Well characterized photon number resolving detectors are a requirement for many applications ranging from quantum information and quantum metrology to the foundations of quantum mechanics. This prompts the necessity for reliable calibration techniques at the single photon level. In this paper we propose an innovative absolute calibration technique for photon number resolving detectors, using a pulsed heralded photon source based on parametric down conversion. The technique, being absolute, does not require reference standards and is independent upon the performances of the heralding detector. The method provides the results of quantum efficiency for the heralded detector as a function of detected photon numbers. Furthermore, we prove its validity by performing the calibration of a Transition Edge Sensor based detector, a real photon number resolving detector that has recently demonstrated its effectiveness in various quantum information protocols.

© 2011 OSA

1. R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nature Photon.3, 696–705 (2009) and ref.s therein. [CrossRef]
2. C. Silberhorn, “Detecting quantum light,” Contemp. Phys.48, 143–156 (2007) and ref.s therein. [CrossRef]
3. J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ’the candela’: evolution in the classical and quantum world,” Metrologia47, R15–R32 (2010). [CrossRef]
4. Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J.Opt. Soc. Am. B27, A170–A174 (2010). [CrossRef]
5. M. Genovese, “Research on hidden variable theories: A review of recent progresses,” Phys. Rep.413, 319–396 (2005) and ref.s therein. [CrossRef]
6. G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon.4, 227–230 (2010). [CrossRef]
7. T. Laenger and G. Lenhart, “Standardization of quantum key distribution and the ETSI standardization initiative ISG-QKD,” New J. Phys.11, 055051 (2009) and ref.s therein. [CrossRef]
8. J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nature Photon.3, 687–695 (2009) and ref.s therein. [CrossRef]
9. N. Gisin and R. Thew, “Quantum communication,” Nature Photon.1, 165–171 (2007) and ref.s therein. [CrossRef]
10. L. A. Jiang, E. A. Dauler, and J. T. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A75, 062325 (2007). [CrossRef]
11. A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nature Photon.2, 302–306 (2008). [CrossRef]
12. D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett.28, 2387–2389 (2003). [CrossRef] [PubMed]
13. M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A68, 043814 (2003). [CrossRef]
14. G. Zambra, M. Bondani, A. S. Spinelli, F. Paleari, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum.75, 2762 (2004). [CrossRef]
15. M. Bondani, A. Allevi, and A. Andreoni, “Light Statistics by Non-Calibrated Linear Photodetectors,” Advanced Science Letters2, 463–468 (2009). [CrossRef]
16. G. A. Morton, RCA Rev.10, 525 (1949).
17. M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B27, 852–862 (2010). [CrossRef]
18. J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett., 74, 902 (1999). [CrossRef]
19. E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron9, 1502–1511 (2003). [CrossRef]
20. K. D. Irwin and G. C. Hilton, “Transition-Edge Sensors,” in Cryogenic Particle Detection (Topics Appl. Phys. Vol. 99), C. Enss eds., (Springer-Verlag, Berlin, 2005), pp. 63–149.
21. A. J. Pearlman, A. Ling, E. A. Goldschmidt, C. F. Wildfeuer, J. Fan, and A. Migdall, “Enhancing image contrast using coherent states and photon number resolving detectors,” Opt. Express18, 6033–6039 (2010). [CrossRef] [PubMed]
22. T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010). [CrossRef]
23. K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express18, 8107–8114 (2010). [CrossRef] [PubMed]
24. A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Today52, 41–46 (1999) and ref.s therein. [CrossRef]
25. G. Brida, M. Genovese, and M. Gramegna, “Twin-photon techniques for photo-detector calibration,” Laser Physics Lett.3, 115–123 (2006) and ref.s therein. [CrossRef]
26. S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” J. Mod. Opt.56, 1045–1052 (2009) and ref.s therein. [CrossRef]
27. D. C. Burnham and D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett.25, 84–87 (1970). [CrossRef]
28. D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron.7, 591 (1977). [CrossRef]
29. P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute efficiency and time-response measurement of single-photon detectors,” Appl. Opt.33, 1844–1853 (1994). [CrossRef] [PubMed]
30. E. Dauler, A. L. Migdall, N. Boeuf, R. U. Datla, A. Muller, and A. Sergienko, “Measuring absolute infrared spectral radiance with correlated photons: new arrangements for improved uncertainty and extended IR range,” Metrologia35, 295 (1998). [CrossRef]
