doi:10.1016/j.micron.2006.07.011
Copyright © 2006 Elsevier Ltd All rights reserved.
Polarization phase in aberration compensation
D. Roychowdhury
, a, K. Bhattacharyaa and A.K. Chakrabortya
aDepartment of Applied Optics and Photonics, University of Calcutta, 92, A.P.C. Road, Kolkata 700 009, India
Available online 31 July 2006.
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Abstract
A phase/amplitude mask on the aperture of an imaging system results in a pupil function that is multiplicative with the lens function, resulting in a morphological transformation of the imaging wavefront. It was shown that such amplitude and phase functions can be implemented using polarization masks, with the advantage that the phase and amplitude can be controlled in real time and in some cases, independently of each other. The phase and amplitude variation over the mask can be controlled either by changing the polarization of the mask or by changing the input beam parameters. Wavefront tailoring using polarization-masked apertures is therefore feasible and may be utilized for focal shift and partial aberration compensation.
For complete compensation of aberration, the phase distribution over the mask should be conjugate to that of the phase error of the aberrant wavefront, which necessitates the use of a continuously variable polarization mask. Since such a mask is difficult to implement, we have considered polarizing masks consisting of discrete polarized zones on the lens aperture, leading to polarization phase steps on the exit pupil of the imaging system. The simulation results presented in this paper show that effects of focal shift, partial compensation of primary spherical aberration and astigmatism can indeed be achieved by the proper use of polarization masked apertures.
Keywords: Polarization phase; Aberration; Compensation
Fig. 1. The schematic diagram of the proposed optical set-up is shown in (a). The mask geometry is shown in (b). P(α) denotes a linear polarizer with its transmission oriented at an angle α to the reference abscissa. The circular symmetric aperture considered for compensation of on-axis aberration is shown in (i). The quadrant masked aperture used for compensation of astigmatism and coma is shown in (ii).
Fig. 2. Normalised axial irradiance for different values of δ for polarisation masked lens aperture. The polarisation parameters are of the system α = 0°, β = 90°, γ = 45°, and a = b = 1,
= 0.707. The values of δ for the plots are as follows: Plot O – δ = 0°, 360°, Plot A – δ = 45°, Plot B – δ = 90°, Plot C – δ = 135°, Plot D – δ = 180°, Plot E – δ = 225°, Plot F – δ = 270°, Plot G – δ = 315°.
Fig. 3. The comparison of the IPSF of a masked lens with δ = 90°, w20=−0.36λ, with that of the diffraction limited IPSF.
Fig. 4. Focal shift in μm against input beam parameter δ in degree.
Fig. 5. Variation of the Strehl ratio with w40 for different values of δ. The polarization parameters are system α = 0°, β = 90°, γ = 45°, and a = b = 1,
= 0.50. The Strehl ratio for an unmasked normal lens aperture is denoted as NRML.
Fig. 6. The IPSF of the polarization-masked lens, unmasked lens, and ideal lens for (a) δ = 60°, (b) δ = 90° and (c) δ = 120°, other parameters same as in Fig. 5.
Fig. 7. The upper half (i) shows the image of an off-axial point source formed by an unmasked lens in presence of astigmatism and the lower half shows the image of similar point source formed by a masked aperture in presence of varying degrees of astigmatism: (a) w22=3λ, (b) w22=5λ, (c) w22=7λ and (d) w22=9λ, computed at w20=−w22/2 for the system polarization parameters α1 = 0°, α2 = 90°, a/b = 1, δ = 90°, γ = 135°.