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I am kind of new to laser physics and signal processing, I hope I am in the right place to ask this question. I am also sorry for my not-great English.

I have been asked to study the transverse intensity profile of a laser beam produced by a $\rm He$-$\rm Ne$ source using a commercial webcam. I am placing the webcam sensor (without any lens) in front of the source and taking a snapshot. Then I am assigning each pixel an intensity value that is simply the recorded value in the red channel ($0-255$). If I choose a row of pixels and plot such value as a function of the pixel, I should expect a Gaussian profile. However it is not what I am observing.

Not really gaussian

In red you can see a Gaussian fit of the data. The actual data is shown in blue. I cannot really call this a good Gaussian shape, although it is some kind of a bell.

  • What could cause such a shape?
  • Could it be due to the laser source which could not be perfectly single-mode?
  • Or could it be due to the sensor?

It is interesting to note that I have also produced an image after making the beam pass through a single mode optical fiber, obtaining similar results; this makes me think that the problem lies in the sensor. However, the only modification the sensor causes and that I am aware of is Gamma correction, and as far as I know, that means that the red (or any channel) value is elevated to a power which is usually $<1$, but that should not change the actual shape. A Gaussian function elevated to a power is still a Gaussian function, although its parameters are different. Can anyone help?

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    $\begingroup$ It's funny, but I would call the blue plot as pretty close to a Gaussian. Plot the histogram of randn() and you're unlikely to get something much better (unless you use many millions of samples). Having said that, the CLT is valid only under certain conditions, you need to make sure they apply here. Also important: digital camera sensors are designed to work with a lens and a LPF in front of them; the light needs to hit the detectors at a certain angle for them to gather light properly. Make sure this is not affecting your results. $\endgroup$ – MBaz Aug 14 '16 at 16:20
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  • What could cause such a shape?
  • Could it be due to the laser source which could not be perfectly single-mode?
  • Or could it be due to the sensor?

There is nothing particularly wrong with the "shape", but there are a few things you can do on the sensor and data processing side, to improve the extraction of an accurate profile.

Your "biggest" problem is going to be the saturation of your web cam's sensor because of the intensity of the beam. This is evident as a flattening of the Gaussian curve's peak. There is a bit of that in this example, but if the $Y$ axis is not scaled, then values in the vicinity of 50 don't look like being saturated....However...

Please make sure that "Automatic Exposure Control" on the web cam is off and then manually set the exposure for minimum distortion (it will probably have to be set to its lowest setting). This will also affect the slopes of the curve as exposure control will strive to maintain contrast across the image.

In addition, you might still need some "analogue" attenuation too. To achieve this, use one or more neutral density filters in front of the camera.

Finally, as it is evident from this profile, it is composed of integer quantities and you are trying to fit a continuous distribution on it. There are two things that can be done here towards improvement: The first, is to shoot a video and then create an average image of the profile over a few hundred frames. This will give you a much smoother real ($\mathbb{R}$) number profile which will vastly improve the fit. The second, is to still shoot a video but produce the beam profile as a boxplot. This will give you the opportunity to observe exactly what the profile "does" over a few hundred (or more) frames. Very briefly, a boxplot would present in one view, information about the distribution of the brightness values at each pixel of the profile over time. You can then fit a Gaussian over the means (or medians) of the profile.

Hope this helps.

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  • $\begingroup$ Thank you, I am already avoiding saturation and controlling exposure manually, although I don't know about minimum distortion, I am just keeping it at a fixed value. Averaging more frames could be interesting and I will try it tomorrow, however I am not sure it will help because all the snapshots I have basically the same shape, flattened at the peak and larger than the gaussian at half maximum. $\endgroup$ – user2668222 Aug 15 '16 at 21:10
  • $\begingroup$ You are welcome. Minimum distortion here meaning tuning the exposure so that it uses as much as possible of the range of outputs of the sensor (0-255) but none of the values appears to be clipped. In this case, your maximum is approximately 50 when it could be 250. If all parameters of data acquisition and processing are checked and controlled then it might really be a characteristic of the beam. Also, you might want to check the wavelength of the laser versus the range of the spectrum the sensor is sensitive in. $\endgroup$ – A_A Aug 16 '16 at 7:50
  • $\begingroup$ The specific example I posted was taken when the laser was really attenuated. I have other images where the output gets closer to 250 but keeps this shape. However, I am wondering if the saturation setting of the camera can be of any importance. I am taking desaturated images so that I am sure that the red channel does not saturate because of artificial (i.e. added by the camera software) gains. Do you think I should change this? $\endgroup$ – user2668222 Aug 16 '16 at 9:17
  • $\begingroup$ No, but that's a good idea anyway. There will be "attenuation" due to conversion but that should be internal and is taken into account already. Is it possible to try a laser with known output characteristics first? Different power levels might excite different modes. $\endgroup$ – A_A Aug 16 '16 at 11:23
  • $\begingroup$ Unfortunately I cannot change the hardware part of my setup right now. $\endgroup$ – user2668222 Aug 19 '16 at 12:14
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Are you sure this should be Gaussian distributed?

Count of photons hitting a detector was the example I was taught for natural occurence of Poisson Distribution.

A high-$\lambda$, but not high enough (that would approach Gaussian) Poisson distribution would in fact have a bell shape that is a bit broader than the Gaussian.

How long is your observation?

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    $\begingroup$ I am not sure about which distribution you are referring to. I think that if a detector is hit by a fixed number of photons repeatedly, the distribution of counts will be Poissonian. However this is different. The distribution I am talking about is on different pixels, hence different detectors, that receive different amount of photons. These different amounts are spatially distributed as a gaussian because the beam itself should be gaussian, being it a laser beam. Note that no real laser is perfectly gaussian, however, mine seems to be particularly far from this approximation. $\endgroup$ – user2668222 Aug 14 '16 at 18:00
  • $\begingroup$ "particularly far"? can't fully agree to that :) $\endgroup$ – Marcus Müller Aug 14 '16 at 18:20
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Any laser beam has not ideal Gaussian profile. There is special term - beam quality factor. There are a lot of reason why laser profile is not gaussian. So your results may be correct. To check it you have to do some test experiments with your measurements system. Try measure some known spacial distribution of light. Uniform may be first step. Then apply some mask before sensor and move it.

Measurements of laser beam profile is common and not easy task. You can see useful article in wiki

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