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  • Editor: Xi-Cheng Zhang
  • Vol. 39, Iss. 15 — Aug. 1, 2014
  • pp: 4603–4606
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Validation of separated source frequency delivery for a fiber-coupled heterodyne displacement interferometer

Arjan J. H. Meskers, Jo W. Spronck, and Robert H. Munnig Schmidt  »View Author Affiliations


Optics Letters, Vol. 39, Issue 15, pp. 4603-4606 (2014)
http://dx.doi.org/10.1364/OL.39.004603


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Abstract

The use of optical fibers presents several advantages with respect to free-space optical transport regarding source-frequency delivery to individual heterodyne interferometers. Unfortunately, fiber delivery to individual coaxial heterodyne interferometers leads to an increase of (periodic) nonlinearity in the measurement, because transporting coaxial frequencies through one optical fiber leads to frequency mixing. Coaxial beams thus require delivery via free-space transportation methods. In contrast, the heterodyne interferometer concept discussed in this Letter is based on separated source frequencies, which allow for fiber delivery without additional nonlinearity. This investigation analyzes the influence of external disturbances acting on the two fibers during delivery, causing asymmetry in phase between the two fibers (first-order effect), and irradiance fluctuations (second-order effect). Experiments using electro-optic phase modulation and acousto-optic irradiance modulation confirmed that the interferometer-concept can measure with sub-nanometer uncertainty using fiber delivered source frequencies, enabling fully fiber-coupled heterodyne displacement interferometers.

© 2014 Optical Society of America

Optical interferometry is a widely applied method for measuring displacement in the fields of metrology and precision engineering. It is used for tracking precision stages [1

1. F. C. Demarest, Meas. Sci. Technol. 9, 1024C (1998). [CrossRef]

] in lithography systems in the semiconductor industry, space-based gravitational wave detection [2

2. T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009). [CrossRef]

], and in atomic force microscopy [3

3. J. Schneir, T. McWaid, J. Alexander, and B. Wilfley, J. Vac. Sci. Technol. B 12, 3561 (1994). [CrossRef]

]. Additionally, it is used as a means for calibrating other measurement tools [4

4. P. de Groot, J. Biegen, J. Clark, X. Colonna de Lega, and D. Grigg, Appl. Opt. 41, 3853 (2002). [CrossRef]

].

There are many error sources that affect the measurement uncertainty of a heterodyne displacement interferometer, especially when aiming for sub-nanometer uncertainty over a large measurement range (i.e., optical measurement pathways of several meters). The impact of several of these error sources, e.g., thermal influence and refractive index fluctuations, can be reduced by external placement of the heat sources (laser source and electronic readout) or operating in vacuum. However, some error sources remain, one of which is periodic nonlinearity (PNL). This error source is attributed by ghost reflections, by imperfections in polarization alignment, and by the polarization quality of both the source frequencies and polarizing optics [5

5. G. Fedotova, Meas. Sci. Technol. 23, 577 (1980). [CrossRef]

9

9. C. Wu and R. D. Deslattes, Appl. Opt. 37, 6696 (1998). [CrossRef]

].

In an effort to meet the industrial need for system layout flexibility and robustness, optical fibers are being employed, replacing free-space optical pathways [see Figs. 1(a) and 1(b)]. The replacement of free-space optical pathways is driven by their inflexible layout and their (high) sensitivity to environmental disturbances. Still, it is difficult for coaxial based interferometer systems to deliver the source frequencies directly to individual interferometers within a host system. Research [10

10. B. A. W. H. Knarren, S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 29, 229 (2005). [CrossRef]

] indicates that fiber delivery of a coaxial beam with one polarization maintaining single-mode fiber is possible, but increases PNL due to frequency mixing within the optical fiber. This necessitates separated source frequency transport using two optical fibers, and coaxially recombining them into a free-space beam inside the host system [see Fig. 1(b)]. The flexibility of optical fibers allows the externally placed equipment to be easily relocated, as seen in current commercial systems from Agilent Technologies.

