High-accuracy MTF measurements are performed with high-cost, high-maintenance diffraction limited objective lenses. These systems are certainly good solutions for R&D, but often not so much for volume manufacturing, where cost and risk are equally as important as measurement accuracy. Using affordable non-diffraction limited optics is a viable solution, since they are much more scalable whilte not compromising measurement accuracy too much. This short article describes the accuracy loss with easy-to-use formulas and proofs them with intuitive examples.
A non-diffraction limited optical system with a system MTF Its non-diffraction limitation doesn’t prevent it from measuring a device-under-test’s (DUT’s) MTF, however, the DUT MTF it reports (1) (2) 
, where 
is the diffraction limit, has MTF curves looking something like this:
will be different from the true DUT MTF 
. This real DUT MTF will be within the interval
For example, if a system with a fidelity 
reports a DUT MTF 
against a diffraction limit 
, then the real DUT MTF will be somewhere between 
and 
. That makes a measurement uncertainty of 
to 
. For R&D applications this might be too large an uncertainty, but for mass production this could already be accurate enough.
For 
, the system is perfectly diffraction limited with 
and its reported DUT MTF is identical to the real DUT MTF , meaning the system reports perfect measurement results.
Proof Of The Lower Bound
The lower bound is found by calculating the largest possible overestimation of the DUT MTF. And this largest possible overestimation happens when the DUT just happens to perfectly compensate all the aberrations that make the measurement system non-diffraction limited.
In such a perfect compensation scenario, the DUT has in fact the exact same MTF as the system, that is
(3) 
(4) 
To correct this error, the reported MTF has to be multiplied with the MTF measurement fidelity 
to retrieve the correct MTF value , and thus the lower bound is
(5) 
Proof Of The Upper Bound
The upper bound is found by calculating the largest possible underestimation of the DUT MTF. And this largest possible underestimation happens when the DUT itself is perfect, e.g. diffraction limited with
(6) 
to be identical to system MTF s with
(7) 
The MTF curves of such a largest possible underestimation look like this:
To correct this error, the reported MTF has to be divided by the MTF measurement fidelity to retrieve the correct MTF value (capped at the diffraction limit , of course), and thus the upper bound is
(8) 
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