31. G. Brida, S. Castelletto, I. P. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Towards an uncertainty budget in quantum-efficiency measurements with parametric fluorescence,” Metrologia37, 629 (2000). [CrossRef]
32. J. G. Rarity, K. D. Ridley, and P. R. Tapster, “Absolute measurement of detector quantum efficiency using parametric downconversion,” Appl. Opt.26, 4616–4619 (1987). [CrossRef] [PubMed]
33. S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Evaluation of statistical noise in measurements based on correlated photons,” J. Opt. Soc. Am. B19, 1247–1258 (2002). [CrossRef]
34. A. Ghazi-Bellouati, A. Razet, J. Bastie, M. E. Himbert, I. P. Degiovanni, S. Castelletto, and M. L. Rastello, “Radiometric reference for weak radiations: comparison of methods,” Metrologia42, 271 (2005). [CrossRef]
35. A. L. Migdall, S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Intercomparison of a Correlated-Photon-Based Method to Measure Detector Quantum Efficiency,” Appl. Opt.41, 2914–2922 (2002). [CrossRef] [PubMed]
36. S.V. Polyakov and A.L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express15, 1390–1407 (2007). [CrossRef] [PubMed]
37. J. Y. Cheung, C. J. Chunnilall, G. Porrovecchio, M. Smid, and E. Theocharous, “Low optical power reference detector implemented in the validation of two independent techniques for calibrating photon-counting detectors,” Opt. Express (submitted). [PubMed]
38. G. Brida, M. Genovese, I. Ruo-Berchera, M. Chekhova, and A. Penin, “Possibility of absolute calibration of analog detectors by using parametric downconversion: a systematic study,” J. Opt. Soc. Am. B23, 2185–2193 (2006). [CrossRef]
39. G. Brida, M. Chekhova, M. Genovese, and I. Ruo-Berchera, “Analysis of the possibility of analog detectors calibration by exploiting stimulated parametric down conversion,” Opt. Express16, 12550–12558 (2008). [CrossRef] [PubMed]
40. G. Brida, I. P. Degiovanni, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Detection of multimode spatial correlation in PDC and application to the absolute calibration of a CCD camera,” Opt. Express18, 20572–20584 (2010). [CrossRef] [PubMed]
41. A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express17, 4397–4411 (2009). [CrossRef] [PubMed]
42. D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98% detection efficiency with index-matched small-gap fiber coupling,” Opt. Express19, 870–875 (2011). [CrossRef] [PubMed]
43. A.E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express16, 3032–3040 (2008). [CrossRef] [PubMed]
44. A. C. Parr, R. U. Datla, and J. L. Gardner, Optical Radiometry (Elsevier Academic Press, Amsterdam2005)
45. C. Portesi, E. Taralli, R. Rocci, M. Rajteri, and E. Monticone, “Fabrication of Au/Ti TESs for Optical Photon Counting,” J. Low Temp. Phys.151, 261–265 (2008). [CrossRef]
46. E. Taralli, C. Portesi, L. Lolli, E. Monticone, M. Rajteri, I. Novikov, and J. Beyer, “Impedance measurements on a fast transition-edge sensor for optical and near-infrared range,” Supercond. Sci. Technol.23, 105012 (2010). [CrossRef]
47. K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett.66, 1998 (1995).
48. L. Lolli, E. Taralli, C. Portesi, D. Alberto, M. Rajteri, and E. Monticone, “Ti/Au Transition-Edge Sensors Coupled to Single Mode Optical Fibers Aligned by Si V-Groove,” IEEE Trans. Appl. Supercond.21215–218 (2011). [CrossRef]
49. D. Drung, C. Assmann, J. Beyer, A. Kirste, M. Peters, F. Ruede, and T. Schurig, “Highly Sensitive and Easy-to-Use SQUID Sensors,” IEEE Trans. Appl. Supercond.17, 699–704 (2007). [CrossRef]
50. S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Theoretical aspects of photon number measurement,” Metrologia37, 613–616 (2000). [CrossRef]
51. Guide to the Expression of Uncertainty in Measurement, ISO (1995).
52. G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, L. Lolli, M. G. Mingolla, F. Piacentini, M. Rajteri, E. Taralli, and M. G. A. Paris, “Full quantum characterization of superconducting photon counters,” http://arxiv.org/pdf/1103.2991 .
53. Incidentally, if one wants to provide a precise estimate of the naked TES based detector quantum efficiency η it is necessary a careful estimation of the optical transmittance τ, accounting for the coupling efficiency in the optical fiber and the optical losses in the non-linear crystal. According to the results of Ref.s [S.V. Polyakov, A.L. Migdall, Opt. Express 15, 1390 (2007); J. Y. Cheung et al., Appl. Opt. (submitted)], one could provide an estimate of this parameter with a less than 1% uncertainty.

