An integrating sphere, which is used for colorimetry or measurements of spectral reflectance, is investigated by theoretical calculations. The calculations are made under the following assumptions. The inner surface of the sphere is a uniform diffuser. Reflectance of samples is obtained by the substitution method, in reference to standard plates which are uniform diffusers.
On the basis of the results, the errors in reflectance measurements are estimated, in cases where the screen is omitted or not and where the specular cup is provided. The effect of flat surface in the sphere can be neglected, unless the light reflected firstly by the sample enters directly the measurement window. When the screen is omitted, a smaller error cannot be expected from a smaller size of the measurement window.