2.1

Multiple-wavelength interferometry with fixed synthetic wavelengths

In this case, multiple-wavelength interferometry can be combined with a commercially available time-of-flight (TOF) technique (e.g. Distomat, Leica) which allows a coarse measurement of the distance with 1 mm accuracy. Then, a chain of synthetic wavelengths can be used to determine the number of optical wavelength λ in the distance L. Finally, the optical fringe is interpolated to achieve 5 nm accuracy. Table 1 shows a possible measurement procedure. This technique has the advantage to enable simultaneous measurements at Λ₁, Λ₂ and λ. However, it requires at least 3 lasers.

Table 1:

Example of multiple-wavelength interferometry combined with time-of-flight technique

2.2

Variable synthetic wavelength

If the phase ϕ of the variable wavelength Λ is monitored during the wavelength tuning, the 2π cycles can be counted and the total phase difference is known absolutely. This allows now an absolute determination of the ranging distance L. The evaluation of the ranging distance from ϕ requires the exact knowledge of the wavelength tuning. This may be determined with the help of an additional Michelson interferometer with an exactly known, calibrated optical path difference L_cal^2,3. The phases of the measuring and reference interferometer will be given by

The distance is then found to be L= L_cal Δϕ /Δϕ_cal.. A possible solution consists of using two-wavelength interferometry (TWI) with variable synthetic wavelength and classical incremental interferometry. The TWI system should allow to determine the number of optical wavelengths. During the frequency chirping, the possible variation of the OPD can be monitored using the incremental interferometer. Table 2 shows a possible configuration

Table 2:

Example of MWI with wavelength tuning mode

This technique has the advantage to be simpler. However, the continuous tunability which is required (> 1 THz) may be very difficult to obtain with commercially available lasers. In addition, the measuring time for the absolute metrology will be limited by the tuning rate of the laser. This system may however be of interest to recover the order of the optical fringe when the incremental interferometer is interrupted.

2.3

Sources

In any case, one of the optical wavelengths has to be stabilized and known with a very high accuracy (< 10^-11 to obtain nm accuracy over 100 m). In order to achieve this day-to-day reproducibility, absolute frequency stabilization is mandatory. Depending on the interferometer concept, the requirement on the coherence length may be very stringent (> 100 m).

In the case of MWI with fixed wavelengths, the different wavelengths must be stabilized with respect to each other with high accuracy. This can be done with the help of a common reference length in the form of a Fabry-Pérot resonator. Absolute accuracy is obtained by stabilizing the Fabry-Pérot with respect to a frequency stabilized master laser⁴, e.g. a laser stabilized on an atomic absorption line, as shown in Fig. 4. A new concept of a multiple-wavelength source was developed recently for which the calibration of the different synthetic wavelengths is obtained by beat-frequency measurements^5,6. This concept may be useful to stabilize and calibrate synthetic wavelengths between 1 mm and 200 mm. Smaller synthetic wavelengths can be achieved by using two lasers which are frequency stabilized on different absorption lines.

Figure 4:

Example of multiple-wavelength source.

Solid-state lasers emitting around 1 µm are of interest because of their high coherence length (>> 100 m). Interesting emission lines can be obtained with Nd:YAG or Nd:YLF lasers at 1047 nm, 1053 nm, 1064 nm, 1320 nm or 1340 nm. Nd:YAG lasers emitting at 1064 nm are continuously tunable over more than 50 GHz. This allows to generate synthetic wavelength larger than 5 mm. The frequency offset between two Nd:YAG lasers can be locked using a commercially available electronic system (e.g. LOLA system from Lightwave). Absolute frequency stabilization can be achieved using a frequency doubling crystal and the I₂ absorption line at 532 nm⁷. Smaller synthetic wavelengths (< 1 mm) could possibly be generated with an additional solid-state laser emitting at 1047 nm (Nd:YLF, CrytaLaser). Indeed, the use of one laser at 1047 nm and one Nd:YAG laser at 1064 nm should allow to generate a synthetic wavelength of 65 µm, which is of a great interest for our application.

In the case of the wavelength tuning mode, the most critical point is the tunability of the laser, which must be at least 1 THz. To our knowledge, only external cavity laser diodes (e.g. New Focus, Velocity Tunable Diode Laser or Photonetics lasers) can achieve such a tunability without mode hops. The fixed wavelength must also be frequency stabilized on an external reference. For the calibration of the wavelength tuning, a temperature-stabilized Fabry-Pérot interferometer (e.g. Newport Super-Cavity) with an exactly known length can act as the reference interferometer. In that case, the wavelength tuning can be determined accurately by counting the resonances at the output of the Fabry-Pérot resonator. The main drawback of external cavity laser diodes is their moderate coherence length (100 m) and their frequency noise spectrum which is usually composed of a white noise part and a 1/f noise, which is a limiting factor for long baseline interferometry⁸.

2.4

Detection techniques

Signal processing is mandatory for practical applications of MWI. Several detection techniques have been proposed which are based on heterodyne or superheterodyne detection. Superheterodyne detection, introduced by Dändliker et al.², enables high-resolution measurements at arbitrary synthetic wavelengths Λ without the need for separation of these wavelengths optically. Different heterodyne frequencies are generated for each wavelength by means of acousto-optic modulators (e.g. 40 MHz and 40.1 MHz). For two-wavelength interferometry, the interference signal is therefore given by

which is the sum of the two heterodyne signals for the wavelengths λ₁ and λ₂, with the corresponding interferometric phases ϕ₁ = 4 L/λ₁ and ϕ₂ = 4 L/λ₂. After amplitude demodulation of the signal I(t) one gets

This signal at f = f₁ – f₂ makes it possible to measure directly the phase difference ϕ = ϕ₁ – ϕ₂ = 4 L/Λ, which is now only sensitive to the synthetic wavelength Λ. We see therefore that the method allows to detect directly the phase difference without optical separation of the wavelengths.