Phase-stepping Interferometry & MATLAB

[n0_3sc]

Homework Statement

I am given 4 files containing the intensities of a fringe pattern with phase-steps of $$\pi/2$$.
I need to do a mesh plot (on MATLAB) of the intensities and phase.

Homework Equations

$$I=A+Bcos(\phi)$$

The Attempt at a Solution

I came up with the following equations:
$$I_1=A+Bcos(\phi)$$
$$I_2=A+Bcos(\phi+\pi/2)$$
$$I_3=A+Bcos(\phi+\pi)$$
$$I_4=A+Bcos(\phi+3\pi/2)$$

After the math I get either:
$$I_4-I_3+I_2-I_1 = 0$$
or
$$0.5(I_4-I_3-I_2+I_1) = B(sin\phi + cos\phi)$$

Obviously the first is not usable because I can't create a plot and the second contains 'B' in it - which doesn't help since I don't know what B is.
Any suggestions at all?

 

[mmwave]

Thank you for sharing your question with us. Based on the information provided, it seems like you are attempting to plot the intensities and phase of a fringe pattern using MATLAB. Your proposed equations for the intensities (I_1, I_2, I_3, I_4) are correct, and they are based on the equation I=A+Bcos(\phi) where A represents the background intensity and B represents the fringe amplitude.

However, in order to plot the intensities and phase accurately, you will need to obtain values for A and B from the data in your files. This can be done by fitting a curve to your intensity data points and extracting the values for A and B from the curve fit.

Once you have values for A and B, you can use the equations you have derived to plot the intensities and phase. The first equation (I_4-I_3+I_2-I_1 = 0) can be used to plot the phase, as it represents the phase difference between consecutive intensity measurements. The second equation (0.5(I_4-I_3-I_2+I_1) = B(sin\phi + cos\phi)) can be used to plot the intensities, as it relates the intensity to the phase.

I hope this helps you with your problem. Let me know if you have any further questions or need clarification on any of the steps.



Scientist

 

[tacman]

Phase-stepping interferometry is a valuable technique for analyzing fringe patterns and determining phase information. In order to create a mesh plot of the intensities and phase, the given equations can be used. It is important to note that the value of B is not necessary for creating the plot, as it only affects the amplitude of the cosine function and does not change the overall shape of the plot.

To create the mesh plot, you can use MATLAB's meshgrid function to create a grid of points for the x and y axes. Then, using the equations you have derived, you can calculate the intensity values for each point on the grid. This will give you a 3D plot with the x and y axes representing the coordinates and the z axis representing the intensity value.

To plot the phase, you can use the same grid of points and calculate the phase values using the inverse cosine function, arccos. This will give you a plot of the phase values at each point on the grid.

It is also important to note that the equations you have derived assume a perfect cosine function for the fringe pattern. In reality, there may be noise or imperfections in the data that can affect the accuracy of the plot. Therefore, it is important to carefully analyze the data and consider any potential sources of error in order to obtain the most accurate results.

In summary, using the equations you have derived and MATLAB's meshgrid function, you can create a mesh plot of the intensities and phase for the given fringe pattern with phase-steps of pi/2. Keep in mind any potential sources of error and carefully analyze the data to obtain the most accurate results.