Applications of a Birefringent Lens as an Optical Image Processing Device

Introduction

The pupil function plays an important role in the final image formation by an optical system. The fact can be understood as some of the image assessment parameters such as the point spread function (PSF), the optical transfer function (OTF) etc. are directly related to the pupil function. Many researchers reported that an imaging system may exhibit an appropriate behavior by modifying either the amplitude or phase or both of the pupil function. An appropriate coating of metal or dielectrics on the pupil may reduce the size of the central spot of the point spread function which in turn may increase the resolving power of the system (Luneberg, 1944). Suppression of the secondary maxima in the diffraction pattern using suitable apodizing masks also gives some advantages which may be utilized in spectroscopy and astronomy (Jacquinot & Roizen-Dossier, 1964). Some researchers reported the use of an appropriate phase filter to improve the resolving power (Osterberg & Wilkins, 1949, 1950; Lit, 1971). A special type of phase filter, known as Walsh filter was also reported for increasing resolution in microscopic imaging (Hazra, 2006).

In some applications such as automatic inspection in microelectronics industry, medical imaging and microscope imagery, imaging systems with high focal depth are required. The use of annular apertures and apodizers for increasing the focal depth as well as reducing spherical aberration was studied by some researchers (Castaneda et al., 1985, 1986, 1988, 1989, 1990). Use of phase filters to decrease the defocus and spherical aberrations was also reported by some scientists (Mezouari & Harvey, 2003).

In almost all of the above cases, the masks used are not versatile and have been utilized for some particular applications. Moreover, on-line modification of these masks and hence, imaging characteristics of the optical systems is not possible. In this connection it may be mentioned that the imaging behavior of such systems has been considered to be independent of the polarization properties of the incident light and only scalar wave theory of light has been employed to study the imaging behavior. Some scientists, however, realized that the polarization properties of light may be used as a parametric variable to modify the complex amplitude of the pupil function. Two orthogonal states of polarization control the nature of the pupil function in this case and their relative contributions can allow real-time modification of the imaging behavior of polarization-based optical systems. Kubota and Inoue (1959), and Kubota and Saito (1960) first demonstrated the application of polarization properties of light in investigating the diffraction images of a pinhole produced by a polarizing microscope with parallel and crossed nicols. Marathay (1969) suggested a versatile analytical technique to realize complex spatial filters using polarizaton properties of light and Polaroid Vectograph film to obtain the desired image. Whiting (2003) utilized polarization properties of light for achieving superresolution for an optical system. The advantage of polarization-based optical systems is that the rotation of any of the two polarizers can modify the imaging properties of the system. This makes the system more versatile for different applications.

However, polarization-based optical devices have certain inherent disadvantages. Manufacturing and proper positioning of polarization masks are very difficult and an appreciable amount of light is always absorbed and/or scattered by the masks. So, research has been carried out to address these problems. Optical imaging systems with their components made from birefringent materials may reduce the associated problems to a certain extent.