Fig. 1. (a) In a free-space system, a coaxial beam (purple) is delivered to interferometers (i) inside a host system to measure stage displacement, using mirrors (m), and a beam splitter (s). (b) A more practical commercial system layout as is found in current lithography machines uses optical-fiber delivery, in which the two source frequencies are coaxially combined by a remote optical combiner (roc), resulting in a free-space beam. (c) The most practical system consists of fully fiber-coupled interferometers, easing system integration. An asterisk denotes the generation of a reference signal. Note that transport of interference signals from interferometers is less stringent and has already proven itself using optical fibers and external readout (not shown).

The two source frequencies are ideally combined into a coaxial beam at the interferometer creating a fully fiber-coupled instrument; unfortunately, this is costly and highly impractical with regard to space consumption and complexity. The solution is to combine the source frequencies into a coaxial beam only once (at the remote optical combiner) and branch off parts of the free-space beam to individual interferometers [see Fig. 1(b)].

Frequency leakage (and thereby PNL) can be prevented by spatially separating the source frequencies throughout the interferometer system until detection [11

11. M. Tanaka, T. Yamagami, and K. Nakayama, IEEE Trans. Instrum. Meas. 38, 552 (1989). [CrossRef]

18

18. J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000). [CrossRef]

]. The main advantage of separated source frequency delivery is that it can take place either free-space as well as via optical fibers, offering a reconfigurable means of optical transport at minimum space consumption and enabling complete fiber-coupled heterodyne displacement interferometers [see Fig. 1(c)].

In this Letter, the Delft interferometer’s ability to operate fiber-coupled will be further investigated, as part of achieving an overall characterization of the interferometer concept. The final aim is to develop a modular heterodyne displacement interferometer that measures with sub-nanometer uncertainty while using optical fibers for the optical transport of both the source frequencies and interference signals.

The experimental setup illustrated in Fig. 2 uses a two-mode helium–neon gas laser (Thorlabs HRS015), and two acousto-optic modulators (aom), (aom1,2 ISOMET OAM-1141-T40-2 and drivers 531C-L, operating at 39 and 41 MHz) generate a 2 MHz split frequency. The applied electro-optic modulator (eom) (eom Thorlabs EO-phase modulator EO-PM-NR-C1) modulates the phase of one of the two source frequencies (simulating air pressure fluctuations, temperature fluctuations, air turbulence, and fiber vibrations) resulting in a time varying phase difference between f1 and f2. Furthermore, standard optical components have been applied from Thorlabs, and a fiber coupled phase-measurement board from Agilent Technologies (N1225A). The setup uses free-space beam delivery in a normal air environment but could be equipped with optical fibers as well. The experiment contains two interferometers, one “classical” interferometer (using PD1,2), and one Delft interferometer (using PD3,4). The classical interferometer interprets the eom’s phase modulation as a displacement, while the Delft interferometer excludes this disturbance, which is analyzed.

Fig. 2. (a) Schematic of the experimental setup where an eom introduces a relative phase difference φeom, between f1 and f2. The half wave plate (hwp) in front of the eom is used for adjusting the polarization alignment between f2 and the eom crystal. (b), (c) Optical pathways of respectively f1 and f2 through the interferometer (dotted lines denote beams in the lower plane whereas solid lines are beams in the upper plane, see also [15,16]). Note that the tested interferometer was not a monolithic structure as suggested. Legend: aomx, acousto-optic modulator; fx, frequency; bs, beam sampler; rb, rhomboid; PDx, photodetector; m, mirror; nbs neutral beam splitter, pbs, polarizing beam splitter; ccx, cube corner reflector; qwp, quarter wave plate; and m′, target mirror.

Two linearly (vertically) polarized beams are delivered to the two interferometers,
J1=E1·[01]ei(ω1t+θ),
(1)
J2=E2·[01]ei(ω2t+φ),
(2)
where ω1,2=2πf1,2 (with f1<f2) and θ and φ represent (unknown and uncontrollable) time varying phase changes in f1 and f2, respectively, caused by the measurement environment. Using rhomboids (rb) for beam overlap in the classical interferometer prevents frequency leakage of f1 into f2. Having both beams vertically polarized removes the need for an analyzer at the PDs. At PD1 the obtained interference signal is
IPD1J1·J2,
(3)
IPD1E1E2ei({ω2ω1}t+φθ).
(4)

Equation (4) shows the reference frequency for the classical interferometer consisting of the frequency difference between f1 and f2 (i.e., ω2ω1).

