# Analyzing movement of fringes

I have taken a series of images of a fringe pattern at regular time intervals. This fringes are generated by shining a laser beam onto the CCD camera. The laser goes through a lot of optics, which is why it creates these fringes.

There is some vibration in the laser system setup which causes these fringes to move around although not by much, couple of pixels at most. I want to analyze how much these fringes are moving around. Is there an easy way to do this?

One idea that I had, and I don't know if it's right, is to take the FFT of the image, and discard the DC (constant) components. I could analyze just one frequency component. Now, if the fringe pattern is moving about, then that should change the phase of that frequency component. Does that make sense?

Thanks.

Update As suggested by A_A, I took one frame as a reference and subtracted it from the rest:

Out of the mess of fringes, I can clearly identify one pattern which is moving about. I particular, the diagonal fringes do not seem to be changing from frame to frame. In the end, I just want to identify if there's any one particular optic which is responsible for this vibration, so I could just set up my live camera feed to display the difference between consecutive images and play around with the optics to see if I can reduce the fringes.

• Why not try it and see what happens? If you want us to take a crack, please upload enough frames to analyze; e.g., as an animated GIF. – Emre May 31 '12 at 6:34
• "take the FFT of the image, and discard the DC" This would be equivalent to subtracting the mean of the pixels. I don't think that's what you want. When these fringes move around, it's just like a translation of the image above? Or do they change in shape and intensity in the process? – endolith May 31 '12 at 13:41

...take the FFT of the image, and discard the DC (constant) components.

That would result in removing the mean brightness from an image. Due to the fact that grayscale images have positive numbers between 0-255, what would be returned from that "high pass" filter (that only "cuts" the DC) would be the image with the same grayscale variance but now centered around 0 (instead of its original mean level).

I want to analyze how much these fringes are moving around. Is there an easy way to do this?

You could obtain the absolute difference between two successive frames and then the sum of all values of that quantitty as a simple metric of how much movement was there.

If you would also like to be able to estimate how much displacement was there between two successive frames then the simplest thing would be to use cross correlation (on successive frames) and track the position of its maximum.

if you want to track the motion of each pixel in the image , there is an algorithm called horn-schunk method that determines the optical flow between two successive images , and the algorithm is simple and based on iterations,implemented here math Works

It should be okay to remove the DC part in the FFT to remove the translations Under the assumption that:

• The images are superpositions of the responses from laser beams (only one laser beam and no interference between timesteps).
• Given a small translation of one laser, the image response from that beam will be translated linearly by the optics.

But then again this is a real-world problem, but it should work in theory, so it make sense''.