Abstract

Quadrant photodiodes (QPDs) are used in laser interferometry systems to simultaneously detect longitudinal displacement of test masses and angular misalignment between the two interfering beams. The latter is achieved by means of the differential wavefront sensing (DWS) technique, which provides ultra-high precision for measuring angular displacements. We have developed a setup to obtain the spatially resolved response of QPDs that, together with an extension of the simulation software IfoCAD, allows us to use the measured response in simulations and accurately predict the desired longitudinal and DWS phase observables. Three different commercial off-the-shelf QPD candidates for space-based interferometry were characterized. The measured response of one QPD was used in optical simulations. Nonuniformities in the response of the device and crosstalk between segments do not introduce significant variations in the longitudinal and DWS measurands with respect to the standard case when a uniform QPD without crosstalk is used.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Laser beam steering for GRACE Follow-On intersatellite interferometry

Daniel Schütze, Gunnar Stede, Vitali Müller, Oliver Gerberding, Tamara Bandikova, Benjamin S. Sheard, Gerhard Heinzel, and Karsten Danzmann
Opt. Express 22(20) 24117-24132 (2014)

Interspacecraft link simulator for the laser ranging interferometer onboard GRACE Follow-On

Josep Sanjuan, Martin Gohlke, Stefan Rasch, Klaus Abich, Alexander Görth, Gerhard Heinzel, and Claus Braxmaier
Appl. Opt. 54(22) 6682-6689 (2015)

Phase stability of photoreceivers in intersatellite laser interferometers

Germán Fernández Barranco, Oliver Gerberding, Thomas S. Schwarze, Benjamin S. Sheard, Christian Dahl, Bernd Zender, and Gerhard Heinzel
Opt. Express 25(7) 7999-8010 (2017)

References

  • View by:
  • |
  • |
  • |

  1. B. Sheard, G. Heinzel, K. Danzmann, D. Shaddock, W. Klipstein, and W. Folkner, “Intersatellite laser ranging instrument for the GRACE follow-on mission,” J. Geod. 86, 1083–1095 (2012).
    [Crossref]
  2. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, “Experimental demonstration of an automatic alignment system for optical interferometers,” Appl. Opt. 33, 5037–5040 (1994).
    [Crossref]
  3. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, “Automatic alignment of optical interferometers,” Appl. Opt. 33, 5041–5049 (1994).
    [Crossref]
  4. H. Gong, L. Hanssen, and G. Eppeldauer, “Spatial and angular responsivity measurements of photoconductive HgCdTe LWIR radiometers,” Metrologia 41, 161–166 (2004).
    [Crossref]
  5. M. Durak, “Spatial non-uniformity analyses of radiometric detectors to identify suited transfer standards for optical radiometry,” Eur. Phys. J. 32, 193–197 (2005).
    [Crossref]
  6. A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, “Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol. 17, 908–912 (2006).
    [Crossref]
  7. F. Seifert, “Power stabilization of high power laser for second generation gravitational wave detectors,” Ph.D. thesis (Leibniz Universität Hannover, 2010).
  8. N. Fox, E. Theocharous, and T. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
    [Crossref]
  9. A. Corrons, J. Fontecha, P. Corredera, J. Campos, A. Pons, and M. Hernanz, “Ultraviolet calibration of detectors with respect to a cryogenic radiometer,” Metrologia 37, 555–558 (2000).
    [Crossref]
  10. M. Durak, F. Samadov, and A. Turkoglu, “Spatial non-uniformity measurements of large area silicon photodiodes,” Turk. J. Phys. 26, 375–380 (2002).
  11. L. C. Alves, F. Reis, M. C. Torres, G. B. Almeida, and I. B. Couceiro, “Spatial uniformity of the silicon photodiodes for establishment of spectral responsivity scale,” in Proceedings of XIX IMEKO World Congress: Fundamental and Applied Metrology (IMEKO, 2009), pp. 164–167.
  12. A. Makynen and J. Kostaniovaara, “Electro-optical instrument for photodetector characterization,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2004), Vol. 3, pp. 2365–2368.
  13. E. Theocharous, M. A. Itzler, J. Cheung, and C. J. Chunnilall, “Characterization of the linearity of response and spatial uniformity of response of two InGaAsP/InP Geiger-mode avalanche photodiodes,” IEEE J. Quantum Electron. 46, 1561–1567 (2010).
    [Crossref]
  14. G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
    [Crossref]
  15. J. A. Arnaud, W. M. Hubbard, G. D. Mandeville, B. de la Clavière, E. A. Franke, and J. M. Franke, “Technique for fast measurement of Gaussian laser beam parameters,” Appl. Opt. 10, 2775–2776 (1971).
    [Crossref]
  16. F. Blumenschein, “Spatially resolved characterization of RF QPDs,” Bachelor’s thesis (University of Konstanz, 2011).