The eom modulates the phase of f2 according to
φeom=Acos(ωeomt),
(5)
where ωeom=2πfeom describes the linear electric field that is applied to the eom’s electro-optic crystal, which gives rise to an electric field dependent birefringence.

Analysis for the other PDs according to Fig. 2 leads to
IPD2E1E2ei({ω2ω1}t+φ+φeomθ),
(6)
IPD3E1E2ei({ω2ω1}t+φ+φeom+φcc1θθcc3θm),
(7)
IPD4E1E2ei({ω2ω1}t+φ+φeom+φcc3+φmθθcc2).
(8)
Since the interferometer, illustrated in Fig. 2, was not monolithic, vibrations of individual components have been taken into account explaining the many additional phase terms. The signs of θm and φm are opposite in Eqs. (7) and (8), which is caused by an opposite shift of the beat frequency at the two detectors. To clarify, when target m displaces toward the interferometer, PD3 encounters a decrease of the beat frequency, fbeat PD3=f2(f1+θm), whereas PD4 encounters an increase of the beat frequency, fbeat PD4=(f2+φm)f1.

The classical interferometer will interpret φeom as an apparent displacement, obtained through a differential operation between PD1 and PD2:
IclassicalE1E2ei[({ω2ω1}t+φ+φeomθ)({ω2ω1}t+φθ)],
(9)
IclassicalE1E2ei(φeom).
(10)

Equation (10) shows that the common noise terms θ and φ, and the frequencies ω1,2 cancel, resulting in the measurement of φeom. The same differential operation is performed for the Delft interferometer:
IDelftE1E2ei[({ω2ω1}t+φ+φeom+φcc3+φmθθcc2)({ω2ω1}t+φ+φeom+φcc1θθcc3θm)],
(11)
IDelftE1E2ei(φcc3φcc1θcc2+θcc3+(φm+θm)).
(12)

The absence of φeom in Eq. (12) shows that any phase difference between the two separately delivered source frequencies is mitigated. This is due to the interferometer’s layout that delivers any fiber induced disturbance to both detectors; a differential operation between the detectors then cancels all common terms.

Note that the phase due to displacement φm+θm is present twice, indicating that this interferometer actually consists of two interferometers that both have an optical resolution of λ/4, due to the differential readout. This results in a final displacement resolution of λ/8.

The results in Eqs. (10) and (12) were verified using the setup shown in Fig. 2. Data from both interferometers was obtained simultaneously and was subsequently fast Fourier transformed (FFT). The combination of the eom operating at a fixed frequency and applying an FFT resulted in a noise level of less than a picometer for the Delft interferometer [see Figs. 3(b)3(d)]. The eom applied a phase modulation at 5 kHz with a modulation depth of 95°, leading to an apparent displacement of 170nm for the classical interferometer. This is indicated by the red peak in Fig. 3(a).

Fig. 3. (a) The eom has a phase modulation depth of 95° nm (170 nm) at feom=5kHz, which is present in the output of the classical interferometer, 170nm (red), while it is absent in the output of the Delft interferometer (blue). (b) Close-up of the result of (a), showing a residual error of 0.03nm. (c) The residual is affected by polarization misalignment between f2 and the eom crystal, which causes both an additional interference signal and a modulation of the irradiance. (d) Influence of irradiance modulation was analyzed by amplitude modulation of aom2 at 50% of the maximum irradiance (15μW interference signal strength at detectors PD3,4), with the eom switched off and the hwp at the position as was used for generating the results illustrated in (a).

The influence of the eom is present in the classical interferometer’s output (red), whereas it is not in the output of the Delft interferometer (blue) [see Fig. 3(a)]. These results are in agreement with Eqs. (10) and (12) and confirm that the disturbance from the eom is cancelled by the differential action between PD3,4.

However, a close up of Fig. 3(a), shown in Fig. 3(b), reveals a peak of 0.03nm and indicates a phase disturbance suppression ratio of 5700 (170nm/0.03nm), which suggests that the eom’s phase disturbance is not completely mitigated. For further robustness improvement it is essential to understand where the residual originates from.

