m8ta
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{1479} | ||
Can we image biological tissue with entangled photons? How much fluorescence can we expect, based on reasonable concentrations & published ETPA cross sections? Start with beer's law: = absorbance; = sample length, 10 μm, 1e-3 cm; = concentration, 10 μmol; = cross-section, for ETPA assume (this is based on a FMN based fluorophore; actual cross-section may be higher). Including Avogadro's number and , Now, add in quantum efficiency (Rhodamine); collection efficiency ; and an incoming photon pair flux of (which roughly about the limit for quantum behavior; n = 0.1 photons / mode; will add this calculation). This is very low, but within practical imaging limits. As a comparison, incoherent 2p imaging creates ~ 100 photons per pulse, of which 10 make it to the detector; for 512 x 512 pixels at 15fps, the dwell time on each pixel is 20 pulses of a 80 MHz Ti:Sapphire laser, or ~ 200 photons. Note the pair flux is per optical mode; for a typical application, we'll use a Nikon 16x objective with a 600 μm Ø FOV and 0.8 NA. At 800 nm imaging wavelength, the diffraction limit is 0.5 μm. This equates to about addressable modes in the FOV. Then an illumination of photons / sec / mode equates to photons over the whole field; if each photon pair has an energy of , this is equivalent to 300 mW. 100mW is a reasonable limit, hence scale incoming flux to pairs /sec. Hence, the imaging mode is power limited, and not quantum limited (if you could get such a bright entangled source). And right now that's the limit -- for a BBO crystal, circa 1998 experimenters were getting 1e4 photons / sec / mW. So, pairs / sec would require 23 GW. Yikes. More efficient entangled sources have been developed, using periodically-poled potassium titanyl phosphate (PPPTP), which (again assuming linearity) puts the power requirement at 23 MW. This is within the reason of q-switched lasers, but still incredibly inefficient. The down-conversion process is not linear in intensity, which is why Goodson pumps with SHG from a Ti:sapphire to yield ~1e7 photons; but this of induces temporal correlations which increase the frequency of incoherent TPA. Still, combining PPPTP with a Ti:sapphire laser could result in 1e13 photons / sec, which is sufficient for scanned microscopy. Since the laser is pulsed, it will still be subject to incoherent TPA; but that's OK, the point is to reduce the power going into the animal via larger ETPA cross-section. The answer to above is a tentative yes. Upon the development of brighter entangled sources (e.g. arrays of quantum structures), this can move to fully widefield imaging. | ||
{1474} | ||
Various papers put out by the Goodson group:
And from a separate group at Northwestern:
Regarding high fluence sources, quantum dots / quantum structures seem promising. |