measuring length in wavelengths of light using interferometer.
in many practical circumstances, , precision work, measurement of dimension using transit-time measurements used initial indicator of length , refined using interferometer. generally, transit time measurements preferred longer lengths, , interferometers shorter lengths.
the figure shows schematically how length determined using michelson interferometer: 2 panels show laser source emitting light beam split beam splitter (bs) travel 2 paths. light recombined bouncing 2 components off pair of corner cubes (cc) return 2 components beam splitter again reassembled. corner cube serves displace incident reflected beam, avoids complications caused superposing 2 beams. distance between left-hand corner cube , beam splitter compared separation on fixed leg left-hand spacing adjusted compare length of object measured.
in top panel path such 2 beams reinforce each other after reassembly, leading strong light pattern (sun). bottom panel shows path made half wavelength longer moving left-hand mirror quarter wavelength further away, increasing path difference half wavelength. result 2 beams in opposition each other @ reassembly, , recombined light intensity drops 0 (clouds). thus, spacing between mirrors adjusted, observed light intensity cycles between reinforcement , cancellation number of wavelengths of path difference changes, , observed intensity alternately peaks (bright sun) , dims (dark clouds). behavior called interference , machine called interferometer. counting fringes found how many wavelengths long measured path compared fixed leg. in way, measurements made in units of wavelengths λ corresponding particular atomic transition. length in wavelengths can converted length in units of metres if selected transition has known frequency f. length number of wavelengths λ related metre using λ = c0 / f. c0 defined value of 299,792,458 m/s, error in measured length in wavelengths increased conversion metres error in measuring frequency of light source.
by using sources of several wavelengths generate sum , difference beat frequencies, absolute distance measurements become possible.
this methodology length determination requires careful specification of wavelength of light used, , 1 reason employing laser source wavelength can held stable. regardless of stability, however, precise frequency of source has linewidth limitations. other significant errors introduced interferometer itself; in particular: errors in light beam alignment, collimation , fractional fringe determination. corrections made account departures of medium (for example, air) reference medium of classical vacuum. resolution using wavelengths in range of Δl/l ≈ 10 – 10 depending upon length measured, wavelength , type of interferometer used.
the measurement requires careful specification of medium in light propagates. refractive index correction made relate medium used reference vacuum, taken in si units classical vacuum. these refractive index corrections can found more accurately adding frequencies, example, frequencies @ propagation sensitive presence of water vapor. way non-ideal contributions refractive index can measured , corrected @ frequency using established theoretical models.
it may noted again, way of contrast, transit-time measurement of length independent of knowledge of source frequency, except possible dependence of correction relating measurement medium reference medium of classical vacuum, may indeed depend on frequency of source. pulse train or other wave-shaping used, range of frequencies may involved.
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