Recent content by Ax_xiom

Apologies That's probably what I was looking for. Thanks for your help

I think the issue is that, for reasons I am not smart enough to understand, the computed diffraction pattern is usually different to the actual diffraction pattern. Compare an airy disk that was computed with a computer: And one observed in real life: The second-order maxima seem to be nearly...

I haven't tried it because I decided to just use Excel's built-in solver. I subsequently abandoned the project when the solver kept on giving solutions that made no physical sense

I'm taking the square root so the image looks brighter compare the regular image to the image when the values are squarerooted The squarerooted version is the closest to what I'm trying to do, but my target image has the centre much brighter and the edges much darker

I'll create a new image with the centre at 0,0 so no shifting is required. Here it is: # fourier_synthesis.py import numpy as np import matplotlib.pyplot as plt image_filename = "HubbleOutline10.jpg" def calculate_2dft(input): ft = np.fft.ifftshift(input) ft = np.fft.fft2(ft)...

I tried it and I get this: Which does have the same general structure as what I'm aiming for, but doesn't "glow" as much Here is the code I'm using, I'm not sure if it uses block swapping

So I'm using python to compute the fourier transform of a black and white image and the images I've been getting have been different to what I expected. Input image: Output FFT: What I expected: Image from MinutePhysics's video Why are Stars Star-Shaped? So why is there a difference?

Not really, but I'll mess around with it as I don't think there is any other reasonable way to solve my problem

After some thinking, I don't think this is possible. For an arbitrary stage i, the expression for the mass ratio will be this $$N_i = \frac{m_i + \alpha_i p + U}{s m_i + \alpha_i p + U}$$ where U is the mass of all upper stages. And we (ideally) want to find ##\frac{m_i + \alpha_i p + U}{U}## in...

s will be around 0.1. These results make sense but this is a solved issue currently. This is the issue I am currently having

the ##c_i##'s and ##V_f## will be variable but the ##c_i##'s will typically be around ##2400-3000ms^{-1}## and ##V_f## will be anywhere from ##2600 - 9000ms^{-1}##

This is nice, but @pasmith pointed out a way to make the Jacobian upper triangular, which makes the computation of ##\Delta X_n## much easier to scale and makes everything much more convenient. The bigger problem I am currently facing is that the system of equations I initially came up with was...

So not related to this specific topic but related to this project. So turns out the equations I was working with are likely wrong. So the method I'm using starts like this: $$ \Delta V = c_1 \ln(\frac{m_1 + m_2 + (\alpha_1 + \alpha_2 + 1)p}{s m_1 + m_2 + (\alpha_1 + \alpha_2 + 1)p}) + c_2...

Do you mean it's possible to solve the linear system without using Excel's matrix operations each time? If that is correct, I believe these would be the solutions to the system: $$ \begin{align} \Delta\lambda = \frac{s\lambda f_6 - \sum_{i=1}^5 \frac{f_i}{N_i}}{\sum_{i=1}^5 c_i (s -...

There's 3 equations in my post, but that's the version for 2 stages. I want to be able to expand it up to 5 stages where the system of equations will be this: $$\begin{align} 1 - c_{1}\lambda + \frac{sN_{1}}{1 - sN_{1}} = 0 \\ 1 - c_{2}\lambda + \frac{sN_{2}}{1 - sN_{2}} = 0 \\ 1 -...