The intercept beta is not related to the actual signal to noise ratio, as was shown by Hocker Litster and Smith more than 40 years ago. Beta is determined by how many coherence areas you are looking at. However, if you open or close the apertures in your collecting optics, within reason, while leaving the laser power and photomultiplier tube gain the same (latter has different phrasings for different photodetectors), beta will change, but the accuracy of your spectral measurement will not. If you open apertures and lower the laser power (as with filters) the count rate may stay the same but the accuracy of the measurement will go down. If you want more accuracy, increase the measrement time.

The fundamental signal to noise ratio is determined by photocounts per relaxation time per coherence area. (Note that coherence is not an on-off thing, so we say per coherence area, but the idea that there is 'one' coherence area misses the point.) As a corollary scattering power goes inversely as wavelength to the fourth power, but shorter wavelength photons each carry more energy, and the relaxation time and size of the coherence areas each scale as wavelength squared, so in net all things being the same you are better off at longer wavelengths, an effect oft-times swamped by the wavelength sensitivity of your detector.

I would be more concerned that you are using some normalization and claiming that the long-time limit of your spectrum is "1", There is noise in the measurement used to normalize, and as a result this claim is imprecise.

In addition, with your picture your polymer spectrum is so noisy that at best you might extract one relaxation rate.

With gels, there is a possiblity that your scatterers cannot move freely, meaning taht if r_n(t) is the position of scattering particle n,

may not (unlike in a solution) average to zero. There are a series of articles on this some decades ago; a keyword is "non-ergodic" with a slightly different meaning than used in some other fields.

If some scatterers are stationary, you may also be doing partial heterodyne detection of the scattered field.

When you say 'asymptotic', did you mean very short-time or very long-time? Which definition of g^(2)(t) are you using, in terms of photocounts in each sampling bin? I am fairly sure I know the answers, but I could waste a lot of your time if I am wrong.

Thank you for responding Professor George Phillies I meant short times. I am unsure on what you mean by the definition of g2(t) -1 being used.

Hi, I follow this question with interest as well and look forward to the feedback from George Phillies.

I think this can be related with the spatial coherence factor, which is related with the aperture area of the photodetector. Larger aperture areas on the detector will increase the number of counts but also lead to a decrease in the spatial coherence factor. Hence, decreasing the aperture area in front of the detector will facilitate the observation of the random fluctuations in the signal of DLS, provided you have a sufficient number of counts.

In our instrument (Horiba sz-100) this aperture can be manually adjusted and I do see this effect (larger apertures -> smaller G2 at short delay times). My guess is that your sample may scatter poorly and to compensate, the instrument automatically opens up the aperture area leading to the low values of G2 that you observe. But I admit my knowledge of this is not too deep and I would like to see what the experts say, and if possible point to suitable literature on the subject.

Good luck

Professor George Phillies to elaborate to a greater extent on what I mean by asymptotic values of the intensity-intensity correlation function (g2(t)-1) I have attached an image. For a dilute polymer solution I observe that the value is 0.6-0.7. But I don't quite understand what controls this number.

A short answer to that is the signal/noise in your system. The higher the intercept, the better the signal to noise (you have enough scattering particles or particles with a good difference in polarizability with respect to your solution), hence you're working with a good signal and you have a high chance of having reliable statistics. The system is really noisy though, and it almost looks like you either have high fluctuations in the polymers conformations, or are your polymers settling down (problems with solubility).

The intercept beta is not related to the actual signal to noise ratio, as was shown by Hocker Litster and Smith more than 40 years ago. Beta is determined by how many coherence areas you are looking at. However, if you open or close the apertures in your collecting optics, within reason, while leaving the laser power and photomultiplier tube gain the same (latter has different phrasings for different photodetectors), beta will change, but the accuracy of your spectral measurement will not. If you open apertures and lower the laser power (as with filters) the count rate may stay the same but the accuracy of the measurement will go down. If you want more accuracy, increase the measrement time.

