Distance measurement by multiple-wavelength interferometry

Transcription

1 J. Opt. 29 (1998) Printed in the UK PII: S15-536X(98) Distance measurement by multiple-wavelength interferometry R Dändliker, Y Salvadé and E Zimmermann Institute of Microtechnology, University of Neuchâtel, Breguet 2, CH-2 Neuchâtel, Switzerland Received 1 October 1997 Abstract. Multiple-wavelength interferometry enables us to increase the range of non-ambiguity and to reduce the sensitivity of classical interferometry. It can also be operated on rough surfaces. The accuracy depends on the stability and the calibration of the different wavelengths. An electronically calibrated three-wavelength source for synthetic wavelengths in the millimetre range with an accuracy of better than 1 5 has been demonstrated. Absolute distance measurements were performed up to 2 mm with a resolution of better than 1 µm. Keywords: Interferometry, multiple-wavelength, distance measurement Mesure de distance par interférométrie à plusieurs longueurs d onde Résumé. L interférométrie à plusieurs longueurs d onde permet d augmenter la zone de non-ambiguïté etderéduire la sensibilité de l interférométrie classique. Elle peut également être utilisée sur des surfaces rugueuses. La précision de mesure dépend de la stabilité et de la calibration des différentes longueurs d onde. Une source à plusieurs longueurs d onde a été réalisée, générant des longueurs d onde synthétiques de quelques millimètres et permettant une calibration électronique de précision meilleure que 1 5. Des mesures de distances absolues ont été effectuées jusqu à 2 mm avec une résolution de 1 µm environ. Mots clés: Interférométrie, longueurs d onde multiples, mesure de distance 1. Introduction Absolute distance measurement with a resolution of better than.1 mm over several metres cannot be covered by classical interferometry or by current time-of-flight metrology. Multiple-wavelength interferometry (MWI) is, similarly to classical interferometry, a coherent method, but it offers great flexibility in sensitivity by an appropriate choice of the different wavelengths [1]. Indeed, the use of two different wavelengths, λ 1 and λ 2, permits the generation of a synthetic wavelength = λ 1 λ 2 / λ 1 λ 2, much longer than the two individual optical wavelengths. This method thus makes it possible to increase the range of non-ambiguity for interferometry and to reduce the sensitivity of the measurement. Moreover, this technique is also applicable to rough surfaces. Invited paper. address: rene.dandliker@imt.unine.ch In order to obtain this new synthetic wavelength, the different optical wavelengths have to be interrelated. Real-time electronic signal processing is mandatory for practical applications. The absolute accuracy of distance measurement by MWI depends essentially on the properties of the source (coherence, stability, power) and on the calibration of the synthetic wavelength. Indeed, for highly accurate measurements, that is for δl/l < 1 5, where L is the working distance and δl is the resolution, the synthetic wavelength has to be known with at least the same accuracy. Therefore the two laser sources must be stabilized and the synthetic wavelength has to be calibrated [1, 2]. This paper presents some solutions for the signal processing and calibration of multiple-wavelength sources. Experimental results of absolute distance measurements with cooperative (reflecting) and non-cooperative (roughsurface) targets will be presented X/98/315+1$19.5 c 1998 IOP Publishing Ltd 15

