Abstract

A photoreceiver (PR) is required for the opto-electrical conversion of signals in intersatellite laser interferometers. Noise sources that originate or couple in the PR reduce the system carrier-to-noise-density, which is often represented by its phase noise density. In this work, we analyze the common noise sources in a PR used for space-based interferometry. Additionally, we present the results from the characterization of the PRs in GRACE-FO, a mission which will pioneer intersatellite laser interferometry. The estimated phase noise is shot-noise limited at 10−4 rad/Hz1/2 down to 10−2 Hz, almost 4 orders of magnitude below the instrument top level requirement (0.5 rad/Hz1/2). Below 10−2 Hz, the PR finite phase response noise dominates but the levels still comply with the instrument requirement. The sub-mHz noise levels and the PR electronic noise have been identified as key design factors for the LISA PR.

© 2017 Optical Society of America

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References

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  1. A. Chaddad, “Low-noise front-end receiver dedicated to biomedical devices: NIRS acquisition system,” Circuits Systems 5, 191–200 (2014).
    [Crossref]
  2. F. Guzmán Cervantes, J. Livas, R. Silverberg, E. Buchanan, and R. Stebbins, “Characterization of photoreceivers for LISA,” Classical Quantum Gravity 28, 094010 (2011).
    [Crossref]
  3. O. Gerberding, “Phase readout for satellite interferometry,” Ph.D. thesis, Leibniz Universität Hannover (2014).
  4. O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
    [Crossref] [PubMed]
  5. B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy. 86, 1083–1095 (2012).
    [Crossref]
  6. K. Case, G. Kruizinga, and S. Wu, GRACE Level 1B Data Product User Handbook (JPL, 2010).
  7. A. Sutton, K. McKenzie, B. Ware, and D. A. Shaddock, “Laser ranging and communications for LISA,” Opt. Express 18, 20759–20773 (2010).
    [Crossref] [PubMed]
  8. G. Fernández Barranco, M. Tröbs, V. Müller, O. Gerberding, F. Seifert, and G. Heinzel, “Spatially resolved photodiode response for simulating precise interferometers,” Appl. Opt. 55, 6688–6693 (2016).
    [Crossref] [PubMed]

2016 (1)

2015 (1)

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

2014 (1)

A. Chaddad, “Low-noise front-end receiver dedicated to biomedical devices: NIRS acquisition system,” Circuits Systems 5, 191–200 (2014).
[Crossref]

2012 (1)

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy. 86, 1083–1095 (2012).
[Crossref]

2011 (1)

F. Guzmán Cervantes, J. Livas, R. Silverberg, E. Buchanan, and R. Stebbins, “Characterization of photoreceivers for LISA,” Classical Quantum Gravity 28, 094010 (2011).
[Crossref]

2010 (1)

Barke, S.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Brause, N.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Buchanan, E.

F. Guzmán Cervantes, J. Livas, R. Silverberg, E. Buchanan, and R. Stebbins, “Characterization of photoreceivers for LISA,” Classical Quantum Gravity 28, 094010 (2011).
[Crossref]

Bykov, I.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Case, K.

K. Case, G. Kruizinga, and S. Wu, GRACE Level 1B Data Product User Handbook (JPL, 2010).

Chaddad, A.

A. Chaddad, “Low-noise front-end receiver dedicated to biomedical devices: NIRS acquisition system,” Circuits Systems 5, 191–200 (2014).
[Crossref]

Danzmann, K.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy. 86, 1083–1095 (2012).
[Crossref]

Delgado, J. E.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Diekmann, C.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Enggaard, A.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Fernández Barranco, G.

Folkner, W. M.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy. 86, 1083–1095 (2012).
[Crossref]

Gerberding, O.

