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High resolution extended image near field optics

7. Further comments

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Copyright (c) Malcolm Kemp 2010

 

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For photolithography and perhaps also for some types of microscopy, having an image the same size as the object is not necessarily a fundamental problem. However for telescopy and most types of microscopy it is. Objects we are interested in viewing through telescopes are typically large and far away, whilst objects we are interested in viewing through microscopes may not be far away but usually we want to incorporate some magnification into the process.

 

It is possible to create aplanatic analogues of double confocal and coaxial ellipsoids introduced in Section 2 that still span the complete range of angles onto a plane, and can thus still in principle make use of nearly fully silvered plane mirrors to support imploding dipole wavefronts. Indeed, the main reason I was led to explore the exact behaviour of solutions to Maxwell’s equations was because I had been considering the possible use of such mirror layouts for solar power concentration and solar powered flight purposes.

 

However:

 

(a)    Whilst equivalent aplanatic layouts that involve magnification can be identified, they do not appear by themselves to create the required boundary conditions to generate perfectly imploding dipole solutions. Instead it seems to be necessary to rotate (and attenuate) by different amounts the light falling on different parts of the telescope or microscope aperture in order to achieve the desired boundary conditions.

 

Such an analysis highlight that is the presence of the plane mirror at the image plane which is of particular importance in achieving superresolution, as we might have surmised from the discussion in Section 6 about how and why this sort of superresolution does not contradict established physical principles.

 

(b)   For astronomical telescopes, it does in principle appear to be possible to achieve a resolution better than that implied by the Rayleigh resolution criterion, by linking two such devices as in (a) of different sizes back-to-back to achieve a suitable level of magnification. However, it is doubtful whether such a device would be as effective as one that involved multiple individual telescopes positioned some way away from each other, which is a well-established technique for boosting resolving power. In particular, we noted in Section 6 that the improvement in accuracy arises principally because we are discarding most of the light falling on the layout, impairing such a telescope’s light gathering ability.

 


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