Diffraction limit · Lobeworks/17

The diffraction limit is the smallest distance between two points that an instrument forming an image with waves can show as separate, set by the wavelength and by the angle of the waves the instrument collects; for a light microscope it is about 200 nanometres.

Diffraction limit. The diffraction limit is the smallest distance between two points that an instrument forming an image with waves can show as separate, set by the wavelength and by the angle of the waves the instrument collects; for a light microscope it is about 200 nanometres.

Ernst Abbe wrote it down in 1873: about the wavelength divided by twice the numerical aperture, a number for the cone of light a lens gathers that reaches about 1.4 for the best oil-immersion lenses. Every point is blurred into a small disc ringed with fainter circles, and two discs closer than the limit merge into one. A wave cannot carry detail finer than its own ripples, the way ocean swells close behind a post but break on a breakwater as wide as they are long.

It is why connectomes use electrons. A synaptic cleft is about 20 nm wide and a vesicle about 40 nm, far under 200 nm; an electron accelerated through 120,000 volts behaves as a wave of about 3 picometres, and electron microscopy resolves around a nanometre.

Fluorescence can step around it. Super-resolution methods, recognised with the Nobel Prize in Chemistry in 2014, locate labelled molecules far more finely than the limit by switching them on a few at a time, but they see only what was labelled, never every membrane in a block.

It is one of the physical limits on reading a brain. With penetration depth and the signal-to-noise ratio, it sets what any method that images the brain can resolve before engineering is even considered.

Questions: Does super-resolution fluorescence break the diffraction limit? It steps around it for labelled molecules. Methods recognised by the 2014 Nobel Prize in Chemistry switch fluorescent labels on a few at a time and locate each one far more finely than the limit. They show only what was labelled, so they can map chosen proteins in a cell but not every membrane in a block of tissue, which a connectome needs. Why can a light microscope not map synapses? Because light cannot separate points closer than about 200 nanometres, its diffraction limit, and a synaptic cleft is about 20 nm wide and a vesicle about 40 nm. An electron accelerated through 120,000 volts behaves as a wave of about 3 picometres, so an electron microscope resolves around a nanometre, enough to follow every membrane and count vesicles.