Abstract

It is difficult to predict where the effective measurement plane is situated with dome-shaped diffusers often used in commercial photometers and radiometers. Insufficient knowledge of this plane could lead to large systematic errors in calibration of the illuminance responsivity of photometers. We propose a method that can be used to determine this reference plane accurately, based on the inverse-square law between the measured signal and the distance from the source. The method is demonstrated with three commercial photometers with dome-shaped diffusers of different geometries. By taking into account the measured shifts of the reference planes (5.0 ± 0.5 mm, 7.8 ± 0.3 mm, and 8.5 ± 0.7 mm), we reduced the systematic measurement errors up to 2% to statistical uncertainty components at the level of 0.2%.

© 2005 Optical Society of America

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References

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  1. Y. Ohno, “Photometric Calibrations,” NIST (Natl. Inst. Stand. Technol.) spec. Publ.250–37 (U.S. Government Printing Office, 1997).
  2. T. M. Goodman, P. J. Key, “The NPL radiometric realization of the candela,” Metrologia 25, 29–40 (1988).
    [CrossRef]
  3. C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
    [CrossRef]
  4. P. Toivanen, P. Kärhä, F. Manoochehri, E. Ikonen, “Realization of the unit of luminous intensity at the HUT,” Metrologia 37, 131–140 (2000).
    [CrossRef]
  5. L. P. Boivin, “Environmental corrections in absolute radiometry,” in Absolute Radiometry, 1st ed., J. Hengstberger, ed. (Academic, 1989).
    [CrossRef]
  6. H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997).

2000 (1)

P. Toivanen, P. Kärhä, F. Manoochehri, E. Ikonen, “Realization of the unit of luminous intensity at the HUT,” Metrologia 37, 131–140 (2000).
[CrossRef]

1996 (1)

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

1988 (1)

T. M. Goodman, P. J. Key, “The NPL radiometric realization of the candela,” Metrologia 25, 29–40 (1988).
[CrossRef]

Boivin, L. P.

L. P. Boivin, “Environmental corrections in absolute radiometry,” in Absolute Radiometry, 1st ed., J. Hengstberger, ed. (Academic, 1989).
[CrossRef]

Cromer, C. L.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Eppeldauer, G.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Goodman, T. M.

T. M. Goodman, P. J. Key, “The NPL radiometric realization of the candela,” Metrologia 25, 29–40 (1988).
[CrossRef]

Hardis, J. E.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Ikonen, E.

P. Toivanen, P. Kärhä, F. Manoochehri, E. Ikonen, “Realization of the unit of luminous intensity at the HUT,” Metrologia 37, 131–140 (2000).
[CrossRef]

Kärhä, P.

P. Toivanen, P. Kärhä, F. Manoochehri, E. Ikonen, “Realization of the unit of luminous intensity at the HUT,” Metrologia 37, 131–140 (2000).
[CrossRef]

Key, P. J.

T. M. Goodman, P. J. Key, “The NPL radiometric realization of the candela,” Metrologia 25, 29–40 (1988).
[CrossRef]

Kostkowski, H. J.

H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997).

Larason, T. C.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Manoochehri, F.

P. Toivanen, P. Kärhä, F. Manoochehri, E. Ikonen, “Realization of the unit of luminous intensity at the HUT,” Metrologia 37, 131–140 (2000).
[CrossRef]

Ohno, Y.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Y. Ohno, “Photometric Calibrations,” NIST (Natl. Inst. Stand. Technol.) spec. Publ.250–37 (U.S. Government Printing Office, 1997).

Parr, A. C.

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Toivanen, P.

P. Toivanen, P. Kärhä, F. Manoochehri, E. Ikonen, “Realization of the unit of luminous intensity at the HUT,” Metrologia 37, 131–140 (2000).
[CrossRef]

J. Res. Natl. Inst. Stand. Technol. (1)

C. L. Cromer, G. Eppeldauer, J. E. Hardis, T. C. Larason, Y. Ohno, A. C. Parr, “The NIST detector-based luminous intensity scale,” J. Res. Natl. Inst. Stand. Technol. 101, 109–132 (1996).
[CrossRef]

Metrologia (2)

P. Toivanen, P. Kärhä, F. Manoochehri, E. Ikonen, “Realization of the unit of luminous intensity at the HUT,” Metrologia 37, 131–140 (2000).
[CrossRef]

T. M. Goodman, P. J. Key, “The NPL radiometric realization of the candela,” Metrologia 25, 29–40 (1988).
[CrossRef]

Other (3)

Y. Ohno, “Photometric Calibrations,” NIST (Natl. Inst. Stand. Technol.) spec. Publ.250–37 (U.S. Government Printing Office, 1997).

L. P. Boivin, “Environmental corrections in absolute radiometry,” in Absolute Radiometry, 1st ed., J. Hengstberger, ed. (Academic, 1989).
[CrossRef]

H. J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, 1997).

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Figures (4)

Fig. 1
Fig. 1

Schematic drawings of the investigated diffusers. Dimensions of the diffusers in the drawings are as follows. (a) D = 24.3 mm, L = 8.0 mm, (b) D = 16.0 mm, L = 7.1 mm, (c) D = 30.0 mm, L = 15.0 mm, W = 26.1 mm.

Fig. 2
Fig. 2

Results of repeated measurements to determine the distance offset ΔdS of the light source with three different reference photometers. Vertical bars indicate the standard deviation of the results for each photometer.

Fig. 3
Fig. 3

Original (crosses) and new (circles) correction factors for the photometer with diffuser (b) in Fig. 1.

Fig. 4
Fig. 4

Coordinate system for the calculation of the distance offset from the geometry.

Tables (1)

Tables Icon

Table 1 Measured Distance Offsets ΔdP of the Reference Planes of the Diffusersa

Equations (8)

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E v = I v / ( d + Δ d S + Δ d P ) 2 ,
E v , test = E v , ref [ ( d + Δ d S ) / ( d + Δ d S + Δ d P ) ] 2 ,
Δ d C = r 0 [ 1 - 2 3 ( 1 - cos 3 θ 0 ) / sin 2 θ 0 ]
Δ d C = R 0 [ 1 - 1 4 ( 2 Θ 0 + sin 2 Θ 0 ) / sin Θ 0 ] ,
r ( θ ) = d + Δ d S + r 0 - r 0 cos θ
d A = 2 π r 0 2 sin θ cos θ d θ .
E C = [ I v / r 2 ( θ ) ] d A d A = 2 I v ( d + Δ d S + r 0 ) 2 sin 2 θ 0 × 0 θ 0 sin θ cos θ d θ [ 1 - r 0 cos θ / ( d + Δ d S + r 0 ) ] 2 ,
E C = I v [ d + Δ d S + r 0 - 2 / 3 r 0 ( 1 - cos 3 θ 0 ) / sin 2 θ 0 ] 2 .

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