Abstract

An alternative payload concept with in-field pointing for the laser interferometer space antenna utilizes an actuated mirror in the telescope for beam tracking to the distant satellite. This actuation generates optical pathlength variations due to the resulting beamwalk over the surface of subsequent optical components, which could possibly have a detrimental influence on the accuracy of the measurement instrument. We have experimentally characterized such pathlength errors caused by a λ/10 mirror surface and used the results to validate a theoretical model. This model is then applied to predict the impact of this effect for the current optical design of the LISA off-axis wide-field telescope.

© 2013 Optical Society of America

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References

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  1. European Space Agency, “LISA, unveiling a hidden universe,” Assessment Study Report (2011).
  2. European Space Agency, “NGO, revealing a hidden universe: opening a new chapter of discovery,” Assessment Study Report (2011).
  3. Astrium GmbH, “Assessment of a next generation gravity mission to monitor the variations of earth’s gravity field,” Executive Summary (2011).
  4. M. Dehne, F. Guzman Cervantes, B. Sheard, G. Heinzel, and K. Danzmann, “Laser interferometer for spaceborn mapping of the earth’s gravity field,” J. Phys. 154, 012023 (2009).
    [CrossRef]
  5. D. Weise, P. Marenaci, P. Weimer, H. R. Schulte, P. Gath, and U. Johann, “Alternative opto-mechanical architectures for the LISA instrument,” J. Phys. 154, 012029 (2009).
    [CrossRef]
  6. D. Weise, P. Marenaci, P. Weimer, M. Berger, H. R. Schulte, P. Gath, and U. Johann, “Opto-mechanical architecture of the LISA instrument,” Proceedings of the 7th ICSO (2008).
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    [CrossRef]
  10. T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gray. 26, 085008 (2009).
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  13. R. Spero, “Optical path error from beamwalk across irregular mirror surfaces,” (1998).
  14. D. Gerardi, PhD thesis currently under submission with the title, “Advanced drag-free concepts for future space-based interferometers,” (Institute of Flight Mechanics, 2009).

2012 (1)

R. Spannagel, T. Schuldt, and C. Braxmaier, “High resolution optical surface investigation based on heterodyne interferometry,” Int. J. Optomechatronics 6, 264–274 (2012).
[CrossRef]

2009 (3)

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gray. 26, 085008 (2009).
[CrossRef]

M. Dehne, F. Guzman Cervantes, B. Sheard, G. Heinzel, and K. Danzmann, “Laser interferometer for spaceborn mapping of the earth’s gravity field,” J. Phys. 154, 012023 (2009).
[CrossRef]

D. Weise, P. Marenaci, P. Weimer, H. R. Schulte, P. Gath, and U. Johann, “Alternative opto-mechanical architectures for the LISA instrument,” J. Phys. 154, 012029 (2009).
[CrossRef]

1994 (2)

1986 (1)

1981 (1)

Berger, M.

D. Weise, P. Marenaci, P. Weimer, M. Berger, H. R. Schulte, P. Gath, and U. Johann, “Opto-mechanical architecture of the LISA instrument,” Proceedings of the 7th ICSO (2008).

Braxmaier, C.

R. Spannagel, T. Schuldt, and C. Braxmaier, “High resolution optical surface investigation based on heterodyne interferometry,” Int. J. Optomechatronics 6, 264–274 (2012).
[CrossRef]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gray. 26, 085008 (2009).
[CrossRef]

Danzmann, K.

M. Dehne, F. Guzman Cervantes, B. Sheard, G. Heinzel, and K. Danzmann, “Laser interferometer for spaceborn mapping of the earth’s gravity field,” J. Phys. 154, 012023 (2009).
[CrossRef]

Dehne, M.

M. Dehne, F. Guzman Cervantes, B. Sheard, G. Heinzel, and K. Danzmann, “Laser interferometer for spaceborn mapping of the earth’s gravity field,” J. Phys. 154, 012023 (2009).
[CrossRef]

Ek, L.

Gath, P.