2012 (2)

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

G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
[Crossref]

2010 (1)

E. Theocharous, M. A. Itzler, J. Cheung, and C. J. Chunnilall, “Characterization of the linearity of response and spatial uniformity of response of two InGaAsP/InP Geiger-mode avalanche photodiodes,” IEEE J. Quantum Electron. 46, 1561–1567 (2010).
[Crossref]

2006 (1)

A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, “Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol. 17, 908–912 (2006).
[Crossref]

2005 (1)

M. Durak, “Spatial non-uniformity analyses of radiometric detectors to identify suited transfer standards for optical radiometry,” Eur. Phys. J. 32, 193–197 (2005).
[Crossref]

2004 (1)

H. Gong, L. Hanssen, and G. Eppeldauer, “Spatial and angular responsivity measurements of photoconductive HgCdTe LWIR radiometers,” Metrologia 41, 161–166 (2004).
[Crossref]

2002 (1)

M. Durak, F. Samadov, and A. Turkoglu, “Spatial non-uniformity measurements of large area silicon photodiodes,” Turk. J. Phys. 26, 375–380 (2002).

2000 (1)

A. Corrons, J. Fontecha, P. Corredera, J. Campos, A. Pons, and M. Hernanz, “Ultraviolet calibration of detectors with respect to a cryogenic radiometer,” Metrologia 37, 555–558 (2000).
[Crossref]

1998 (1)

N. Fox, E. Theocharous, and T. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[Crossref]

1994 (2)

1971 (1)

Almeida, G. B.

L. C. Alves, F. Reis, M. C. Torres, G. B. Almeida, and I. B. Couceiro, “Spatial uniformity of the silicon photodiodes for establishment of spectral responsivity scale,” in Proceedings of XIX IMEKO World Congress: Fundamental and Applied Metrology (IMEKO, 2009), pp. 164–167.

Alves, L. C.

L. C. Alves, F. Reis, M. C. Torres, G. B. Almeida, and I. B. Couceiro, “Spatial uniformity of the silicon photodiodes for establishment of spectral responsivity scale,” in Proceedings of XIX IMEKO World Congress: Fundamental and Applied Metrology (IMEKO, 2009), pp. 164–167.

Arnaud, J. A.

Blumenschein, F.

F. Blumenschein, “Spatially resolved characterization of RF QPDs,” Bachelor’s thesis (University of Konstanz, 2011).

Campos, J.

A. Corrons, J. Fontecha, P. Corredera, J. Campos, A. Pons, and M. Hernanz, “Ultraviolet calibration of detectors with respect to a cryogenic radiometer,” Metrologia 37, 555–558 (2000).
[Crossref]

Cheung, J.

E. Theocharous, M. A. Itzler, J. Cheung, and C. J. Chunnilall, “Characterization of the linearity of response and spatial uniformity of response of two InGaAsP/InP Geiger-mode avalanche photodiodes,” IEEE J. Quantum Electron. 46, 1561–1567 (2010).
[Crossref]

Chunnilall, C. J.

E. Theocharous, M. A. Itzler, J. Cheung, and C. J. Chunnilall, “Characterization of the linearity of response and spatial uniformity of response of two InGaAsP/InP Geiger-mode avalanche photodiodes,” IEEE J. Quantum Electron. 46, 1561–1567 (2010).
[Crossref]

Corredera, P.

A. Corrons, J. Fontecha, P. Corredera, J. Campos, A. Pons, and M. Hernanz, “Ultraviolet calibration of detectors with respect to a cryogenic radiometer,” Metrologia 37, 555–558 (2000).
[Crossref]

Corrons, A.

A. Corrons, J. Fontecha, P. Corredera, J. Campos, A. Pons, and M. Hernanz, “Ultraviolet calibration of detectors with respect to a cryogenic radiometer,” Metrologia 37, 555–558 (2000).
[Crossref]

Couceiro, I. B.

