Recent content by omg!

i think this is a much simpler thought experiment: imagine you have two clocks C1, C2 in an inertial frame and showing the same time. a third clock C3 moves uniformly on a trajectory parallel to the line made by C1, C2. at time 0, C3 crosses the point of shortest distance to C1 on its...

landau's argument goes like this: for two infinitely close events, he defines the infinitesimal interval to be ds^2=c^2 dt^2 - dx^2 we know that ds=0 iff the events describe the propagation of signals at the speed of light. in this case, by the constancy of the speed of light, ds'=0 also in...

the data is only ONE pair of 2D coordinates, that's right! I suppose that could be the reason for the bias, as it was pointed out that MLE is asymptotically unbiased. And I would like to quantify the uncertainty of the estimation of x_c, y_c, alpha. i'm afraid i don't know how to compute the...

thank you very much for your interest. the maximum likelihood estimator of the aforementioned center coordinate \vec{x}_c=x_(\vec{x}_1+\vec{x}_2)/2 is given by x_c=(\frac{x_1+d\cos\alpha}{\sigma_1^2}+\frac{x_2-d\cos\alpha}{\sigma_2^2})/(1/\sigma_1^2+1/\sigma_2^2)...

hi all, i would appreciate any help you can offer for the following problem. consider coordinates x_1, x_2 in the plane for which ||x_1-x_2||=d. suppose that this pair of coordinates can be measured independently, and that the measurements are 2D normally distributed with means x_1, x_2 and...

thank you for your clear explanation. forgive my ignorance, but could you point out an example of a non-transversal EM wave? i'm trying to calculate the intensity on the CCD resulting from a focused light beam. the two formulas give slightly different values, the more general one has a...

intuitively, i would say that in a CCD, the photoelectrons are being "created" only by the electric field of the incident light, so that the intensity is proportional to |E_x|^2+|E_y|^2, with the xy-plane coinciding with the CCD plane. But I have several papers here saying that the intensity...

the graph that i showed previously used randomly generated data. data from an actual measurement is attached with this post. note that the data is not stationary, it doesn't have zero mean. i need to know whether there are vibrations "on top" of the curve, so i first subtract the moving average...

thank you very much for the suggestion to use a band pass filter. i have tried it, but it merely filters out the band passed part of the spectrum without changing the amplitudes (see attachment). the data was generated with sines with amplitudes 0.37 and 0.24, added with normally distributed...

hi everyone, i would be grateful for suggestions for the following problem: i have a set of measurements, discrete samples from a continuous function of time. with each measurement comes a estimate of its uncertainty (standard error). by doing a discrete Fourier transform, i have seen some...

thank you very much for your clarification! what I'm still asking myself is whether or not the cover glass correction corrects a phase factor of the electromagnetic field that it acquires by traveling through the cover glass. in other words, if the cover glass is thicker or thinner than it is...

hi everybody, i would appreciate it if someone could clarify the concept of spherical aberrations in the context of high NA objectives in which use lenses are used that are not exclusively of the spherical type. a common thing that you hear is that some objective is corrected for 0.17mm...

1. Find the minimum point of I(p, q, r, s)=\int_{\mathbb{R}^2}\,dxdy\,\left[exp(-(x-d)^2-y^2)+exp(-(x+d)^2-y^2)-exp(-(x-p)^2-(y-q)^2)-exp(-(x-r)^2+(y-s)^2)\right]^2 +\int_{\mathbb{R}^2}\,dxdy\,\left[exp(-(x-\delta_x)^2-(y-\delta_y)^2)-exp(-(x-p)^2+(y-q)^2)\right]^2 for given d, \delta_x...

ok, let me describe the problem I'm really facing. the version above is badly formulated and too confusing, please forget it. the thing is, i measure the state of a system as a function of time. The state can be 0,1 or 2. the measuring apparatus samples the state in a finite time period...

thank you for your answer. but the state need not necessarily end up in 2, e.g. a sequence like this ...11000000 where the last state is the nth time step would give rise to a sequence where the last observed 1 state is at the n-6th time step. my current approach is like this...