Uncertainty analysis of photometer directional response index f₂ using Monte Carlo simulation

The uncertainty of the photometer directional response index f₂ is investigated using Monte Carlo simulations and error models derived for the characterization measurements of three photometers. Both random and biased types of errors are used simultaneously to model the measurement noise, drift of the light source, alignment of the photometer, and the errors of the rotary stage. The values of f₂ obtained for each azimuth angle of the photometer are sensitive to the asymmetry of the directional response. It is shown by variation of the photometer symmetry that the changes in the value of f₂ calculated as an average of all simulated values are small. It is further demonstrated that with typical measurement distances the quality index f₂ can be sensitive to the position of the axis of rotation with respect to the receiving plane of the photometer. The simulated f₂ values of the three photometers with expanded uncertainties (k = 2) are (4.325 ± 0.035)%, (1.698 ± 0.027)% and (4.315 ± 0.030)%.