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01-07-2011, 12:34 AM   #1
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Combined effect of defraction, lens defocus and sensor/film size on resolution

I was inspired by comments in another post entitled 645N II vs. 67 II, in particular those by Luc Ibanec, to perform an analysis of resolution, taking into account the combined effects of diffraction, lens defocus and sensor type (film/digital) & size. I tried to use as realistic assumptions as practicable, though some of you may have differing opinions about what is appropriate. Please post whatever constructive comments as you wish, but please, no flaming - I have given this my best effort but do not claim to have any special knowledge of the truth so I would appreciate only responses in kind.

This analysis only looks at the issue of resolution. One may prefer digital over film or vice versa because of other issues such as the extent of micro-contrast, the type and quality of grain/noise, or the rendition of colour - but these issues are not addressed here.

The analysis is applied to nine different sensor/film and lens combinations and has two objectives: 1) to determine the maximum dimensions of a photo for each combination; and 2) to determine the maximum f-number that each combination is capable of when producing a photo of fixed 24in horizontal dimension and similar resolution. In all cases, the photos are assumed to be viewed at the limit of visual perception for 1m setback where details are resolved to MTF50. Below I list the assumptions and then the results.

FILM/SENSOR

I considered three digital sensor configurations and three film sizes assuming two different types of film:

DIGITAL:
Nikon D300: 12.3 MP, DX 15.8mm x 24.6mm, MTF50: 90.8 lp/mm;
Nikon D3x: 25.4 MP, FX 24mm x 35.5mm; MTF50: 84.8 lp/mm;
Pentax 645D 40 MP, MF 33mm x 44mm; MTF50: 83 lp/mm;

FILM - MTF50: 1) Velvia 100 - 50 lp/mm; and 2) B&W - 100 lp/mm
35mm: 24mm x 36mm;
Pentax 645: 41.5mm x 56mm; and
Pentax 67: 56mm x 69mm.

The MTF50's for film are taken from manufacturer's data; for digital from pixel density, assuming 2 pixels per line pair to resolve to MTF50 with no account of aliasing. Thus, the MTF50's may be optimistic for digital on both accounts, but my experience leads me to believe that state-of-the-art digital sensors are currently out resolving the best colour films at the pixel density/film grain level so the assumption stands.

LENS DEFOCUS

By lens defocus, I mean blurriness caused by aberrations, but not diffraction. I assume and MTF50 of 150 lp/mm for the 35mm and smaller sensors/film and 105 lp/mm for medium format. These MTF's correspond to the very best lenses of each type used at optimum f-stops in the range of f/5.6 to f/8. The effect of increased aberrations at lower f-numbers is not accounted for, and the effect of diffraction is taken account separately.

LENS DIFFRACTION

The Rayleigh diffraction limit given in lp/mm by 1/(1.22*N*lambda), where N is the f-number and lambda is the wavelength of light, assumes an MTF of zero. At MTF50, I have used lp/mm = 0.38/(N*lambda), and assume lambda = 0.5 microns, which is the wave length of daylight.

OVERALL RESOLUTION AT MTF50

I have assumed the overall serial model:

1/lp/mm(overall) = 1/lp/mm(film/semsor) + 1/lp/mm(lens) + 1/lp/mm(diffraction)

This is a common model for the combined effect of the sensor and the lens. One can determine with greater accuracy the combined effect of lens defocus and diffraction by numerical integration, but I have found that the serial model above provides a pretty good approximation, good enough to resolve trends, which is really the objective of this study.

VISUAL ACUITY

I have assumed a visual acuity of 300 ppi at 25cm setback. This corresponds to 1.15 arcminutes, which is a little lower than 1 arcminute (350 ppi at 25cm) for 20/20 vision. Some say that the ultimate limit for humans is about 0.6 to 0.8 arcminutes for centre vision, but since most people who view photos in galleries and most people who use these cameras are not 18 year olds with perfect vision, the 300 ppi limit seems appropriate to me.

OVERALL METHOD

Use the visual acuity assumption of 1.15 arcminutes to determine pixel density for viewing at 1m setback, convert to lp/mm (assuming 2 pixels per line pair), and match with the lp/mm(overall) for each sensor/lens combination at a given f-number. Repeat for all combinations and f-numbers.

RESULTS FOR MAXIMUM COLOUR PHOTO SIZE

Results are given at f/8, 1m setback, and limit of visual acuity, rounded to the nearest inch:
12.3 MP DX sensor: 15in x 22in;
35mm film: 17in x 25in;
25.4 MP FX sensor: 22in x 32in;
40 MP MF sensor: 27in x 36in;
645 film: 27in x 37in; and
67 film: 37in x 45in.

