Help with the 3D gaussian function

[PythagoreLove]

Hi,
I need help with the gaussian function in 3D. I'm using the form:
z=A*exp( (x-xo)^2/(2σx^2)+(y-yo)^2/(2σy^2))

I know that A is the amplitude and xo,yo are the center coordinate.

I found that formula on http://en.wikipedia.org/wiki/Gaussian_function and they say that σx and σy are the spread of the blob. But if I put σx=σy=1, the function is from -3 to 3... Why is that ?

 

[phyzguy]

They only plotted it from -3 to 3. It extends to +/-infinity in both x and y, but once |x-x0|/sigmax is much larger than 3.0, the value of the function is very close to zero.

 

[PythagoreLove]

But is there a pretty good way to find σx and σy, graphically speaking. I have a gaussian curve and want to find what is the function.

 

[phyzguy]

A good way is to use FWHM(Full Width at Half Maximum). In other words, you measure the width of the curve at half of the peak value. This is then easily converted into sigma using the formula on this page:

http://en.wikipedia.org/wiki/Fwhm

Since you have a 2D Gaussian, you need to measure the FWHM in the x-direction with y=y0 to find sigmax, then do the same in the y-direction with x=x0 to find sigmay.

 

[blue_raver22]

Hello, thank you for reaching out for assistance with the 3D gaussian function. I would be happy to help you understand the formula and why it may produce a range from -3 to 3 when σx=σy=1.

First, let's break down the formula and understand what each component represents. The gaussian function is a mathematical function commonly used in statistics and physics to describe the distribution of data. In the context of 3D, it is used to describe the distribution of data in three dimensions, with x, y, and z coordinates.

The formula you provided is a specific form of the gaussian function that includes the amplitude (A), center coordinates (xo, yo), and spread (σx, σy). The amplitude represents the maximum value of the function, while the center coordinates represent the location of the peak of the function. The spread, also known as the standard deviation, determines the width of the function's curve.

When σx=σy=1, this means that the spread is equal in both the x and y directions. This results in a symmetrical distribution, with a range from -3 to 3 in both the x and y directions. This is because the formula is exponential, meaning that as the distance from the center coordinates increases, the value of the function decreases rapidly. This leads to a range that is limited to -3 to 3 in both directions.

If you would like to change the range of the function, you can adjust the spread (σx, σy) to be larger or smaller than 1. A larger spread will result in a wider distribution, while a smaller spread will result in a narrower distribution. This will change the range of the function accordingly.

I hope this helps to clarify the 3D gaussian function for you. If you have any further questions, please don't hesitate to ask. I am always happy to help others understand complex concepts. Best of luck with your research!