number by 17.44, which is the result of (3.14/180)(1000) in the equation above.

(24/320) x 17.44 = 1.308 mrad

Knowing that the IFOV is 1.308 mrad, you then must find your IFOV in millimetres with this formula:

IFOV (mm): (1.308/1000) x 15000 = 19.62 mm

*In the formula above, the 15000 figure is the distance from your target.

So what does this number mean? The spot size ratio is 19.62:15000. This number is the measurable size of one single pixel (1 x 1). To put it in more simple terms, this calculation tells you that **your camera can measure a 19.62 mm spot from 15 metres away**.

This single-pixel measurement is called **theoretical spot size ratio**. Some manufacturers list theoretical spot size ratio in their product specifications. While this may be considered the true spot size ratio, it is misleading because it is not necessarily the most accurate. This can be because it only gives you the temperature of a very small area within a single pixel. As previously mentioned, you want to get as many pixels as possible on your target for the greatest accuracy. One or two pixels may be enough to qualitatively determine that a temperature difference exists, but it may not be enough to provide an accurate representation of the average temperature of an area.

A single pixel measurement may be inaccurate for various reasons:

- Thermal cameras can develop bad pixels
- Objects reflect – a scratch or solar reflection would cause a false positive and a false high reading
- The object that is hot – say a bolt head – might be close to the same width as a pixel but those are square whereas a bolt head is hexagonal
- No optics are absolutely perfect – there are always some distortions in optical systems which impact measurements

Due to a phenomenon called optical dispersion, radiation from a very small area will not give one detector element enough energy for correct value. We recommend making sure that the hot area where the spot value requested is at least 3 x 3 pixels. Just multiply your theoretical spot size ratio in millimetres by three, which gives you a spot size ratio of 3 x 3 pixels instead of 1 x 1. This number is going to be more accurate.

So if you multiply IFOV in mm (19.62) by 3, you get: 58.86 mm

This means you can measure a 58.86 millimetre spot from 15 metres away.

### How far away can you measure a given spot size?

Let us say you want to measure a 20mm spot. From how far away you can accurately measure that specific spot size? You need to use a little cross-multiplication:

IFOV in mm : Distance in mm

5.886:15000

20 mm : x

15000*2 = 58.86*x

300000/58.86 = x

x = 5096.8 mm

This tells us you can measure a 20mm spot from approximately 5m away from the target with your 320 x 240 resolution camera.

Other manufacturers may not use this number when they discuss IFOV or SSR; but, in truth, this number will give you a more accurate temperature reading on an anomaly.

Ultimately, spot size ratio matters because it will help you understand whether your thermal camera is capable of accurately measuring temperature at the distance that you need it to. If you need to measure small targets from long distances, knowing the spot size ratio of the camera and whether you are standing within accurate measurement range is crucial.

If you are planning a thermography survey, think about whether you can get close enough to a target to get an accurate reading. Accurate should be interpreted as 'good enough for proper interpretation.' This does not necessarily even mean within the accuracy specification of your camera. You can make the mistake of being off by several – even hundreds – of degrees if you do not consider the spot size ratio.

To make the calculations quicker, Flir has a FOV calculator for each of its cameras at **flir.custhelp.com**. Just click on the Flir camera series you are using, which will take you to a list of all the cameras in that series. Click on 'FOV Calc' next to the correct camera and it will show you your camera's spot size ratio.