Is it possible electronically to amplify an expected signal with a S/N close to 1, or 1? If yes, how? I already tried to use an Lock-In-Amplifier, but that was not useful after the noise itself is also chopped. Are there other possibilities?
Clarification: I have a photo multiplier tube which detects reflected light (shape is depending on sample which reflects light). The noise is the dark current. If I reduce the light on the sample, the dark current goes down, but so does the signal. If I reduce the amount of reflected light by slits, both signals are also going down. The dark current is random, and therefore not predictable.
Concerning the signal itself: I do not know where I can expect the signal, and I do not know the shape of the signal.
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1\$\begingroup\$ What's the nature of the signal? What's the nature of the noise? \$\endgroup\$– Nick AlexeevCommented Oct 12, 2015 at 20:55
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\$\begingroup\$ You need to clarify what you require. Of course you can amplify a signal with a low S/N, but you will just end up with a larger amplitude signal with a low s/n. \$\endgroup\$– Kevin WhiteCommented Oct 12, 2015 at 20:56
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2\$\begingroup\$ I'm not sure you're understanding your noise sources correctly. Dark current is usually a property of the receiver (the PMT, in this case). It is the output current seen when there's no light input at all. It does not depend on whether some light source is turned on or not. If you have noise that increases when your source is turned on, that is something else other than dark current. \$\endgroup\$– The PhotonCommented Oct 12, 2015 at 22:35
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\$\begingroup\$ If I understand your situation correctly, what you might need to do is redesign your optical system so that the only light that reaches the PMT from the source is the light reflected off the sample. If there is leakage from the source to the PMT other than off the sample, there's not really anything you're going to be able to do electronically to make that go away. \$\endgroup\$– The PhotonCommented Oct 12, 2015 at 22:37
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\$\begingroup\$ If you don't know where (when?) you can expect the signal, you can't benefit from periodic techniques, and if you don't know the shape, correlation won't help. Your signal is completely indistinguishable from noise. You need to redesign the experiment to improve the optical SNR. \$\endgroup\$– Neil_UKCommented Oct 13, 2015 at 4:35
3 Answers
Of course you can amplify the signal but in doing so you will also amplify the noise. I'm guessing that is not what you want.
Fundamentally if you want to measure a signal of similar magnitude to the noise you have to know something about the signal. The more you know about the signal the more you can design a system to measure it while reducing the impact of the noise.
If you want more help you are going to have to give us more information about your signal.
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\$\begingroup\$ Is the information I added enough? \$\endgroup\$ Commented Oct 12, 2015 at 22:22
Yes, it is possible to amplify a signal, regardless of its S/N ratio, however, you will also be amplifying the noise. With a perfect noise-free amplifier, you will be able to maintain the SNR. With any real amplifier, the SNR will be degraded somewhat.
As a first step in improving things, you must make your detector as narrow band as possible with a bandpass filter, to reduce the noise power, while maintaining the signal power. This improves the SNR compared to a wideband detector, an example of which is an oscilloscope trace.
A lock-in amplifier is a method of reducing the noise bandwidth of the detector system to a much higher degree than is possible with a simple bandpass filter. Where the signal is periodic, the noise bandwidth can be reduced, almost arbitrarily reduced if you average for long enough.
When the signal is wider band, and the noise power reduction of a lock-in amp cannot be used, you can still use correlation, at least if the signal waveform is known. In a way, this is just a generalisation of the principle of the lock-in amp, which can only correlate with periodic signals.
If you're talking about a signal where a lock-in might be useful, you might consider whether ensemble averaging techniques would give you a grip on this problem. If you're measuring a noisy response to a well-defined stimulus, you can average in time, locking onto the stimulus to line up the epochs. The noise goes down by \$ \sqrt{N} \$ for N ensembles in your data set.