D. Weise, P. Marenaci, P. Weimer, H. R. Schulte, P. Gath, and U. Johann, “Alternative opto-mechanical architectures for the LISA instrument,” J. Phys. 154, 012029 (2009).
[CrossRef]

D. Weise, P. Marenaci, P. Weimer, M. Berger, H. R. Schulte, P. Gath, and U. Johann, “Opto-mechanical architecture of the LISA instrument,” Proceedings of the 7th ICSO (2008).

Gerardi, D.

D. Gerardi, PhD thesis currently under submission with the title, “Advanced drag-free concepts for future space-based interferometers,” (Institute of Flight Mechanics, 2009).

Gohlke, M.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gray. 26, 085008 (2009).
[CrossRef]

Guzman Cervantes, F.

M. Dehne, F. Guzman Cervantes, B. Sheard, G. Heinzel, and K. Danzmann, “Laser interferometer for spaceborn mapping of the earth’s gravity field,” J. Phys. 154, 012023 (2009).
[CrossRef]

Heinzel, G.

M. Dehne, F. Guzman Cervantes, B. Sheard, G. Heinzel, and K. Danzmann, “Laser interferometer for spaceborn mapping of the earth’s gravity field,” J. Phys. 154, 012023 (2009).
[CrossRef]

Johann, U.

D. Weise, P. Marenaci, P. Weimer, H. R. Schulte, P. Gath, and U. Johann, “Alternative opto-mechanical architectures for the LISA instrument,” J. Phys. 154, 012029 (2009).
[CrossRef]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gray. 26, 085008 (2009).
[CrossRef]

D. Weise, P. Marenaci, P. Weimer, M. Berger, H. R. Schulte, P. Gath, and U. Johann, “Opto-mechanical architecture of the LISA instrument,” Proceedings of the 7th ICSO (2008).

Marenaci, P.

D. Weise, P. Marenaci, P. Weimer, H. R. Schulte, P. Gath, and U. Johann, “Alternative opto-mechanical architectures for the LISA instrument,” J. Phys. 154, 012029 (2009).
[CrossRef]

D. Weise, P. Marenaci, P. Weimer, M. Berger, H. R. Schulte, P. Gath, and U. Johann, “Opto-mechanical architecture of the LISA instrument,” Proceedings of the 7th ICSO (2008).

Meers, B. J.

Morrison, E.

Pantzer, D.

Peters, A.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gray. 26, 085008 (2009).
[CrossRef]

Politch, J.

Robertson, D. I.

Robertson, D.I.

Schuldt, T.

R. Spannagel, T. Schuldt, and C. Braxmaier, “High resolution optical surface investigation based on heterodyne interferometry,” Int. J. Optomechatronics 6, 264–274 (2012).
[CrossRef]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gray. 26, 085008 (2009).
[CrossRef]

Schulte, H. R.

D. Weise, P. Marenaci, P. Weimer, H. R. Schulte, P. Gath, and U. Johann, “Alternative opto-mechanical architectures for the LISA instrument,” J. Phys. 154, 012029 (2009).
[CrossRef]

D. Weise, P. Marenaci, P. Weimer, M. Berger, H. R. Schulte, P. Gath, and U. Johann, “Opto-mechanical architecture of the LISA instrument,” Proceedings of the 7th ICSO (2008).

Sheard, B.

M. Dehne, F. Guzman Cervantes, B. Sheard, G. Heinzel, and K. Danzmann, “Laser interferometer for spaceborn mapping of the earth’s gravity field,” J. Phys. 154, 012023 (2009).
[CrossRef]

Sommaergren, G. E.

Spannagel, R.

R. Spannagel, T. Schuldt, and C. Braxmaier, “High resolution optical surface investigation based on heterodyne interferometry,” Int. J. Optomechatronics 6, 264–274 (2012).
[CrossRef]

Spero, R.

R. Spero, “Optical path error from beamwalk across irregular mirror surfaces,” (1998).

Ward, H.

Weimer, P.

