FZ200 Diffraction Limit - Panasonic Tech Service

Started Aug 27, 2013 | Discussions thread
Stephen Barrett Contributing Member • Posts: 683
Are 2 pixels per line-pair enough?

J C Brown's assessment of the FZ50 (Section 7 of his paper for Black & white resolution) is that it can resolve at least 1850 lpph (line-pairs per picture height).

The Cameralabs review says 2100 lpph at f/4.0.

The sensor has 3648 x 2738 pixels, so the number of pixels per line-pair is
2738 pixels / 2100 line-pairs = 1.3 pixels per line-pair. This seems to give somewhere around 10% MTF total camera resolution, including the sensor, lens and and all the "filters", demosaicing algorithms and crosstalk etc.

In view of this, 1.3 pixels per line-pair appears to be enough to give approximately 10% MTF total resolution, and possibly more than enough for the sensor alone.  A large number of lines in a test pattern would probably exhibit aliasing and other distortions, but the pattern would not be extinguished everywhere.

Some Crude Calculations
With my Canon SX30 at full optical zoom f/5.8 (wide open for full zoom) and infinite focus, the camera resolution (approx 10% MTF) is approximately 30 microradians.

30 x 10 ^ -6 radians x 150.5 mm = 0.0045 mm (test value)
4.55 mm sensor height / 3240 pixels = 0.0014 mm per pixel

Lens resolution (old Zeiss formula for white light & nearly-perfect optics)
= 1600 / 5.8 = 276 line-pairs / mm or 0.0036 mm line-pair separation.

Sensor resolution assuming 2 pixels per line-pair = 2 x 0.0014 mm = 0.0028 mm

Total resolution (approx 10% MTF) from square root of the sum of the squares
= 0.0046 mm or approx 30 microradians, in good agreement with the test result.
Frequency = 1 line-pair / 0.0045 mm = 222 line-pairs / mm.

Even though the this method seems to give good agreement with several types of tests (telephoto, macro & telemacro) for my camera, I am not satisfied with it because it is hard to justify the 2 pixels per line-pair in the calculation when the final image on the sensor has about 3 pixels per line-pair. The MTF calculations (frequency domain) that Detail Man advocates do not suffer from such inconsistencies.

Better Calculations in the Frequency Domain
At the observed frequency of 222 line-pair per mm, the lens has more than 10% MTF, and so does the sensor with approximately 3 pixels per line-pair. When the MTFs of the lens, sensor and all the "filters" are all multiplied together , the result is the total MTF. This computation can be performed as a function of frequency until the estimated test value of approximately 10% is obtained. The corresponding calculated frequency, which is a measure of the resolution, can then be compared with the test value of 222 line-pairs per mm.

Tentative Conclusion

Tentatively, I would conclude that in my tests, I was obtaining approximately 10% MTF total resolution at frequencies corresponding to about 1 line-pair per every 3 pixels. J C Brown and Camerlabs showed some test results on the Panasonic FZ50 with similar resolution at frequencies above 1 line-pair per every 1.5 pixels. We are looking at fairly poor resolution, close to extinction but, for that purpose, it appears that 2 pixels per line-pair are sometimes enough.

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