This paper presents a method for sampling a ray from a distribution of rays leaving a light source to illuminate objects for measurements of bidirectional reflectance distribution function (BRDF). The BRDF measurements of real objects are required to preserve and reproduce the objects in Internet museum, telemedicine, E-commerce and so on. In conventional methods for BRDF measurements, huge measurement space is required to collimate rays from a light source to target objects. In this paper, we sample a ray from a distribution of rays leaving a light source by using a mirrored ball and a pinhole camera, and use the light source to illuminate objects from a short distance for BRDF measurements. By using a mirrored ball, the proposed method can expand a directional distribution of original rays leaving a light source. Based on this expansion, rays leaving a light source are captured at each pixel in images taken by a pinhole camera with high directional resolution. Radiant intensity and a direction of a ray from a distribution of rays leaving a light source are estimated from the taken images by using a ray tracing technique. The accuracy of the estimation in the proposed method was evaluated by a numerical simulation and the result showed an effectiveness of the proposed method. As a preliminary experiment, we measured BRDF of a real object illuminated from a short distance by the light source whose rays was sampled by the proposed method. From the measured data, we estimated diffuse reflectance of the object more accurately than conventional methods.