Fraunhofer diffraction experiment- neural density filters

[Strides]

I'm currently carrying out an experiment with Fraunhofer diffraction. It involves shining a laser beam through neural density filters, a lens and a diffraction grating, to create a diffraction pattern which is then picked up with a CCD camera, to find the intensity of the maximal peaks.

However I'm having an issue with my results, the diffraction pattern is clear and has no issues, however the measured intensity of the peaks isn't decreasing substantially enough with the increase of the neural density filters (i.e. from D = 1.8, D = 2.0, ... to D = 3.4), and thus according to the following equation:

D = log₁₀(Io/Id)

D = value of the neural density filter
Id = Light intensity after filter
Io = original light intensity

The results aren't giving me a constant value for the original light intensity from the laser, and instead just increases with each iteration of neural density filter. I was thus wondering if anyone could please help me explain what the issue is and help identify any source of errors I can use to correct my result (I've already corrected for background noise, although this could still potentially be a source of error).

 

[BvU]

The results

What results ? I don't see any. At least not first hand. Hard to comment this way (well, you do specify that I₀ increases with D). The most likely explanation up front is that the few CCD pixels that do get hit (burned?) are way over saturation, so you get almost the same response each time.

Oh, and: Hello Strides,
(although in your case it seems to be a ' welcome back! ' )

 

[Strides]

Thanks for the help, saturation could be part of the problem, but that's why the ND filters were used, which seemed to give quite defined peaks in the diffraction pattern.

My results are rather large to post in the forum, but I can try to attach an excel document, if that's possible?

Here's an image I took using an image of the pattern with a webcam, with a filter of D = 2:

 

[Strides]

Here's a rough excel spreadsheet I've put together, containing my results for each neural density filter (haven't been able to add appropriate units yet):

 

[BvU]

I plotted your I_D-DS and on the picture you can see the peaks of order $\pm$ 4 and higher drop by a factor of about 10 for an increase in density from 2 to 3 -- which is what you expect. But the central maximum and the three peaks on either side drop off less than that. My conclusion: CCD is linear up to approximately 55000, so with a dark signal of 36000 you only have linearity up to 20000 things. No way to reduce DS ? Work in a darkroom ? If not, you can try to extrapolate the seven central peak intensities from density 3 through 3.5 back to density 0 -- because in that range the CCD does exhibit the expected linearity on the log plot.

 

[Strides]

Thanks, that's a great help. The CCD camera and accompanying program is already quite limited in the range that it can measure intensity, so I'll definitely try repeating my experiment in a darker room to help compensate for the issue.

 

[BvU]

repeating my experiment in a darker room

That will help for the measurements that are in the range 20000 -- 50000 so for the central peaks you can only hope for a slightly longer linear section (on the log plot)

Note also that subtracting a large DS from a measured value that is only a little bit more gives considerable error if DS isn't determined very precisely.
e.g. $37400\pm 100 - 36800\pm 100 = 600 \pm 140$ or 25% if you are reasonably optimistic...

 

[Ibix]

I'll definitely try repeating my experiment in a darker room

The senior technician in my old lab insisted that it wasn't an optics experiment if there wasn't some black card involved in it somewhere. He was over-stating slightly, but had a point. It's worth considering building a matt black cardboard cover for your experiment - it may be enough and easier and/or cheaper than finding a dark room to work in.