Abstract

We describe a non-traditional optical power meter which measures radiation pressure to accurately determine a laser’s optical power output. This approach traces its calibration of the optical watt to the kilogram. Our power meter is designed for high-accuracy and portability with the capability of multi-kilowatt measurements whose upper power limit is constrained only by the mirror quality. We provide detailed uncertainty evaluation and validate experimentally an average expanded relative uncertainty of 0.016 from 1 kW to 10 kW. Radiation pressure as a power measurement tool is unique to the extent that it does not rely on absorption of the light to produce a high-accuracy result. This permits fast measurements, simplifies power scalability, and allows high-accuracy measurements to be made during use of the laser for other applications.

Full Article  |  PDF Article
OSA Recommended Articles
Onsite multikilowatt laser power meter calibration using radiation pressure

Paul A. Williams, Joshua A. Hadler, Brian J. Simonds, and John H. Lehman
Appl. Opt. 56(34) 9596-9600 (2017)

Direct measurement of radiation pressure and circulating power inside a passive optical cavity

Ryan Wagner, Felipe Guzman, Akobuije Chijioke, Gurpreet Kaur Gulati, Matthias Keller, and Gordon Shaw
Opt. Express 26(18) 23492-23506 (2018)

Use of radiation pressure for measurement of high-power laser emission

Paul A. Williams, Joshua A. Hadler, Robert Lee, Frank C. Maring, and John H. Lehman
Opt. Lett. 38(20) 4248-4251 (2013)

References

  • View by:
  • |
  • |
  • |

  1. P. A. Williams, J. A. Hadler, R. Lee, F. C. Maring, and J. H. Lehman, “Use of radiation pressure for measurement of high-power laser emission,” Opt. Lett. 38(20), 4248–4251 (2013).
    [Crossref] [PubMed]
  2. M. Stimler, Z. I. Slawsky, and R. E. Grantham, “Torsion Pendulum Photometer,” Rev. Sci. Instrum. 35(3), 311–313 (1964).
    [Crossref]
  3. J. J. Cook, W. L. Flowers, and C. B. Arnold, “Measurement of Laser Output by Light Pressure,” Proc. IRE 50, 1693 (1962).
  4. Y. P. Yuan, “A New Pulse Laser Energy Meter,” Rev. Sci. Instrum. 61(6), 1743–1746 (1990).
    [Crossref]
  5. V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, “A new facility to realize a nanonewton force standard based on electrostatic methods,” Metrologia 46(3), 277–282 (2009).
    [Crossref]
  6. K. Agatsuma, D. Friedrich, S. Ballmer, G. DeSalvo, S. Sakata, E. Nishida, and S. Kawamura, “Precise measurement of laser power using an optomechanical system,” Opt. Express 22(2), 2013–2030 (2014).
    [Crossref] [PubMed]
  7. D. K. Ma, J. L. Garrett, and J. N. Munday, “Quantitative measurement of radiation pressure on a microcantilever in ambient environment,” Appl. Phys. Lett. 106(9), 091107 (2015).
    [Crossref]
  8. J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
    [Crossref]
  9. J. A. Hadler, C. L. Cromer, and J. H. Lehman, NIST Measurement Services: cw Laser Power and Energy Calibrations at NIST, NIST Special Publication (2007), Vol. 250–75.
  10. C. Crespy, D. Villate, M. Soscia, F. Coste, and R. Andre, “RLCYC 75: a 2 kW electrically calibrated laser calorimeter designed for Laser MegaJoule diagnostics calibration,” Metrologia 50(1), 37–48 (2013).
    [Crossref]
  11. F. Brandt, H. Lecher, and S. Kuck, “Traceable measurement of high laser power in the 1-um spectral range,” in NewRad 2014, (Helsinki, 2014), pp. 269–271.
  12. R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, “Calorimeter for High-Power CW Lasers,” IEEE Trans. Instrum. Meas. 21(4), 434–438 (1972).
    [Crossref]
  13. C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” in 11th Conference on New Developments and Applications in Optical Radiometry, (Maui, 2011), pp. 180–181.
  14. J. C. Maxwell, A Treatise on Electricity and Magnetism, 1st ed. (Oxford University, 1873).
  15. E. E. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 25 (1903).
  16. P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, “Determination of a cantilever’s mechanical impedance using photon momentum,” Appl. Phys. Lett. 102(18), 184103 (2013).
    [Crossref]
  17. P. Williams, J. Sowards, and B. Simonds, “Measuring Laser Beam Welding Power Using the Force of Light,” Weld. J. 95, 30–34 (2016).
  18. F. C. Maring, “High resolution offset electronic weighing devices and methods,” U.S. Patent 7,315,003 B2 (2008).
  19. B. S. Wherrett, “Scaling Rules for Multiphoton Interband Absorption in Semiconductors,” J. Opt. Soc. Am. B 1(1), 67–72 (1984).
    [Crossref]
  20. A. Obeidat, J. Khurgin, and W. Knox, “Effects of two-photon absorption in saturable Bragg reflectors used in femtosecond solid state lasers,” Opt. Express 1(3), 68–72 (1997).
    [Crossref] [PubMed]
  21. B. N. Taylor and C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurement results, NIST Technical Note 1297 (1994).
    [Crossref]
  22. X. Li, J. A. Hadler, C. L. Cromer, J. H. Lehman, and M. L. Dowell, NIST Measurement Services: High power laser calibrations at NIST, NIST Special Publication 250–77 (2008).
  23. P. Williams, B. Simonds, J. Sowards, and J. Hadler, “Measuring laser power as a force: A new paradigm to accurately monitor optical power during laser-based machining operations,” Proc. SPIE 9741, L1–L8 (2016).

