Since you mentioned spacial frequency, I assume that you're familiar with MTFs. An MTF comparison between a pinhole size, optimized for the Airy disk, compared to one optimized for the Rayleigh criterion reveals the difference. If someone is after the optimum pinhole size, one must decide what to optimize it for. Our eyes have a clear preference for contrast over resolution, and therefore, the Airy disk is commonly preferred. However, the Raleigh criterion results in higher resolution at the cost of contrast and perceived sharpness.
Diffraction optics dictates that the pinhole is as large as possible to minimize light spreading, and geometric optics dictates that an ideal pinhole is as small as possible to optimize image clarity. Considering the Airy disc and the Rayleigh criterion leads to two theorems for an ideal pinhole diameter and suggests that there may be more than one right answer.
1. The smallest pinhole possible is based on the Airy disc to optimize image sharpness.
d = sqrt(2.44 * wave length * focal length)
2. The largest pinhole necessary satisfies the Rayleigh criterion to optimize image resolution.
d = sqrt(3.66 * wave length * focal length)
Again, the quest for the optimal pinhole diameter is generally fueled by the desire to create the sharpest pinhole image possible. Contrast and resolution are both aspects of sharpness, but human perception typically considers high-contrast images to be sharper than high-resolution images. Consequently, unless resolution is more important than perceived sharpness, my proposal for the optimal pinhole diameter is based on George Airy’s diffraction-limited disc.
I hope this explains it a bit better.
Ah okay, thanks Ralph, I figured it was an MTF argument. Interesting. I was guessing that it was all a wash when one takes into account wavelength spread, but I will think about it some more. Interesting!