# Accuracy of an Optical Spectrum Analyzer (OSA)

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1. May 4, 2015

Hey!
I've a simple (and maybe stupid) question about the accuracy of an OSA. The datasheet report a level accuracy of 0.4 dB but this seems quite strange to me. Indeed level measurements are done in dBm thus, as long as dB measures a relative power, I assume that even the 0.4 dB are referred to 1 mW as in the case of dBm. Am I correct?
If yes what sounds strange to me is that if I measure a power near to 1 mW than the relative error will be quite high (I'm measuring something like 0 dBm) and as the power that I'm measuring decreases also the relative error decreases.
An example to explain my problem:
1) P=0.4 dBm, the relative error is equal to 100%. Expressed in mW means that I'm measuring a power of 1.096 mW
2) P=-65 dBm (the minimum detectable level for my OSA), the relative error is equal to 0.6%. Expressed in watt: $P= (0.316 \pm 0.002)~nW$, that would mean an accuracy of 2 pW: quite amazing!

So where is the bug in my reasoning?

Thanks to everyone

2. May 4, 2015

### sophiecentaur

Hello
It might be a good idea to give a reference to that particular data sheet. I agree that what you seem to have read is a bit confusing. There should be some indication of the lowest power value it can register, at least.

3. May 5, 2015

Ok, my OSA is MS9710C from Anritsu, you can find the datasheet here (appendix A).
In any case the minimum detectable power should be -65 dBm as i wrote above (for the sake of completeness i have to say that it changes accordingly to the wavelength range in which you are working, but we can focus on that value). Maybe my example is not correct because I'm working at the lower limit of my detector but the conceptual problem is still present even if we consider an higher value.
Moreover i've read datasheets from some other osa and i saw that is quite common to express accuracy in terms of dB, so there must be an error in my reasoning!
In any case thank you for the answer!

4. May 5, 2015

### Andy Resnick

It's been a while since I've used this type of instrument, but the level specification (page A-3) is given as +/- 0.4 dB with an input level of -23 dB. Since the linearity spec is +/- 0.05 dB with input levels between -50 and 0 dB, I expect the accuracy spec to be approximately linear with changing input levels- curse you, log scales!

5. May 5, 2015

### sophiecentaur

...and why not? It's only an alternative to percentage for showing the ratio. On a dB scale, it'd really just what you want, I would have thought. You could argue that, in many measurements, the uncertainty is often the same, whatever scale you are using - so it would be more appropriate to use an absolute measure of accuracy. In the end, the choice would depend upon what is being measured and the method being used.

6. May 6, 2015

Thank you very much for the answers.
Andy Resnick you get the solution to my problem, i didn't thought about a linear relation between the accuracy and the input level but it seems to be the right answer