2016 (2)

P. Williams, J. Sowards, and B. Simonds, “Measuring Laser Beam Welding Power Using the Force of Light,” Weld. J. 95, 30–34 (2016).

P. Williams, B. Simonds, J. Sowards, and J. Hadler, “Measuring laser power as a force: A new paradigm to accurately monitor optical power during laser-based machining operations,” Proc. SPIE 9741, L1–L8 (2016).

2015 (1)

D. K. Ma, J. L. Garrett, and J. N. Munday, “Quantitative measurement of radiation pressure on a microcantilever in ambient environment,” Appl. Phys. Lett. 106(9), 091107 (2015).
[Crossref]

2014 (2)

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

K. Agatsuma, D. Friedrich, S. Ballmer, G. DeSalvo, S. Sakata, E. Nishida, and S. Kawamura, “Precise measurement of laser power using an optomechanical system,” Opt. Express 22(2), 2013–2030 (2014).
[Crossref] [PubMed]

2013 (3)

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, “Determination of a cantilever’s mechanical impedance using photon momentum,” Appl. Phys. Lett. 102(18), 184103 (2013).
[Crossref]

C. Crespy, D. Villate, M. Soscia, F. Coste, and R. Andre, “RLCYC 75: a 2 kW electrically calibrated laser calorimeter designed for Laser MegaJoule diagnostics calibration,” Metrologia 50(1), 37–48 (2013).
[Crossref]

P. A. Williams, J. A. Hadler, R. Lee, F. C. Maring, and J. H. Lehman, “Use of radiation pressure for measurement of high-power laser emission,” Opt. Lett. 38(20), 4248–4251 (2013).
[Crossref] [PubMed]

2009 (1)

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, “A new facility to realize a nanonewton force standard based on electrostatic methods,” Metrologia 46(3), 277–282 (2009).
[Crossref]

1997 (1)

1990 (1)

Y. P. Yuan, “A New Pulse Laser Energy Meter,” Rev. Sci. Instrum. 61(6), 1743–1746 (1990).
[Crossref]

1984 (1)

1972 (1)

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, “Calorimeter for High-Power CW Lasers,” IEEE Trans. Instrum. Meas. 21(4), 434–438 (1972).
[Crossref]

1964 (1)

M. Stimler, Z. I. Slawsky, and R. E. Grantham, “Torsion Pendulum Photometer,” Rev. Sci. Instrum. 35(3), 311–313 (1964).
[Crossref]

1903 (1)

E. E. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 25 (1903).

Agatsuma, K.

Andre, R.

C. Crespy, D. Villate, M. Soscia, F. Coste, and R. Andre, “RLCYC 75: a 2 kW electrically calibrated laser calorimeter designed for Laser MegaJoule diagnostics calibration,” Metrologia 50(1), 37–48 (2013).
[Crossref]

Ballmer, S.

Brand, U.

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, “A new facility to realize a nanonewton force standard based on electrostatic methods,” Metrologia 46(3), 277–282 (2009).
[Crossref]

Case, W. E.

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, “Calorimeter for High-Power CW Lasers,” IEEE Trans. Instrum. Meas. 21(4), 434–438 (1972).
[Crossref]

Cervantes, F. G.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

Coste, F.

