# How Numerical is your Aperture?

Planning another optogenetics study, and I needed to cut the optic fibre cannulae ready for implantation. One of the other postdocs in the lab had been super organised and bought in a bunch of implants from Thorlabs at a variety of numerical apertures (thanks Amy). But, which is the best numerical aperture (NA) for my experiment?

I won’t go into details (because I’m not a physicist), but Wikipedia defines the NA of an optical system as “a dimensionless number that characterises the range of angles over which the system can accept or emit light”.

Essentially, as far as we are concerned for fibre optics, the NA is relevant for two things:

1. The bigger the NA, the more light from the source will travel down the optic fibre – for a laser system, this doesn’t matter much because the coherent light can easily be focused down it, but for an LED, this can make a big difference for how much light is captured by the fibre (rather than scattering away)
2. It determines how much the light spreads after exiting the fibre (for in vivo opto’s, this will be in the mouse’s brain) – the higher the NA, the greater the cone of light dispersion

So, back to cutting fibres, and I had to decide which ones to use – I normally use the 0.22 NA fibres out of habit, but I have read multiple recommendations to use as high an NA fibre as possible when using an LED system (which is what we have); the idea being to get as much light power as possible into the mouse’s brain, which is important considering LED systems can struggle to be bright enough for in vivo opto’s. Both Prizmatix and Doric suggest using 0.66 NA fibres for LED-connected systems, which is actually higher than the ones we have available from Thorlabs.

To test the light output, I hooked up fibres of different NA’s to our LED optogenetics system, and recorded the light power out the end of the fibre using a light meter, both under constant illumination and during 10 Hz flashing with 10 ms on times (Table 1).

True to form, the higher the NA of a fibre, the more light that is passed down it. Great, so at this point I’d pretty much settled on the 0.50 NA fibre, because it emitted approx. 50 % more power than the 0.22 NA fibre. However, for the sake of completeness, I decided to input the values into Karl Deisseroth’s irradiance predictor, to check how deep I would get good ChR2 activation. This is a useful step when planning placement of your optic fibres.

I plotted the values for all three NA fibres (Figure 1), and I’ve included the threshold level of 1 mW/mm2 that I’ve talked about previously (this is the measured EC50 of ChR2 H134R, which I use as a threshold irradiance to assume good activation).

Now I’ll be honest, I was surprised by this outcome – despite having lower light output from the lower NA fibres, the irradiance was higher as soon as you go deeper than about 0.2 mm into the tissue. I can only assume this is because the lower NA results in less light spread coming out of the fibre – the 0.50 NA fibre remains above the critical 1 mW/mm2 down to about 1.0 mm, whereas the 0.22 NA fibre goes to about 1.4 mm.

The answer is simple – I’m going to use the 0.22 NA fibres, because they have the dual benefit of activating ChR2 to a greater depth, and also having lower brightness at the end of the fibre, which means less heating of the tissue and phototoxicity.