Investigation of a concentric black and white hexagonal pupil and its application in confocal microscopic imaging

We constructed a new concentric black and white (B/W) hexagonal aperture, and we resized the image in a matrix of dimensions 1024 × 1024 pixels using MATLAB code. We derived a new formula for the point spread function (PSF) corresponding to the B/W hexagonal aperture. We computed the PSF using the Fast Fourier transform and compared the results with the case of a transparent hexagonal shape. In addition, we computed the coherent transfer function (CTF) for two symmetric objectives provided with the B/W hexagonal aperture. Finally, we reconstructed the image from the input object located in the confocal plane of the microscope provided with the modulated hexagonal apertures. We showed that the full width of the central lobe is smaller than that corresponding to the transparent hexagonal aperture hence improved resolution is attained in the case of B/W hexagonal aperture. In addition, we showed significant Legs of diffraction pattern corresponding to the B/W concentric hexagonal aperture. Then the PSF is dependent on the geometry of the B/W hexagonal aperture. We conclude that the image resolution which depends on the PSF is improved in the case of B/W hexagonal aperture while the image contrast is affected by the transmitted intensity in the detection plane of the confocal microscope. The coherent transfer function (CTF) or the autocorrelation corresponding to the B/W concentric hexagonal aperture has triangular decaying fringing as compared to that corresponding to the uniform hexagonal and circular apertures.