If we have a cascaded microscope system made of :
1. Microscope objective of numerical aperture NA1
2. Tube lens
3. Microscope objective of numerical aperture NA2
4. Tube lens
5. A recording device
Then what is effective NA of this whole system for the purpose of resolution limit calculation? It makes sense that the combined NA should be product of NA1 and NA2.
Does this imply that it is possible to increase the resolution by using a >1 NA objective remotely to any existing microscopy system?
Let's make more fun out of this!
What happens if second cascaded microscopy system is flipped to undo the magnification of 1st microscopy system? Does effective resolution (theoretical) of this new system also follow the rule of product of individual NA or do aberrations cancel out and the effective resolution tends to diffraction limit?
So, in summary how do we actually know the effective NA of a cascaded system?
Unfortunately, it does not work that way.
The light from your sample is collected by your objective with a given NA. This (and the condenser) determines the resolution limit due to diffraction--your ability to discriminate between two points of light. Your 2nd lens is just enlarging the image, but it cannot increase the amount of information collected--much like zooming in on an image on your computer screen--it just serves to increase the magnification. There is no "limit" to how much you can magnify an image, but at some point it's worthless. In fact it is not uncommon to reduce the image obtained by the objective to better match the dimensions of your detector.
Unfortunately, it does not work that way.
The light from your sample is collected by your objective with a given NA. This (and the condenser) determines the resolution limit due to diffraction--your ability to discriminate between two points of light. Your 2nd lens is just enlarging the image, but it cannot increase the amount of information collected--much like zooming in on an image on your computer screen--it just serves to increase the magnification. There is no "limit" to how much you can magnify an image, but at some point it's worthless. In fact it is not uncommon to reduce the image obtained by the objective to better match the dimensions of your detector.
@Peter
Thank you.
I understand that magnification and resolution are totally independent things. My question is all about resolution. Does a second cascaded microscope affect resolution in any way? (I don't care for practicality, detector resolution and magnification while considering this!)
Let me add this to the discussion. So far your responses are based on IDEAL resolution limited by the NA, where-ever it may be limited. As a designer and empirical optical engineer, I can tell you, without reservation, that each lens in the system is reducing resolution, no matter how you define it. Numerical aperture is a first order concept as is its effect on resolution. Microscope objectives and tube lenses have real, higher order, terms that affect resolution. No lens design is perfect, no lens surface is perfect in radius or surface figure, no lens is assembled without some residual misalignments.
A good design ensures that the lens design and tolerances give performance (margin) approaching or exceeding the first order diffraction limit. A good fabrication house will meet those requirements, but there will always be residuals. Also, the alignment of the separate components will not be perfect and there will be debris that will also degrade the image. A lens is a Low pass filter to optical spatial frequencies. Just be aware it is not a perfect low pass filter and exhibits higher order behavior than you might expect. Hopefully it is small enough to be insignificant and that depends largely on your budget and discipline.
Thank you everyone for adding your perspective. It definitely helps in better understanding.
I think I have found the answer I was looking for :
For a cascaded system, the system NA is defined/approximated (in ray optics approach) by the largest angle effectively collected by the 1st objective.
So,
1. effective NA can never increase beyond the specified NA of 1st objective.
2. if there is a cascaded system where 2nd microscope re-images the 1st image formed by 1st microscope then assuming everything else (tube lenses, alignment) being perfect, the system effective NA is NOT a product of individual NA but the least of two NA (follows easily with simple ray optics picture).
Please, feel free to add on your views.
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