By using a fairly rigid aperture grille with sparse randomly placed holes of different sizes, including a large number that are very small, it should be possible to do very high resolution microscopy, including subwavelength near-field light microscopy of flat objects, using only low-resolution, low-quality lenses or mirrors to focus light.
You put the grille on top of the sample, in contact with it, and shine light through the sample and the grille, taking a picture of the starfield pattern that comes through. Where a hole is over a clear spot in the sample, a white point of light will show; where it’s over a transparent red spot, a red point of light will show; where it’s over an opaque part, no light will show. The holes are much smaller than the camera pixels, but they are sparse enough that typically only one hole or less makes a significant contribution to each camera pixel. The consequence is that moving the grille by a hole diameter or so scans many such high-resolution pixels over the sample, and by taking many such frames, eventually the whole sample can be covered redundantly by many holes.
It’s necessary to estimate the relative positions of the holes to deep subpixel resolution, and it may be necessary to do this simultaneously with estimating the image of the surface, a problem similar to the simultaneous localization and mapping (SLAM) problem in robotics. Alternatively, if the grille is rigid enough, it may be possible to estimate the hole positions ahead of time, using, for example, a known microscopic image or many high-resolution photographs of the grille.
Using a variety of different sizes of holes in such a grille is a way to reduce the difficulty of this estimation problem. The larger holes provide a blurrier image, but their positions are much easier to estimate to the desired precision, and the blurry image helps in estimating the position of the smaller holes.
A very practical way to produce such a grille is by perforating a thin metal surface, such as gold leaf; aluminum foil peeled from a gum wrapper; the aluminum coating on metallized Mylar/boPET or polyimide, such as a discarded potato chip bag; or the silvering of a first-surface mirror. A very practical way to perforate such a metal sheet is with a short-lived arc, triggered by bringing an electrode close to the surface; the hole diameter, if not its position, can be controlled fairly precisely by controlling the energy released in the arc, which can be measured fairly precisely by measuring the charge and voltage loaded onto a capacitor before the discharge.
Gold leaf is typically 0.2 microns thick; Mylar is commonly 10 microns thick, but only about 0.5 microns of that is the metallized film, sometimes as little as 0.1 microns. Regular kitchen aluminum foil is on the order of 20 microns thick. Vaporizing a 1-micron-diameter hole in an 0.5-micron-thick metal film requires vaporizing about 0.4 (μm)³ of metal, which at 2.7 g/cc for aluminum works out to about a picogram. Solid aluminum's specific heat is 24.20 J/mol/K, its heat of fusion is 10.71 kJ/mol, its heat of vaporization is 284 kJ/mol, and it boils at 2470°, so we're looking at (2470 - 20) K 24.20 J/mol/K + 10.71 kJ/mol + 284 kJ/mol = 354 kJ/mol, and its atomic weight is about 27.0 g/mol, so that’s 14 kJ/g = 14 nJ/pg = 14 nJ per hole. That’s the energy of a 280 pF capacitor at 10 V.
If the capacitor’s capacitance were to increase or decrease by 1% (for example due to temperature, ferroelectric, or soak effects), which is a typical precision for low-capacitance capacitors like this, that would increase or decrease the diameter of the hole by about ½%. It should be straightforward to measure the charge deposited on the capacitor during the charging process to within about 0.1%.
I say it’s probably not practical to control the location of the hole precisely because you need to bring the electrode close enough to the foil to provoke a dielectric breakdown of the air; for 10 V to be adequate, for example, the distance needs to be about 3 microns. But if the tip has a spherical radius of 3 microns, then a corona discharge will be occurring around the tip at the same time. This seems undesirable to me for a variety of reasons (uncontrolled loss of energy, ionic erosion) so it would be better to make the tip diameter much larger than this. But this means that the position of the arc will be uncertain to within several microns, controlled by small asperities on the tip or on the foil or by stray ions that wander by. You’re depending on the positive feedback of the arc itself to channel all the energy into a small area, but that same positive feedback creates unpredictability.
Using lower voltages would help if it were possible, but it probably is not practical; Paschen’s law has its minimum for nitrogen at about one torr cm and about 300 V. An atmosphere is 760 torr, so we reach one torr cm at about 13 microns. Using higher voltages makes the lateral uncertainty larger.
XXX now that I know about Paschen’s law I need to rethink the above for a higher voltage.
Coloring the grille black, for example with a layer of carbon black deposited by smoke, should reduce stray light contamination which will damage SNR and require algorithmic rejection after the fact. This should be especially helpful for imaging using reflected light rather than transmitted light.
This approach doesn’t seem like it would offer any advantages for electron microscopy, and without very exotic materials, it probably doesn’t extend very far into the ultraviolet.
Doing telescopy rather than microscopy with this approach probably will not work very well, because diffracting light through small holes like that will lose a lot of information about which direction it came from. But in telescopy, the whole point is to determine which direction it came from. A more purely diffractive approach, where the incoming light diffracts through a random aperture grille and then falls on a focal plane with no intervening lens, might work better.