2 R Dändliker et al 2. Signal processing Two-wavelength heterodyne interferometry was reported by Fercher et al [3]. By simultaneous phase measurement at both wavelengths, the interference phase at the synthetic wavelength can be determined directly. This method provides fast measurement and also works for rough surfaces. However, because the two wavelengths must be optically separated (prism, grating) before detection, the technique can only be used for relatively large wavelength differences and thus small synthetic wavelengths. Superheterodyne detection, introduced by Dändliker et al [4], enables high-resolution measurements at arbitrary synthetic wavelengths without the need for interferometric stability at the optical wavelengths λ 1 and λ 2 or for separation of these wavelengths optically. This is of great importance for range finding and industrial distance measuring with sub-millimetre resolution. Two laser sources of different optical frequencies ν 1 and ν 2, corresponding to the wavelengths λ 1 and λ 2, are used to simultaneously illuminate a Michelson-type heterodyne interferometer. For this purpose, each source is followed by a device which creates two orthogonal polarizations of slightly different frequency. These frequency differences can be produced by acousto-optical modulators and are typically f 1 = 4. MHz and f 2 = 4.1 MHz. Two photodetectors behind appropriate polarizers produce reference and interferometer signals I r (t) and I(t) of the form I(t) = a +a 1 cos(2πf 1 t + φ 1 ) + a 2 cos(2πf 2 t + φ 2 ) (1) which is the sum of the two heterodyne signals for wavelengths λ 1 and λ 2, with the corresponding interferometric phases φ 1 and φ 2. For an interferometric path difference L, the phases φ 1 and φ 2 are given by φ 1 = 4πL/λ 1 and φ 2 = 4πL/λ 2. (2) They are sensitive to path changes L of the order of the optical wavelength. Therefore, to determine the phase difference φ = φ 1 φ 2, the phases φ 1 and φ 2 must be measured accurately, which requires interferometric stability of the set-up. However, if the two heterodyne signals are fed to a quadratic detector (mixer), the phase difference φ = φ 1 φ 2 can be measured directly. Because f 1 f 2 is chosen to be small compared with f 1 and f 2, the detector output (equation (1)) has the form of a carrier-suppressed amplitude-modulated signal with carrier (f 1 + f 2 )/2 and modulation frequency (f 1 f 2 )/2. After amplitude demodulation, one therefore finds I dem (t) = a 12 cos[2π(f 1 f 2 )t + (φ 1 φ 2 )]. (3) This signal at f = f 1 f 2 makes it possible to measure the phase difference directly, φ = φ 1 φ 2 = 4πL/λ 1 4πL/λ 2 = 4πL/ (4) which is now only sensitive to the synthetic wavelength. Successful application of superheterodyne detection has been reported for multiple-wavelength interferometry with Λ distance (2L) Figure 1. Interference signal for two wavelengths λ 1 and λ 2 as a function of the distance L (equation (5) with f 1 =) and the corresponding modulation power of this interference signal (equation (6)). different types of sources, namely two detuned singlefrequency Ar lasers ( = 6 mm) [4], a diode laser and an acousto-optic modulator for a 5 MHz frequency shift ( =.6 m) [5], a two-wavelength HeNe laser ( = 55.5 µm) [6] and tunable Nd:YAG lasers ( = m) [7 9]. However, simpler detection methods, which do not need separate modulation of the two wavelengths might be of interest [1]. If the two heterodyne frequencies f 1 and f 2 are chosen equal (f 1 = f 2 ), equation (1) becomes I(t) = a +a 1 cos(2πf 1 t + φ 1 ) + a 2 cos(2πf 1 t + φ 2 ). (5) The interference fringe function for the synthetic wavelength is then obtained by detecting the electrical power of the AC part of this signal, which is P ac = 1 2 [a2 1 + a a 1a 2 cos(φ 1 φ 2 )]. (6) Figure 1 shows the detected interference signal for two wavelengths λ 1 and λ 2 as a function of the distance L (equation (5) with f 1 = ) and the corresponding modulation power of this interference signal (equation (6)). Equation (6) looks like a typical interference signal, but now for the synthetic wavelength rather than for the optical wavelength λ. The interference phase φ = φ 1 φ 2 = 4πL/ of the synthetic wavelength can now be determined by techniques similar to those used for phase interpolation in interferometry. In practice, the frequency shift f 1 can be obtained by an acousto-optical modulator or by path length modulation in the interferometer. Assuming that the interferometer is scanned at a constant speed v, we get a frequency shift of f 1 = 2v/λ. Both techniques have been used to obtain the experimental results reported later in this paper. 3. Calibrated multiple-wavelength sources Multiple-wavelength interferometry can be operated with fixed wavelengths or in a wavelength tuning mode [1]. 16

