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Resolution Limits

So what are the resolution limits?

We can work out this fairly directly for the camera sensor by knowing the number pixels and sensor size and applying the Nyquist Sampling Theorem. The anti-alias or blur filter will introduce some additional losses that can't be removed by sharpening, I have assumed this to be say 25%.

Table-1

The lens will also limit the resolution, Canon define simulated MTF curves for most lenses and some organizations have a database of measured MTF data.

Here I have taken the measured data for various Canon lenses from Photodo, who provide data at 10, 20 and 40 lp/mm. For the EF-S lenses I have had to use the Canon Data as Photodo have not measured any EF-S lenses. Canon only provide 10 and 30 lp/mm.

An example is shown below:

Figure-1

This shows that the spatial resolution roll-off is different for different image offsets from the lens optical axis.

Although two or three data points is not much to base a trend on, I have used the method of Norman Koren to estimate the lens resolution for the 10% MTF point in the worst case line orientation, at edge of format using Eq-1.

Eq-1

This curve fit done on MTF values at 10 and 30 lp/mm is a quite good fit of real measured lens data up to about 40-50 lp/mm after which it tends to over estimate by 0.1 to 0.3, this over estimation is probably due to the camera anti-alias filter. As an example the very sharp EF 200mm f2.8L USM II both measured and model error for three locations near the centre of the lens.

An example of the fit operation is shown graphically below:

Figure-2

The 10% MTF level is chosen as a reasonable limit for when detail starts to become illegible, resulting in the below table.

Table-2

We can see by comparing the values in Table-1 and Table-2 that we are probably at or getting close to the point of diminishing returns with the current crop of APS-C sensor sized DSLRs for wide angle lenses (EF 20mm and EF-S 17mm). 

For the equivalent angle of view on the 1Ds the EF 35mm would be nearest. The slightly longer focal length makes the lens easier to design and produce with a corresponding increase in resolution. 

Thus there is more headroom in full frame 35mm over APS-C due to better available lens resolution in addition to the increase in sensor resolution. Further increases in resolution in APS-C sensors will have limited advantages at wide angle focal lengths.

At longer focal lengths the lens performance is improved and 10% MTF resolutions in excess of 100 lp/mm seem possible.

To take full advantage of this resolution would require APS-C sensors of 40Mpixel and full frame 35mm sensors of 100Mpixel. So for longer focal lengths there is plenty of headroom for further sensor development.

Probably a more important factor is the 30 to 40 lp/mm MTF value as this will define the perceived detail reproduction in the currently available DSLRs.

Comparing Figure-1 and Figure-3 gives an idea how much the APS-C sensor is at a disadvantage for wide angle detail in this respect, despite the image being cropped at about 13mm offset.

Figure-3

To see this more clearly in Figure-4 and Figure-5 I plot a comparison between the APS-C wide angle EF 20mm f2.8 and the 35mm wide angle EF 35mm f1.4L, both with almost exactly the same angle of view. The APS-C spatial frequencies have been interpolated and regressesed to correct for the crop factor so that 16, 32 and 64 lp/mm correspond to 10, 20 and 40 lp/mm on the 35mm lens. Additionally the image height, or offset from the optical axis, is relabeled as percent of frame diagonal to compare the relative image height.

Figure-4

Figure-5

This exercise shows the lenses compare quite well for contrast (10 and 16 lp/mm), however for detail (20 to 40 and 32 to 64 lp/mm) the MTF curves diverge limiting the available wide angle lens detail for the smaller format.

Some comparisons between APS-C and full frame are available at these references [1], [2], [3].

Another direction to look at this from is the diffraction limited resolution, this is the best a lens can be and so places an upper limit on the required resolution.

The diameter of the diffraction spot is D=2.44 X N X lambda, where N is the f-stop number and lambda is the wavelength of light (green = 0.53 micron = 0.53E-3 mm).

If we then have detail represented by two spot widths representing a light and dark line pair we can calculate the detail frequency as 1/D/2 lp/mm if  we have used mm as length units. To sample this at the Nyquist rate without alias effects the pixel frequency needs to be twice this value.

In conjunction with the sensor and anti-alias filter MTF characteristics this permits Table 3 and Table 4 to be calculated.

Table 3

Table 3 shows the case where no anti-alias filter is used, the sensor 70% MTF case representing the sample rate and sensor resolution required for the Nyquist rate of 0.5 cycles per pixel at the diffraction detail level and the sample rate and sensor size for the sensor MTF to be 90%. Lenses are unlikely to approach the diffraction limit until they are stopped down to f5.6 or f8, marked by the red text. The yellow text indicates the current resolution of top end DSLRs.

Table 4

With Table 4 the case when an anti-alias filter is used is presented. The Nyquist rate being suppressed has a low MTF of 8% to achieve higher MTFs of 50% and 90% much higher sensor resolutions are needed. This suggests that is anti-alias filters are used sensor resolutions of 13-66Mp are  needed to reproduce the diffraction limited detail.

Looking now at the circle of confusion based measure of the required sensor resolution in Table 5.

Table 5

This shows the required sensor resolution in the first row for the normally accepted size of circle of of confusion for acceptable focus and a sensor MTF of 50% with a quartz anti-alias filter, starting at around 4Mp. Depending on what is acceptable for the sharp focus area, some fraction of the acceptable focus, we then get a lower bound for  useful sensor resolution. The current sensors are in the 0.4c to 0.7c area. 

Conceivably sharp focus on a large print might be defined by something in the 0.2c to 0.5c range indicating minimum sensor resolutions of 18Mp to 96Mp. Comparing this to the diffraction limited resolution for 50% MTF sensor resolution with an anti-alias filter we see this corresponds to the limit of resolution for optics at f5.6 to f8 and f4 to f11 for APS-C and 35mm respectively. So it seems likely that 20-40Mp cameras will be developed but after that it is at best diminishing returns. 

The only other justification for larger sensor resolutions would be to dispense with anti-alias filters without risking alias artifacts. The image can then be down sampled to a manageable frame size. This would technique is often used in 1D sampling systems and has advantages of reducing quatization noise (increasing the sampling bit depth) and removing the need for anti-alias filters and the subsequent effects of sharpening to compensate for them without compromising pixel noise (as the noise will be averaged across the pixels in the down sample process). 

For me the increased maximum resolution and improved optical performance at wide angles is a major reason to be able move to a full frame 35mm sensor at some point in the future. See my lens system trade-off study. 

Other advantages of full frame over APS-C are improved noise performance and reduced diffraction limited resolution (ref). Clearly the difference is small, but about a factor of 2. Clearly there will always be a need for larger formats to get the best quality, it seems likely that full frame 35mm and medium format will survive the digital revolution for critical professional application.

However, chromatic aberration can be an issue at the edge of frame for full frame SLRs, this may be partly due to the a steep exit angle from the lens and so be lens dependant. There are other issues also, see Joseph S. Wisniewski's Digital Lens FAQ and  discussion of the likely future of APS-C and full frame 35mm DSLRs. The suggestion being the FF sensor may be affordable in the 5 year time frame.

Last Updated 05/06/2008

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