The error is the result of a differential operation between PD3,4 and can therefore only consist from signal differences between the two detectors. These differences could consist from a number of effects: the presence of additional interference signals, an unbalanced irradiance distribution between the detectors, or optical pathway asymmetry between the reference and measurement pathways (affecting the differential operation by a non-simultaneous arrival of a disturbance).

It is most likely that the residual consists of ghost reflections, which are a well-known source of additional interference signals. The target’s first reflection can partially be transmitted by the polarizing beam splitter via polarization leakage, and could eventually be reinjected from the feeding direction (see Fig. 2). The amount of irradiance required for explaining the residual is already present even when using good antireflection coatings [19

19. C. Wu, Opt. Commun. 215, 17 (2003). [CrossRef]

].

Another source of additional interference signals is formed by the eom. The eom consists of a birefringent crystal that is modulated over one axis, which makes it sensitive to polarization misalignment. When the linear polarization orientation of f2 mismatches with the crystal’s birefringent index, the beam is only partially phase modulated. This results in a primary interference signal at 5 kHz between f1 and f2 [clearly visible with the classical interferometer in Fig. 3(a)] together with a secondary interference signal from f2 itself, also at 5 kHz.

This hypothesis was verified by inducing polarization misalignment by rotation of a half-wave plate in front of the eom [Fig. 2(a)]. Increasing the polarization misalignment of f2 resulted in a nonlinear increase of the error [see Fig. 3(c)]. Placing a Glan–Taylor polarizer behind the eom only resulted in a limited reduction of the effect, indicating that this error adds little to the residual.

Timing issues due to optical pathway asymmetry between the reference and the measurement pathway are present, but can be considered negligible in comparison to the influence from ghost reflections.

Additionally, polarization misalignment between f2 and the eom crystal not only leads to an additional interference signal, it also results in an irradiance modulation at 5 kHz, due to the use of polarizing optics. When the eom was modulating phase using equal settings as used for generating the results illustrated in Figs. 3(a) and 3(b), an irradiance modulation of less than 0.5% was measured.

The influence of irradiance modulation of f2 was further analyzed by modulating the amplitude of the driving signal of aom2, with the eom switched off [see Fig. 2(a)]. The irradiance was modulated up to ±2.5μW around 7.5μW (AC-signal at detector), with a peak-to-peak modulation amplitude of 10%, 20%, and 30%. The results are illustrated in Fig. 3(d) and show a linear increase of the error as the modulation amplitude was enlarged.

The graphs illustrated in Figs. 3(c) and 3(d) show that the influence of the irradiance modulation on the residual error of 0.03 nm, Fig. 3(b), is much smaller than the influence of polarization misalignment between f2 and the eom’s birefringent crystal.

It can be concluded that the residual of 0.03 nm consists of multiple effects. However, some of them will not be encountered during normal operation and some can be reduced. This holds for partial phase modulation by the eom when using single mode optical fibers and for ghost reflections and optical symmetry when employing monolithic optical structures, respectively.

The research in this Letter has demonstrated that the discussed interferometer can achieve subnanometer measurement uncertainty while using separated source frequency delivery. The interferometer can significantly mitigate time variant phase disturbances and irradiance fluctuations that result from external disturbances acting on source frequency transport.

These findings are an important step toward a PNL free heterodyne displacement interferometer that can measure with subnanometer uncertainty while being fully fiber coupled. For this instrument, the use of optical fibers leads to system modularity, which eases the integration into complex host systems. An additional advantage worth mentioning is that the pluggable nature of optical fibers potentially results in fast component replacement, which helps minimizing downtime of a host system upon component failure.

This work was supported by the Dutch IOP (IPT04001) in the Netherlands. The authors are thankful for the support by Agilent Technologies for providing equipment used during this research.

References

1.

F. C. Demarest, Meas. Sci. Technol. 9, 1024C (1998). [CrossRef]

2.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009). [CrossRef]

3.

J. Schneir, T. McWaid, J. Alexander, and B. Wilfley, J. Vac. Sci. Technol. B 12, 3561 (1994). [CrossRef]

4.

P. de Groot, J. Biegen, J. Clark, X. Colonna de Lega, and D. Grigg, Appl. Opt. 41, 3853 (2002). [CrossRef]

5.

G. Fedotova, Meas. Sci. Technol. 23, 577 (1980). [CrossRef]

6.