D. Weise, P. Marenaci, P. Weimer, H. R. Schulte, P. Gath, and U. Johann, “Alternative opto-mechanical architectures for the LISA instrument,” J. Phys. 154, 012029 (2009).
[CrossRef]

D. Weise, P. Marenaci, P. Weimer, M. Berger, H. R. Schulte, P. Gath, and U. Johann, “Opto-mechanical architecture of the LISA instrument,” Proceedings of the 7th ICSO (2008).

Weise, D.

D. Weise, P. Marenaci, P. Weimer, H. R. Schulte, P. Gath, and U. Johann, “Alternative opto-mechanical architectures for the LISA instrument,” J. Phys. 154, 012029 (2009).
[CrossRef]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gray. 26, 085008 (2009).
[CrossRef]

D. Weise, P. Marenaci, P. Weimer, M. Berger, H. R. Schulte, P. Gath, and U. Johann, “Opto-mechanical architecture of the LISA instrument,” Proceedings of the 7th ICSO (2008).

Appl. Opt. (4)

Class. Quantum Gray. (1)

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gray. 26, 085008 (2009).
[CrossRef]

Int. J. Optomechatronics (1)

R. Spannagel, T. Schuldt, and C. Braxmaier, “High resolution optical surface investigation based on heterodyne interferometry,” Int. J. Optomechatronics 6, 264–274 (2012).
[CrossRef]

J. Phys. (2)

M. Dehne, F. Guzman Cervantes, B. Sheard, G. Heinzel, and K. Danzmann, “Laser interferometer for spaceborn mapping of the earth’s gravity field,” J. Phys. 154, 012023 (2009).
[CrossRef]

D. Weise, P. Marenaci, P. Weimer, H. R. Schulte, P. Gath, and U. Johann, “Alternative opto-mechanical architectures for the LISA instrument,” J. Phys. 154, 012029 (2009).
[CrossRef]

Other (6)

D. Weise, P. Marenaci, P. Weimer, M. Berger, H. R. Schulte, P. Gath, and U. Johann, “Opto-mechanical architecture of the LISA instrument,” Proceedings of the 7th ICSO (2008).

European Space Agency, “LISA, unveiling a hidden universe,” Assessment Study Report (2011).

European Space Agency, “NGO, revealing a hidden universe: opening a new chapter of discovery,” Assessment Study Report (2011).

Astrium GmbH, “Assessment of a next generation gravity mission to monitor the variations of earth’s gravity field,” Executive Summary (2011).

R. Spero, “Optical path error from beamwalk across irregular mirror surfaces,” (1998).

D. Gerardi, PhD thesis currently under submission with the title, “Advanced drag-free concepts for future space-based interferometers,” (Institute of Flight Mechanics, 2009).

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Figures (17)

Fig. 1.
Fig. 1.

Schematic of the LISA off-axis wide-field telescope for IFP ( M = mirrors , F = folding mirrors , EP = external pupil ). The actuated mirror implements the beam tracking, which will result in considerable beamwalk over the mirror surfaces of the mirrors F1, M3, and F2. Three different positions of the actuated mirror are indicated using different colors of the optical paths, blue (0°), red ( + 2 ° ), and green ( 2 ° ). The EP in the present design is virtual so that the transmit beam will actually be reflected from mirror M1 to leave the telescope toward the left.

Fig. 2.
Fig. 2.

Photograph of the heterodyne interferometer (top) and schematic of its highly symmetric optical paths (bottom). SMF = single-mode fiber , COL = collimator , POL = polarization filter , ESC = energy separator cube , PBS = polarizing beamsplitter , WIN = window , BS = beamsplitter .

Fig. 3.
Fig. 3.

Performance of the measurement setup: LSD for translation (top) and LSD for tilt (bottom).

Fig. 4.
Fig. 4.

Photograph of the pendulum with mounted mirror support for two test mirrors and the linear piezo actuator PI Nexline N-111, mounted on the left side.

Fig. 5.
Fig. 5.