Advanced Science Letters

• M. Bondani, A. Allevi, and A. Andreoni, “Light Statistics by Non-Calibrated Linear Photodetectors,” Advanced Science Letters2, 463–468 (2009). [CrossRef]

Appl. Opt.

• P. G. Kwiat, A. M. Steinberg, R. Y. Chiao, P. H. Eberhard, and M. D. Petroff, “Absolute efficiency and time-response measurement of single-photon detectors,” Appl. Opt.33, 1844–1853 (1994). [CrossRef] [PubMed]
• J. G. Rarity, K. D. Ridley, and P. R. Tapster, “Absolute measurement of detector quantum efficiency using parametric downconversion,” Appl. Opt.26, 4616–4619 (1987). [CrossRef] [PubMed]
• A. L. Migdall, S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Intercomparison of a Correlated-Photon-Based Method to Measure Detector Quantum Efficiency,” Appl. Opt.41, 2914–2922 (2002). [CrossRef] [PubMed]

Appl. Phys. Lett.

• J. Kim, S. Takeuchi, Y. Yamamoto, and H. H. Hogue, “Multiphoton detection using visible light photon counter,” Appl. Phys. Lett., 74, 902 (1999). [CrossRef]

Contemp. Phys.

• C. Silberhorn, “Detecting quantum light,” Contemp. Phys.48, 143–156 (2007) and ref.s therein. [CrossRef]

IEEE J. Sel. Top. Quantum Electron

• E. Waks, K. Inoue, W. D. Oliver, E. Diamanti, and Y. Yamamoto, “High-efficiency photon-number detection for quantum information processing,” IEEE J. Sel. Top. Quantum Electron9, 1502–1511 (2003). [CrossRef]

IEEE Trans. Appl. Supercond.

• L. Lolli, E. Taralli, C. Portesi, D. Alberto, M. Rajteri, and E. Monticone, “Ti/Au Transition-Edge Sensors Coupled to Single Mode Optical Fibers Aligned by Si V-Groove,” IEEE Trans. Appl. Supercond.21215–218 (2011). [CrossRef]
• D. Drung, C. Assmann, J. Beyer, A. Kirste, M. Peters, F. Ruede, and T. Schurig, “Highly Sensitive and Easy-to-Use SQUID Sensors,” IEEE Trans. Appl. Supercond.17, 699–704 (2007). [CrossRef]

J. Low Temp. Phys.

• C. Portesi, E. Taralli, R. Rocci, M. Rajteri, and E. Monticone, “Fabrication of Au/Ti TESs for Optical Photon Counting,” J. Low Temp. Phys.151, 261–265 (2008). [CrossRef]

J. Mod. Opt.

• S. V. Polyakov and A. L. Migdall, “Quantum radiometry,” J. Mod. Opt.56, 1045–1052 (2009) and ref.s therein. [CrossRef]

J. Opt. Soc. Am. B

• S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Evaluation of statistical noise in measurements based on correlated photons,” J. Opt. Soc. Am. B19, 1247–1258 (2002). [CrossRef]
• G. Brida, M. Genovese, I. Ruo-Berchera, M. Chekhova, and A. Penin, “Possibility of absolute calibration of analog detectors by using parametric downconversion: a systematic study,” J. Opt. Soc. Am. B23, 2185–2193 (2006). [CrossRef]
• M. Ramilli, A. Allevi, V. Chmill, M. Bondani, M. Caccia, and A. Andreoni, “Photon-number statistics with silicon photomultipliers,” J. Opt. Soc. Am. B27, 852–862 (2010). [CrossRef]

J.Opt. Soc. Am. B

• Y. Gao, P. M. Anisimov, C. F. Wildfeuer, J. Luine, H. Lee, and J. P. Dowling, “Super-resolution at the shot-noise limit with coherent states and photon-number-resolving detectors,” J.Opt. Soc. Am. B27, A170–A174 (2010). [CrossRef]

Laser Physics Lett.