L. C. Alves, F. Reis, M. C. Torres, G. B. Almeida, and I. B. Couceiro, “Spatial uniformity of the silicon photodiodes for establishment of spectral responsivity scale,” in Proceedings of XIX IMEKO World Congress: Fundamental and Applied Metrology (IMEKO, 2009), pp. 164–167.

Danzmann, K.

G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
[Crossref]

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

de la Clavière, B.

Durak, M.

M. Durak, “Spatial non-uniformity analyses of radiometric detectors to identify suited transfer standards for optical radiometry,” Eur. Phys. J. 32, 193–197 (2005).
[Crossref]

M. Durak, F. Samadov, and A. Turkoglu, “Spatial non-uniformity measurements of large area silicon photodiodes,” Turk. J. Phys. 26, 375–380 (2002).

Eppeldauer, G.

H. Gong, L. Hanssen, and G. Eppeldauer, “Spatial and angular responsivity measurements of photoconductive HgCdTe LWIR radiometers,” Metrologia 41, 161–166 (2004).
[Crossref]

Folkner, W.

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

Fontecha, J.

A. Corrons, J. Fontecha, P. Corredera, J. Campos, A. Pons, and M. Hernanz, “Ultraviolet calibration of detectors with respect to a cryogenic radiometer,” Metrologia 37, 555–558 (2000).
[Crossref]

Fox, N.

N. Fox, E. Theocharous, and T. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[Crossref]

Franke, E. A.

Franke, J. M.

Gong, H.

H. Gong, L. Hanssen, and G. Eppeldauer, “Spatial and angular responsivity measurements of photoconductive HgCdTe LWIR radiometers,” Metrologia 41, 161–166 (2004).
[Crossref]

Hanssen, L.

H. Gong, L. Hanssen, and G. Eppeldauer, “Spatial and angular responsivity measurements of photoconductive HgCdTe LWIR radiometers,” Metrologia 41, 161–166 (2004).
[Crossref]

Heinzel, G.

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

G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
[Crossref]

Hernanz, M.

A. Corrons, J. Fontecha, P. Corredera, J. Campos, A. Pons, and M. Hernanz, “Ultraviolet calibration of detectors with respect to a cryogenic radiometer,” Metrologia 37, 555–558 (2000).
[Crossref]

Hubbard, W. M.

Hyyppa, T.

A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, “Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol. 17, 908–912 (2006).
[Crossref]

Ikonen, E.

A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, “Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol. 17, 908–912 (2006).
[Crossref]

Itzler, M. A.

E. Theocharous, M. A. Itzler, J. Cheung, and C. J. Chunnilall, “Characterization of the linearity of response and spatial uniformity of response of two InGaAsP/InP Geiger-mode avalanche photodiodes,” IEEE J. Quantum Electron. 46, 1561–1567 (2010).
[Crossref]

Karha, P.

A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, “Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol. 17, 908–912 (2006).
[Crossref]

Klipstein, W.

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

Kochkina, E.

G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
[Crossref]

Kostaniovaara, J.

A. Makynen and J. Kostaniovaara, “Electro-optical instrument for photodetector characterization,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2004), Vol. 3, pp. 2365–2368.

Lamminpaa, A.

A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, “Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol. 17, 908–912 (2006).
[Crossref]

Mahrdt, C.

G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
[Crossref]

Makynen, A.

A. Makynen and J. Kostaniovaara, “Electro-optical instrument for photodetector characterization,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2004), Vol. 3, pp. 2365–2368.

Mandeville, G. D.

Manoocheri, F.

A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, “Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol. 17, 908–912 (2006).
[Crossref]

Meers, B. J.

Morrison, E.

Noorma, M.

A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, “Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol. 17, 908–912 (2006).
[Crossref]

Pons, A.

A. Corrons, J. Fontecha, P. Corredera, J. Campos, A. Pons, and M. Hernanz, “Ultraviolet calibration of detectors with respect to a cryogenic radiometer,” Metrologia 37, 555–558 (2000).
[Crossref]

Reis, F.

L. C. Alves, F. Reis, M. C. Torres, G. B. Almeida, and I. B. Couceiro, “Spatial uniformity of the silicon photodiodes for establishment of spectral responsivity scale,” in Proceedings of XIX IMEKO World Congress: Fundamental and Applied Metrology (IMEKO, 2009), pp. 164–167.

Robertson, D. I.

