A detection limit and an averaging time are a pair. Separated, neither one carries information. Put them back together and something uncomfortable appears: in the example above, the module quoting 5 ppm is the better one.

Below is the conversion, the point where it stops working, and what this means for the specification you are about to publish on your own product.

Averaging buys sensitivity, at a fixed exchange rate

A detection limit is set by noise. Averaging reduces noise, so averaging lowers the detection limit.

While the noise is white — random and uncorrelated — the exchange rate is fixed: detection limit scales as 1 / √τ, where τ is the averaging time. Four times the averaging time buys a factor of two. A hundred times buys a factor of ten.

The same two published figures, converted onto a common time base using 1 / √τ.
Quoted specification At 1 sAt 10 s At 60 s
1 ppm at 60 s 7.7 ppm2.4 ppm1.0 ppm
5 ppm at 1 s 5.0 ppm1.6 ppm0.65 ppm
0 2 4 6 8 Detection limit, ppm 7.7 5.0 at 1 s 2.4 1.6 at 10 s 1.0 0.65 at 60 s quoted 1 ppm at 60 s quoted 5 ppm at 1 s
On a common time base the module quoting the larger number reaches the lower limit. Neither supplier has to be dishonest for this to happen — each quoted a real measurement at a time base that suited them.

At a common 60 seconds, the second module reaches 0.65 ppm against the first module’s 1.0 ppm. The datasheet quoting the larger number describes the quieter instrument.

Where the conversion stops working

The 1 / √τ relationship holds only while white noise dominates. It does not hold forever, and the point where it stops is a property of the instrument.

Beyond some averaging time, drift takes over — temperature, optical alignment, laser wavelength stability. Past that point averaging longer makes the result worse, not better. Extrapolating a quoted figure past it produces a number the instrument cannot reach at any setting.

Allan deviation Averaging time τ → Minimum ask for this time 1 / √τ holds here the conversion above is valid drift dominates averaging makes it worse
Past the minimum, averaging longer makes the result worse. A headline figure without this curve is a point you have not been shown.

Two practical consequences:

  • A quoted figure at a very long integration time may sit past the minimum, in which case it is not achievable.
  • Two instruments with identical detection limits can have minima an order of magnitude apart in time, and for a control loop that difference matters more than the ppm figure.

Back to the specification you are writing

Your control loop’s allowed response time sets your averaging time. Your averaging time sets your achievable detection limit. You cannot specify the two independently.

If your instrument has to respond within 2 seconds, you are working on the left of the Allan curve and you get whatever detection limit that region gives. Publishing a detection limit measured at 60 seconds alongside a 2-second response claim describes an instrument that does not exist — yours or anyone’s.

Required response a process requirement Averaging time what is left after transport Detection limit read off the curve Compare against what you must resolve Response time and detection limit are one decision, not two.
Response time and detection limit are one decision, not two. Fixing either one constrains the other.

Work in this order:

  1. Fix the response your application requires. That is a process requirement, not a negotiable one.
  2. Convert it to an averaging time. Response also includes gas transport and cell displacement — the averaging window is only part of it.
  3. Read the detection limit at that averaging time, from the curve rather than from the headline.
  4. Check it against the concentration you actually need to resolve, not against the bottom of the range.

Step 4 catches a common over-specification. A detection limit far below anything your process produces costs response time you may need elsewhere.

What published figures actually look like

Two reference points from the engineering literature, with their conditions attached:

  • Near-infrared wavelength modulation spectroscopy typically reaches low ppb to ppm levels at around one second of integration.
  • A portable laboratory system measured a CO₂ detection limit of 0.13 ppm at 18 seconds and H₂O of 3.7 ppm at 35 seconds, with a system response of about 10 seconds.

How to read those two figures

These are laboratory implementations reported in the literature. They are not an industrial product baseline and should not be read as one — they are here to show what a properly conditioned figure looks like: a number, a time, and a system context.

Mid-infrared wavelengths produce stronger absorption than near-infrared for many gases, which shifts the whole curve down. That is a wavelength property, not a product claim, and it comes with different laser and detector hardware. → What a multi-gas TDLAS platform can and cannot share

Five things to ask a supplier

  1. The integration time behind every detection limit figure.
  2. The Allan deviation minimum — value and the time it occurs at.
  3. The background gas the figure was measured in. A limit measured in nitrogen does not describe a stream carrying CO₂ and water vapour.
  4. Whether the module had finished warming up, and how long that takes.
  5. The temperature the measurement was made at.

Any figure you intend to design around needs all five. A datasheet that gives you a table and no conditions block has given you a marketing document.

Why we do not publish a platform detection limit

Our box-level extractive module carries four standard gases across eight ranges. We do not publish a platform-wide detection limit for any of them.

The reason follows directly from this page. A single figure would need one integration time, one background gas and one range to be true of, and it would then be quoted against configurations it was never measured in. It would make this page look more complete and make the number less usable.

Detection limit, cross-interference and gas path material are confirmed at configuration, against your gas, your range and your background composition. What we publish instead is what holds across configurations: segmented accuracy per gas and per range, with the reference conditions stated.

We are aware that this is the less convenient answer. A number that has not been measured against your background is not a number you can design with, and putting one on a page does not change that.