Two-photon microscopy

A fluorescent molecule can be excited by two long-wavelength photons instead of one short one, provided they arrive within a fraction of a femtosecond of each other. Because that depends on the square of the photon flux, it happens at a meaningful rate only where the beam is most tightly focused — inside a volume around a femtolitre, and essentially nowhere else along the beam path.

That quadratic dependence is the whole trick, and it is what a femtosecond pulsed laser is for: packing enough photons into brief bursts to make the two-photon event likely at the focus while keeping average power low enough not to cook the tissue.

What it buys

Optical sectioning without a pinhole. Since only the focal volume fluoresces, all emitted light can be collected as signal, even light that scattered on the way out. A confocal microscope has to reject out-of-focus light and throws away scattered photons with it, which is exactly the wrong trade in tissue that scatters.

Depth. Near-infrared excitation scatters and is absorbed less than visible light, so imaging works hundreds of micrometres into cortex rather than tens.

Less damage where it matters. Photobleaching and phototoxicity are confined to the focus instead of the whole illuminated cone.

Worth being clear that the depth owes more to the first of these than to the longer wavelength. The excitation has already fixed where a photon came from, so the detector does not need to: a large detector close to the objective can count every fluorescence photon it catches, scattered or not. Comparing identical sections in 1998, Centonze and White found that two-photon excitation reached at least twice as deep as confocal imaging in every specimen they tried, and traced the confocal image’s decline mainly to scattered emission.

A prediction that waited for the laser

Maria Göppert-Mayer worked out the theory of an atom absorbing two light quanta in a single act for her doctorate at Göttingen, taken in 1930 with Max Born guiding her and published in 1931. The unit of two-photon cross-section, the GM, is named after her.

Nothing could test it for three decades, because no light source was intense enough. In 1961, with the ruby laser a year old, Kaiser and Garrett shone its 694.3 nm light into a crystal of calcium fluoride doped with europium and saw blue fluorescence — more energy per photon out than any single red photon brought in. Those pulses were too long to reach the peak intensity that imaging living tissue would need; femtosecond lasers, arriving in the 1980s, removed that obstacle. The idea of building a scanned image from a nonlinear signal was in print by 1978, when Sheppard and Kompfner discussed nonlinear interactions in the scanning optical microscope.

Winfried Denk, James Strickler and Watt Webb made it work at Cornell in 1990. As their patent describes the demonstration, a standard laser-scanning microscope had its continuous argon-ion laser replaced by a 25 mW colliding-pulse mode-locked dye laser — pulses of about 100 fs at about 80 MHz, near 630 nm — of which about 3 mW reached the sample. The targets carried dyes that normally need ultraviolet. For the images of fluorescent beads the confocal pinhole was opened as far as it would go, and the stacks were sectioned anyway: fluorescence rose with the square of the intensity, and fluorescence and bleaching both stayed near the focal plane.

Seven years later Svoboda, Denk, Kleinfeld and Tank took it into the intact brain. In rat whisker cortex they imaged calcium in the dendrites of layer 2/3 pyramidal neurons while stimulating the whiskers and recording the cell’s voltage through an intracellular electrode. Whether such dendrites generate their own calcium spikes had been argued over from slice experiments; here calcium rose only with sodium action potentials, roughly in proportion to their number, and fell off steeply with distance from the soma, with little reaching the distal branches in layer 1.

The laser and the scanner

The reason for pulses is a duty cycle. At 80 MHz with 100 fs pulses the laser is on for about one part in $10^5$ of the time. Two-photon excitation follows the square of instantaneous power, so concentrating a given average power into those pulses multiplies the time-averaged excitation by the inverse of the duty cycle — about $10^5$ — while heating, which follows the average, stays where it was. Continuous light would need a few hundred times the average power for the same signal.

The source that became standard is titanium-doped sapphire. Moulton’s 1986 characterisation of the crystal reported tuning from 660 to 986 nm, a band that covers the two-photon absorption of most common fluorophores. In January 1991 Spence, Kean and Sibbett reported 60 fs pulses straight from a Ti:sapphire laser that mode-locked itself. Within the year Salin, Squier and Piché tied the effect to self-focusing in the crystal; with an aperture in the cavity, that self-focusing becomes a loss that falls as power rises, so the laser prefers to pulse — Kerr-lens mode-locking, as Brabec, Spielmann, Curley and Krausz analysed it in 1992. By the mid-2000s commercial Ti:sapphire lasers were sold as turnkey systems, tunable over roughly 700–1000 nm, with pulses near 100 fs at 80–90 MHz.

