# How large can you print?

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How large can you print?
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Hi,

This is a very simple analysis, probably a bit too simple.

The image here was shot with a Hasselblad 180/4 CFi on a P45+ back at f/5.6. Blue curve is interpolated green channel in Lightroom, with sharpening set to zero. Red curve is the same image sharpened in FocusMagic.

Note that the red curve is pretty flat up to around 1500 cy/PH.

Let's assume that we need like 90% MTF for an excellent print.

The question is, how many cycles do we need for an excellent print? The figure 180 PPI is often used. Giving the rationale for this is beyond the scope of this posting.
Looking at the MTF curve, we could sharpen more, but that would just yield supernatural sharpness. We probably want sharpening that keeps MTF just below 1.0 over a wide range of frequencies.

Using these presumptions, the maximum vertical size of an 'excellent' print would be

2* 1470/180 -> 16.5". The P45 has 49/37 aspect ratio, so that would convert to:

16.5 * 49/37 -> 22"

So, the P45+ would be able to deliver an excellent print up to 16"x22", with proper sharpening.

Having a better lens/sensor combo would deliver the same IQ with less sharpening, but may not deliver a sharper image as we don't want to oversharpen.

The weak point of this reasoning is the 90% at 180 PPI criterium.

A small point is that I don't suggest we print at 180 PPI, having 90% MTF at 180 PPI would cause a lot of aliasing. So, we would rather print at 360 or 720 PPI, which would much reduce aliasing.
Best regards

Erik

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Erik Kaffehr
Website: http://echophoto.dnsalias.net
Magic uses to disappear in controlled experiments…
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