1. I am currently using a 532nm laser and NA = 0.6 objective lens for laser focusing, (the spot size of the laser outlet is 2mm, then expand the beam 4 times, and finally through several mirrors into the objective lens) according to the formula d = 1.22 * λ / NA = 1.08um, but in fact the spot size in the camera is much larger than this value, should be more than 10um, this is why. 2. When I use the bias film to attenuate the laser, the spot size at the focal plane will become smaller, but according to the previous formula, the smallest spot should be and the light intensity of no light, but now adjust the light intensity but change the spot size is why, this condition can become very low spot but the light intensity is also very weak, this is why. This is also the case when a neutral density filter is used instead of a skewed film. 3. The final laser is shown on the camera as a circle, not a circle, which is why
The actual numerical aperture of your system is based on the focal length of the lens and the aperture pf the lens being used. You mention the diameter of the laser beam is 2mm and you have expand the beam by 4. Is the beam gaussian and is the final diameter ~8mm? You need to find the focal length of the lens you are using. The f/no of the system is the focal length divided by the diameter of the input light. The diameter of the focused spot should be of the order of λ* f/no. A gaussian beam typically appears about 3-4 times its "1/e radius". My guess is that you are not using (filling) the entire aperture of your 0.6 NA lens and the result is a much higher effective f/no, resulting in a larger spot at focus.
Assuming your laser beam shape is "gaussian" - you might want to look into the optics of gaussian beams. Many diode lasers don't have a well characterized beam shape.
The optical properties of the system should have no relation to the number of photons passing through the system - or the attenuation in the system. A camera looking at a scene has the same image size and resolution as the same camera looking through a strong attenuating filter - it just has a lot less light at the image plane.
"3. The final laser is shown on the camera as a circle, not a circle, which is why" ????
Dick Horton 505/417-6846
I want to emphasize what R. F. Horton said. Just because the lens aperture allows an NA up to 0.6 doesn’t mean your beam is actually 0.6 NA. If the beam does not fill the input aperture of the 0.6 NA lens, your actual NA is something less than 0.6.
Also, 1.22 lambda / NA is what you would get if and ONLY if the input beam is uniform, i.e. a top hat profile (for example if you were tremendously over filling the lens and the lens was clipping out an almost uniform part of the middle of the beam) which produces an Airy spot. By the way, 1.22 lambda / NA is not the expected diameter, but rather the radius to the first Airy minimum.
If, on the other hand, most of your Gaussian profile fits within the aperture of the lens (for example if the hard aperture clips at something > 2 sigma) then the spot size is not an Airy disk with a first minimum at 1.22. Instead, if the input beam’s 1/e^2 diameter is D, the spot is a Gaussian with a 1/e^2 diameter d ~= 2*f*lambda/(pi*D/2)
What R. F. Horton and Mike Albert said has accuratedly answered your question. But one thing I want to point out is that how do you ensure that the spot size measured by CCD is the waist spot size after focusing? Maybe three issues should be considered:
1. For 0.6NA objective lens, its work distance is generally small. The position of the waist after focusing is very close to the working distance. In other words, the CCD surface should be palced at the waist spot, how to ensure this?
2. The divergence angle of gaussian beam is very large after focusing. Maybe the sopt size you measured is a spot after divergence.
3. The pixel size of CCD is generally in the order of um. Is it accurate to use a detector with an accuracy of um to detect the size of um?
I can add that you should also consider possible abberations in optics as well as initial imperfections of the laser beam, like astigmatism.
This is about the Helmholtz-Lagrange invariant. Pay attention to my article: Fabry-Perot interferometer with conjugate convex-concave mirrors as wide-angle spectrometer for scattered light
R. F. Horton Thank you so much for your response. The size of the beam spot after expanding the beam should be larger than the entrance pupil diameter of the objective lens. Thirdly, I want to mention that the focused beam spot should be circular, but the actual beam spot may not be circular and may cause distortion. Is it possible that this problem is due to an angular tilt between the laser axis and the objective lens axis?
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