Why is the Rayleigh Criterion not a definitive resolution limit for microscopes?

[KFC]

From Rayleigh criterion, the resolution of microscope is given by

$$\sin\theta = 1.22\frac{\lambda}{D}$$

where D is the separation b/w two objects. Suppose D is constant, image and object distances are fixed, if we want to increase the resolution, we should increase the angle (theta) right? So we should use long wave-length light instead of short one? But in the text, they said short wavelength is preferred (in some case even use electron wave), why is that?

 

[mgb_phys]

Isn't D the aperture of the objective?
theta is the minimum separation between two points (on the object) - so you want to make theta as small as possible

 

[KFC]

Isn't D the aperture of the objective?
theta is the minimum separation between two points (on the object) - so you want to make theta as small as possible

Oh! D is the separation between two points (for example, the distance between to pinholes) and I forget that theta estimates the size of zero-order disc of the diffraction pattern, so we should make it as small as possible. What was I thinking!? :(

 

[turin]

Oh! D is the separation between two points (for example, the distance between to pinholes)

mgb_phys is correct. D is the apperture size. The formula that you present is for the diffraction limited resolution. θ is the minimum angular separation between two points that can be resolved.

 

[KFC]

mgb_phys is correct. D is the apperture size. The formula that you present is for the diffraction limited resolution. θ is the minimum angular separation between two points that can be resolved.

Yes, D is the aperture size. Thanks for pointing that out. I still have a question. From Rayleigh's criterion, at small angle approxmiation, the limit of resolution gives

$$\theta = 1.22\frac{\lambda}{D}$$

where $$\theta$$ gives the minimum angular separation of two patterns that can barely be resolved. That is, this criterion is applied on the diffraction pattern. But in the text, this also works on objects. Namely, the minimum angular separation of two objects that can barely be resolved is also equal to $$\theta = 1.22\frac{\lambda}{D}$$, why MINIMUM SEPARATION OF DIFFRACTION PATTERNS = MINIMUM SEPARATION OF OBJECTS?

 

[Andy Resnick]

Again, these criteria are based on heuristic arguments about how much signal-to-noise is required to differentiate an object from background. The Rayleigh criterion claims that neighboring airy discs can be separated if the central dip from the combined pattern is 20% below the maximum intensity. There are many resolution criteria- Sparrow's criterion is another. There are still more for pixelated detectors.

Even moreso, the Rayleigh limit is for two mutually incoherent points, something that may not be the case for a scene illuminated with partially coherent light.

The bottom line is that "maximum resolution" or "resolution limit" or all those other marketing buzzwords are not hard limits.