Interferometry is a family of optical measurement techniques that superimpose two coherent light waves (a reference beam and a beam reflected from the test surface). Where the two waves are in phase they add up (bright fringe) and where they are out of phase they cancel (dark fringe). Because each fringe corresponds to a path-length change of half a wavelength (λ/2 ≈ 0.3 μm for visible light), the method resolves height differences down to the nanometre scale.

Why measuring surface roughness is the correct choice:

• Modern non-contact optical profilometers use phase-shifting and white-light (coherence scanning) interferometry to map the height of every point on a surface.
• From this height map the instrument computes standard roughness parameters (R_a, R_q, etc.), so surface roughness/texture is a well-established interferometric measurement.
• The vertical resolution is far finer than the roughness features being measured, making the technique ideal for fine finishes.

Why the other choices are less appropriate in this context:

• Frequency of vibration is normally obtained from accelerometers or vibration sensors that read frequency directly; it is a dynamic/time-domain quantity, not the static surface-height information interferometry is meant to capture here.
• Linear displacement and depth of micro-grooves are dimensional (length/depth) quantities. While specialised interferometers can also gauge displacement, in a standard shop-metrology sense micro-groove depth is typically taken with a contact stylus profilometer, so "surface roughness" is the answer that most directly and characteristically belongs to interferometry.