Derivative of Axial Resolution from Rayleigh's Limit

In summary, the derivation of axial resolution from Rayleigh's limit is a mathematical process that shows the relationship between the axial resolution and the numerical aperture of an optical system. This relationship is described by the formula: Axial Resolution = 0.61 * λ / NA, where λ is the wavelength of light and NA is the numerical aperture. The axial resolution is a measure of the ability of an optical system to distinguish between two points along the direction of the optical axis, and it is affected by the numerical aperture and the wavelength of light. Other factors such as aberrations, scattering, and noise can also limit the axial resolution in an optical system. Optimizing these factors is important for achieving the best possible axial resolution in imaging.
  • #1
TS Wong
1
0
I am currently studying optical microscope and discover that the axial resolution is limited as r(z) = 2pi / (NA)^2.
However, while I got hints that it is due to the Rayleigh's limit, I can't derivative the equation using numerical method.
It would be huge thanks if anyone can help me on the solution.
 
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  • #2
Born and Wolf derive this in section 8.8 (7th edition). My hint is that you are evaluating the diffraction integral on-axis.
 

FAQ: Derivative of Axial Resolution from Rayleigh's Limit

What is the derivation of axial resolution from Rayleigh's limit?

The derivation of axial resolution from Rayleigh's limit is a mathematical process that shows the relationship between the axial resolution and the numerical aperture of an optical system. It is based on the Rayleigh criterion, which states that two point sources can be distinguished if the peak of one source falls on the first dark ring of the other source's diffraction pattern.

How is the axial resolution affected by the numerical aperture?

The axial resolution is inversely proportional to the numerical aperture. This means that as the numerical aperture increases, the axial resolution decreases. This relationship is described by the formula: Axial Resolution = 0.61 * λ / NA, where λ is the wavelength of light and NA is the numerical aperture.

What is the significance of the axial resolution in imaging?

The axial resolution is a measure of the ability of an optical system to distinguish between two points along the direction of the optical axis. It is an important factor in imaging, as it determines the smallest distance between two objects that can be resolved in an image. A higher axial resolution allows for more detailed and accurate imaging.

How does the wavelength of light affect the axial resolution?

The wavelength of light is directly proportional to the axial resolution. This means that as the wavelength decreases, the axial resolution also decreases. This is because shorter wavelengths of light can diffract more, resulting in a larger diffraction pattern and a lower axial resolution.

What are some factors that can limit the axial resolution in an optical system?

Some factors that can limit the axial resolution in an optical system include the numerical aperture, the wavelength of light, and the quality of the optics. Other factors such as aberrations, scattering, and noise can also affect the axial resolution. It is important to optimize these factors in order to achieve the best possible axial resolution in imaging.

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