The image is then built a point at a time. Galvanometer mirrors raster the focus across the field; run at its mechanical resonance, a galvanometer sweeps lines fast enough for about 30 frames a second, and a photomultiplier turns each pixel’s fluorescence into one number. The instrument is a single detector time-multiplexed across a population of cells, so neurons trade against frame rate: across the systems Lecoq, Orlova and Grewe compared in 2019, the number recorded falls as the rate rises.

Why it changed neuroscience

Combined with calcium indicators, it made it possible to watch hundreds of identified cells in a living brain, return to the same cells days or weeks later, and see them in their anatomical context — which electrode recording cannot do. Knowing which cell is which, and what type it is, turned out to matter as much as recording many of them.

Each part of that rests on a different piece of engineering. In a living brain is the optics above. Identified is genetics: an indicator encoded as a gene can be expressed in a chosen class of cells. Nakai, Ohkura and Imoto built one from a single green fluorescent protein in 2001, G-CaMP, which let go of calcium with a time constant of about 200 ms; successive generations improved until GCaMP6 (Chen and colleagues, 2013) reliably reported single action potentials from cell bodies in mouse visual cortex. Over days needs the indicator to stay expressed and a window that stays clear: a glass coverslip cemented in place of a piece of skull can be imaged through for months, each site logged against the pattern of blood vessels on the dura so that it can be found again (Holtmaat and colleagues’ 2009 protocol).

Put together, they let the same identified cells be watched for days in an intact brain. In 2008 Mank and colleagues could still write that no technique reliably followed changes in identified neurons across repeated sessions; with their indicator, TN-XXL, they measured the orientation tuning of the same neurons in mouse visual cortex over days and weeks. By 2014 Peters, Chen and Komiyama were imaging the same hundreds of layer 2/3 neurons in motor cortex through two weeks of mice learning to press a lever, with excitatory and inhibitory cells told apart by a transgenic label.

What it trades away

The trade against electrical recording is timing. Calcium is a slow, indirect proxy for spiking, so temporal precision is far worse than an electrode’s, and imaging speed is limited by having to scan the focus point by point. Depth is still bounded by scattering. The two methods answer different questions, and most labs now run both.

Each of those comes with numbers. Neuron count and timing both trade against photon noise. In Lecoq, Orlova and Grewe’s estimate, the detectability of a single spike, $d'$, goes as

$$d' \approx \frac{\Delta F}{F}\sqrt{\frac{F_0\,\tau}{2}}$$

where $\Delta F/F$ is the fractional brightening one spike produces, $F_0$ the photons per second detected from the resting cell, and $\tau$ the indicator’s decay time; $d' = 5$ corresponds to about 99% correct detection. For GCaMP6f, about 15% and 0.2 s, that takes at least 11,000 photons a second from each cell. The Allen Brain Observatory’s standard rigs, scanning 512 × 512 pixels at 30 Hz, collected on average 0.89 photons per pixel per dwell time — about 2,700 a second from a cell body, a $d'$ of 2.4, enough for bursts of five spikes but not for single ones. Giving each cell five times the pixels clears $d' = 5$ and records a fifth as many neurons. The slower GCaMP6s gives more per spike, about 25% over 0.6 s, at a further cost in spike timing.

More laser power would buy photons, until the heat budget runs out. Podgorski and Ranganathan measured it in mouse cortex in 2016: illuminating a square millimetre continuously raised the temperature by about 1.8 °C per 100 mW, worst hundreds of micrometres below the focus because the cranial window draws heat out through the surface, and more than 250 mW sustained left lasting damage. Higher powers were tolerable in experiments that illuminated only part of the time; heat follows average power.

Depth fails in its own way. Unscattered excitation light falls off exponentially with depth, so keeping the focus bright means raising the power at the surface exponentially, until two-photon excitation near the surface outshines the focus. Theer, Hasan and Denk imaged 1 mm into mouse neocortex in 2003, using pulses from a regenerative amplifier, and came close to that limit. Routine instruments stop well short of it; beyond about 500 µm, Lecoq and colleagues note, they need adapting.