Comparing lens MTF figures with sensor resolution

[Class A]

I'm interested in comparing lens MTF-50 resolution figures with sensor resolution. It would be interesting to know at which point (in terms of choosing a lens or aperture) a lens would be sharp enough to outresolve the sensor.

MTF-50 figures are given in LW/PH. For instance 2000 LW/PH means that 2000 line widths are resolved across the vertical length of the picture with a 50% loss of relative contrast. Because one looks at a pattern of alternating white and black lines, one can speak of 1000 lines (say black lines on a white background) or 2000 line widths.

Now we can assume the vertical height of the picture to be the height of the sensor, say 15.7mm (ignoring unused pixels). This allows to relate the LW/PH resolution to the number of vertical pixels.

I believe in order to achieve a relevant comparison one has to do the following: Find out how many line widths per millimetre cause a 50% loss of relative contrast when viewed through a grid with the resolution of the vertical sensor resolution. Is it as simple as saying that 1.3 x the number of line widths will cause that resolution loss? If I see 1.3 N line width through a N line width grid, then each grid line blurs 1 + 1/3 line widths so the contrast between adjacent grid line widths should be 1/3 : 2/3 = 0.5 (50%).

So am I right that 2008 vertical pixels correspond to ~2677 LW/PH?

This assumes a monochrome image. Due to the bayer array structure of the sensor, the colour resolution will be reduced. The minimum should be ~1339 LW/PH, but in reality it should be somewhere between these values as interpolation can recover information for say image positions occupied by red pixels by using information from adjacent green pixels. This will lead to real resolution gains as long the light that hit the red pixel had some green component.

Is there an error in my thoughts and/or is it meaningful/reasonable to use such an assumed sensor MTF-50 figure to reason about a sensor being outresolved by a lens?

In the aboveI omitted the anti-aliasing filter. What could be considered to be a very aggressive anti-aliasing filter? One that spreads the light for one pixel so that adjacent pixels are covered half?

Also, I'm wondering how to correctly interpret the PH (picture height) in LW/PH. It seems that one cannot simply assume say 15.7mm PH for a measurement that was taking on a sensor with 24mm height. The only way I think that PH can be independent from sensor size is if it is independent of sensor size but refers to the image circle size of a lens. Does that mean that one has to convert MTF-50 resolution figures given for full frame lenses in order to understand their resolution on a APS-C sensor?

EDIT: I edit the above because I realised I made a hash of the multiplication factor. Should be 1.3 instead of 3x. At 2x the contrast is already completely gone.

[Colin Southern]

"Does that mean that one has to convert MTF-50 resolution figures given for full frame lenses in order to understand their resolution on a APS-C sensor? "

To be honest, I wouldn't have a clue! My understanding is that the 50D currently has the highest pixel density - and I read somewhere that the sensors still had a ways to go before it could out-resolve top lenses, but it's not something I've gotten in to. One thing to consider though (outside of the test tube) is that correct sharpening can have a far greater effect on the quality of an image than "this lens over that lens" or "this sensor over that sensor" - and most people don't understand correct sharpening. In reality we've had sensors with more than enough MP for many years now that are quite capable of producing more than acceptable images at normal viewing distances.

Welcome to the forums by the way - it's great to have another Kiwi with us (rumour has it we're mounting a takeover!) (4 that I know of so far).

Cheers,

Colin (in Nelson)

[McQ]

Does that mean that one has to convert MTF-50 resolution figures given for full frame lenses in order to understand their resolution on a APS-C sensor?

My understanding is that full frame lenses list their MTF values according to the line pairs per picture height of a full frame sensor. In order to understand their impact on a smaller APS-C sensor you will indeed need to do a conversion. This is in part one of the big drawbacks of the APS-C sensors: that they will have slightly worse micro contrast and extinction resolution for a given print size, when compared to a full frame sensor. On the other hand, the best MTF is in the center of the frame anyways, and APS-C sensors crop out the lower MTF edges of the full frame...

I believe in order to achieve a relevant comparison one has to do the following: Find out how many line widths per millimetre cause a 50% loss of relative contrast when viewed through a grid with the resolution of the vertical sensor resolution. Is it as simple as saying that 3 x the number of line widths will cause that resolution loss?

You cannot always extrapolate to an extinction resolution based on the MTF-50 resolution. It all depends on the slope and shape of the MTF curve. A lens with some vaseline on it would have a very poor MTF-50, but may very well still have a great extinction resolution (the so called MTF-0).

Cambridge in Colour sorely needs a page on this topic in the "advanced topics" section...someone should really get around to that

[Class A]

Hi Colin,

good to see another Kiwi photog! I'm from Welly, BTW.

I read somewhere that the sensors still had a ways to go before it could out-resolve top lenses

It depends on the aperture. According the quite substantial "Do Sensors “Outresolve” Lenses?" article at luminous landscapes, you "only" need 16MP on a full frame sensor to capture the resolution at f/11 (assuming the lens is diffraction limited at that point). This is in accord with the calculator at one of the great cambridge in colour tutorial at https://www.cambridgeincolour.com/tu...hotography.htm.

One thing to consider though (outside of the test tube) is that correct sharpening can have a far greater effect on the quality of an image than "this lens over that lens" or "this sensor over that sensor"

I think you are quite right there. With proper sharpening I have achieved astonishing sharpness without causing havoc to areas of the image that shouldn't be sharp. Sharpness is a combination of resolution and contrast and it appears a lot can be gained by bringing back contrast with PP.

[Class A]

My understanding is that full frame lenses list their MTF values according to the line pairs per picture height of a full frame sensor.

That would make sense. I wish the unit were "per mm" instead of "per picture height". The later appears to have been introduced to be agnostic about sensor sizes, but it seems the contrary has been achieved.

On the other hand, the best MTF is in the center of the frame anyways, and APS-C sensors crop out the lower MTF edges of the full frame...

Yes. Someone has a funny signature along theses lines: "Ah, full frame. At last we get our blurry corners back. But luckily we cannot see them as well because of the vignetting."

You cannot always extrapolate to an extinction resolution based on the MTF-50 resolution. It all depends on the slope and shape of the MTF curve.

Makes sense. I just didn't know how to sensibly approach the comparison between lens and sensor resolution. Any further hints or even a tutorial(!) would be very much appreciated.

Please note that I have corrected an error in my original posting. I got the algebraic part of working out the number of LWs right, but then forgot to add a 1 to the fraction (1/3) I had figured out.

[Colin Southern]

"Sharpness is a combination of resolution and contrast and it appears a lot can be gained by bringing back contrast with PP."

As a "typical borderline excessive/compulsive photographer" - and one who also sells prints commercially, I'm often "torn between two masters" - on one hand there's the compulsive desire for "the best" - more MP - greater clarity - more resolution etc, but in reality it doesn't add any commercial value to the product for sale.

My typical print size on canvas is 22 x 44 inches - and I can't say that at normal viewing distances that I'm seeing any great differences between the images from my old 20D compared to ones from my 1Ds3; I think people rightly work out that images look poor at a certain distance below a certain resolution - and yet they forget about the law of diminishing returns when it comes to the opposite direction - and they compound the erronious thinking with poor or non-existant capture sharpening, so you get wonderful statements like "I don't like to print under 360ppi" and in the same breath "What's capture sharpening?"

My personal solution to the great dilema is to just go out and take some photos

Cheers,

Colin - pbase.com/cjsouthern