Question

I try to calculate the beam diameter after a high NA objective that focuses on a point-like emitter that emits fluoresence light.

To my basic understanding, I get this by computing the Entrance pupil (EP) of the objective, thus
EP=2∗NA∗feff=2∗NA∗fnomX
where NA
is the numerical aperture, X
the magnification and feff
would be the effective focal length. However, this information seems not to be available anymore for modern objectives. I am looking at a 40x Olympus objective. I get the magnification, the Parfocalizing distance and the Back focal plane position as well as the objective field number. How can I get the beam width? Furthermore, if I compute the beam diameter like this, is this the 1/e2
diameter or the 99% diameter?
Options:

A) Utilize the given data along with the field number and the known magnification to estimate the beam diameter, adjusting for the numerical aperture's effects. The computed diameter is typically the 1/e² diameter.

B) Calculate the beam diameter by taking the product of the objective's magnification and the field number. This value corresponds to the 99% diameter.

C) Employ the Parfocalizing distance and Back focal plane position to infer the effective focal length and subsequently derive the beam diameter using the formula EP = 2 * NA * feff. The resulting diameter represents the 1/e² diameter.

D) Estimate the beam diameter using the numerical aperture and the magnification, assuming a Gaussian distribution, thereby computing the 99% diameter.

Answer 1

The beam diameter of fluorescence light after a high NA objective is typically calculated using the numerical aperture and effective focal length, but if the latter is not available, it can be estimated from other given parameters. The calculated diameter represents the 1/e² (about 13.5%) intensity diameter.

Step-by-step explanation:

To calculate the beam diameter of a fluorescence light after passing through a high NA objective, you would typically use the numerical aperture (NA) and the effective focal length (feff). However, if the effective focal length is not provided, another approach must be used. You can use the given Parfocalizing distance and Back focal plane position to infer the effective focal length, but this is not directly provided here. The calculated beam diameter usually represents the 1/e² diameter, which describes the diameter at which the intensity drops to 1/e² (about 13.5%) of its maximum value. The correct approach seems to be Option C, which suggests using the Parfocalizing distance and Back focal plane position to derive the effective focal length and then calculate the beam diameter with the formula EP = 2 * NA * feff. Note that the optical properties such as numerical aperture influence the light-gathering ability and resolving power of the lens.