3 Distance measurement by multiple-wavelength interferometry λ1, λ2, λ3 Fabry-Perot resonator high speed photodetector LD3, λ3 electronic feedback PD LD2, λ2 electronic feedback frequency counter LD1, λ1 electronic feedback 75 GHz.75 GHz ν1 ν2 ν3 N ν Figure 2. Multiple-wavelength source using laser diodes with absolute calibration by electronic beat-frequency measurement. Instead of one phase measurement for a fixed separation λ = λ 1 λ 2 of the two wavelengths, two phase measurements are performed before and after a change of the wavelength difference λ between the two sources. If the phase φ of the variable synthetic wavelength is monitored during the wavelength tuning, the 2π cycles can be counted and the total phase difference is known absolutely. This now allows an absolute determination of the ranging distance L. The evaluation of the ranging distance from φ requires 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 (4). In the case of fixed wavelengths, the laser sources for the different wavelengths must be stabilized with respect to each other. This can be done with the help of a common reference length in the form of a Fabry Perot resonator. Absolute accuracy can be obtained if the Fabry Perot is stabilized with respect to a frequency-stabilized master laser [1, 1]. Another concept of a stabilized multiplewavelength source, for which the calibration of the different synthetic wavelengths is obtained by the use of optoelectronic beat-frequency measurements, has been reported recently [1, 2]. Figure 2 shows the concept of a three-wavelength source with absolute calibration by electronic beatfrequency measurement [2]. This source consists of three diode lasers operating at the frequencies ν 1, ν 2 and ν 3. Two of them (ν 1 and ν 2 ) are stabilized on two consecutive resonances of a common stable Fabry Perot resonator. In our experiment, the Fabry Perot resonator has a free spectral range of.75 GHz, as shown in the bottom part of figure 2. The corresponding beat frequency ν 21 = ν 2 ν 1 =.75 GHz is detected and measured by a frequency counter with electronic accuracy. The third laser is tuned (without mode hopping) over N resonances of the Fabry Perot. The frequency difference ν 31 = ν 3 ν 1 is then known with the same relative accuracy as the electronically calibrated beat frequency ν 21. For N = 1 we obtain ν 31 = Nν 21 = 75 GHz ( 31 = 4 mm). To get an accuracy of δl/l = 1 6, the free spectral range of the Fabry Perot must be calibrated with an accuracy of δν 21 /ν 21 = 1 6, or in our case δν 21 =.75 khz, which is feasible for a stable Fabry Perot by long-time averaging. The required short-time stability of the laser diodes for the high-resolution distance measurement with 31 is obtained from δν 31 /ν 31 = 1 6, which in our case is δν 31 = 75 khz. With such a multiple-wavelength source it would be possible to measure distances without ambiguity within 2 mm ( 21 = 4 mm) and with a resolution of 2 µm ( 31 = 4 mm with 2π/1 interpolation). Experimental investigations were performed with commercial GaAlAs monomode laser diodes (Sharp LT27MD) emitting at 78 nm with a maximum optical power of 1 mw. The optical set-up used for the calibration of the synthetic wavelength by comparison with an HP laser interferometer is depicted in figure 3. This set-up is similar to a wavemeter. We used ν 1 and ν 3 to illuminate the heterodyne Michelson interferometer. A number of 17

4 R Dändliker et al phase stepping CC Λ/8 HP-interferometer νi + F2 νi + F1 CC PBS photodetector P HP-counter (i = 1 and 3) high speed photodetector ν21 νi + F1 νi + F2 3λ-source + Heterodyning module lock-in amp. phase measurement Figure 3. Calibration of the synthetic wavelength by comparison with an HP laser interferometer: PBS, polarizing beamsplitter; CC, corner cubes; P, polarizer; AOM, acousto-optic modulators. N = 1 resonances of the Fabry Perot were counted while tuning the laser diode LD 3 from ν 1 to ν 3. The detection at the output of the two-wavelength interferometer is achieved by a photodiode and a lock-in amplifier to obtain the interference signal by heterodyne detection. To this end, the multiple-wavelength source is followed by a device which creates two orthogonal polarizations of slightly different frequencies. This frequency difference is produced by two acousto-optic modulators operating at F 1 = 4. MHz and F 2 = 4.1 MHz. As shown in figure 3, a polarizing beamsplitter directs the optical frequencies ν i + F 1 (i = 1, 3) toward a reference mirror, while the optical frequencies ν i + F 2 go to the target. The output of the interferometer is then detected by a photodiode and a lock-in amplifier, which performs the detection at the heterodyne frequency of 1 khz. The interference fringe function for the synthetic wavelength 31 is then obtained by detecting the electrical power of the AC part of the photodiode signal (equation (6)). The phase φ(l) of the synthetic wavelength is determined by moving the reference mirror in steps of 31 /8 =.5 mm to get five 9 phase steps. From the corresponding measured values of the heterodyne signal power the phase is calculated with a five-frame error-compensation algorithm [11]. By measuring over a common path difference of about 1 m, using both the multiple-wavelength and the HP laser interferometer, a calibrated value of the synthetic wavelength is obtained. From this calibration procedure [1] and taking into account the atmospheric conditions (group index n g = ), we found 31 = ±. 6 mm, corresponding to an interpolation accuracy of better than 2π/1. On the other hand, we determined the beat frequency from ten values obtained with the frequency counter. For a gate time of 1 s, we measured ν 21 = ±.1 MHz. We found with this value a synthetic wavelength 31 = c/(n g ν 31 ) = c/(n g Nν 21 ) of ±. 5 mm (in air as above). This result proves that an absolute calibration of the synthetic wavelength with an accuracy of at least is achieved by means of electronic beat-frequency measurements at ν 21 [2]. The synthetic wavelength 31 can be chosen anywhere within the tuning range of the laser diode LD 3, which is about 1 GHz, by selecting the number N of resonances of the Fabry Perot counted while tuning the laser diode LD 3 from ν 1 to ν Absolute distance measurement The set-up of the three-wavelength heterodyne interferometer is shown in figure 4. Assuming a fringe interpolation of at least 2π/2, for the synthetic wavelength, it should be possible with the above-described threewavelength source to measure distances without ambiguity within 2 mm ( 21 = 4 mm) and with a resolution of 1 µm ( 31 = 4 mm). The technique consists of two successive two-wavelength interferometric measurements, the first one using ν 3 and ν 1 and the second one using ν 3 and ν 2 to illuminate simultaneously the Michelson-type interferometer. The corresponding synthetic wavelengths are 31 = 4mmand 32 = 4.4 mm, respectively. The detection of the modulation power is performed by a photodiode followed by a lock-in amplifier. For an interferometric path difference L, the phases φ 31 and φ 32, obtained by moving 18