The fundamental signal to noise ratio is determined by photocounts per relaxation time per coherence area. (Note that coherence is not an on-off thing, so we say per coherence area, but the idea that there is 'one' coherence area misses the point.) As a corollary scattering power goes inversely as wavelength to the fourth power, but shorter wavelength photons each carry more energy, and the relaxation time and size of the coherence areas each scale as wavelength squared, so in net all things being the same you are better off at longer wavelengths, an effect oft-times swamped by the wavelength sensitivity of your detector.

I would be more concerned that you are using some normalization and claiming that the long-time limit of your spectrum is "1", There is noise in the measurement used to normalize, and as a result this claim is imprecise.

In addition, with your picture your polymer spectrum is so noisy that at best you might extract one relaxation rate.

With gels, there is a possiblity that your scatterers cannot move freely, meaning taht if r_n(t) is the position of scattering particle n,

may not (unlike in a solution) average to zero. There are a series of articles on this some decades ago; a keyword is "non-ergodic" with a slightly different meaning than used in some other fields.

If some scatterers are stationary, you may also be doing partial heterodyne detection of the scattered field.

Professor George Phillies thank you very much for your much awaited insightful reply! If you could please share the specific citation of Hocker Litster and Smith it would be great. What could be the remedy if I can't change the aperture at my collecting optics? Just run for long times?

I do not know if that paper was ever published. I think there was a hangup at some point. Changing the aperture on your colelcting optics will not give you a more accurate measurement of g(t). Run for longer times. Are you stuck at a single laser power? What is your current photocount rate?

Thanks for your reply Professor George Phillies ! No, I can change the incident laser power. I am currently working at 2W and I can go up to 7.5W. I have at 30 degrees tried to measure the correlation function as a function of incident light intensity. It didn't improve the beta either. For the above graph the mean count rate is 258 kHz. The correlation function as you can see is very smooth

You may be interested to know that a related method (phase analysis light scattering) can measure directly the first order autocorrelation function. There's no incoherent background and the function decays to zero instead of an arbitrary number based on the optics of the instrument and other factors already mentioned. All commercial DLS instruments that also incorporate electrophoretic light scattering have all the hardware necessary to do this.

"...measure the correlation function as a function of incident light intensity. It didn't improve the beta either..."

Beta is determined by the optics, and, as you found, has nothing to do with the incident laser power. A smaller beta is neither better nor worse than a larger beta. If you want to convince me that the g(t) is smooth, you need to replace the linear ordinate with a log ordinate, so that you are plotting log (g(t) -g(baseline channels)) against (preferably linear as well as log, in two graphs) time.

Per George Phillies comment about assuming a single relaxation time, if you do then you can very easily get the time constant even without knowing the values at the start and end of the decay. This is the Swinbourne plot method and is something that seems to have been forgotten.

I will try to find the method and reply - it's been many years since I last needed to do such a plot.

Excellent details by George Phillies.

In terms of practical suggestions for your sample, the intercept of 0.3 is still reasonable. In some older ALV goniometer systems with a choice of different pinholes in the detection optics, the choice of that pinhole would influence the intercept. Assuming that both optical setups are the same (i.e. either the same pinhole, or you have a more recent goniometer with fiber optic detection) then the main reason you observe the low intercept is the low relative scattering intensity from your sample with respect to the 'background'. If you want to convince yourself of that fact, try to increase or decrease the gel concentration and observe any change in the correlation function intercept. [[and as you observed, the ratio between fluctuating and background will not change with increased laser power - however this may change as a function of angle: if your scattering angle is near a form factor minimum then the intercept could be affected by that. Think of the intercept as a measure of 'fluctuating' signal to 'static' background.]]

You could also look at the scattering intensity of your sample and of the 0.1 M NaCl buffer - and compare that to the scattering intensity of the polymer sample in relation to the buffer used in that sample. That is one part of the contribution, the other part could be a static contribution from the gel network that is so slow that it becomes part of the background.