Abstract

A straightforward method for estimating the position of the optical receiving plane of a spherical, dome-shaped diffuser from its spatial responsivity data is presented. The method is tested with two diffusers, types J1002 and J1015 from CMS Schreder, commonly used in solar UV spectroradiometers. The shift of the receiving plane from its nominal position determines a potential measurement error that occurs when measurements and calibrations are carried out with sources at different distances from the diffuser. Such information is particularly valuable for voluminous solar UV monitoring spectroradiometers that cannot easily be transported to laboratory calibrations. The results suggest that systematic measurement errors are at least of the order of 1%, if the position of the receiving plane is not properly taken into account, thus indicating a need to study the effect more carefully. This method can also be used to minimize measurement errors when designing diffusers.

© 2009 Optical Society of America

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References

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  1. G. Bernhard and G. Seckmeyer, Photochem. Photobiol. 65, 923 (1997).
    [CrossRef]
  2. J. G. Schreder, M. Blumthaler, and M. Huber, Internet Photochem. Photobiol. (1998), http://www.photobiology.com/UVR98/schreder/index.htm, retrieved September 29, 2009.
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    [CrossRef] [PubMed]
  4. J. Hovila, M. Mustonen, P. Kärhä, and E. Ikonen, Appl. Opt. 44, 5894 (2005).
    [CrossRef] [PubMed]
  5. P. Manninen, J. Hovila, L. Seppälä, P. Kärhä, L. Ylianttila, and E. Ikonen, Metrologia 43, S120 (2006).
    [CrossRef]
  6. J. Gröbner and M. Blumthaler, Opt. Lett. 32, 80 (2007).
    [CrossRef]
  7. G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
    [CrossRef]
  8. P. Manninen, P. Kärhä, and E. Ikonen, Appl. Opt. 47, 4714 (2008).
    [CrossRef] [PubMed]
  9. K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
    [CrossRef]

2008 (3)

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

P. Manninen, P. Kärhä, and E. Ikonen, Appl. Opt. 47, 4714 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

P. Manninen, J. Hovila, L. Seppälä, P. Kärhä, L. Ylianttila, and E. Ikonen, Metrologia 43, S120 (2006).
[CrossRef]

2005 (1)

2003 (1)

1997 (1)

G. Bernhard and G. Seckmeyer, Photochem. Photobiol. 65, 923 (1997).
[CrossRef]

Arola, A.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Bernhard, G.

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

G. Bernhard and G. Seckmeyer, Photochem. Photobiol. 65, 923 (1997).
[CrossRef]

Blumthaler, M.

J. Gröbner and M. Blumthaler, Opt. Lett. 32, 80 (2007).
[CrossRef]

J. G. Schreder, M. Blumthaler, and M. Huber, Internet Photochem. Photobiol. (1998), http://www.photobiology.com/UVR98/schreder/index.htm, retrieved September 29, 2009.

Booth, C. R.

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

Ehramjian, J. C.

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

Gröbner, J.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

J. Gröbner and M. Blumthaler, Opt. Lett. 32, 80 (2007).
[CrossRef]

J. Gröbner, Appl. Opt. 42, 3516 (2003).
[CrossRef] [PubMed]

Heikkilä, A.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Hovila, J.

P. Manninen, J. Hovila, L. Seppälä, P. Kärhä, L. Ylianttila, and E. Ikonen, Metrologia 43, S120 (2006).
[CrossRef]

J. Hovila, M. Mustonen, P. Kärhä, and E. Ikonen, Appl. Opt. 44, 5894 (2005).
[CrossRef] [PubMed]

Huber, M.

J. G. Schreder, M. Blumthaler, and M. Huber, Internet Photochem. Photobiol. (1998), http://www.photobiology.com/UVR98/schreder/index.htm, retrieved September 29, 2009.

Hülsen, G.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Ikonen, E.

Johnston, P.

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

Kärhä, P.