Samadov, F.

M. Durak, F. Samadov, and A. Turkoglu, “Spatial non-uniformity measurements of large area silicon photodiodes,” Turk. J. Phys. 26, 375–380 (2002).

Schuster, S.

G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
[Crossref]

Seifert, F.

F. Seifert, “Power stabilization of high power laser for second generation gravitational wave detectors,” Ph.D. thesis (Leibniz Universität Hannover, 2010).

Shaddock, D.

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

Sheard, B.

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

G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
[Crossref]

Theocharous, E.

E. Theocharous, M. A. Itzler, J. Cheung, and C. J. Chunnilall, “Characterization of the linearity of response and spatial uniformity of response of two InGaAsP/InP Geiger-mode avalanche photodiodes,” IEEE J. Quantum Electron. 46, 1561–1567 (2010).
[Crossref]

N. Fox, E. Theocharous, and T. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[Crossref]

Torres, M. C.

L. C. Alves, F. Reis, M. C. Torres, G. B. Almeida, and I. B. Couceiro, “Spatial uniformity of the silicon photodiodes for establishment of spectral responsivity scale,” in Proceedings of XIX IMEKO World Congress: Fundamental and Applied Metrology (IMEKO, 2009), pp. 164–167.

Turkoglu, A.

M. Durak, F. Samadov, and A. Turkoglu, “Spatial non-uniformity measurements of large area silicon photodiodes,” Turk. J. Phys. 26, 375–380 (2002).

Wanner, G.

G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
[Crossref]

Ward, H.

Ward, T.

N. Fox, E. Theocharous, and T. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[Crossref]

Appl. Opt. (3)

Eur. Phys. J. (1)

M. Durak, “Spatial non-uniformity analyses of radiometric detectors to identify suited transfer standards for optical radiometry,” Eur. Phys. J. 32, 193–197 (2005).
[Crossref]

IEEE J. Quantum Electron. (1)

E. Theocharous, M. A. Itzler, J. Cheung, and C. J. Chunnilall, “Characterization of the linearity of response and spatial uniformity of response of two InGaAsP/InP Geiger-mode avalanche photodiodes,” IEEE J. Quantum Electron. 46, 1561–1567 (2010).
[Crossref]

J. Geod. (1)

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

Meas. Sci. Technol. (1)

A. Lamminpaa, M. Noorma, T. Hyyppa, F. Manoocheri, P. Karha, and E. Ikonen, “Characterization of germanium photodiodes and trap detector,” Meas. Sci. Technol. 17, 908–912 (2006).
[Crossref]

Metrologia (3)

N. Fox, E. Theocharous, and T. Ward, “Establishing a new ultraviolet and near-infrared spectral responsivity scale,” Metrologia 35, 535–541 (1998).
[Crossref]

A. Corrons, J. Fontecha, P. Corredera, J. Campos, A. Pons, and M. Hernanz, “Ultraviolet calibration of detectors with respect to a cryogenic radiometer,” Metrologia 37, 555–558 (2000).
[Crossref]

H. Gong, L. Hanssen, and G. Eppeldauer, “Spatial and angular responsivity measurements of photoconductive HgCdTe LWIR radiometers,” Metrologia 41, 161–166 (2004).
[Crossref]

Opt. Commun. (1)

G. Wanner, G. Heinzel, E. Kochkina, C. Mahrdt, B. Sheard, S. Schuster, and K. Danzmann, “Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams,” Opt. Commun. 285, 4831–4839 (2012).
[Crossref]

Turk. J. Phys. (1)

M. Durak, F. Samadov, and A. Turkoglu, “Spatial non-uniformity measurements of large area silicon photodiodes,” Turk. J. Phys. 26, 375–380 (2002).

Other (4)

L. C. Alves, F. Reis, M. C. Torres, G. B. Almeida, and I. B. Couceiro, “Spatial uniformity of the silicon photodiodes for establishment of spectral responsivity scale,” in Proceedings of XIX IMEKO World Congress: Fundamental and Applied Metrology (IMEKO, 2009), pp. 164–167.

A. Makynen and J. Kostaniovaara, “Electro-optical instrument for photodetector characterization,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (IEEE, 2004), Vol. 3, pp. 2365–2368.

F. Seifert, “Power stabilization of high power laser for second generation gravitational wave detectors,” Ph.D. thesis (Leibniz Universität Hannover, 2010).

