Sub-micron inline thickness measurement of cold-rolled metal strips by multi-wavelength interferometry and laser triangulation.

Thin metal foils of thicknesses below 100 µm are finding increasing use in high-tech applications. For such foils it is essential that production be controlled inline with sub-micron accuracy in highly challenging environments. An optical thickness gauge combining laser triangulation with multi-wavelength interferometry has now been developed for this purpose. Modulation-based 2f-3f-interferometry was used to realize a compact and robust sensor. A thorough measurement uncertainty analysis of the complete thickness measurement process yielded an expanded measurement uncertainty of U=(0.30µm)2+4π R a2, which is dependent on the roughness average Ra. The influence of oil remnants on measurement results is significantly weaker in the interference measurement than in geometric optical systems. Verification measurements against tactile reference measurements support the derived measurement uncertainty, and initial measurements in actual rolling mill environments have proven the real-world capability of this measurement technique over relevant process time scales at metal strip speeds of 200 m/min.

Refractive index of air. 2. Group index: comment.

Philip E. Ciddor and Reginald J. Hill published an analytical expression and a detailed procedure in 1999 on how to compute the group refractive index of air [Appl. Opt.38, 1663 (1999).APOPAI0003-693510.1364/AO.38.001663]. The International Association of Geodesy (IAG) has been referring to this procedure in its official recommendations for the compensation of the index of refraction in geodetic observations since then. Equation (B2) of the published procedure, however, contains a sign error. For proper application, this error must be corrected accordingly.

Analysis of a highly efficient phase-locking stabilization method for electro-optic comb generation.

We theoretically show that a slightly modified Pound-Drever-Hall (PDH) stabilization scheme can lead to the optimum time-domain characteristics for electro-optic comb generators (EOCG). The ideal locking point is located by analyzing the EOCG output pulse width. By summing up the electrical field reflected by the EOCG front mirror, a model of the phase-locking error signal is derived with the Jacobi-Anger identical transformation. The simulation and experiment show that the zero-locking point of the error signal of the modified scheme coincides well with the ideal locking point in contrast with the direct application of the PDH scheme. Finally, a power efficiency of up to 2.9% is achieved with this EOCG stabilization scheme. A relative instability of better than 2.6×10-8 is demonstrated by a dual comb interferometer with fixed paths. The Allan deviations of the comb mode frequencies are smaller than 2.8×10-9 and 1.1×10-10 for average times of 1 and 100 s, respectively.

Overcoming the refractivity limit in manufacturing environment.

We present a tracking interferometer with an intrinsic compensation of the refractive index of air. By using both wavelengths of a frequency doubled Nd:YAG laser the refractive index of air can be determined and compensated by the dispersion. One dimensional benchmark verification experiments in air conditioned and typical harsh, uncontrolled environment show an asymptotic length dependent uncertainty in the order of 0.1 µm/m for distances over 10 m, proofing the potential of this approach for high accuracy measurements in industrial environments.

Heterodyne multi-wavelength absolute interferometry based on a cavity-enhanced electro-optic frequency comb pair.

We present a heterodyne absolute distance interferometer with a macroscopic range, based on a promising optical source. The basis of the heterodyne measurement principle, a frequency comb pair with slightly different repetition rates and offset frequencies, is realized coherently by synchronized cavity-enhanced electro-optic frequency comb generators. The unknown distance is determined absolutely from the interferometric phases of distinct comb modes, by a parallel digital lock-in scheme. Comparison experiments with a reference HeNe incremental interferometer show an agreement well within 15 µm, for a range up to 10 m.

Diode-laser-based high-precision absolute distance interferometer of 20 m range.

We present a hybrid absolute distance measurement method that is based on a combination of frequency sweeping, variable synthetic, and two-wavelength, fixed synthetic wavelength interferometry. Both experiments were realized by two external cavity diode lasers. The measurement uncertainty was experimentally and theoretically demonstrated to be smaller than 12 microm at a measurement distance of 20 m.