• G. Brida, M. Genovese, and M. Gramegna, “Twin-photon techniques for photo-detector calibration,” Laser Physics Lett.3, 115–123 (2006) and ref.s therein. [CrossRef]

Metrologia

• S. Castelletto, I. P. Degiovanni, and M. L. Rastello, “Theoretical aspects of photon number measurement,” Metrologia37, 613–616 (2000). [CrossRef]
• J. C. Zwinkels, E. Ikonen, N. P. Fox, G. Ulm, and M. L. Rastello, “Photometry, radiometry and ’the candela’: evolution in the classical and quantum world,” Metrologia47, R15–R32 (2010). [CrossRef]
• A. Ghazi-Bellouati, A. Razet, J. Bastie, M. E. Himbert, I. P. Degiovanni, S. Castelletto, and M. L. Rastello, “Radiometric reference for weak radiations: comparison of methods,” Metrologia42, 271 (2005). [CrossRef]
• E. Dauler, A. L. Migdall, N. Boeuf, R. U. Datla, A. Muller, and A. Sergienko, “Measuring absolute infrared spectral radiance with correlated photons: new arrangements for improved uncertainty and extended IR range,” Metrologia35, 295 (1998). [CrossRef]
• G. Brida, S. Castelletto, I. P. Degiovanni, M. Genovese, C. Novero, and M. L. Rastello, “Towards an uncertainty budget in quantum-efficiency measurements with parametric fluorescence,” Metrologia37, 629 (2000). [CrossRef]

Nature Photon.

• G. Brida, M. Genovese, and I. Ruo Berchera, “Experimental realization of sub-shot-noise quantum imaging,” Nature Photon.4, 227–230 (2010). [CrossRef]
• J. L. O’Brien, A. Furusawa, and J. Vučković, “Photonic quantum technologies,” Nature Photon.3, 687–695 (2009) and ref.s therein. [CrossRef]
• N. Gisin and R. Thew, “Quantum communication,” Nature Photon.1, 165–171 (2007) and ref.s therein. [CrossRef]
• R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nature Photon.3, 696–705 (2009) and ref.s therein. [CrossRef]
• A. Divochiy, F. Marsili, D. Bitauld, A. Gaggero, R. Leoni, F. Mattioli, A. Korneev, V. Seleznev, N. Kaurova, O. Minaeva, G. Gol’tsman, K. G. Lagoudakis, M. Benkhaoul, F. Lvy, and A. Fiore, “Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths,” Nature Photon.2, 302–306 (2008). [CrossRef]

New J. Phys.

• T. Laenger and G. Lenhart, “Standardization of quantum key distribution and the ETSI standardization initiative ISG-QKD,” New J. Phys.11, 055051 (2009) and ref.s therein. [CrossRef]

Opt. Express

• G. Brida, M. Chekhova, M. Genovese, and I. Ruo-Berchera, “Analysis of the possibility of analog detectors calibration by exploiting stimulated parametric down conversion,” Opt. Express16, 12550–12558 (2008). [CrossRef] [PubMed]
• G. Brida, I. P. Degiovanni, M. Genovese, M. L. Rastello, and I. Ruo Berchera, “Detection of multimode spatial correlation in PDC and application to the absolute calibration of a CCD camera,” Opt. Express18, 20572–20584 (2010). [CrossRef] [PubMed]
• A. P. Worsley, H. B. Coldenstrodt-Ronge, J. S. Lundeen, P. J. Mosley, B. J. Smith, G. Puentes, N. Thomas-Peter, and I. A. Walmsley, “Absolute efficiency estimation of photon-number-resolving detectors using twin beams,” Opt. Express17, 4397–4411 (2009). [CrossRef] [PubMed]
• D. Fukuda, G. Fujii, T. Numata, K. Amemiya, A. Yoshizawa, H. Tsuchida, H. Fujino, H. Ishii, T. Itatani, S. Inoue, and T. Zama, “Titanium-based transition-edge photon number resolving detector with 98% detection efficiency with index-matched small-gap fiber coupling,” Opt. Express19, 870–875 (2011). [CrossRef] [PubMed]
• A.E. Lita, A. J. Miller, and S. W. Nam, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express16, 3032–3040 (2008). [CrossRef] [PubMed]
• K. Tsujino, D. Fukuda, G. Fujii, S. Inoue, M. Fujiwara, M. Takeoka, and M. Sasaki, “Sub-shot-noise-limit discrimination of on-off keyed coherent signals via a quantum receiver with a superconducting transition edge sensor,” Opt. Express18, 8107–8114 (2010). [CrossRef] [PubMed]
• A. J. Pearlman, A. Ling, E. A. Goldschmidt, C. F. Wildfeuer, J. Fan, and A. Migdall, “Enhancing image contrast using coherent states and photon number resolving detectors,” Opt. Express18, 6033–6039 (2010). [CrossRef] [PubMed]
• S.V. Polyakov and A.L. Migdall, “High accuracy verification of a correlated-photon-based method for determining photoncounting detection efficiency,” Opt. Express15, 1390–1407 (2007). [CrossRef] [PubMed]

Opt. Lett.

