Date
2018-06-29
- On the long journey towards clearer and better laser technologies, scientists reveal previously-unsuspected aperture-induced astigmatism, and show how to remedy it -
Scientists have discovered a new property
of wave propagation, that leads to an all-new way to improve the resolution of
virtually all optical technologies, including: microscope lenses,
telecommunications, laser-based lithography, biological and astronomical
imaging. All these systems transmit information and energy through wave propagation.
Researchers at the Center for Soft and
Living Matter, within the Institute
for Basic Science (IBS, South
Korea) have discovered that, if light passes through asymmetric apertures, astigmatism
arises and can degrade image resolution. Having identified this
previously-unsuspected problem, the researchers showed how to remedy it.
As you read this article, the eye lens focuses
light from the screen to the back of the eye. However, if the lens’s horizontal
and vertical focusing power is different, this text will appear blurred: for
example, the vertical and horizontal lines, which form the letter “T” will not be
brought in focus together. To avoid this focusing defect, artificial lenses are
optimally designed to change the shape of the light wavefronts from planar into
perfectly spherical wavefronts, because it is believed that spherical
wavefronts necessarily focus at their unique center of curvature. Published in Proceedings of the National Academy of
Sciences of the USA (PNAS), this
study shows that scientists should re-examine this belief and revisit their
design strategies.
Examples of wave propagation are circular
waves created by a pebble
dropped into a pond. The exact point where the pebble hits the water determines
the position and the shape of the waves. If you could go back in time, those circular
waves would refocus on the initial impact point precisely, because the
information on the point location is not lost during wave propagation. This 2D example can be extended to a 3D situation, where waves are
spherical and refocus exactly at the center of the sphere. However, in real
life, one generally focuses light from one side, along some direction and not
from all directions, and the ideal picture of focusing from a full circle or a
full sphere is never exactly relevant.
“A full spherical wave is symmetric and has
its focus exactly at the center of the sphere. However, to keep this spherical
symmetry, light should propagate from all directions onto the sample. And this
virtually never happens. Practically, wavefronts are passed through an aperture
that is limited to a portion of a sphere, instead of the full sphere.
Consequently, spherical symmetry is broken and information is lost,” says Francois
Amblard, co-author of the study. In the case of the pond, this would be similar to going back in time to
try to refocus a limited wave arc, instead of the full circular waves: these
arc waves would not necessarily converge on the same impact point, because
information about the center location is partially lost.
The IBS team has explained and given the
experimental proof that, as the aperture gets smaller, the focus shifts more
and more backwards towards the lens, such that the initial focus is no longer
“in focus.” As a consequence, if the aperture is not equal in the vertical and
horizontal planes, focal shifts will differ between these directions, leading
to astigmatism. “Astigmatism can occur even with the most perfect lens if it is
used with a non-circular aperture,” explains Kai Lou, first author of the study.
Figure 1: Information loss by asymmetry
and small aperture. (A) A stone falling in a pond produces full circular waves
that are centered on the impact point, and those waves would back propagate
onto that same point if time could be reversed. Using this time-reversal
argument, if one generates back propagating circular waves from a limited arc,
they will not necessarily focus at the center. (B) Representation of how diffraction
effects compete with focusing for a beam of different initial size, that is
different aperture. Going from left to right on the x-axis, the input beam size (aperture size W_A, orange
line) increases. For a large beam, focusing is strong, leading to a small cross
section in the focal plane W_F (blue line). If the aperture W_A is
reduced, a critical situation is reached (dashed line) where W_A is same as W_F. At the critical
point where the two lines cross, focusing and diffraction effects are equal, and
energy (red) is best focused between the lens and the initial focal plane,
which means that the effective focal plane has shifted towards the lens. Extremely
small apertures correspond to a point source and produce diffraction without
focusing.
The team applied the idea to improve a
technique called line-temporal
focusing microscopy (LTFM, also named spatiotemporal focusing), which makes use
of a naturally asymmetric input beam. As LTFM is a method used to visualize
deep biological structures, the researchers tested their focal shift correction
strategy with mouse lung tissues. An unprecedented resolution was obtained, that
even outperformed a classical technique called point scanning microscopy (PSM).
Figure
2: Comparison of two bioimaging techniques: line-temporal focusing microscopy (LTFM) and point scanning microscopy (PSM). IBS researchers increased LTFM resolution, by restoring the circular
symmetry of the LTFM beam. Images of a fluorescently-labelled mouse lung slice
show that the improved LTFM achieves a higher resolution than PSM: a result
never reached before.
How does this knowledge help to improve
resolution? Even though this effect is very small and can be neglected for
ordinary applications, correcting for aperture-induced astigmatism could make a
significant difference in delicate systems, like advanced microscopy used to
acquire a large volume of images. Understanding that astigmatism is intrinsic
to the broken circular symmetry could help design corrections tailored to the
aperture shape, especially in fields such as astronomy, telecommunication, or
with ultrasounds, where non-circular apertures cannot be avoided.
“In the future, we plan to apply
aperture-induced astigmatism to even more complex information transfer
technologies,” said Steve Granick, co-correspondent author of this study.
“Moreover, the study opens avenues to basically improve the design of any equipment
handling electromagnetic waves, ultrasounds, or particles beams. For example,
it also applies to waves, used with space antennas to focus on satellite or
spaceship. We believe it can contribute to design better systems in synthetic
microscopic eyesight, telecommunications, and even microwave devices.”