G. Fernández Barranco, M. Tröbs, V. Müller, O. Gerberding, F. Seifert, and G. Heinzel, “Spatially resolved photodiode response for simulating precise interferometers,” Appl. Opt. 55, 6688–6693 (2016).
[Crossref] [PubMed]

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

O. Gerberding, “Phase readout for satellite interferometry,” Ph.D. thesis, Leibniz Universität Hannover (2014).

Guzmán Cervantes, F.

F. Guzmán Cervantes, J. Livas, R. Silverberg, E. Buchanan, and R. Stebbins, “Characterization of photoreceivers for LISA,” Classical Quantum Gravity 28, 094010 (2011).
[Crossref]

Hansen, T.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Heinzel, G.

G. Fernández Barranco, M. Tröbs, V. Müller, O. Gerberding, F. Seifert, and G. Heinzel, “Spatially resolved photodiode response for simulating precise interferometers,” Appl. Opt. 55, 6688–6693 (2016).
[Crossref] [PubMed]

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy. 86, 1083–1095 (2012).
[Crossref]

Jennrich, O.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Klipstein, W. M.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy. 86, 1083–1095 (2012).
[Crossref]

Kruizinga, G.

K. Case, G. Kruizinga, and S. Wu, GRACE Level 1B Data Product User Handbook (JPL, 2010).

Kullmann, J.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Livas, J.

F. Guzmán Cervantes, J. Livas, R. Silverberg, E. Buchanan, and R. Stebbins, “Characterization of photoreceivers for LISA,” Classical Quantum Gravity 28, 094010 (2011).
[Crossref]

McKenzie, K.

Müller, V.

Pedersen, S.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Rasmussen, T.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Reiche, J.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Schwarze, T. S.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Seifert, F.

Shaddock, D. A.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy. 86, 1083–1095 (2012).
[Crossref]

A. Sutton, K. McKenzie, B. Ware, and D. A. Shaddock, “Laser ranging and communications for LISA,” Opt. Express 18, 20759–20773 (2010).
[Crossref] [PubMed]

Sheard, B. S.

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy. 86, 1083–1095 (2012).
[Crossref]

Silverberg, R.

F. Guzmán Cervantes, J. Livas, R. Silverberg, E. Buchanan, and R. Stebbins, “Characterization of photoreceivers for LISA,” Classical Quantum Gravity 28, 094010 (2011).
[Crossref]

Sodnik, Z.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Stebbins, R.

F. Guzmán Cervantes, J. Livas, R. Silverberg, E. Buchanan, and R. Stebbins, “Characterization of photoreceivers for LISA,” Classical Quantum Gravity 28, 094010 (2011).
[Crossref]

Suess, M.

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Sutton, A.

Tröbs, M.

G. Fernández Barranco, M. Tröbs, V. Müller, O. Gerberding, F. Seifert, and G. Heinzel, “Spatially resolved photodiode response for simulating precise interferometers,” Appl. Opt. 55, 6688–6693 (2016).
[Crossref] [PubMed]

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Ware, B.

Wu, S.

K. Case, G. Kruizinga, and S. Wu, GRACE Level 1B Data Product User Handbook (JPL, 2010).

Appl. Opt. (1)

Circuits Systems (1)

A. Chaddad, “Low-noise front-end receiver dedicated to biomedical devices: NIRS acquisition system,” Circuits Systems 5, 191–200 (2014).
[Crossref]

Classical Quantum Gravity (1)

F. Guzmán Cervantes, J. Livas, R. Silverberg, E. Buchanan, and R. Stebbins, “Characterization of photoreceivers for LISA,” Classical Quantum Gravity 28, 094010 (2011).
[Crossref]

J. Geodesy. (1)

B. S. Sheard, G. Heinzel, K. Danzmann, D. A. Shaddock, W. M. Klipstein, and W. M. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geodesy. 86, 1083–1095 (2012).
[Crossref]

Opt. Express (1)

Rev. Sci. Instrum. (1)

