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I'm currently a physics student studying the optics unit. I learned that the Rayleigh Criterion is usually used to define minimum optical resolution. The equation for the criterion is θ=1.22 λ/d where θ is the angular resolution, λ is the wavelength of the light being emitted, and d is the diameter of the aperture. I would think that the intensity of the light would factor into this equation, but it is strangely absent. My intuition tells me that a brighter light would be easier to resolve just because it is more visible at a distance. Does anyone have an explanation about the relationship between the intensity and the angular resolution?

The reason that I am asking this question is because I am thinking about structuring an experiment around it. Would this experiment be worth conducting, or am I wasting my time looking into this?

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  • $\begingroup$ The Rayleigh criterion of one of a number of arbitrary resolution limits that can be overcome with super-resolution techniques that make proper use of the available signal-to-noise ratio in the images. Before you start re-inventing the wheel, though, get yourself a few textbooks about super-resolution techniques. $\endgroup$
    – CuriousOne
    Jun 6, 2016 at 2:42

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The Rayleigh criterion provides an ideal best-case. The details of the Rayleigh criterion are arbitrary, and might not be appropriate for every case, but it does represent an accepted starting point.

As you have intuited, there is more to the issue. It's essential to consider the capabilities of your optical and detection system. First we recognize that the criterion applies to diffraction limited optics. No real system is diffraction limited, thus the Rayleigh criterion provides a lower limit to resolution.

But that's not really the kernel of your question. Ultimately, any measurement is limited by how much the signal being measure exceeds the noise level. There are many sources of noise: thermal noise in the amplifiers, dark noise from the detector, shot noise, quantization noise (relating to the resolution of digital to analog conversion). Most of these are independent of the intensity, but shot noise in particular does depend on intensity. The more intense, the lower the noise, and the closer you will get to the Rayleigh limit. Higher intensity might also better fill the dynamic range of the analog to digital conversion, resulting in better resolution.

But there is a limit to the benefits of increasing the intensity. All detectors will saturate, that is they have a maximum intensity they can detect. Any intensity brighter than the saturation level will be recorded as being equal in intensity to the saturation level. Two spots that would resolve at a lower intensity appears to be one big unresolved blob at intensities above the saturation level.

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  • $\begingroup$ What do you mean when you write that the Rayleigh Criterion is "arbitrary?" Are there other equations that can be used to define angular resolution? $\endgroup$
    – LPC16
    Jun 7, 2016 at 2:17
  • $\begingroup$ There's nothing compelling about "peak overlapping zero". Rayleigh might just as well have chosen "the distance when the dip at the peak is 5%. Or maybe 6%. It is merely the generally accepted criterion. $\endgroup$
    – garyp
    Jun 7, 2016 at 10:58

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