| Author | Message | ||
     Dusan Kojic (dkojic) Junior Member Username: dkojic Post Number: 7 Registered: 7-2011 |
Dear Howard and Dave, This are all great advices. Thanks a lot ! I will do what you suggested. Actually, I'm not really suspecting in the performance quality of my instrument; I'm just trying to figure out the accuracy since I'm dealing with really tough samples (different types of water whose spectra are significantly overlapping) and I want to somehow delineate the extent to which instrumental variability is an issue. Again, many thanks and I'll get back to you after I run long-term tests. BRegards, Dusan | ||
| Howard Mark (hlmark) Senior Member Username: hlmark Post Number: 470 Registered: 9-2001 |
Dusan - I would also suggest that you do the long-term drift test first, before the tests that Dave suggests. That way you will know that you've taken your "noise" data at a time when the instrument has stabilized, since that really represents the only conditions when you can expect the sqrt (n) rule to hold. If you try to collect the noise data too early, then the SD you calculate will be dominated by the drift, and you will certainly not see sqrt (n) behavior. It's sometimes hard to be patient about this, but trying to rush these sorts of tests is the surest way to generate confusing results. If the instrument hasn't settled down, even after a day, then there's no point in rushing to collect and calculate the noise values. That will surely bring you back here to the discussion group with the same questions. In fact, if that happens, you may want to contact the instrument manufacturer, to find out why it hasn't settled down after such a long time. \o/ /_\ | ||
| David W. Hopkins (dhopkins) Senior Member Username: dhopkins Post Number: 212 Registered: 10-2002 |
Hi Dusan, It's hard to say what is not quite in line. It appears that both the results for 64 and 128 are lower than expected, in comparison to the result for 32 coadds, and they are certainly closer to each other than you would expect from the sqrt(n) "law". You should consider repeating the measurements, with more repeats, so you can get some insight into the statistics. One expects a straight line when the noise [40 17 15] is plotted vs the log10 of x [32 64 128]. It is hard to say what values are out of line, with only 3 x levels, and single observations of the y values. It would be useful to compute noise spectra, so you can observe the noise as a function of wavelength, with 10 or more spectra at each level of coadding. Summary statistics of the noise at each level of coadding are nice, but observing the PCA of the noise spectra can help you learn about the noise structure of your instrument. Best regards, Dave | ||
| Dusan Kojic (dkojic) Junior Member Username: dkojic Post Number: 6 Registered: 7-2011 |
David and Howard, Thank you both for your insightful comments. Regarding the validation of SNR increase: before placing the actual sample I took background spectra and immediately after another spectra with empty sample chamber. The latter spectra should have a constant value of 0 after compensation with background. In this case the differences between 32, 64 and 128 scans, shown as maximum deviations from 0 were (for 32,64,128) as follows: 40, 17, 15 (all times E-05). This would mean that sqrt(n) is ok for 32 to 64 scans but not so much for 64 to 128. Right ? (If the validation method is ok.) BRegards, Dusan | ||
| Howard Mark (hlmark) Senior Member Username: hlmark Post Number: 469 Registered: 9-2001 |
David makes a good point. Various effects, that we can loosely classify under the heading "drift", can give rise to long-term variations that are above and beyond the "noise". Since those effects are often systematic but appear random when captured sporadically, it would require some experimental designs that are beyond the scope of this discussion, to examine properly. One simple experiment that could be done, however, is to set the instrument up to collect spectra continuously (without averaging) over some moderately long period, say a day, then plot the readings at each of several given wavelengths versus time. The most likely result is that depending on the wavelength plotted, the early spectra would show some drift in the readings, which would eventually decrease as the instrument stabilized, then display a steady-state result. If nothing else, this will tell you how long you need to let your instrument stabilize before collecting sample spectra. \o/ /_\ | ||
| David W. Hopkins (dhopkins) Senior Member Username: dhopkins Post Number: 211 Registered: 10-2002 |
Hi Dusan, An important point that is often overlooked is, you need to verify that the noise reduction in going from 32 to 64 or 128 scans coadded for each spectrum does actually decrease the noise as expected by the sqrt(n). It can (frequently!) be the case that after a certain number of coadds, further scans include new sources of instability that corrupt the reduction of noise. In that case, it may be advantageous to include sample rescans in your experimental design, to capture, identify and reject those other sources of variation. Best regards, Dave | ||
| Dusan Kojic (dkojic) New member Username: dkojic Post Number: 5 Registered: 7-2011 |
Howard, Thank you for your precise answer. I will try to get a hold of your book. Seem like just the right kind of literature for me in this moment ! Best regards, Dusan | ||
| Howard Mark (hlmark) Senior Member Username: hlmark Post Number: 467 Registered: 9-2001 |
Dusan - Yes, if you take (let's say) two replicates and take 64 scans of each, then average together those 128 scans, that will have the same noise-reduction effect as taking 128 scans of one of those replicates (i.e., sqrt (128)). In addition, that process will reduce the effect of the variations between the replicates by a factor of sqrt (2). If, on the other hand, you collect 64 scans of each of thw two replicates as before, and average together each set of 64 but don't average together the two replciates' data, the noise will be reduced by a factor of only sqrt (64). In addition there will not be an explicit reduction of the inter-replicate variability, but the model calculated from the data will change slightly so as reduce the effect of inter-replicate variability on the precision of the final predicted values (at the expense of sightly reduced precision due to the increased noise). This is all discussed in detail (with mathematical proofs) in "Principles and Practice of Spectroscpic Calibration", Wiley, (1991). \o/ /_\ | ||
| Dusan Kojic (dkojic) New member Username: dkojic Post Number: 4 Registered: 7-2011 |
I'm using an FT instrument (MPA) and I want to improve signal-to-noise ratio so I'm taking 128 scans to obtain one spectra, and I need advice in comparing this setting to taking replicate spectra (with fewer number of scans). My understanding is that increasing scans improves signal-to-noise ratio while replicates (i.e. its average) serve as optical perturbation. Is 128 scans adequate substitution for taking replicates ? I understand that these are two different things, but can the first setting also compensate the benefits of the second ? Thanks a lot ! Dusan |