Is MTF50 a good proxy for perceived sharpness? It turns out that the spatial frequencies that are most closely related to our perception of sharpness vary with the size and viewing distance of the displayed image.

For instance if an image captured by a Full Frame camera is viewed at ‘standard’ distance (that is a distance equal to its diagonal) the portion of the MTF curve most representative of perceived sharpness appears to be around MTF90.

The explanation starts with the human Contrast Sensitivity Function (aka the visual system’s ‘MTF’) as measured and used by Granger, translated by Bob Atkins, validated by Harvard and modeled more recently by Matkovic. It looks as follows when expressed in cycles per degree on the retina, log scale on the left (also often seen as the outline of a Campbell-Robson chart) and the less familiar linear scale on the right:

The two graphs show the average Human Visual System’s Contrast Sensitivity as a function of cycles per degree on the retina for persons with 20/20 vision, on a log (left) and Linear (right) scales. As a result of these measurements, maximum human acuity is often assumed to be 50 cycles/degree.

Granger says that the spatial frequencies on the retina that are most representative of the perception of sharpness are those between 3 and 12 cycles/degree (he worked off data in log scale). With a little geometry we can easily convert cycles per degree on the retina to cycles per mm on a displayed photograph:

(1)

with p the period typically in mm, d viewing distance in the same units, and the angle on the retina in degrees for one period, representing cycles/degree. We can then project the corresponding spatial frequency in cycles/mm (1/p) onto the sensor by multiplying it by the ratio of the diagonal of the camera’s sensor to the diagonal of the displayed photograph. The corresponding spatial frequency on the sensor can then be expressed as follows:

(2)

in cycles per the same units as viewing distance , with the ratio of the diagonals of the displayed photo and sensor respectively.

#### MTF50 not Relevant at Standard Distance

For instance, = 3 cycles per degree on the retina corresponds to about 4 lp/mm on a Full Frame sensor with a diagonal of 43.3mm when the photograph is viewed at standard distance, a distance equal to the photograph’s diagonal with m = . Here is the HMV’s Contrast Sensitivity Function at standard distance, with the MTF curve of a D610 for reference:

Granger’s most sensitive 3-12 cycles per degree on the retina map to 4-16 lp/mm on a FF sensor when its captures are viewed at standard distance – multiply by crop factor when referring to other sensor formats. The area of interest is shown below together with the measured MTF of a D4/s for reference, but the same area applies to the graph above and to that of any camera with a sensor of about 24mm sensor height when the photograph is viewed at standard distance:

Shown in gray above is the area Granger says best correlates to perceived sharpness for an image captured by a D4s sensor and viewed at Standard distance. So if we mostly view our images at standard distance we should really focus on their combined MTF performance at around MTF90 +/-10 as far as expected perceived sharpness is concerned, according to Granger. That’s the portion of the MTF curve related to image **contrast**. It may come in handy to know when evaluating lenses for purchase.

The statement above is theoretically valid whether you look at your FF captures as 5x7s from 218mm away, 8x12s from 366mm away, fit to your 24″ monitor from 611mm away or 10x15m billboards from 18m away: they are all standard distances equal to the diagonal of the displayed image, hence project the same cycles per degree on the retina.

#### MTF50 Relevant when Pixel Peeping

Of course the pixel peeper in me would also want to choose a lens for my camera that will provide good perceived sharpness also when watching a final photograph from closer than standard distance, say when pixel peeping on my monitor. Pre-solving equation (2), the representative spatial frequency range of interest becomes

(3)

with CF crop factor relative to FF (1 for FF, 1.5 for APS-C, 2 for mFT etc.).

I currently have a 5.9um pitch D610 4000×6000 pixel FF camera and pixel peep at 100% from 400mm (16″) away on a U2410 24″ 1920×1200 monitor so the fraction above works out to about 5. The frequencies of interest are therefore in the range of 20 to 80 lp/mm. This is what the scaled CSF would look like then (D610 MTF shown):

For a 3.9um pitch, 24MP APS-C camera like the Sony a7 mark II the range in the same conditions becomes 30 to 120 lp/mm, and this is how the area of interest would look like for it:

On the other hand the 4928×3280 pixel, 7.1um pitch Full Frame D4s produces a smaller overall image when pixel peeping at 100% on a monitor because it has fewer pixels. The ‘pixel peeping’ photo diagonal to viewing distance ratio would therefore be about 4 for it on my monitor. Below are what Granger would call critical frequencies for perceived sharpness then (D4s MTF shown):

And here is a 4.85um pitched, 7360×4912, Full Frame, D810 mounting an AF-S 85mm f/1.4G in the same conditions, this time with spatial resolution expressed in cycles per pixel

When evaluating images up close MTF50 looks like it is right in the thick of things. So keeping in mind that these curves are derived from unsharpened raw data, perhaps when pixel peeping at 100% zoom on a 24″ monitor from 400mm (16″) away MTF50 is not such a bad proxy for perceived sharpness after all*.

Resizing an image also results in changed magnification and similar effects as discussed above. This article deals with it from a downsizing perspective.

*Since MTF curves tend to be approximately linear around MTF50, MTF50 can also often be seen to be proportional to the area under the curve in the Granger frequency range, which is another well accepted sharpness metric: Subjective Quality Factor (SQF).

Hi Jack,

thank you for your very informative articles. – What would you think would be the main region of interest for a viewing distance of 2x the format diagonal? Which I think is a more “normal” viewing distance for *images* in real life. I assume the blue curve in fig.2 would be pushed to the right, in the direction of pixel peeping.

Hello Hening,

Spatial frequency in cycles per mm is one over the period (p) defined in formula 1. If we keep visual acuity constant (controlled by theta) when distance (d) to the displayed image is doubled the relative linear spatial frequency is halved.

So the blue line/area moves to the left. In other words, the further you are from the image, the less lp/mm you are able to detect in it, the more important the low MTFs (contrast) become as an indicator of perceived sharpness. This is true at any starting distance.

Jack

Thanks for your reply, Jack. I should have known it: everything math is always exactly the other way ’round (than I think)…

I have only recently begun to learn optics. Where can I find info at what MTF for 50cy/mm can human eye discern for Visual Acuity (VA) 20/20?

For 100 cyc/mm, what MTF will be for eye to discern for 20/20 VA?

What is the maximum cycles/mm retina can discern beyond which MTF is 0? For example, is retina capable of clearly viewing a pattern as small as 200 cy/mm? If so, what would be the MTF?

Hi Jack,

Good questions, I would suggest wikipedia and online course material from well known universities.

I currently have a 5.9um pitch D610 4000×6000 pixel FF camera and pixel peep at 100% from 400mm (16″) away on a U2410 24″ 1920×1200 monitor so the fraction above works out to about 5.

how the 5 be calculated?

Should the unit of fig1 be cycles/degree?

The factor of 5 is calculated as photograph diagonal divided by viewing distance. If pixel peeping from 40cm a 6000×4000 image at 100% on that 24″ 1920×1200 monitor it means that

picture diagonal = 24″ x 2.5cm/inch x (4000/1200) = 200cm

so the factor is 200/40 = 5.

And good catch about Figure 1, it should indeed be cycles/degree. Thanks for that, I’ll correct it when I have time.