Context: Trying to comprehend the Frequency ratio method(fringe counting method) which employs a Michelson interferometer, used for calibrating accelerometers.
A Michelson interferometer is depicted above. Its components are the laser source, a fixed mirror, a beam splitter (not depicted, but assume it's there), a detector (photo-diode) and a mobile mirror that's glued to the arm of an shm shaker that produces a sinusoidal displacement (ξ(t)=ξsin(2πft)); the accelerometer is not relevant for my questions.
The concern is to derive the number of averaged fringes that land on the detector. The following formula has been suggested:
Where λ is the wavelength of the laser.
Question: Where do all the multiplicative constants originate from (ξx2x2x2)?
Further info: More details are described in the following reference: G. S. Pineda,L. F. Argote,Vibration measurement using laser interferometry,pp 6-8. It's available online for free.