Optik 124 (2013) 729–733 Contents lists available at SciVerse ScienceDirect Optik jou rnal homepage: www.elsevier.de/ijleo Vector wave diffraction by a circular aperture using semicircular polarization mask Mohammad Tahir a,∗ , K. Bhattacharya b , A. Ghosh b a Jhikra High School (H.S), Jhikra, Joypur, Howrah 711 401, India b Department of Applied Optics and Photonics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Calcutta 700 009, India a r t i c l e i n f o Article history: Received 4 September 2011 Accepted 11 January 2012 Keywords: Semicircular aperture Polarization masking Polarization phase Intensity PSF a b s t r a c t It is well-known that the imaging properties of optical systems are determined by the diffraction proper- ties of their apertures or pupils. This enables us to study the diffraction properties of different apertures in presence of zonal masking devices. Many authors have studied the effect of circular aperture masked by circularly symmetric polarization masks. In the present paper we study the diffraction properties of a circular aperture divided into two equal semicircular apertures each of which is masked by a linear polarizer. With such masking polarizers it may be possible to compensate for asymmetric aberrations. © 2012 Published by Elsevier GmbH. 1. Introduction To modify the imaging characteristic of an optical system scalar wave properties of light are usually considered. In recent studies on the modification of the optical imaging system using the polariza- tion properties of light is highly rewarding. The most important feature of an optical system using polarization mask is that its imaging properties can be continuously varied by changing the ori- entation of an analyzer placed at the output side or by changing the state of polarization of an input beam. This flexibility is unachiev- able in system using scalar waves. The effect of polarization masks on different zones of a lens aperture for the modification of its imag- ing characteristics was studied by Chakraborty and Ghosh [1–4]. The modification of the characteristics of an optical imaging system can be largely extended by the possibility of utilizing the polariza- tion – induced phase in imaging as was shown by Bhattacharya [5,6]. It may be mentioned in this connection that recent studies have convincingly proved that the polarization properties of light can be utilized for compensating Seidel aberrations as well that has also been shown by Roychoudhury [7,8]. In Fourier optics we usually ignore the vector nature of light; because the Fraunhofer diffraction pattern of an object wave is not dependent on the polarization of the incident beam if the object itself does not alter the state of polarization of incident beam. Recently, Moreno et al. have extended the scalar Fourier optics to a vectorial theory by using Jones matrix formalism and analyzed the ∗ Corresponding author. E-mail address: mail2mdtahir@gmail.com (M. Tahir). variable intensity and polarization distribution in the Fourier plane for a typical aperture having polarizing devices used as masks [9]. As a matter of fact they have studied the variation of the state of polar- ization in the far-field pattern of a slit masked by two orthogonal polarizers. Gori et al. [10] have studied the diffraction properties of a square aperture divided into two halves each of which is masked by a linear polarizer. They have studied the case where one half of the aperture is masked by a polarizer having its transmission axis along the horizontal direction and the other half masked by a polarizer whose principal transmission axis is along the vertical direction. The system referred to above is, however, not circular symmet- ric. In our previous publications we have considered the effect of circular symmetric polarization masks on the imaging characteris- tic of a lens [11]. These systems naturally have circular symmetric optical transfer functions. In this section we consider the effects of sector shaped polarization masks on the imaging characteristic of a lens. It is well expected that an imaging system using an asym- metric aperture mask will possess imaging characteristic which is asymmetric in the sense that the PSF and OTF of such a system will be different along different azimuths. In this paper we have stud- ied the Fraunhofer diffraction pattern of a circular aperture divided into two semicircular apertures, which are masked by orthogonally oriented linear polarizers. 2. Theory In this problem we consider the far-field diffraction pattern of an elementary area element of a circular aperture over which the amplitude and phase are constant. Such an area element in Fig. 1 obviously is that area confined by the annular aperture whose 0030-4026/$ – see front matter © 2012 Published by Elsevier GmbH. doi:10.1016/j.ijleo.2012.02.001