C. Crespy, D. Villate, M. Soscia, F. Coste, and R. Andre, “RLCYC 75: a 2 kW electrically calibrated laser calorimeter designed for Laser MegaJoule diagnostics calibration,” Metrologia 50(1), 37–48 (2013).
[Crossref]

Crespy, C.

C. Crespy, D. Villate, M. Soscia, F. Coste, and R. Andre, “RLCYC 75: a 2 kW electrically calibrated laser calorimeter designed for Laser MegaJoule diagnostics calibration,” Metrologia 50(1), 37–48 (2013).
[Crossref]

Cromer, C. L.

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” in 11th Conference on New Developments and Applications in Optical Radiometry, (Maui, 2011), pp. 180–181.

DeSalvo, G.

Dowell, M. L.

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” in 11th Conference on New Developments and Applications in Optical Radiometry, (Maui, 2011), pp. 180–181.

Friedrich, D.

Frumin, L. L.

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, “A new facility to realize a nanonewton force standard based on electrostatic methods,” Metrologia 46(3), 277–282 (2009).
[Crossref]

Garrett, J. L.

D. K. Ma, J. L. Garrett, and J. N. Munday, “Quantitative measurement of radiation pressure on a microcantilever in ambient environment,” Appl. Phys. Lett. 106(9), 091107 (2015).
[Crossref]

Grantham, R. E.

M. Stimler, Z. I. Slawsky, and R. E. Grantham, “Torsion Pendulum Photometer,” Rev. Sci. Instrum. 35(3), 311–313 (1964).
[Crossref]

Hadler, J.

P. Williams, B. Simonds, J. Sowards, and J. Hadler, “Measuring laser power as a force: A new paradigm to accurately monitor optical power during laser-based machining operations,” Proc. SPIE 9741, L1–L8 (2016).

Hadler, J. A.

Hull, G. F.

E. E. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 25 (1903).

Kawamura, S.

Khurgin, J.

Knox, W.

Lee, R.

Lehman, J. H.

P. A. Williams, J. A. Hadler, R. Lee, F. C. Maring, and J. H. Lehman, “Use of radiation pressure for measurement of high-power laser emission,” Opt. Lett. 38(20), 4248–4251 (2013).
[Crossref] [PubMed]

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” in 11th Conference on New Developments and Applications in Optical Radiometry, (Maui, 2011), pp. 180–181.

Li, X.

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” in 11th Conference on New Developments and Applications in Optical Radiometry, (Maui, 2011), pp. 180–181.

Ma, D. K.

D. K. Ma, J. L. Garrett, and J. N. Munday, “Quantitative measurement of radiation pressure on a microcantilever in ambient environment,” Appl. Phys. Lett. 106(9), 091107 (2015).
[Crossref]

Maring, F. C.

Melcher, J.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

Mueller, M.

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, “A new facility to realize a nanonewton force standard based on electrostatic methods,” Metrologia 46(3), 277–282 (2009).
[Crossref]

Munday, J. N.

D. K. Ma, J. L. Garrett, and J. N. Munday, “Quantitative measurement of radiation pressure on a microcantilever in ambient environment,” Appl. Phys. Lett. 106(9), 091107 (2015).
[Crossref]

Nesterov, V.

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, “A new facility to realize a nanonewton force standard based on electrostatic methods,” Metrologia 46(3), 277–282 (2009).
[Crossref]

Nichols, E. E.

E. E. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 25 (1903).

Nishida, E.

Obeidat, A.

Pratt, J. R.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, “Determination of a cantilever’s mechanical impedance using photon momentum,” Appl. Phys. Lett. 102(18), 184103 (2013).
[Crossref]

Rasmussen, A. L.

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, “Calorimeter for High-Power CW Lasers,” IEEE Trans. Instrum. Meas. 21(4), 434–438 (1972).
[Crossref]

Russell, T. W.

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, “Calorimeter for High-Power CW Lasers,” IEEE Trans. Instrum. Meas. 21(4), 434–438 (1972).
[Crossref]

Sakata, S.

Shaw, G. A.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, “Determination of a cantilever’s mechanical impedance using photon momentum,” Appl. Phys. Lett. 102(18), 184103 (2013).
[Crossref]

Simonds, B.

P. Williams, J. Sowards, and B. Simonds, “Measuring Laser Beam Welding Power Using the Force of Light,” Weld. J. 95, 30–34 (2016).

