A laser generating TEM00 mode has a Gaussian light intensity distribution. You can try to take a photo with appropriate filters and a macro lens. A good laser pointer might be good enough as a light source.

A 20 nm fluorescent plastic balls also produce quite nice Gaussian distribution when imaged by a scanning confocal microscope, somewhat elliptical due to linear polarization of exciting light. This is optomechanics, though.

Hi Vladimir I Chukharev, thanks a lot for your answer. But actually I want to implement the random Gaussian matrix (randn(size1,size2)), instead of the normal Gaussian distribution. Is there any method which could generate the random patterns?

Dear Qiuliang Ye ,

You can set up a geiger counter to register the electrons coming from the radioactive decay of a source, let's say strontium. You count the pulses generated over an arbitrary period of time and that is one random number, from a Gaussian distribution. Subtract that number from the mean value that you expect (empirically determined). Then repeat as many times as necessary to get size1*size2 numbers and arrange them in your matrix.

Several clever researchers have found various ways to implement the inherent randomness associated quantum mechanics to generate random numbers. One particularly elegant possibility is to used the path taken by single photons at a beam splitter. An often cited article describing the technical details of implementing this idea is " Optical quantum random number generator " by Stevanov et al published in the Journal of Modern Optics (Vol 47, p595) in 2000 which can be accessed at

https://doi.org/10.1080/09500340008233380

Qiuliang Ye, if the image is acquired by a CCD camera in the small signal mode, then each point of the image has a random value with quantum (Chi2) distribution and average according to the Gaussian distribution across the matrix. With bigger signal, the distribution at a point approaches normal. Soon, it is determined by electronic noises, and thus hardly it can be called optically obtained.

Frankly, I do not completely understand what you want to achieve, and why you think it can be better than ordinary techniques of collecting real randomness in the computer, and using that in the matrix.

Vladimir I Chukharev , I want to implement the optical mask which is the random Gaussian matrix as what I said. Random Gaussian distribution has nice property in mathematics, therefore I want to find some methods or optical instruments to approximate the random matrix. I think a possible answer is via SLM (spatial light modulator), but I want to find another possible techniques.

Qiuliang Ye, Just some ideas for the optical mask. You can try photochromic material (bleaching or induced absorption) or photo-induced refractive index modulation like in doped KTP.

Long long time ago I used (IIRR) a KTP:Fe crystal for tuning the setup for measuring transient photo-induced diffraction grating.