When pointing my presentation laser at a semi glossy object like stained wood or my skin I see noise, almost like TV static (it also appears to be moving). Is this a property of the laser's refraction on the object? or something with the eye?
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You are observing speckle noise, which appears in coherent illumination. It can also be seen in radar images, sonar images, and sonograms.
Although the radiant intensity illuminating the scene is uniform, or at least slowly varying, the image appears speckled or "salt and peppered".
Consider a single image resolution cell (labeled $i$) that is much larger than the wavelength of the incident radiation. It is made up of many individual scattering cells, each which reflects a (roughly) uniform amount of power with a random phase.
The total (transverse) field is then the sum of many equal magnitude phasors with random phase. If you split the field into a horizontal and veritcal component, each independently random walks away from $E=0$, and will be gaussian distribution about zero, e.g.:
$$ P(E_{H,l}) \propto e^{-E_{H,i}^2/4} $$
(This is normalized to unit power, so each channel has a variance of $\frac 1 2$).
The total electric field amplitude is the vector sum:
$$ \vec E_i = \vec E_{H, i} + \vec E_{V, i} $$
whose magnitude is Rayleigh distributed:
$$ P(E_i) \propto E_i e^{-E^2_i/2} $$
and phase is random.
The intensity $I_i$ goes as $||E_i||^2$, and the square of a Rayleigh distributed variable is exponentially distributed:
$$ P(I_i) \propto e^{-I_i} $$
So a uniform illumination is modulated by an exponential intensity distribution. For a non-uniform image, this is a multiplicative factor (hence it is sometimes called multiplicative noise).
The most probably value is $I=0$, hence all the dark spots, and the maximum brightness is unbound (one reason even low power lasers can damage your retina). This leads to the appearance of speckle. Note that the speckle is spatially correlated, so if you move your eye, the speckle pattern moves with you for a coherence length.
In coherent imaging, speckle noise is a significant and fundamental problem. Since it is coherent, you cannot reduced it with more data. That is, an image that is a coherent sum of 25 images has the same speckle noise as 2500 images, summed.
One way to deal with it is to sum independent "looks"; that is, if you have 2500 coherent sets of data, you break it into 100 sets (looks) of 25 coherent images. Each batch of 25 images is coherently processes (with random speckle), and then all 100 are added after squaring.
In that case, each pixel is the average of 100 exponential distributions, and the speckle noise is reduced by $\sqrt{100}=10$. Averaging exponentially distributions leads to a gamma distribution:
$$ P(I_i) \propto I_i^{N-1}e^{-I_i} $$
which has variance N.
Note that the gamma distribution is the same as the chi-squared distribution with $2N$ degrees of freedom, and you are essentially adding $2N$ gaussian deviations from $E=0$.
Finally, if you do this in the presence of noise, the final distribution is the non-central-chi-squared distribution (https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution), which does not depend on how the noise (e.g. RF interference in a SAR image) is distributed in the data, and depends only on the total interference power versus signal power.