P. Williams, B. Simonds, J. Sowards, and J. Hadler, “Measuring laser power as a force: A new paradigm to accurately monitor optical power during laser-based machining operations,” Proc. SPIE 9741, L1–L8 (2016).

Slawsky, Z. I.

M. Stimler, Z. I. Slawsky, and R. E. Grantham, “Torsion Pendulum Photometer,” Rev. Sci. Instrum. 35(3), 311–313 (1964).
[Crossref]

Smith, R. L.

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, “Calorimeter for High-Power CW Lasers,” IEEE Trans. Instrum. Meas. 21(4), 434–438 (1972).
[Crossref]

Soscia, M.

C. Crespy, D. Villate, M. Soscia, F. Coste, and R. Andre, “RLCYC 75: a 2 kW electrically calibrated laser calorimeter designed for Laser MegaJoule diagnostics calibration,” Metrologia 50(1), 37–48 (2013).
[Crossref]

Sowards, J.

P. Williams, J. Sowards, and B. Simonds, “Measuring Laser Beam Welding Power Using the Force of Light,” Weld. J. 95, 30–34 (2016).

P. Williams, B. Simonds, J. Sowards, and J. Hadler, “Measuring laser power as a force: A new paradigm to accurately monitor optical power during laser-based machining operations,” Proc. SPIE 9741, L1–L8 (2016).

Stimler, M.

M. Stimler, Z. I. Slawsky, and R. E. Grantham, “Torsion Pendulum Photometer,” Rev. Sci. Instrum. 35(3), 311–313 (1964).
[Crossref]

Stirling, J.

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

Villate, D.

C. Crespy, D. Villate, M. Soscia, F. Coste, and R. Andre, “RLCYC 75: a 2 kW electrically calibrated laser calorimeter designed for Laser MegaJoule diagnostics calibration,” Metrologia 50(1), 37–48 (2013).
[Crossref]

Wherrett, B. S.

Wilkinson, P. R.

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, “Determination of a cantilever’s mechanical impedance using photon momentum,” Appl. Phys. Lett. 102(18), 184103 (2013).
[Crossref]

Williams, P.

P. Williams, J. Sowards, and B. Simonds, “Measuring Laser Beam Welding Power Using the Force of Light,” Weld. J. 95, 30–34 (2016).

P. Williams, B. Simonds, J. Sowards, and J. Hadler, “Measuring laser power as a force: A new paradigm to accurately monitor optical power during laser-based machining operations,” Proc. SPIE 9741, L1–L8 (2016).

Williams, P. A.

Yuan, Y. P.

Y. P. Yuan, “A New Pulse Laser Energy Meter,” Rev. Sci. Instrum. 61(6), 1743–1746 (1990).
[Crossref]

Appl. Phys. Lett. (3)

D. K. Ma, J. L. Garrett, and J. N. Munday, “Quantitative measurement of radiation pressure on a microcantilever in ambient environment,” Appl. Phys. Lett. 106(9), 091107 (2015).
[Crossref]

J. Melcher, J. Stirling, F. G. Cervantes, J. R. Pratt, and G. A. Shaw, “A self-calibrating optomechanical force sensor with femtonewton resolution,” Appl. Phys. Lett. 105(23), 233109 (2014).
[Crossref]

P. R. Wilkinson, G. A. Shaw, and J. R. Pratt, “Determination of a cantilever’s mechanical impedance using photon momentum,” Appl. Phys. Lett. 102(18), 184103 (2013).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

R. L. Smith, T. W. Russell, W. E. Case, and A. L. Rasmussen, “Calorimeter for High-Power CW Lasers,” IEEE Trans. Instrum. Meas. 21(4), 434–438 (1972).
[Crossref]

J. Opt. Soc. Am. B (1)

Metrologia (2)

C. Crespy, D. Villate, M. Soscia, F. Coste, and R. Andre, “RLCYC 75: a 2 kW electrically calibrated laser calorimeter designed for Laser MegaJoule diagnostics calibration,” Metrologia 50(1), 37–48 (2013).
[Crossref]

V. Nesterov, M. Mueller, L. L. Frumin, and U. Brand, “A new facility to realize a nanonewton force standard based on electrostatic methods,” Metrologia 46(3), 277–282 (2009).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (1)

E. E. Nichols and G. F. Hull, “The pressure due to radiation,” Phys. Rev. 17, 25 (1903).

Proc. SPIE (1)

P. Williams, B. Simonds, J. Sowards, and J. Hadler, “Measuring laser power as a force: A new paradigm to accurately monitor optical power during laser-based machining operations,” Proc. SPIE 9741, L1–L8 (2016).

