Michelson Interferometer fringe counter

Question

For a lab report on the Michelson Interferometer, I want to write a code on Python that automatically counts the fringes (right now we have to count them manually and it is not precise). I took a video for the purpose.

A frame of the video

How would you start? Many thanks.

Answer 1

I'd check out openCV, an open source computer vision library for python. Since the fringes are likely to be fairly different from the background, you can take the derivative of the image (https://docs.opencv.org/2.4/doc/tutorials/imgproc/imgtrans/sobel_derivatives/sobel_derivatives.html), and count the places where there's a large gradient. My solution on the image you posted is below. I think this should get you started on the right track.

import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import numpy as np
import cv2
from scipy.signal import find_peaks
from scipy.ndimage.filters import gaussian_filter1d

fig = plt.figure(tight_layout=True)
gs = gridspec.GridSpec(2, 2)
ax1 = fig.add_subplot(gs[0, 0])
ax2 = fig.add_subplot(gs[0, 1])
ax3 = fig.add_subplot(gs[1, :])
ax1.set_xticks([])
ax1.set_yticks([])
ax2.set_yticks([])
ax2.set_xticks([])

img = cv2.imread('michelson.jpg', 0) # read in the image as grayscale

ax1.imshow(img, cmap='gray')
ax1.set_title("Original image (grayscale)")

img[img < 10] = 0 # apply some arbitrary thresholding (there's
# a bunch of noise in the image

yp, xp = np.where(img != 0)

xmax = max(xp)
xmin = min(xp)

target_slice = (xmax - xmin) / 2 + xmin # get the middle of the fringe blob

sobely = cv2.Sobel(img,cv2.CV_64F,0,1,ksize=5) # get the vertical derivative

sobely = cv2.blur(sobely,(7,7)) # make the peaks a little smoother

ax2.imshow(sobely, cmap='gray') #show the derivative (troughs are very visible)
ax2.plot([target_slice, target_slice], [img.shape[0], 0], 'r-')

slc = sobely[:, int(target_slice)]
slc[slc < 0] = 0
ax2.set_title("vertical derivative (red line indicating slice taken from image)")

slc = gaussian_filter1d(slc, sigma=10) # filter the peaks the remove noise,
# again an arbitrary threshold

ax3.plot(slc) 
peaks = find_peaks(slc)[0] # [0] returns only locations 

ax3.plot(peaks, slc[peaks], 'ro')
ax3.set_title('number of fringes: ' + str(len(peaks)))
plt.show()