Laser power, photons per second, speed of light in different mediums (media?)
One thing I'd like to have is a theoretical model of the confocal microscope, in order to understand noise sources and to be able to quantify the measurement results.
So, I started at the beginning, looking at the laser source.
Goal 1: to express the number of photons per second as a function of the laser power (in Watts) and the wavelength.
The energy per photon is E = h * f (where h is Planck's constant ≈ 6.6 * 10-34, f is the frequency in Hz, and the energy E is in Joules). Or more relevantly for us, using the wavelength rather than frequency (f = c / λ), E = h * c / λ (where c is the speed of light).
Question: What c should be used? The speed of light in vacuum? Or the speed of light in the gas in the laser? Or the speed of light in the air outside the laser?
Assuming that photons maintain their energy when passing through matter with different densities, does the wavelength of the light change to compensate? (That seems like the most likely event). But if so, is the wavelength of the laser specified for vacuum? Probably all this is academic because of the small change in speed of light in vacuum and air, but to be completely accurate I'd still like to know the answer.
Taking the power of the laser in plaser [Watts] = [Joules * second], multiplying it by one second, and dividing it by the photon energy should then give us the number of photons per second:
fphotons [Hz] = plaser [W] * c [m/s] / λ [m].
For a 1 W laser, this works out to be c / λ = f ! (In other words, about 600 * 1012 photons / second.
In the confocal microscope I think we're using voxel times of about 1 μs, so at 500 nm we should be getting 600*106 photons per voxel from the laser.
So, I started at the beginning, looking at the laser source.
Goal 1: to express the number of photons per second as a function of the laser power (in Watts) and the wavelength.
The energy per photon is E = h * f (where h is Planck's constant ≈ 6.6 * 10-34, f is the frequency in Hz, and the energy E is in Joules). Or more relevantly for us, using the wavelength rather than frequency (f = c / λ), E = h * c / λ (where c is the speed of light).
Question: What c should be used? The speed of light in vacuum? Or the speed of light in the gas in the laser? Or the speed of light in the air outside the laser?
Assuming that photons maintain their energy when passing through matter with different densities, does the wavelength of the light change to compensate? (That seems like the most likely event). But if so, is the wavelength of the laser specified for vacuum? Probably all this is academic because of the small change in speed of light in vacuum and air, but to be completely accurate I'd still like to know the answer.
Taking the power of the laser in plaser [Watts] = [Joules * second], multiplying it by one second, and dividing it by the photon energy should then give us the number of photons per second:
fphotons [Hz] = plaser [W] * c [m/s] / λ [m].
For a 1 W laser, this works out to be c / λ = f ! (In other words, about 600 * 1012 photons / second.
In the confocal microscope I think we're using voxel times of about 1 μs, so at 500 nm we should be getting 600*106 photons per voxel from the laser.
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