Rev. Sci. Instrum. (2)

Y. P. Yuan, “A New Pulse Laser Energy Meter,” Rev. Sci. Instrum. 61(6), 1743–1746 (1990).
[Crossref]

M. Stimler, Z. I. Slawsky, and R. E. Grantham, “Torsion Pendulum Photometer,” Rev. Sci. Instrum. 35(3), 311–313 (1964).
[Crossref]

Weld. J. (1)

P. Williams, J. Sowards, and B. Simonds, “Measuring Laser Beam Welding Power Using the Force of Light,” Weld. J. 95, 30–34 (2016).

Other (8)

F. C. Maring, “High resolution offset electronic weighing devices and methods,” U.S. Patent 7,315,003 B2 (2008).

J. J. Cook, W. L. Flowers, and C. B. Arnold, “Measurement of Laser Output by Light Pressure,” Proc. IRE 50, 1693 (1962).

F. Brandt, H. Lecher, and S. Kuck, “Traceable measurement of high laser power in the 1-um spectral range,” in NewRad 2014, (Helsinki, 2014), pp. 269–271.

J. A. Hadler, C. L. Cromer, and J. H. Lehman, NIST Measurement Services: cw Laser Power and Energy Calibrations at NIST, NIST Special Publication (2007), Vol. 250–75.

C. L. Cromer, X. Li, J. H. Lehman, and M. L. Dowell, “Absolute high-power laser measurements with a flowing water power meter,” in 11th Conference on New Developments and Applications in Optical Radiometry, (Maui, 2011), pp. 180–181.

J. C. Maxwell, A Treatise on Electricity and Magnetism, 1st ed. (Oxford University, 1873).

B. N. Taylor and C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurement results, NIST Technical Note 1297 (1994).
[Crossref]

X. Li, J. A. Hadler, C. L. Cromer, J. H. Lehman, and M. L. Dowell, NIST Measurement Services: High power laser calibrations at NIST, NIST Special Publication 250–77 (2008).

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 (7)

Fig. 1
Fig. 1 Schematic of radiation pressure power meter (RPPM). The complete meter fits within a cube of roughly 30 cm on each side.
Fig. 2
Fig. 2 Calibration discrepancy (disagreement between the mass measured by the scale and the mass’s calibrated value). The mass is reported in mg and the equivalent optical power in watts. Error bars are dominated by measurement repeatability and not by mass artifact calibration uncertainty.
Fig. 3
Fig. 3 (a) Raw scale response (in mass units) for a 125 s laser injection at nominally 10 kW power. The mass offset on the scale reading is arbitrary. Heating of the scale and its housing cause the upward slope visible and indicated by the blue dashed line. (b) Corrected measurement from (a) scaled to units of optical power using Eq. (1).
Fig. 4
Fig. 4 Standard deviation of repeated RPPM measurements of CW laser power (circles). Solid line is Eq. (3) with σp = 10 W and γT = 0.001. The low value of the 750 W point (second from left) is attributed to quiet measurement conditions. Removing this point does not significantly alter the fitting coefficients.
Fig. 5
Fig. 5 (a) Traditional setup for high-accuracy laser power meter calibration. (b) Calibration scenario used for simultaneous comparison of the radiation pressure power meter. (c) expanded view of the standard used in the validation test including a reflective chopper to attenuate light before the thermopile.
Fig. 6
Fig. 6 Radiation pressure power meter (red solid) and thermopile (blue dashed) measurements of injected power (a) nominally 2 kW injected power and (b) nominally 10 kW.
Fig. 7
Fig. 7 Measured percent difference Δρ (circles) between RPPM and thermopile versus injected power. Expanded relative uncertainties are: RPPM (blue error bars) and thermopile (red dashed line).

Tables (1)

Tables Icon

Table 1 RPPM measurement uncertainties.

Equations (4)

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

P = c F / 2 r   c o s ( θ ) ,
u s t a t = ( σ p P ) 2 + γ T 2   .
u s t a t = ( σ p P 60 Δ t ) 2 + γ T 2   .
2 U ( P , Δ t ) = 2 u s c a l e 2 + u H V 2 + u m i r r o r 2 + u a n g l e 2 + ( σ p P 60 Δ t ) 2 + γ T 2 ,

Metrics