LCD pixel shape and far field diffraction patterns - Páginas de ...

268ARTICLE IN PRESSM. Fernández Guasti et al. / Optik 116 (2005) 265–269Fig. 4. Diffraction pattern of squircle with s ¼ 0:9; contourplot for iso-amplitudes shown on the top and 3D mesh withheight representing the field amplitude on the bottom.Fig. 5. Image of a single LCD pixel (top) and the correspondingdiffraction pattern in the far field (bottom).frequencies on the aperture have stronger influence onhigher-order rings or further away from the axis in thediffraction pattern [7].Let us now exhibit the images and diffraction patternsobtained with the LCD mask. The microscope image ofa single LCD pixel together with its far-field diffractionpattern is shown in Fig. 5. The low resolution of thetraveling microscope yields an image whose squarishshape may only be approximately guessed from thephotograph. However, comparison of the diffractionpattern of the pixel with the previous patterns showsthat the pixel is not a perfect square with sharp corners.The most similar diffraction image is 3c, which indicatesthat the pixel has blunt corners with a squarenessparameter around s ¼ 0:9: The reference wavefront in aPDI will have this pattern when implemented with anLCD pixel of this type. Departure from the point sourcecircular symmetry is expected even if only the centralportion is considered as may be seen from the contourplot in Fig. 4. This discrepancy with the sphericalwavefront should then be taken into account so that it isnot associated, for example, with aberrations of anoptical system under test.In Fig. 6, the image and diffraction pattern of anarray of nine apertures are shown. The contribution ofthe square pixels blunt corners is still clear in thediffraction pattern. On the one hand, full rings ratherthan the spots expected from the square array are clearlyvisible. On the other hand, the rings are not circular butare flattened at 45 from the Cartesian axes. Furthermore,the rings are more intense in the regions whereperfect squares would exhibit their maxima. Thediffraction pattern, according to Fourier optics theory,should correspond to the convolution of the single pixelaperture that is shifted to the other eight positions in theaperture plane.5. ConclusionsThe far-field diffraction from apertures whose shapelies between a square and a circle has been experimentallystudied. The main features of the observeddiffraction patterns are qualitatively in accordance withpreviously reported computer simulations. From atopological point of view, these results no longer exhibitthe square and the circle as isolated aperture cases but asa continuous deformation, which may be tackled withnumerical evaluations that can be qualitatively comparedwith experimental observations.