Low stress mounting concept of the test mirrors in the pendulum’s mirror support: (1) fixation screws, (2) teflon rings for reduction of torsional stress, (3) Viton O-rings for homogeneous pressure distribution, (4)  λ / 10 test mirrors, and (5) fused silica limiting plate for parallel adjustment of the test mirrors.

Fig. 6.
Fig. 6.

Measurement configurations: (A) initial setup, (B) setup with tilted window for testing any influence of parasitic pendulum movements, and (C) setup with lens for improving the lateral resolution.

Fig. 7.
Fig. 7.

Correction process for translational errors due to parasitic tilts of the pendulum during measurement.

Fig. 8.
Fig. 8.

Measurement results with unfocused laser beams. Top: initial measurement. Middle: measurement with tilted window for excluding an influence of parasitic pendulum movements in the measurement results. Bottom: measurement with removed tilted window → initial measurement. The standard deviation σ for the different runs of each measurement is indicated in the respective legend.

Fig. 9.
Fig. 9.

Measurement results with focused measurement beam, resulting in higher translation amplitudes and an improved lateral resolution. The standard deviation σ for the different runs of each measurement is indicated in the respective legend.

Fig. 10.
Fig. 10.

Results of the PTB interference microscopy measurements. Raw data (top) and data filtered with simulated laser beam of diameter 1300 μm (middle) and 13 μm (bottom).

Fig. 11.
Fig. 11.

PSDs of the piston obtained from the interferometry measurement with lens, the unfiltered and filtered interference microscopy measurement, and the theoretical model filtered with 13  μm beam diameter.

Fig. 12.
Fig. 12.

PSDs of the piston due to beamwalk with 10 mm (mirror F1) and 40 mm (mirror F2, M3) laser beam diameter.

Fig. 13.
Fig. 13.

Pointing angle (top) and derived pointing velocity (bottom) for one of the three LISA satellites, caused by their individual orbital dynamics.

Fig. 14.
Fig. 14.

LSD of the piston in the LISA telescope due to a regular pointing of ± 0.4 ° beam steering, considering a worst case scenario by using a constant pointing velocity of 3.65 × 10 6 mrad / s .

Fig. 15.
Fig. 15.

LSD of the jitter beamwalk on the three telescope mirrors F2, M3, and F1, caused by pointing-jitter within the requirement.

Fig. 16.
Fig. 16.

PSD of the surface topography gradient on the three telescope mirrors F2, M3, and F1.

Fig. 17.
Fig. 17.

LSDs of the piston in the LISA telescope caused by pointing-jitter of the IFP and the linear summation of them.

Tables (2)

Tables Icon

Table 1. Input Data for Calculating Piston Due to Regular Pointing

Tables Icon

Table 2. Input Data for Calculating Piston due to Pointing Jitter

Equations (12)

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Δ s corr ( x ) = Δ s ( x ) ± tan ( α meas + α ref 2 ) × l .
p ( x 0 , y 0 ) = j = 1 n i = 1 n s ( x i , y j ) × g ( x i , y j , x 0 , y 0 ) ,
g ( x , y , x 0 , y 0 ) = 2 π r 2 exp [ 2 [ ( x x 0 ) 2 + ( y y 0 ) ] 2 r 2 ] ,
p ˜ ( f ) s ˜ ( f ) × g ˜ ( f ) = k f 2 × g ˜ ( f ) ,
g ˜ ( f ) = exp [ ( π 2 d f ) 2 ] .
q ˜ pist ( ν ) = 3 pm Hz × 1 + ( 2.8 mHz ν ) 4 .
ν = f × v ,
p ˜ orbit ( ν ) p ˜ orbit ( f ) v ,
p ˜ jitt ( ν ) 3 c × j ˜ ( ν ) .
q ˜ jitt ( ν ) = 10 nrad Hz × 1 + ( 2.8 mHz ν ) 4 .
c = rms ( g ˜ ( f ) ) = 0 g ˜ ( f ) d f ,
g ˜ ( f ) = p ˜ ( f ) × ( 2 π f ) 2 .

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