O. Gerberding, C. Diekmann, J. Kullmann, M. Tröbs, I. Bykov, S. Barke, N. Brause, J. E. Delgado, T. S. Schwarze, J. Reiche, K. Danzmann, T. Rasmussen, T. Hansen, A. Enggaard, S. Pedersen, O. Jennrich, M. Suess, Z. Sodnik, and G. Heinzel, “Readout for intersatellite laser interferometry: Measuring low frequency phase fluctuations of high-frequency signals with microradian precision,” Rev. Sci. Instrum. 86, 074501 (2015).
[Crossref] [PubMed]

Other (2)

K. Case, G. Kruizinga, and S. Wu, GRACE Level 1B Data Product User Handbook (JPL, 2010).

O. Gerberding, “Phase readout for satellite interferometry,” Ph.D. thesis, Leibniz Universität Hannover (2014).

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Figures (10)

Fig. 1
Fig. 1

Block diagram of the PR stages within the interferometer metrology chain. The optical beat note, represented as a red sinusoid, arrives at the PR (dashed line). A photodetector, commonly a photodiode (PD), absorbs the photons of the incoming light and produces a current. This current is converted into voltage by the transimpedance amplifier (TIA). The signal at the output of the TIA passes through an anti-aliasing filter (AAF) to filter out undesired signals and noise above the Nyquist frequency. Once the signal is filtered, it is transmitted from the output of the PR to the phasemeter (PM), where the signal is digitized and its phase measured.

Fig. 2
Fig. 2

Phase noise budget for one PR channel obtained using the PR requirements and expected interferometer parameters for GRACE-FO. The values used are summarized in Table 1. The red curve represents the total noise in the PR ϕ̃N from the noise sources described along Section 2. The PR is shot-noise limited at 10−4 rad/Hz1/2 down to 10−2 Hz, where the finite phase response noise begins to dominate. The blue curve shows the top level noise requirement for the LRI ϕ̃LRI, which needs to be fulfilled between 2·10−3 Hz and 10−1 Hz (solid line) but was extended in this plot (dashed line) for comparison with the PR phase noise. In the shot-noise limited section, ϕ̃N is almost 4 orders of magnitude below ϕ̃LRI. This margin decreases towards low frequencies due to the influence of the finite phase response noise contribution. This noise level in the sub-mHz range complies with the extended top level requirement, but indicates that post-processing correction might be chosen for further reduction of this noise contribution.

Fig. 3
Fig. 3

Electrical diagram of the TIA from the GRACE-FO PR. The current from the reverse-biased photodiode (Vbias = 5 V) splits into an AC (main signal) and a DC path. Two OpAmp-based TIAs, featuring the LMH6624 (AC) and the OP284 (DC), convert the current into voltage (VAC, VDC).

Fig. 4
Fig. 4

Block diagram of the hot redundancy configuration: two photoreceiver front-ends (PRFs) with independent PDs and TIAs sharing a common photoreceiver back-end (PRB), which includes a summing amplifier and the AAF. The output voltages of the two PRFs are combined in the summing amplifier of the PRB prior to the AAF. The topology is essentially the same for the DC and the AC paths, differing in the OpAmp used for the summing amplifier (LT1498 for DC and AD8001 for AC).

Fig. 5
Fig. 5

Input noise density ι̃en for a single channel measured using cold redundancy (only one PRF). The requirement for GRACE-FO in this configuration is 5 pA/Hz1/2 at 16 MHz. The value obtained is around 3.5 pA/Hz1/2, fulfilling the requirement. The measurement was repeated for all channels of all PRFs obtaining similar results.

Fig. 6
Fig. 6

Block diagram of the setup used during the TVAC test. The full PR (PRFs and PRB) was placed inside the TVAC, together with infrared LEDs for beat note simulation. The LEDs were amplitude-modulated using a frequency sweep from 4 to 16 MHz. The phases of the PR signals ϕX = {ϕA, ϕB, ϕC, ϕD} were measured against the reference signal from the LED driver source ϕREF. The TVAC temperature changed during the test with a nominal range of [−10,60] °C for the PRFs and [−15,55] °C for the PRB. The real temperature of the PRB was sensed by a PT1000 resistance temperature detector (RTD) inside the unit. Using this temperature and the phasemeter data, the temperature coefficient that defines the thermal-induced noise in the PR phase was experimentally measured.

