A novel setup for the efficient constant optical measurements of biological tissues in the near infrared is presented. The system combines the use of a fiber-based supercontinuum source with a simple optics fiber collimator. This configuration allows a wide spectral range of measurement and, at the same time, can efficiently filter the straightforward transmitted light while avoiding scattered light. As a performance example, the optical characterization of rat brain and retina tissues are shown. The attenuation coefficient for both tissues in the near infrared region is also obtained. This technique could be applied in clinical research as a noninvasive method with several potential practical applications.