Detection periodic elements in image
You could apply a 2d FFT. You will get a frequency spectrum as z values on a 2d plane:

 ← That's log(abs(fftshift(fft2(image))))) where image is from the question, but with white borders trimmed

From the z values you can determine the highest peak and calculate its position on the 2d plane. With some geometric calculation, you can derive wavelength, direction and phaseshift from this.