Fig. 7
Fig. 7

A picture of all 3 PR flight models prior to the TVAC test. The three PRBs are placed on the top base plate and the six PRFs (only 3 visible) on the lower base plate. The LEDs were mounted underneath the PRFs.

Fig. 8
Fig. 8

Diagram with the relation between the different quadrants and the longitudinal and differential phases. The main longitudinal phase ϕL is an average of the 4 different channels measured against the reference phase ϕREF. The differential phase between the channels ϕDiff is needed to derive the angular misalignment between the interfered beams.

Fig. 9
Fig. 9

Representative example of the longitudinal phase stability obtained during the TVAC test (from flight model #1). The longitudinal phase ϕL was recorded for a total of 61 PRB temperatures (between −6.4 °C and 63.2 °C) at each 1 KHz-frequency bin within the GRACE-FO Doppler frequency range. The plot on the left shows ϕL for the minimum and maximum temperatures. Since the results showed a mostly linear dependence of ϕL on temperature, a linear fit was performed to obtain the temperature coefficient ϕLT plotted on the right. The maximum ϕLT obtained (in absolute terms) is below −5 mrad/K at 16 MHz. This value is not exactly the coefficient from the PR, since the LED source used has also a temperature dependency of about −2.5 mrad/K at 16 MHz. The value measured is nonetheless suitable as an upper limit for the longitudinal phase stability. The requirement of 25 mrad/K is fulfilled.

Fig. 10
Fig. 10

Representative example of the differential phase stability (ϕAϕD of PR flight model #1). The differential phase ϕDiff is plotted on the left for the minimum and maximum PRB temperatures measured during the test. A mostly linear dependence of ϕDiff on temperature was observed. Therefore a linear fit provided again the temperature coefficient ϕDiffT plotted on the right. Since the differential phase does not require the use of a phase reference, the temperature coefficient of the LED does not couple. The maximum temperature coefficient obtained in absolute terms is about −100 μrad/K, 2 orders of magnitude below the 10 mrad/K requirement from GRACE-FO.

Tables (1)

Tables Icon

Table 1 PR requirements and expected interferometer parameters for GRACE-FO. Values with an asterisk (*) show only the noise floor at 1 Hz for simplification. In reality, they increase towards low frequencies as seen in Fig. 2. Based on the expected orbit dynamics in GRACE-FO, Doppler changes along the measurement band and therefore no specific value is given in this table. Experimentally measured values for ι̃en and ϕLT of the GRACE-FO PR flight model are given in Section 4.

Equations (7)

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i bn = R ( 2 γ P LO P RX ) 1 / 2 [ A ] ,
ι ˜ sn = ( 2 q R ( P LO + P RX ) ) 1 / 2 [ A / Hz 1 / 2 ] ,
ϕ ˜ sn = ι ˜ sn i bn = ( q ( P LO + P RX ) R γ P LO P RX ) 1 / 2 [ rad / Hz 1 / 2 ] .
ϕ ˜ en = ι ˜ en i bn = ι ˜ en R ( 2 γ P LO P RX ) 1 / 2 [ rad / Hz 1 / 2 ] .
ϕ ˜ tin = T ˜ PR ϕ LT [ rad / Hz 1 / 2 ] .
ϕ fpn = ( f ˜ laser 2 + f ˜ Doppler 2 ) 1 / 2 ϕ LF [ rad / Hz 1 / 2 ] .
ι ˜ en = ( 2 q I DC ( v ˜ sn v ˜ dark ) 2 1 ) 1 / 2 [ A / Hz 1 / 2 ] ,