Angular Response Correction Procedure
angular cosine response

Last Updated: January 12, 2015

The instrument's most recent cosine responses, determined in the laboratory of the testing agency prior to the date of the data being corrected, are used.

The laboratory measurements are used to derive a single correction factor for any combination of solar azimuth and elevation angle. In the laboratory, measurements are made for light incident from directions along axes aligned in the south to north and west to east directions relative to the orientation of the instrument as it is in the field. Measurements are made as the instrument is rotated in 1 degree increments relative to the incoming beam along each of these axes.

Cosine correction values are formed using the solar elevation angle in an interpolation scheme to mix the laboratory values in the SN and WE tables. In order to specify which portions of the SN and WE tables to mix, the laboratory measurements are first grouped in pairs according to quadrant of solar azimuth angle. Quadrants of the solar azimuth angles are indexed from 0 to 3 by taking the integer part of the solar azimuth angle divided by 90 degrees. This division is represented in the table below. When the cosine correction values are downloaded into a .csv or MS EXCEL file, 14 rows of 179 values are available. The first seven rows are for the SN direction, one row for each wavelength channel, and the second seven rows for the WE direction. Cosine correction data in each row are ordered by the angle from the vertical to the direction of incident radiation along the SN or WE axes. In each row the values start with the measurements near the instrument horizon along the SN direction, the first value being the SN M89 value where M represents the minus direction from vertical. The row ends with the SN P89 value where the P represents positive values or values near the north horizon. For example, in the SN portion (top seven rows of the downloaded data) , SN P15 refers to the laboratory data measured for light incident 15 degrees from the normal to the instrument in the positive direction (north), while WE M45 refers to a direction of light incident 45 degrees off the vertical from the west. Note that west and south are considered as negative directions. Light vertically incident is identified as P0. All laboratory values are normalized by the value at P0 so P0 is always unity. As mentioned above, the table below is used to group two portions of the coordinate axes for use in the mixing or interpolation of SN and WE measurements to determine the cosine correction for any incident solar zenith and azimuth. To download the cosine correction data please see our Download section under Instrument Characteristics .

Quadrant IndexSolar Aximuth AngleAxis 1Axis 2
00 - 89SN P89 - P0WE P89 - P0
190 - 179WE P89 - P0SN M89 - P0
2180 - 269SN M89 - P0WE M89 - P0
3270 - 359WE M89 - P0SN P89 - P0

In the simplest case we assume that the solar elevation and azimuth angles are integer degrees so we can use these values as pointers to count along the portions of the axes shown in the Axis1 and Axis2 columns. But first, two weighting factors awt2 and awt1, are determined. Awt2 is just the fractional weight given to the leg of the axis named in the Axis2 column; awt2 = fractional part of (solar azimuth / 90.0). Awt1 weights the contribution from the leg of the axis indicated in the Axis1 column, and; awt1 = 1.0 – awt2. Next, using the solar azimuth to choose the quadrant row in the table, the cosine correction is simply given as: c = r1 x awt1 + r2 x awt2., where r1 and r2 represent the responses obtained by starting at the positions identified in the Axis1 and Axis2 columns and counting forward from the M directions or backward from the P direction by a count equal to the elevation angle. For example if the solar azimuth and elevation are 120 and 35 degrees respectively, one would use the starting points WE P89 and SN M89 and find r1 and r2 in the 35th positions from the ends (WE P89 SN M89). Note that this requires indexing backward from the P ends of the axes. The actual process is slightly more complicated in that linear interpolation is used to account for the fractional parts of the solar elevation angle. Please contact UVMRP for a more complete description of the process.

If the raw direct component voltage is greater than 0.00009, divide it by the correction factor. Otherwise, no correction is made.