Combination pupil filter enables efficient superresolution

July 1, 2005
The point-spread function (PSF) of an optical system can be altered by inserting a spatially varying filter at the pupil plane; if the filter is properly designed, the width of the central peak of the PSF can be narrowed.

The point-spread function (PSF) of an optical system can be altered by inserting a spatially varying filter at the pupil plane; if the filter is properly designed, the width of the central peak of the PSF can be narrowed. In real terms, this means that the focused spot of a laser beam, for example, can be made smaller without increasing the numerical aperture of the system.

So why doesn’t every focusing lens include a filter like this? The answer is that, although the spot can be made smaller, the shrinkage comes at the expense of intensity. A pupil filter-which can have spatial variations in amplitude, phase, or both-invariably shifts much of the energy from the central spot to the outlying diffraction rings (for a phase version) or absorbs almost all the light (for an amplitude version). But the resulting “superresolved” spot, though lower in intensity, can be useful for measurement ­purposes such as scanning microscopy or for boosting the displacement sensitivity of the spot on a quadrant detector. Pupil filters can also be used to sharpen astronomical images of stars.

A focused spot of 532-nm laser light has a diameter of 1540 µm (left). When a combination of phase and amplitude pupil filters is inserted into the optical system, the spot size is reduced to 990 µm while maintaining a Strehl ratio of about 0.1 and relatively low side-lobe intensities (right).
Click here to enlarge image

Two things are desirable in a superresolving pupil filter. One is a relatively high Strehl ratio and the other is a high ratio of the peak intensity to the intensity of the first side lobe, also known as gamma (Γ). Conventional amplitude filters can have a Γ of 7 when producing small spots (less than 0.7 the size of the original), but suffer a Strehl ratio of 1 × 10-3 or less; phase filters can achieve a Strehl ratio of 0.2 but may have a Γ of only about 2. Now, researchers at EMPA (Dubendorf, Switzerland) and the Ecole Polytechnique Fédérale de Lausanne (Lausanne, Switzerland) have developed a complex (both phase and amplitude) pupil filter that achieves a good Strehl ratio and a high Γ at the same time.1

The researchers first modeled conventional amplitude filters with continuously varying transmission profiles and phase filters with radial zones, determining their properties. They then modeled a combination filter consisting of a three-zone phase filter and a continuous amplitude filter, which could produce a spot 64% the diameter of the original while maintaining a Γ of 4 and shifting less of the energy into the side lobes than would an all-phase filter.

SLM setup

To realize the filter experimentally, the researchers used two spatial light modulators (SLMs), one for phase (up to π rad) and one for amplitude (intensity variation of up to 96%). Proper orientation of polarizers ensured phase- and amplitude-only operation for the two different SLMs, each of which had an 832 × 624-pixel resolution. An optical system containing two separate pupil planes allowed easy placement of the SLMs. Laser light at 532 nm was sent through the system; a CCD camera with an 11-μm pixel spacing captured the spot.

Without the filters, the spot was measured to be 1540 μm in size. With the filters, the spot shrank to 990 μm in size (64% of the original; see figure). The Strehl ratio was about 0.1, according to Phanindra Gundu, one of the researchers. In addition, the Γ was about 4-a combination of characteristics that will boost the efficiency of superresolution via pupil filtering.


1. P. N. Gundu et al., Optics Express13(8) (April 18, 2005).

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