The attached illustrate what I'm trying to convey.
I am trying to follow your train of thought Bill. If the Exposure is kept constant with both unaberrated lenses at f/4 by varying the exposure time, all else equal, the Airy disks on the image plane should be the same size. Both lenses will produce the same MTF curve, with the same x-axis in lp/mm, and the same diffraction extinction frequency.
In visual astronomy, the better analog would be looking at and discerning an extended object such as a faint galaxy. Just as two lenses of any focal length at f/4 deliver the same exposure to the sensor, two telescopes of any aperture and focal length deliver an image of a galaxy having the same surface brightness at magnifications producing the same exit pupil diameter. In fact, if we take into consideration the reality that no optical system is perfect, every galaxy displays its greatest surface brightness to the naked eye. Increasing aperture doesn't increase an object's apparent surface brightness. At best the 20-inch Obsession Dob delivers an image of a distant galaxy having the same surface brightness as that produced by a 60mm refractor.
Continuing the visual astronomy analogy, the advantage of the larger aperture is that - while the galaxy (a faint extended object) can have the same apparent surface brightness in a wide range of apertures being larger at the eyepiece translates to delivering more total light to the eye. As you mentioned earlier, increased total light from the subject translates to an improved SNR and less prominent photon noise. This results in objects that appear as low having contrast against the surrounding dark sky being visible - or more easily so - in larger aperture telescopes. It's how the observer using the 20-inch Dob is able to see more galaxies in the Virgo cluster than the person set up next to them using the 60mm refractor. Though, one would hope the Obsession owner would offer to share the view
And, of course, it's possible the images I posted aren't as effective at illustrating the point as others might be.If the lenses are perfect, and sensors have infinite resolution, only the aperture size matters for the ability do discern.
What if they have different focal lengths? Photographers take them into consideration through f-number, approximated by f/D, i.e. focal length divided by aperture diameter. The relative blurring function on the image plane, call it an Airy disk, would be 1.22lambdaN.
It depends on the shape of the relative MTF curve and what you mean by resolution. The MTF curve of a diffraction limited lens with a circular aperture is not linear, though not far from it. The diffraction extinction spatial frequency is D/(f*lambda).
It is more accurate to multiply MTF curves, but that ignores anisotropy and phase.Roger is never wrong, but perhaps sometimes not accurate as he explained above ;-)
I do not know if this was referred to in any of the posts above, but with only a few days left of DPReview, there is no time to check
The link below gives an approximation of a formula for total system resolution, i.e. the combination of camera and lens : https://www.pbase.com/lwestfall/image/52085939
So
1/Res(total) = 1/Res(sensor) + 1/Res(lens)
Some formulas use the square for all the resolutions.
In any case, it shows that even if one part has a higher resolution than the other, both still contribute to the total resolution.
However, it also shows that if one is much much greater than the other, the total resolution will be largely limited by the part with the lowest resolution.
I.e., if both sensor and lens have arbitrary resolution values of 10, then total system resolution will be 5, but if the lens resolution is 10 and the sensor resolution is 100, then total system resolution will be 9.1 - probably an extreme case, but mathematically possible
In the latter case some might argue that the sensor out-resolved the lens, but other might argue that is does not as total system resolution is not 10.
So do the two formulas above ;-)
True enough. I didn't mean to imply otherwise.
Ignoring aliasing and Anti-Aliasing filters, there are typically two main drivers to system 'resolution' In modern Interchangeable Lens Cameras: lens blur and sensor blur.
Thank you Jack for this data and the analysis. I am curious on how the lens mtf can be measured without the camera itself but let's not go there for now.Based on the discussion and the shapes of the curves above one can surmise that the relationship between effective pixel aperture and System MTF50 is roughly linear in the interval of interest all else equal. In fact:
No AA, green channel, perfectly square effective pixel aperture, with the same Nikon Z 24-70mm 4 S kit at 24mm and f/5 in the center
So approximately 10 lp/mm in System MTF50 are lost for every micron increase in effective pixel aperture, with this setup.
Jack
It's approximately reverse engineered from a measured System MTF curve fit to defocus, SA3 and pixel aperture. It should be a decent enough approximation in the center of the FOV as shot. Should you be interested some of the detail is described hereThank you Jack for this data and the analysis. I am curious on how the lens mtf can be measured without the camera itself but let's not go there for now.Based on the discussion and the shapes of the curves above one can surmise that the relationship between effective pixel aperture and System MTF50 is roughly linear in the interval of interest all else equal. In fact:
No AA, green channel, perfectly square effective pixel aperture, with the same Nikon Z 24-70mm 4 S kit at 24mm and f/5 in the center
So approximately 10 lp/mm in System MTF50 are lost for every micron increase in effective pixel aperture, with this setup.
Jack
I am not sure what matrix resolution means, the gradient refers to MTF50 as a proxy for pixel-peeping sharpness. My discussion above ignores aliasing. Monochrome Nyquist would be at 1/2 cycles per pixel pitch. With 4um per pixel that would be 1/2/.004 = 125 lp/mm, well above MTF50. As pixel size decreases the monochrome Nyquist frequency increases accordingly. In other words, as far as aliasing is concerned you want a poorer lens with larger pixels - and vice versa.
Very helpful, clear and concise description.Ignoring aliasing and Anti-Aliasing filters, there are typically two main drivers to system 'resolution' In modern Interchangeable Lens Cameras: lens blur and sensor blur.
Lens blur is caused by diffraction and aberrations due to the physical set up of the lens.
Sensor blur is introduced by filtering right on top of silicon in combination with the shape and size of the active area of the pixel. To simplify things we will assume a perfectly square aperture that fills the pixel entirely - and measure resolution horizontally or vertically in the center of the field of view only.
Each of these two main components results in an MTF curve. If we multiply them together frequency-by-frequency we get the System MTF curve as shown below for a modern ILC:
4.35um perfectly square pixel aperture, f-number = 5, Aberrations of a good 24-70mm zoom in the center
So what's resolution? Choose a threshold that is relevant for the purpose at hand. Often online one finds MTF50, the spatial frequency at which the captured contrast is half of what would be possible. This may be relevant when pixel peeping .
System MTF50 above is about 84.6 lp/mm, lens MTF50 is about 125.0 lp/mm and pixel aperture 138.7 lp/mm.
Can we say that as set up the lens brings down system MTF50 more than the sensor does? We could, though that answer depends on lens and pixel aperture readings not at MTF50 - but at about MTF65 and MTF80 respectively. Does that mean that the sensor 'outresolves' the lens in general? No, because if we instead chose MTF10 as a threshold, as required by a different application, the opposite would be true. And then there are Nyquist and aliasing to contend with.
As pixels get smaller the dashed line of pixel aperture and its null above move more to the right, bigger to the left. The null for a 6um pixel aperture is 167lp/mm, for 3.7um 270lp/mm. On the other hand the dotted MTF curve of the lens depends only on aberrations and f-number so unless those change it stays put. This should give an intuition on how system resolution is affected by varying pixel size in this case.
Jack
PS The 1/r formula yields a system MTF50 of 65.7 and the 1/r^2, 92.9 lp/mm versus the actual 84.6.
I agree. If you want to capture all the information from a lens, you need a sensor with higher resolution than the lens.
The nyquist limit (better nyquist frequency) is an attribute of the sampling process. What you mean is that a grid with maximum contrast has unlimited upper frequency (like a square wave), and the amplitude of high frequencies is proportional to 1/f.
Hi,