• D. Achilles, C. Silberhorn, C. Sliwa, K. Banaszek, and I. A. Walmsley, “Fiber-assisted detection with photon number resolution,” Opt. Lett.28, 2387–2389 (2003). [CrossRef] [PubMed]

Phys. Rep.

• M. Genovese, “Research on hidden variable theories: A review of recent progresses,” Phys. Rep.413, 319–396 (2005) and ref.s therein. [CrossRef]

Phys. Rev. A

• L. A. Jiang, E. A. Dauler, and J. T. Chang, “Photon-number-resolving detector with 10 bits of resolution,” Phys. Rev. A75, 062325 (2007). [CrossRef]
• M. J. Fitch, B. C. Jacobs, T. B. Pittman, and J. D. Franson, “Photon-number resolution using time-multiplexed single-photon detectors,” Phys. Rev. A68, 043814 (2003). [CrossRef]
• T. Gerrits, S. Glancy, T. S. Clement, B. Calkins, A. E. Lita, A. J. Miller, A. L. Migdall, S. W. Nam, R. P. Mirin, and E. Knill, “Generation of optical coherent-state superpositions by number-resolved photon subtraction from the squeezed vacuum,” Phys. Rev. A82, 031802 (2010). [CrossRef]

Phys. Rev. Lett.

• D. C. Burnham and D. L. Weinberg, “Observation of Simultaneity in Parametric Production of Optical Photon Pairs,” Phys. Rev. Lett.25, 84–87 (1970). [CrossRef]

Phys. Today

• A. Migdall, “Correlated-photon metrology without absolute standards,” Phys. Today52, 41–46 (1999) and ref.s therein. [CrossRef]

RCA Rev.

• G. A. Morton, RCA Rev.10, 525 (1949).

Rev. Sci. Instrum.

• G. Zambra, M. Bondani, A. S. Spinelli, F. Paleari, and A. Andreoni, “Counting photoelectrons in the response of a photomultiplier tube to single picosecond light pulses,” Rev. Sci. Instrum.75, 2762 (2004). [CrossRef]

Sov. J. Quantum Electron.

• D. N. Klyshko, “Utilization of vacuum fluctuations as an optical brightness standard,” Sov. J. Quantum Electron.7, 591 (1977). [CrossRef]

Supercond. Sci. Technol.

• E. Taralli, C. Portesi, L. Lolli, E. Monticone, M. Rajteri, I. Novikov, and J. Beyer, “Impedance measurements on a fast transition-edge sensor for optical and near-infrared range,” Supercond. Sci. Technol.23, 105012 (2010). [CrossRef]

Other

• K. D. Irwin, “An application of electrothermal feedback for high resolution cryogenic particle detection,” Appl. Phys. Lett.66, 1998 (1995).
• J. Y. Cheung, C. J. Chunnilall, G. Porrovecchio, M. Smid, and E. Theocharous, “Low optical power reference detector implemented in the validation of two independent techniques for calibrating photon-counting detectors,” Opt. Express (submitted). [PubMed]
• Guide to the Expression of Uncertainty in Measurement, ISO (1995).
• G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, L. Lolli, M. G. Mingolla, F. Piacentini, M. Rajteri, E. Taralli, and M. G. A. Paris, “Full quantum characterization of superconducting photon counters,” http://arxiv.org/pdf/1103.2991 .
• Incidentally, if one wants to provide a precise estimate of the naked TES based detector quantum efficiency η it is necessary a careful estimation of the optical transmittance τ, accounting for the coupling efficiency in the optical fiber and the optical losses in the non-linear crystal. According to the results of Ref.s [S.V. Polyakov, A.L. Migdall, Opt. Express 15, 1390 (2007); J. Y. Cheung et al., Appl. Opt. (submitted)], one could provide an estimate of this parameter with a less than 1% uncertainty.
• K. D. Irwin and G. C. Hilton, “Transition-Edge Sensors,” in Cryogenic Particle Detection (Topics Appl. Phys. Vol. 99), C. Enss eds., (Springer-Verlag, Berlin, 2005), pp. 63–149.
• A. C. Parr, R. U. Datla, and J. L. Gardner, Optical Radiometry (Elsevier Academic Press, Amsterdam2005)

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