Recent content by Skaiserollz89

Great! I think I've got it now. Ill attempt to work it through here... Given the initial problem $$ \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}d\vec{r}d\vec{r'}W(\vec{r})W(\vec{r'}) \vec{r} \cdot \vec{r'}$$ It seems like you are referring to Green's Theorem to turn a line integral into a...

Thank you for clarifying. But I think I am a little confused. Would you mind elaborating? I think you are saying that my line that reads ##cos(\phi) \int_{0}^{R}r dr\int_{0}^{R}r' dr'## is incorrect, and should be ##cos(\phi) \int_{0}^{R}r d\vec{r}\int_{0}^{R}r'd\vec{r'}## which simplifies to...

I agree. After performing the dot product I am working with scalars at that point, correct? So ##d\vec r## and ##d\vec r'## goes to ##dr## and ##dr'##? Do you think I am missing something?

So the statement in the published paper is assuming that integration with respect to ##\phi## must also be performed for it to go to zero, without explicitly saying so?

This homework statement comes from a research paper that was published in SPIE Optical Engineering. The integral $$\int\int_{-\infty}^{\infty}drdr'W(\vec{r})W(\vec{r'}) \vec{r} \cdot \vec{r'}=0$$ is an assumtion that is made via the following statement from the paper : "Since...

I have 2 lenses. L1 and L2 with focal lengths f1=910mm and f2=40mm, respectively. They are separated by a distance d=f1+f2. The magnification of the system is M1=-f2/f1=.044. If I have a normally incident, collimated beam pass through my system I will have a beam, parallel to the optic axis exit...

Here, ##\Phi(f_{x_n},f_{y_m})=|\mathscr{F(\phi(x,y))}|^2 ## is the Power Spectral Density of ##\phi(x,y)## and ##\mathscr{F}## is the Fourier transform operator. Parseval's Theorem relates the phase ##\phi(x,y)## to the power spectral density ##\Phi(f_{x_n},f_{y_m})## by...

In my system I am trying to represent two lenses. L1 with focal length f1=910mm and the other lens, L2 with focal length f2=40mm. These lenses are space such that there is a distance of f1+f2 between the lenses. I have a unit amplitude plane wave incident on L1. My goal is to find the...