rjlittlefield wrote: ↑Sun Nov 14, 2021 11:49 am
This graph incorporates the combined effects of diffraction and finite pixel size. What is shown is system MTF = lens MTF * sensor MTF.
Lens MTF is computed from diffraction only, using the equations quoted at
viewtopic.php?p=124831#124831 . Sensor MTF assumes perfect pixels (box filter width = pixel width) and is computed as a sinc function as described at
http://mtfmapper.blogspot.com/2012/05/p ... d-mtf.html and shown in the
5th chart there. Lambda = 0.00055 mm.
Bottom line, the NA 0.21 image will look sharper and will reveal finer detail, unless you post-process the images so as to compensate for the differences in MTF.
In this particular case, a strong sharpening filter applied to the NA 0.14 image could bring its overall MTF up to match the NA 0.21. But that would come at the cost of also increasing fine scale noise by almost 4X.
The one downside to the NA 0.21 objective is that it provides a lot more opportunity for aliasing, if the subject contains fine detail that resolves above the Nyquist limit of the sensor. The beauty of Nikon's rule is that it guarantees no aliasing, because it matches the cutoff frequency of the objective with the Nyquist limit of the sensor. Unfortunately, for users who don't understand what's going on, that rule can also result in "recommending" an objective with small NA, which will produce an inferior image.
--Rik
Great links there, I'll have a closer look. Sinc functions bring back all the computational nightmares from university, FT and convolution... what's in my mind? The Fourier Transform of a square wave results in that, it probably does have something to do with it, vaguely from memory. I'll read the articles.
I didn't consider MTF at all and never bothered to incorporate it into my calculator, perhaps I should now. It'll require a lot of work in Excel, a program I don't exactly like working with -- too bad my SAS subscription from the university days is gone.
By "fine scale noise", do you mean noise factors such as read-out noise and photon shot noise? So basically, all the noise factors are amplified. As a standard practice, I will decrease the "radius" slider to minimum and apply maximum sharpening and some noise reduction. Sort of similar to "deconvolution", they do make a huge difference especially when down-sampled.
I would generally recommend the cheaper option considering the price of one 5x HR gets the user an array of objectives. It's equivalent to a 5x, 10x, 20x and perhaps even 50x and 7.5x if one's patient. The cheapest 5x HR Mitutoyo I've seen so far is $2500. Below are some typical, lower bound used prices. The 50x fluctuates a lot, sometimes they go for as high as $1200. Must be patient with this one!
- 5x: $450 (as low as $250)
- 10x: $450 (as low as $400)
- 20x: $600 (as low as $550)
- 50x: $700 (as low as $600)
- Carman Haas clone TTL200-A tube lens: $180
At the cost of the cheapest 5x HR I've ever seen online.
I'm not the one to say "the HR is useless because your 24MP sensor wouldn't resolve it" when clearly my tests and far more precise calculations here prove otherwise. The funny thing is, my D810's 36MP shows a far smaller difference, it's worse in some instances compared to the BSI 24MP sensor on the Z6, at ISO100 and with a lowpass filter (vs. 64 and without). I'll attribute this to generational differences and "raw baking" which is yet two more factors in the optical system.