Determining the size of a light source I have an incoherent light source that is of unknown size, and I was wondering about the possible methods to measure its size. The issue is that I am expecting it to be very small (few micrometers), and if I try to use a pinhole camera much smaller than the source size I will not gain enough light to actually resolve the image.
If I use a reasonable sized pinhole camera (50um) - I will only image the pinhole - not gaining any new information about the source itself.
Right now, I am thinking of calculating it by looking at how quickly the light intensity falls off when it passes a sharp absorbing feature such as a knife edge or a slit. If the source was infinitely small I assume what I would see would be a fall-off that would be approximately as long ('smudged') as the effective mean wavelength of the light. If the source is larger than the wavelength, then the speed at which the light intensity falls off at the edge should be approximately equal to the size of the light source (corrected for the magnification of the imaging system). I guess what I am essentially saying is that the image will be something like the source intensity spatial distribution convoluted with the transmission map, am I correct here?
Are there any methods of estimating the source size by looking at the image of the source through a pinhole that is larger than the source itself, or by looking at the image of the source passing through a slit (two knife edges)?
Are there any other simple ways one can measure or estimate the source size?
It's also worth mentioning that I am dealing with light that is approximately 0.1-0.01nm in wavelength.
 A: You are working in a spectral range for which finding lenses will be a problem, so we'll reject the idea of using a lens.
Making a small pinhole comparable to the wavelength will be difficult or expensive, but you're right that the spot of light that makes it through the pinhole would be the convolution of the source with the pinhole.
A knife edge should work as well as a pinhole, and should be a lot easier to arrange.  Place a razor blade a distance X from the source, then a detector a distance X' beyond the razor blade. Measure the width W of the transition between the fully-shadowed area on the detector and the fully-illuminated area on the detector.  The width $S$ of the source is $S = W (X/X')$.
A: Here is an off the wall thought. Some glues are set with UV light. Are there any that work with xrays? Cover the source with a thin film of glue. Expose it enough to set it. Pry the glue off and look at it under a microscope.
Or the other way around. Cover the source with something that is damaged by xrays. Pry it off and look at the damage with a microscope. Or if it is thin, leve it in place and look at how big the hole burned through it is.
Infrared laser beam diameters are measured with fluorescence. A light source makes a flat plate fluoresce. The infra-rad beam suppresses the fluorescence. You measure the dark spot. With this approach, you could use a visible light telescope to measure the size of the spot.
How small can you make a thermocouple? How intense is the light? Move it around in front of the source and measure the temperature as a function of position.
Some microbes survive radiation pretty well. Cover a flat plate with microbes, put it against the source, and expose them. Check where they are dead.
Frances Helman at UC Berkeley came up with a thin film bolometer sensitive enough to measure the metabolism of a single cell. It has a free standing thin film that bridges a hole in the substrate. The film has simple circuit elements on it. This might be used to combine a knife edge and thermocouple approach.
A: Use a good objective lens->imaging lens->camera with decent magnification and an OK camera. Shouldn't be a problem. Details follow.
Use an objective with a moderately high numerical aperture(>0.1) and low aberrations. (https://www.thermofisher.com/order/catalog/product/NX1004X#/NX1004X). If you can't get this close to the sample because you don't want to spring for a vacuum compatible objective use a longer focal length but bigger (2" dia) lens. Use an imaging lens with a long effective focal length to achieve a high magnification. Use any cheap ccd or cmos camera with a smallish (few micron) pixel size.  Use achromatic lenses.
If chromatic aberrations are an actual problem use a interference filter with a ~10+ nm pass band (https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=1001). Sill should have plenty of signal. I can see single-atom florescence with such a setup.
If the light source is VERY dim, use a cooled CCD camera with good gain and low noise. and a longer exposure time.
If visible wavelengths are emitted, this is well above the diffraction limit so shouldn't be a big problem to view.
What's the desired precision?