Kaurola, J.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Koskela, T.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Kotkamp, M.

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

Kyrö, E.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Lakkala, K.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Lindfors, A.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Manninen, P.

P. Manninen, P. Kärhä, and E. Ikonen, Appl. Opt. 47, 4714 (2008).
[CrossRef] [PubMed]

P. Manninen, J. Hovila, L. Seppälä, P. Kärhä, L. Ylianttila, and E. Ikonen, Metrologia 43, S120 (2006).
[CrossRef]

McKenzie, R. L.

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

Meinander, O.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Mustonen, M.

Nichol, S. E.

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

Schreder, J. G.

J. G. Schreder, M. Blumthaler, and M. Huber, Internet Photochem. Photobiol. (1998), http://www.photobiology.com/UVR98/schreder/index.htm, retrieved September 29, 2009.

Seckmeyer, G.

G. Bernhard and G. Seckmeyer, Photochem. Photobiol. 65, 923 (1997).
[CrossRef]

Seppälä, L.

P. Manninen, J. Hovila, L. Seppälä, P. Kärhä, L. Ylianttila, and E. Ikonen, Metrologia 43, S120 (2006).
[CrossRef]

Tanskanen, A.

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

Wood, S.

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

Ylianttila, L.

P. Manninen, J. Hovila, L. Seppälä, P. Kärhä, L. Ylianttila, and E. Ikonen, Metrologia 43, S120 (2006).
[CrossRef]

Appl. Opt. (3)

Atmos. Chem. Phys. (1)

K. Lakkala, A. Arola, A. Heikkilä, J. Kaurola, T. Koskela, E. Kyrö, A. Lindfors, O. Meinander, A. Tanskanen, J. Gröbner, and G. Hülsen, Atmos. Chem. Phys. 8, 3369 (2008).
[CrossRef]

J. Geophys. Res. (1)

G. Bernhard, R. L. McKenzie, M. Kotkamp, S. Wood, C. R. Booth, J. C. Ehramjian, P. Johnston, and S. E. Nichol, J. Geophys. Res. 113, D14310 (2008).
[CrossRef]

Metrologia (1)

P. Manninen, J. Hovila, L. Seppälä, P. Kärhä, L. Ylianttila, and E. Ikonen, Metrologia 43, S120 (2006).
[CrossRef]

Opt. Lett. (1)

Photochem. Photobiol. (1)

G. Bernhard and G. Seckmeyer, Photochem. Photobiol. 65, 923 (1997).
[CrossRef]

Other (1)

J. G. Schreder, M. Blumthaler, and M. Huber, Internet Photochem. Photobiol. (1998), http://www.photobiology.com/UVR98/schreder/index.htm, retrieved September 29, 2009.

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Figures (2)

Fig. 1
Fig. 1

Geometric parameters in determining the location of the effective optical receiving plane of a spherical diffuser with a dome surrounded by a planar diffusing surface. The thick line describes the surface of the diffusing material. R 0 is the radius of the diffuser, r 0 is the radius of curvature of the diffuser dome, and θ 0 is the opening angle of the dome. The origin of the coordinates is on the symmetry axis at depth r 0 from the top of the diffuser. The geometric distance offset of the diffuser is defined as Δ d g = r 0 d eff .

Fig. 2
Fig. 2

Relative spatial responsivity S ( r ) of (a) a Bentham spectroradiometer equipped with diffuser J1002 and (b) Brewer spectroradiometers #037 and #107 equipped with diffuser J1015. The solid lines show the height profiles d ( r ) of the diffusers.

Equations (3)

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d eff = A d ( r ) S ( r ) d A A S ( r ) d A ,
d ( r ) = { r 0 2 r 2 , when r [ 0 , r 0 sin θ 0 ] r 0 cos θ 0 , when r [ r 0 sin θ 0 , R 0 ] } ,
S ( r ) = i = 0 N c i r i ,

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