Abstract
We analyze the symmetry properties of the focal plane distribution when light is focused with an element characterized by a periodic angular dependent phase, sin (mφ) or cos (mφ). The majority of wave aberrations can be described using the said phase function. The focal distribution is analytically shown to be a real function at odd values of m, which provides a simple technique for generating designed wave aberrations by means of binary diffractive optical elements. Such a possibility may prove useful in tight focusing, as the presence of definite wave aberrations allows the focal spot size to be decreased. The analytical computations are illustrated by the numerical simulation, which shows that by varying the radial parameters the focal spot configuration can be varied, whereas the central part symmetry is mainly determined by the parity of m: for even the symmetry order is 2m and for odd is m.
Highlights
Various aberrations in the focusing system are known to result in a wider, distorted focal spot with disturbed axial symmetry [1]
The analytical computations are illustrated by the numerical simulation, which shows that by varying the radial parameters the focal spot configuration can be varied, whereas the central part symmetry is manily determined by the even value of the angular parameter m
We have analyzed symmetry properties of the light distribution generated in the focal plane by focusing the light beam with a periodic angular dependent phase given by sin(mφ) or cos(mφ)
Summary
Various aberrations in the focusing system are known to result in a wider, distorted focal spot with disturbed axial symmetry [1] Such an effect is normally considered to be a negative factor. We analyze symmetry properties of the distribution formed in the focal plane by an optical element characterized by a periodic angular dependent phase function in the form of sin(mφ) or cos(mφ). Based on this phase relation, it is possible to describe the majority of wave aberrations, which can be represented [14] as the decomposition in terms of Zernike functions [1]. The analytical computations are illustrated by the numerical simulation, which shows that by varying the radial parameters the focal spot configuration can be varied, whereas the central part symmetry is manily determined by the even value of the angular parameter m
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