5 Distance measurement by multiple-wavelength interferometry 3λ-source ν1, ν2, ν3 frequency shifter module F1 = 4 MHz F2 = 4.1 MHz frequency counter ν21 = ν2 ν1 resonances counter N νi + F1 νi + F2 Lock-in amp. phase measurement P Λ/8 PBS target νi + F2 λ/4 νi + F1 reference Michelson interferometer Figure 4. Three-wavelength heterodyne interferometer. The phases of the synthetic wavelengths 31 and 32 are detected by five phase steps of /8 =.5 mm. the reference mirror in steps of 31 /8 =.5 mm, are given by φ 31 = 4π L and φ 32 = 4π L. (7) The phase difference φ 21 = φ 31 φ 32 can then be calculated and is related to the path difference L by φ 21 = 4π L (8) 21 which is now sensitive to the synthetic wavelength 21 = 4 mm. Assuming that the resolution of φ 21 is better than 2π/2, this phase measurement can be used to evaluate the fringe order M of the synthetic wavelength 31 without ambiguity, using the algorithm { } 1 M = Round 2π (Nφ 21 φ 31 ) (9) where N = 1 is the number of resonances of the Fabry Perot between ν 1 and ν 3. The path difference L can then be calculated by ( L = M + φ ) π 2. (1) We checked the resolution of the set-up by measuring distances over a range of 2 mm, corresponding to a displacement of 31 /2. Once again, we used the HP laser interferometer as a reference. The measuring time was 5 ms (5 1 ms, using a five-phase stepping algorithm). For each distance, the measurement was repeated 1 times, yielding a repeatability of the order of 8 µm, which corresponds to a phase accuracy of approximately 2π/25. We then measured the phase φ 21 as described above over a range of 2 mm. The standard deviation δφ 21 was about 2π/4, which is better than expected for independent measurements of δφ 31 and δφ 32. After fringe order estimation, the distance has been determined using equation (1). The lower trace of figure 5 reports the multiple-wavelength interferometry (MWI) results versus the HP laser, whereas the upper graph shows the corresponding deviation of the MWI mean value from the reference value given by the HP interferometer. The standard deviation is about 9 µm. Combining time-of-flight distance measurement and the described multiple-wavelength interferometry allows one to get micrometre accuracy over even larger distances. However, the coherence length of the laser diodes may become a limiting factor for the maximum distance to be measured. With the measured linewidth of 9 MHz for the Sharp LT27MD, which corresponds to a coherence length of L c = 1.6 m, absolute distance measurements up to 5.3 m should be possible. However, the phase fluctuations due to the frequency noise of the lasers become more important for increasing distance. From the measured frequency noise spectrum we estimate a phase error of about.2 rad 2π/3 for a path difference equal to the coherence length and an observation time of T = 1 ms [12]. 19

