Mathamatically working out average power over time

[VW]

I was wondering, how do you mathamatically work out the average power of a laser over a set period of time?  I noticed a lot of people seem to base an average on the point where a laser rests for the longest.  That's all fine and well if the laser holds an average long enough for you to be able to determine it off hand.  But what about more unstable lasers?  For example and primarally, while read on a thermal unit my Spartan BP climbs slowly and drops slowly, so it never holds an average long enough to say, "that is the average."  What would be the method to record and work out the mathamatical average power over a set period of time?  

 

[FrothyChimp]

Re: Mathamatically working out average power over

Statistical analysis. Select a sample to use such as the measurement at >15 minutes or whatever the warmup time is for the laser. Take samples. Use that population in the arithmetic mean function. Your sample can really be anywhere on the curve or all of the curve but for average power you should use the output after warmup.

I should point out that statistical mean reports central tendency so using results from startup which often include the peak output can skew the average and should be considered before blindly using all data points.

Modify once again: I almost forgot there are ways to determine if data points are truly representative of a population by measuring standard deviation and setting what is called an alpha which is the point where the data value is rejected as not being part of the population sample. This helps eliminate those sometimes weird fluctuations and bring the average closer to the actual average.

 

[VW]

Re: Mathamatically working out average power over

Thanks for the fast reply. Cool, I remember the idea of calculating the mean, but I've forgotten how to work it out. From what I can remember you would need to mark down the power at set intervals over a given length of time (say a minute), but I can't remember how to set up the numbers to get the exact mean (or as close to).

 

[FrothyChimp]

Re: Mathamatically working out average power over

I believe you can enter the data points into excel and it will calculate mean and deviation for you. You can also simplify your rough data by using moving averages or even linear regression to better visualize what is happening inside the measurements.

Mean = add up all your data points and divide by the number of samples. But you have to be sure the data points are representing the most stable portion of the output. This can be an educated guess based on experience but if you are not sure you should use deviation and some other analysis to determine what should be included in the population for the average.

Modify: Now you have me on a statistical roll. One cool thing is you can use that average as the central point of a normal distribution and plot data points that go above that average and data points that go below that average. Find the range of a single standard deviation and you can calculate whether the power stability advertised is what you are getting.

 

[VW]

Re: Mathamatically working out average power over

Awesome man, thanks. Deffinately re-jogged my memory. The laser I need this for reads pretty stable anyway on a thermal unit, it's always concistant in the speed of it's power climb and drop, so marking accurate data points shouldn't be too hard.

If I'm wanting an average over a period of time, I would need to mark down it's power, would you say, every 5 seconds or so?

 

[FrothyChimp]

Re: Mathamatically working out average power over

Yes, every 5 seconds will work if the unit is fairly stable. That's the magic and the horror of statistics. Sample to little and you may miss important swings in the curve. Sample too much and your math can become too unwieldy or you have to justify throwing out data points.

 

[VW]

Re: Mathamatically working out average power over

Okay cool man, thanks.

 

[NovoRei]

Re: Mathamatically working out average power over

You could take a 2 minutes, 5-5secs, then apply the mean theorem. The area below the graph divided by the lenght will give the mean power.

Linear regression then derivation can be done too.


Ah, and cut the first 5 seconds.

 

[Hemlock_Mike]

Re: Mathamatically working out average power over

Frothy --

Thanks for reminding me why I hated Stat 101 ;D

Mike