T Q: Resolving Power - Theory & Wave Character

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In summary, the resolution of an image is limited by the aperture of the detector and the distance from the source. Provided the signal we are trying to detect is reasonably stable with time, we can obtain images with resolutions that exceed the maximum resolution allowed in the far-field.
  • #1
Dr.Brain
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I want theoretical reason . When using microscopes , we can magnify the image as much as we want by adjascently using lenses in such a way that all aberrations are removed. But magnifying is not the solution , because there is something called 'Resolving' , like ability of the microscope to differentiate between two ends of a bacterium . As we magnify further , the two end points that smoothly define the boundaries of the image are smeared up and it is rather difficult to make out the two points. I think the reason is that as per Fermat's P. , the rays from both end points of bacterium take the approx. the same time to reach the focussing point , so they give approx. the same smeared images.So solution lies in making the rays from both end points reach the focussing point at different intervals.

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I found in a book that this difference in time interval for both rays should be more than one time period.

But what wonders me is that the wavelength of light is very small as compared to the instrument used, we should study light using 'geometrical optics' and not 'wave character', so what do they exactly mean by "one time period difference"?

BJ
 
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  • #2
When you want to assemble an image using waves, you can't do it using
waves that are longer (crest-to-trough) that the image you want to assemble.

This is a very crude analogy but since you are using a computer it should make
sense- if your computer monitor only has 100 dots/inch, it can't display a picture
which is smaller than 1/100th of an inch.
 
  • #3
If you had an infinite numerical aperture, you could resolve an object with infinite precision. The problem is, the best numerical apertures available to us are around 1.5. This means that the resolution we are able to achieve in the far-field is approximately [itex] \lambda/2 [/itex], so if we are imaging something using a 500 nm source, the maximum resolution we can achieve is 250 nm.

There are a few theories as to why this is so, essentially the theory depends on what criterion you use to define an object as being resolved.

Basically if your Numerical Aperture is finite you cannot image something with infinite precision because you have lost some of the scattered light and hence some of the information about the object (This is commonly referred to as Abbe's theory of imaging).

Note that these restrictions only apply only to the far-field. In the near-field (roughly defined as distances smaller than [itex] \lambda [/itex]), resolution is only limited by the aperture of our detector and the distance from the source. Provided the signal we are trying to detect is reasonably stable with time, we can obtain images with resolutions that exceed the maximum resolution allowed in the far-field. For more info, I suggest doing a google on SNOM (or NSOM) which stands for Scanning Near-field Optical Microscopy.

Claude.
 

What is T Q: Resolving Power?

T Q: Resolving Power is a theoretical concept in the field of optics that measures the ability of an optical instrument to distinguish between two closely spaced objects. It is often used in the study of microscopy and telescopes.

How is T Q: Resolving Power calculated?

T Q: Resolving Power is calculated using the formula R = λ/Δλ, where R is the resolving power, λ is the wavelength of the light being used, and Δλ is the smallest difference in wavelength that can be distinguished by the instrument.

What factors affect T Q: Resolving Power?

The main factors that affect T Q: Resolving Power include the quality and design of the optical instrument, the wavelength of light being used, and the size of the aperture or lens. Higher quality instruments and shorter wavelengths generally result in higher resolving power.

How is T Q: Resolving Power related to wave character?

T Q: Resolving Power is closely related to the wave character of light. The ability to resolve two objects depends on the wavelength of light and the diffraction pattern produced by the instrument’s aperture. Light waves with shorter wavelengths produce smaller diffraction patterns, resulting in higher resolving power.

Why is T Q: Resolving Power important in scientific research?

T Q: Resolving Power is important in scientific research because it allows scientists to accurately observe and study objects that are too small or distant to be seen with the naked eye. It also helps to improve the quality and accuracy of images produced by optical instruments, leading to more precise measurements and discoveries in various fields such as biology, astronomy, and physics.

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