6 R Dändliker et al Errors [µm] MWI Measurements [mm] HP Reference [mm] 15 2 Figure 5. Absolute distance measurements over a range of 2 mm using three-wavelength interferometry. Figure 6. Schematic layout of improved lock-in CCD (developed and designed by CSEM/PSIZ). 5. Two-dimensional detection In view of the application of multiple-wavelength interferometry to non-cooperative targets (rough surfaces), a new type of CCD image sensor for two-dimensional synchronous detection at the heterodyne frequency was proposed and developed recently [13]. For each pixel, modulated light is detected with four 9 phase-shifted samples per period. The corresponding photo-charges are stored at four different locations (buckets). The cycle of integrating and storing can be repeated over many periods. The four samples are then read out by charge transfer. The amplitude, phase or power of the modulation (beat frequency) can then be determined for each pixel. Using an increased number of spatially separated detectors in an array improves the detection probability of the interference signal between the reference beam and the speckled return beam from a rough target [14]. The layout of an improved version of a lock-in CCD is shown in figure 6. Arrays with 5 12 pixels have been designed and fabricated with a standard CMOS process. To further simplify the optical set-up (figure 7), we use a moving mirror on a magnetic translator (loudspeaker) to provide the phase stepping at the synthetic wavelength and to generate the frequency shift for the heterodyne detection. This mirror moves at a nearly constant speed of about 2 mm s 1 over a distance of about 3 mm, which produces a heterodyne frequency of 2v/λ 5 khz. The control signals for the lock-in CCD and the phase-shifting algorithm are obtained from the interference signal I ref. Preliminary results were obtained by using a cooperative target (mirror) and one pixel of the lock-in CCD. The power of the modulated signal was computed from the CCD output. The phase of the synthetic wavelength 31 was measured over a length L of 4 mm. Results are shown in figure 8. The charge was collected over 1 modulation periods (.2 ms) for five quadrature positions (.5 mm) of the mirror. The standard deviation of the error between the MWI and the HP interferometer is about 4 µm, which corresponds to a phase resolution of 2π/5. This resolution is good enough to perform absolute distance measurements over 2 mm with the reported three-wavelength source. 6. Measurements on non-cooperative targets The problems with non-cooperative targets (rough surfaces) are: the statistical properties of returning light (speckles) and low coherent power (diffused light, speckles). There are different possibilities to increase the source power. Two solutions have been studied. The first one 11

7 Distance measurement by multiple-wavelength interferometry Detection technique frequency f TTL signal generator Phase shifting control Master clock CCD Driver Trigger t I ref PD Lock-In CCD Multiple- Wavelength Source νi νi + f νi target v reference Multiple-Wavelength Interferometer Magnetic Translator Figure 7. Multiple-wavelength interferometer using a movable mirror on a magnetic translator to produce simultaneously the heterodyne frequency and the phase shifting at the synthetic wavelength. 1 error [µm] Distance [mm] Reference [mm] 3 4 Figure 8. Distance measurements over a range of 4 mm, using a lock-in CCD detector (HP interferometer used as a reference). 111

8 R Dändliker et al Reference signal PD Moving reference Target Lens Multiplewavelength source Figure 9. Multiple-wavelength speckle inteferometer set-up. T = 133 ms Modulation power 6 ms 1 ms Time Figure 1. Integration phase (dark bars) and read-out phase (light bars) during the measurement time. consists of using a semiconductor optical amplifier after the low-power source. For this task, we used a tapered amplifier chip at 785 nm (SDL 863). For a few mw of input power, we obtained an output power of about 1 mw at each wavelength, yielding a gain of about 1. In this MOPA (master oscillator power amplifier) configuration, the spectral characteristics are only determined by the lowpower diode lasers. The main drawback is the high optical isolation (>7 db) which is required between the lowpower source and the optical amplifier to avoid spectral disturbance of the master oscillator due to the feedback sensitivity of diode lasers. The second solution consists of using directly highpower distributed Bragg reflectors diode lasers (SDL- 5722H). The maximal ouput power is about 15 mw. A multiple-wavelength source similar to the low-power source described above was mounted with such diode lasers. The frequency tunability with temperature is modehop free over at least 1.5 nm (62 GHz). This allows us to choose the most appropriate synthetic wavelength with great flexibility between.5 and 2 mm, depending on the number of Fabry Perot resonances between both 112

