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Programmable vector point-spread function engineering

Michael R. Beversluis, Lukas Novotny, and Stephan J. Stranick

Open Access Open Access

Abstract

We use two nematic liquid crystal spatial light modulators (SLM’s) to control the vector point spread function (VPSF) of a 1.3 numerical aperture (NA) microscope objective. This is achieved by controlling the polarization and relative phase of the electric field in the objective’s pupil. We measure the resulting VPSF’s for several different pupil field polarization states. By using single fluorescent molecules as local field probes, we are able to map out the focal field distributions and polarization purity of the synthesized fields. We report the achieved field purity and address the experimental issues that currently limit it.

©2006 Optical Society of America

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Figures (3)
Fig. 1.
Fig. 1. VPSF experimental schematic drawing using a 1.3 NA oil-immersion objective fluorescence microscope. Each SLM is located in an image plane of the objective’s pupil. (ND = Neutral Density filter, Pol. = polarizer, λ/2 = half-wave plate, λ/4 = quarter-wave plate, Ex. and Em. = excitation and emission filters, respectively, and APD=Avalanche Photodiode.)

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Fig. 2.
Fig. 2. Successive images of a single molecule sample for pupil polarizations that are: (A) Linear polarized along x (horizontally), (B) azimuthally-polarized, and (C) radially-polarized. The field of view is 10 microns square.

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Fig. 3.
Fig. 3. A comparison of theoretical and experimental images for pupil polarizations that are: (A) Linear along x̂, (B) azimuthally-polarized, and (C) radially-polarized. Each image is 2 microns square and has been displayed with a normalized gray scale.

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

T xy = exp ( − i θ xy / 2 ) 2 1 − i − i 1 exp ( − i θ xy / 2 ) 0 0 exp ( i θ xy / 2 ) 1 i i 1
· exp ( − i ϕ xy / 2 ) 0 0 exp ( i ϕ xy / 2 )
= exp [ − i ( ϕ xy + θ xy / 2 ) ] cos ⁡ ( θ xy / 2 ) sin ⁡ ( θ xy / 2 ) − sin ⁡ ( ϕ xy / 2 ) cos ⁡ ( θ xy / 2 )
E ( r ) ∝ ∬ Ω E ref ( s ) s z e is · r d s
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