Quality of the diffuser

Quality factors: Relative cosine error, Q and DCE

Relative cosine error

The quality of the diffuser is defined with the following quality factors.

The "relative cosine error" is defined by:

Q correction factor

Q is a correction factor for isotropic radiation:

This factor 'Q' is greater than 1 if the diffuser overestimates and less than 1 if the diffuser underestimates.

Diffuse Cosine Error (DCE)

The "Diffuse Cosine Error" shows the actual quality of the cosine response response.

Physical meaning of the DCE: If the diffuser has a perfect cosine response this factor will be zero. If there are cosine errors they are expressed as a percentage of the ideal cosine response.

The DCE does not show the sense of the error (ie whether "under-" or "over-estimating").

DCE versus "f2"

The DCE is quite simular to the "f2" error described in DIN standards . The difference between these two is that the DCE’s integration interval is Solar Zenith Angle (SZA)= -pi/2 to +pi/2 whereas the "f2"’s integration interval is SZA= 0 to +0.47pi. The " f2" error assumes that there are no errors between 0.47pi and 0.5pi and makes the assumption that the relative cosine error is the same for SZA = -0.47pi to 0 and for SZA = 0 to +0.47pi. Most often this is not true. Practical examples are azimuth errors and alignment errors. The "f2" error does not show these errors or does not show these errors in the right way. The DCE has a better probability of showing these errors. A graph of the relative error for SZA= -pi/2 to +pi/2 together with Q and the DCE pr oves to be of great practical value.


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Emeritus Researcher – Atmospheric Radiation