9 Distance measurement by multiple-wavelength interferometry Error [mrad] Phase [rad] Reference distance [mm] 3 4 Figure 11. Phase measurements on non-cooperative targets over a range of 4 mm, after signal processing. frequencies. Moreover, the linewidth measured from the beat note spectrum is only 2.6 MHz, which corresponds to a coherence length of about 4 m, i.e. four times longer than for the standard low-power diode lasers. The system was adapted for measurements on noncooperative targets. The final set-up, shown in figure 9, is similar to the one used for ESPI (electronic speckle pattern interferometry), except for the moving reference and the lock-in CCD. Two-dimensional measurements are important to overcome the problem of speckles produced by light scattering on rough surfaces. With appropriate statistical averaging, the probability to detect bright speckles is increased. We therefore used the 2D version of the lock-in CCD which is composed of 5 12 pixels. The modulation power of the interference signal is detected in ten intervals of 1 ms duration and 6 ms separation, phase shifted by 45 (see figure 1). Five 9 phase-shifted values are obtained by adding two consecutive samples. The phase of the synthetic wavelength is then calculated using the fiveframe error compensation algorithm [11]. The effective integration time is thus about 1 ms. To improve the statistical signal quality, only 3 pixels (5% of 5 12) were retained for the phase evaluation. The final phase value was obtained by averaging over these 3 phase measurements. Distance measurements at 4 cm from the imaging lens indicate a phase resolution of about 2π/2, as shown in figure 11, corresponding to a distance resolution of about 1 µm. 7. Conclusions Multiple-wavelength interferometry has been chosen as the most promising approach for absolute distance measurements with high resolution. A novel concept of a multiple-wavelength source, using tunable diode lasers, with absolute calibration by electronic beat-frequency measurements has been developed. Experimental results of the comparison with an HP interferometer prove that a calibration of the synthetic wavelength in the millimetre range with an accuracy better than 1 5 is feasible. With the reported three-wavelength source, absolute distance measurements were performed up to 2 mm (synthetic wavelength of 4 mm), and with a resolution better than 1 µm (synthetic wavelength of 4 mm, phase resolution better than 2π/2). Distance measurements to noncooperative targets using MWI have been demonstrated, using a custom-designed lock-in CCD and appropriate signal processing. Future tasks are the measurements at larger distances (>1 m) by combining time-of-flight distance measurements with MWI and the development of a more compact set-up. Acknowledgments The authors thank P Seitz and T Spirig (CSEM, Centre Suisse d Electronique et de Microtechnique, formerly Paul Scherrer Institute, Zürich) for providing the lock-in CCD detectors. This work was supported by the Swiss Priority Programme OPTIQUE. References [1] Dändliker R, Hug K, Politch J and Zimmermann E 1995 High accuracy distance measurement with multiple-wavelength interferometry Opt. Eng

10 R Dändliker et al [2] Zimmermann E, Salvadé Y and Dändliker R 1996 Stabilized three-wavelength source calibrated by electronic means for high accuracy absolute distance measurement Opt. Lett [3] Fercher A F, Hu H Z and Vry U 1985 Rough surface interferometry with a two-wavelength heterodyne speckle interferometer Appl. Opt [4] Dändliker R, Thalmann R and Prongué D 1988 Two-wavelength laser interferometry using superheterodyne detection Opt. Lett [5] Manhart S and Maurer R 199 Diode laser and fiber optics for dual-wavelength heterodyne interferometry Proc. SPIE [6] Sodnik Z, Fischer E, Ittner T and Tiziani H J 1991 Two-wavelength double heterodyne interferometry using a matched grating technique Appl. Opt [7] Gelmini E, Minoni U and Docchio F 1994 Tunable, double-wavelength heterodyne detection interferometer for absolute-distance measurement Opt. Lett [8] Salewski K-D, Bechstein K-H, Wolfram A and Fuchs W 1996 Absolute Distanzinterferometrie mit variabler synthetischer Wellenlänge Technisches Messen [9] Bechstein K-H and Fuchs W 1997 Absolute interferometric distance measurements applying a variable synthetic wavelength Optoelectronic Distance/Displacement Measurements and Applications (EOS Topical Meeting Digest Series 14) (Nantes: Ecole des Mines) [1] Dändliker R 1992 Distance measurements with multiple wavelength techniques 2nd Int. Workshop on High Precision Navigation ed K Linkwitz and U Hangleiter (Bonn: Dümmlers) pp [11] Schmit J and Creath K 1995 Opt. Lett [12] Salvadé Y, Zimmermann E and Dändliker R 1996 Limitations of multiple-wavelength interferometry due to frequency fluctuations of laser diodes Proc. IWI 96, Int. Workshop on Interferometry (Optical Society of Japan, Japan Society of Applied Physics) pp 9 1 [13] Spirig T, Seitz P, Vietze O and Heitger F 1995 The lock-in CCD two dimensional synchronous detection of light IEEE J. Quantum Electron. QE [14] Dändliker R, Geiser M, Giunti C, Zatti S and Margheri G 1995 Improvement of speckle statistics in double-wavelength superheterodyne interferometry Appl. Opt