Sensors and lenses resolution

[iangreenhalgh1]

I don't understand why some lenses are listed as being suitable for 16mpx max.

Why? The resolution of the lens is surely high enough for a 36mp sensor. The D800 sensor has 102.3lp/mm resolution, this is still much less than what a good film can resolve - Velvia 50 can resolve 160lp/mm.

So is it true that the D800 sensor is more demanding? I'm not sure I understand the maths here.

[iangreenhalgh1]

I found this list of sensors and their resolutions in lp/mm:

[twinquartz]

[sichko]

[twinquartz]

Hi John!
Yes, I used the formula 1/T = 1/S + 1/L, where T = total res, S = sensor res, L = lens res.

In order not to complicate things, let us just consider the Helios-103 (and skip the decimals):
Using my formula, the total resolution values become max 40, min 30, depending on which sensor we use.
Using your square formula, the total resolution values will have a span of max 51, min 43.
Were we to use a third formula, we would most probably arrive at other values.

Can we agree on which is the "correct" formula?

And, before we set off WorldWar 2.5 by hi-jacking this thread, shall
we start a new one (thread, that is, not a WW) someplace else?

[sichko]

[Orio]

OK, I split the thread (and put this in Lenses forum, since it does not seem to be limited to DSLR cameras).
Enjoy

[twinquartz]

Splendid! Thank you.

[Orio]

[sichko]

Thanks Orio !

[twinquartz]

No need to re-calcuate my Excel sheet with the 1.5 value you just brought into the picture,
the resulting values would sort of fall in between my original set and the squared one.

One of the German forum members is skilled in lp/mm, especially when it comes
to reprographic lenses. Let us hope that he will be able to straighten out the problem...

[twinquartz]

I found a reference to your square formula: Higgins, G.C.Appl. Opt. 3, v.1, 9, Jan 1964.
And here is a good discussion (with lots of graphs!) http://www.diax.nl/pages/Lens_res_uk.html
Enjoy!

Ah, just found another good one:
http://www.dpreview.com/articles/4110039430/detail-of-sx3040-vs-compact-slr

[buerokratiehasser]

You call that sharp?

My comment on this issue would be that most lenses, especially old zooms, would be lucky to field 70 lp/mm on a good day.

lp/mm values for lenses can be tricky. They depend on where you measure (center or corners) and what level of constrast degradation is considered OK. I think they are usually given as MTF50, i.e. where MTF drops contrast to 50 %.

The maximum resolution would be where contrast drops to zero - MTF01 or something. Same for those 160 lp/mm from Velvia.
For Bayer sensors, correction factor like 1.5..2 to compensate for RGB pattern.

I can imagine you would, with these insane-resolution-sensors at 100% zoom, see a drastic improvement swapping a so-so 90 lp/mm lens against a gold standard one, like Sigma 50 Macro, because with sensors, the MTF goes 100% almost until the maximum resolution.

Film would profit a lot, too (the MTFs multiply), but most people never had the equipment (or cared) to examine the 100 lp/mm range.

[iangreenhalgh1]

[SXR_Mark]

The correct way to combine resolutions will be to do a mathematical process called convolution. Conveniently, Gaussian functions convolve so that the widths add in quadrature. Thus the total width T when Gaussians of widths A and B are convolved is given by T^2=A^2+B^2. This will (I assume) be the origin of the formula with squares in it. The reciprocal will be because the resolution is expressed in reciprocal units (lp/mm). This convolution means that if one part has much worse resolution than the other part, the combined resolution is determined basically only by the worst part, as one would expect from a common sense point of view.

However, I would say combing lp/mm figures in this way will be a very dodgy procedure. The problem comes from how one defines the resolution when using pairs of black and white lines. Specifically, the contrast across the lines is an important part of the definition. Thus, one lens resolution figure may be at, say, 80% contrast (very well resolved) whilst another may be at 20% contrast (much less well resolved).

Another issue is how the resolution of the sensor is calculated. Because of the Bayer pattern of the pixels in the sensor and the interpolation used to create the final image, it is not correct to simply say the spatial resolution is determined by the pixel spacing and thus the spatial-frequency resolution, limited by Nyquist, is given by 0.5*(1/pixel spacing). A more realistic calculation would be to take square-root(2)*(pixel spacing) as this is the spacing between green pixels in the Bayer sensor and the green channel gives most of the spatial information. The Nyquist limit for a sensor would thus be 1.414 times smaller than the figures quoted by Ian.

[coon]

To what was said above, I only want to add that the formula 1/Res_tot = 1/Res_1 + 1/Res_2 comes from the fact that two Lorentzians instead of Gaussians are convoluted, which gives again a Lorentzian but with a width parameter equal to the sum of the original two: http://en.wikipedia.org/wiki/Cauchy_distribution (see the remark with the stable distribution)
The connection to optics is - I think - that the envelope of the Airy disc is a Lorentzian, therefore it might be more appropriate if one estimates resolutions for diffraction-limited optics.

But I also think it should be taken with a grain of salt, because digital sensors have the box distribution ( http://en.wikipedia.org/wiki/Box_blur ) instead of a Gaussian/Lorentzian as 'blur operator'. So in principle one should describe it as the convolution of the point spread function (which can be rather ugly with all sorts of aberration) with this box filter, and then it is not so easy to give a simple equation for the resulting resolution or blur width.

coon

[paulhofseth]

when I did optics and maths , Cauchy had in the past documented interesting consequences in his sphere for functions crossing it, and Gauss made an impression with a bell curve which begat standard deviations, but i never heard of a box function (apart fromthe monte carlo method), so please explaina bit further for the benefit of us ignorant oldtimers.

p

[fermy]

[coon]

[Ray Parkhurst]

Much of my photographic effort last couple years has been toward maximizing sharpness in my coin photography. The macro nature of photographing coins places a special emphasis on diffraction effects due to the magnification near 1:1 (most all my work is on Lincoln Cents at M=0.8 or so). Most recently I have been using a Canon T2i, which has particularly small (4.3um) pixels, with 18MP on a APS-C sensor. This has placed a burden on my lenses since the Diffraction Limited Aperture of the sensor is around f7. To achieve effective aperture of f7 at M=0.8 you need a lens that has 116lp/mm MTF50 at f4 across at least 16mm (the coin is round, so corners don't matter much). Few lenses can do this, and in fact I'm only aware of a handful. Lower magnifications widen the field of available lenses significantly.

[sammo]

[SonicScot]

I forced myself to read every post in this thread, despite not understanding most of it.

My brain just imploded.

[twinquartz]

This must be a potent thread: so far, one Italian headache and one Scottish implosion.
Apart from that: one of my hopes is that in the end, we will be able to find
a suitable approximation which most can agree on.

[Himself]

[NikonD]

I just take photos and don't worry about the resolution not being constiti.... my brain ran away