Design of a free-form diffuser for the entrance optic to correct the cosine error in the photometer

The entrance optic is an important part of the photometer head. It can match the directional response of the photometer to the cosine function. In this paper, an entrance optic consisting of a free-form diffuser, a shadow ring, and an integrating cavity is introduced. An iterative optimization algorithm is presented to design a freeform diffuser that exhibits better cosine response characteristics. Diffusers of different materials and sizes are designed in a simulation experiment. After a finite number of iterations, in the absence of the shadow ring, the integral cosine error of the free-form diffuser is less than 1%. The directional cosine error is less than 3% for incidence angles between 0° and 70°. After adding a shadow ring to correct the directional response of the incident angle greater than 80°, for incident angles between 0° and 85°, the cosine errors are typically less than 3%, except that the cosine errors of very few large incident angles are close to 5%. The experimental results show the effectiveness and robustness of the proposed method. In addition, the influence of an important percentage constant s on iterative optimization is studied. It is found that the larger the parameter s, the fewer the number of iterations, and the directional cosine error may be slightly larger but still acceptable. The wide range of values of s further embodies the versatility and flexibility of the proposed method.