F. Blumenschein, “Spatially resolved characterization of RF QPDs,” Bachelor’s thesis (University of Konstanz, 2011).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1. Schematic description of the experimental setup to measure the spatial response of photodiodes. The light of a fiber-pigtailed laser diode is collimated and injected onto a small optical bench. A focusing lens is used to focus the beam onto the device under test (DUT). The DUT is connected to a four-channel transimpedance amplifier (TIA). The DUT position in the horizontal plane and the vertical position of the optical bench are set by translation stages. Motion of the stages and data sampling are controlled by a PC.
Fig. 2.
Fig. 2. Normalized spatially resolved response of the QP22 by First Sensor. The sum of the four QPD segments was used for the plot. The measurement shows a distribution of spots across the photodiode surface with a 20% reduced responsivity.
Fig. 3.
Fig. 3. Normalized spatially resolved response of the GAP9119 by OEC GmbH. The sum of the four QPD segments was used for the plot. The responsivity deviation within the active area is around 1%.
Fig. 4.
Fig. 4. Normalized spatially resolved response of the FCIQ1000 by OSI Optoelectronics. The sum of the four QPD segments was used for the plot. The responsivity deviation within the active area is around 1%.
Fig. 5.
Fig. 5. Flowchart of an IfoCAD simulation including the extension for measured QPD responses. First, the two interfering beams and the QPD are created and their parameters specified. At this stage, we can choose between the standard QPD model or a measured QPD response. Then, IfoCAD propagates the beams until they reach the QPD position and integrates the electric fields over the given surface. After that, the main interferometric signals can be obtained.
Fig. 6.
Fig. 6. Scheme of the simulation setup used, based on the interferometer conditions in an intersatellite laser ranging mission like GRACE-FO. A 1.675-mm-waist radius Gaussian beam (in blue) was used for the local beam with the waist located at the pivot point. The red line represents the received top-hat beam. Yaw and pitch tilts from 10 to 10 mrad were applied to both beams simultaneously, which would ideally lead to zero longitudinal and DWS signals. Three different QPD positions with respect to the pivot point ( P e ) were used: 0, 0.5, and 1 mm, in order to study deviations from the ideal case.
Fig. 7.
Fig. 7. Horizontal DWS signal for yaw tilts obtained in the simulations. Results for the vertical DWS signal using different pitch tilts are equivalent and are omitted for the sake of clarity. The tilt is applied to both beams simultaneously. Simulations were performed using three different distances between the pivot point and the photodiode ( P e ), represented by different colors. The lines correspond to simulations with the standard IfoCAD QPD, and the markers to ones with the measured QP22 response.
Fig. 8.
Fig. 8. Example of a single segment response of the standard QPD model (Case 1), the modified profiles for additional simulations (Cases 2 and 3), and the unmodified measured QPD response (Case 4). In Case 2, the QPD response is uniform within the segment and nonzero outside. That includes not only the gap but also the crosstalk from adjacent segments. Case 3 is the opposite: the response is nonuniform within the segment but zero outside.
Fig. 9.
Fig. 9. Horizontal DWS signal for yaw tilts at P e = 1 mm for all four cases of Fig. 8. Results for the vertical DWS signal are equivalent and are omitted for the sake of clarity.
Fig. 10.
Fig. 10. Main longitudinal signal for yaw tilts obtained in the simulations. Results for tilts in pitch are equivalent and are omitted for the sake of clarity. The tilt is applied to both beams simultaneously. Simulations were performed using three different distances between the pivot point and the photodiode ( P e ), represented by different colors. The lines correspond to simulations with the standard IfoCAD QPD, and the markers correspond to ones with the measured QP22 response.
Fig. 11.
Fig. 11. Main longitudinal signal for yaw tilts at P e = 1 mm for all four cases of Fig. 8. Results for tilts in pitch are equivalent and are omitted for the sake of clarity.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

c ˜ i = d A E 1 E 2 * R ˜ i d A E 1 E 1 * R ˜ i d A E 2 E 2 * R ˜ i ,
LPS = λ 2 π arg ( c ˜ A + c ˜ B + c ˜ C + c ˜ D ) [ m ] ,
DWS H = arg ( c ˜ A + c ˜ C c ˜ B + c ˜ D ) [ rad ] ,
DWS V = arg ( c ˜ A + c ˜ B c ˜ C + c ˜ D ) [ rad ] .

Metrics