R. Quenelle, Hewlett-Packard J. 34, 10 (1983).

7.

C. Sutton, J. Phys. E 20, 1290 (1987). [CrossRef]

8.

W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992). [CrossRef]

9.

C. Wu and R. D. Deslattes, Appl. Opt. 37, 6696 (1998). [CrossRef]

10.

B. A. W. H. Knarren, S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 29, 229 (2005). [CrossRef]

11.

M. Tanaka, T. Yamagami, and K. Nakayama, IEEE Trans. Instrum. Meas. 38, 552 (1989). [CrossRef]

12.

C.-M. Wu, J. Lawall, and R. D. Deslattes, Appl. Opt. 38, 4089 (1999). [CrossRef]

13.

T. Schmitz and J. Beckwith, J. Mod. Opt. 49, 2105 (2002). [CrossRef]

14.

K.-N. Joo, J. D. Ellis, J. W. Spronck, P. J. M. van Kan, and R. H. M. Schmidt, Opt. Lett. 34, 386 (2009). [CrossRef]

15.

J. D. Ellis, A. J. H. Meskers, J. W. Spronck, and R. H. M. Schmidt, Opt. Lett. 36, 3584 (2011). [CrossRef]

16.

A. J. H. Meskers, J. W. Spronck, and R. H. Munnig Schmidt, Opt. Lett. 39, 1949 (2014). [CrossRef]

17.

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012). [CrossRef]

18.

J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000). [CrossRef]

19.

C. Wu, Opt. Commun. 215, 17 (2003). [CrossRef]

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments
(120.4820) Instrumentation, measurement, and metrology : Optical systems
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: April 29, 2014
Revised Manuscript: June 27, 2014
Manuscript Accepted: June 30, 2014
Published: July 31, 2014

Citation
Arjan J. H. Meskers, Jo W. Spronck, and Robert H. Munnig Schmidt, "Validation of separated source frequency delivery for a fiber-coupled heterodyne displacement interferometer," Opt. Lett. 39, 4603-4606 (2014)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-39-15-4603


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References

  1. F. C. Demarest, Meas. Sci. Technol. 9, 1024C (1998). [CrossRef]
  2. T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009). [CrossRef]
  3. J. Schneir, T. McWaid, J. Alexander, and B. Wilfley, J. Vac. Sci. Technol. B 12, 3561 (1994). [CrossRef]
  4. P. de Groot, J. Biegen, J. Clark, X. Colonna de Lega, and D. Grigg, Appl. Opt. 41, 3853 (2002). [CrossRef]
  5. G. Fedotova, Meas. Sci. Technol. 23, 577 (1980). [CrossRef]
  6. R. Quenelle, Hewlett-Packard J. 34, 10 (1983).
  7. C. Sutton, J. Phys. E 20, 1290 (1987). [CrossRef]
  8. W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992). [CrossRef]
  9. C. Wu and R. D. Deslattes, Appl. Opt. 37, 6696 (1998). [CrossRef]
  10. B. A. W. H. Knarren, S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 29, 229 (2005). [CrossRef]
  11. M. Tanaka, T. Yamagami, and K. Nakayama, IEEE Trans. Instrum. Meas. 38, 552 (1989). [CrossRef]
  12. C.-M. Wu, J. Lawall, and R. D. Deslattes, Appl. Opt. 38, 4089 (1999). [CrossRef]
  13. T. Schmitz and J. Beckwith, J. Mod. Opt. 49, 2105 (2002). [CrossRef]
  14. K.-N. Joo, J. D. Ellis, J. W. Spronck, P. J. M. van Kan, and R. H. M. Schmidt, Opt. Lett. 34, 386 (2009). [CrossRef]
  15. J. D. Ellis, A. J. H. Meskers, J. W. Spronck, and R. H. M. Schmidt, Opt. Lett. 36, 3584 (2011). [CrossRef]
  16. A. J. H. Meskers, J. W. Spronck, and R. H. Munnig Schmidt, Opt. Lett. 39, 1949 (2014). [CrossRef]
  17. C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012). [CrossRef]
  18. J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000). [CrossRef]
  19. C. Wu, Opt. Commun. 215, 17 (2003). [CrossRef]

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