Conclusions: In terms of resolution, 35mm film is slightly better than that of the 12.3 MP DX sensor, but not as good as the 25.4 MP FX sensor, which is capable of producing a large size print at 22in x 32in. The 645D and the 645 film cameras produce almost the same size photo, which leads one to wonder if this was the intention of the Pentax designers. At 27in by 36in, the 645D photo is larger than that produced by the FX sensor, but not so much larger that one could not consider using the two camers interchangeably in many instances. The 67 still reigns as the camera capable of producing the largest photo by a significant margin.

RESULTS FOR MAXIMUM B&W PHOTO SIZE

Results are given at f/8, 1m setback, and limit of visual acuity, rounded to the nearest inch:
12.3 MP DX sensor: 15in x 22in;
25.4 MP FX sensor: 22in x 32in;
35mm film: 23in x 35in;
40 MP MF sensor: 27in x 36in;
645 film: 39in x 49in; and
67 film: 49in x 60in.

Conclusions: In terms of resolution, B&W film still rules the day. The 35mm film produces a photo size about the same as the 25.4 MP FX sensor. The 645 film produces a photo significantly larger than that of the 645D, and the 67 produces a huge 49in x 60in print.

RESULTS FOR MAXIMUM f-NUMBER ASSUMING FIXED COLOUR PHOTO DIMENSION

Results are given for a colour print with 24in horizontal dimension viewed at 1m setback for the largest f-number possible satisfying the same limit of visual acuity:

12.3 MP DX sensor: f/5.6;
35mm film: f/10;
25.4 MP FX sensor: f/16;
40 MP MF sensor: f/20;
645 film: f/25; and
67 film: f/35.

Conclusions: The results do indeed show that the effect of diffraction on resolution is predominantly dependent on both the diffraction limit of the lens and the size of the sensor/film. In this regard, the new 645D demonstrates better performance than the FX sensor, but not as good as the 645 or 67 film cameras, with significantly bigger film/sensor areas.


Last edited by ARCASIA; 01-07-2011 at 02:55 AM.
01-07-2011, 02:01 AM   #2
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Great work!

I'm just trying to figure out what you're saying here.

So, first of all, do your results for f-stop and diffraction relate to focal length at all? I mean, f/32 at 33mm (33-55mm lens) results in a 1mm aperture. However, f/32 on a 300mm lens results in a 9.4mm aperture. A 1mm is like a pinhole and that would seem to result in greater diffraction than a hole that's almost 3/8" wide (9.4mm). Am I right?

Regarding these results:

12.3 MP DX sensor: f/5.6;
35mm film: f/10;
25.4 MP FX sensor: f/16;
40 MP MF sensor: f/20;
645 film: f/25; and
67 film: f/35.

Are you saying that an image with 645 film @ f/25 will look the same as 40 MP MF sensor @ f/20?

So, if I'm shooting my 645NII at f/22 to f/32 most of the time, that's the equivalent of f/18 to f/25 on the 645D (based on the crop factor). Since I'll be at these small apertures most of the time, does digital in any way "magnifiy" the effects of diffraction over what you'd see with film? I remember talking to an engineer at Schneider who said that diffraction becomes a big problem after f/8. And, I'm thinking, huh? If that's the case, then I'm screwed!

Thanks for your help and the great work.
01-07-2011, 02:45 AM   #3
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Hi Mike,

Welcome to the Pentax MF Forum and thank you for your kind remarks. I will try to answer your three questions:

1) Yes, the MTF50 equation for defraction I used, which is based on the Rayleigh diffraction limit, gives the lp/mm resolution as a function of the f-number, which if you recall. is the ratio of the lens focal length divided by the exit pupil diameter. So the focal length is taken into account'

2) Yes, but more precisely, when viewed at 1m setback, a print with 24in horizontal dimension will have the same resolution if the picture were to be taken with the 645D set at f/20 or with the 645 film camera set to f/25. There may be a difference in appearance between the two photos due to other factors.

3) A very good question. The pixels of digital sensors are located at the bottom of structural wells. If light leaves the lens parallel to the optical axis, as in a telecentric lens design, the well structure will not affect the (vertical) incidence of light onto the pixels. Modern lenses made for use with digital sensors are designed as practicable to achieve this. If however, the light from the lens is not vertically incident, the light will hit the corner of the well and be diffracted towrds the pxel, causing distortions, often in the form of chromatic aberration. The extent to which this may be a problem depends on the particulars of the sensor and lens design. I have not taken this into account in my analysis.

Best, Alan

QuoteOriginally posted by chicagonature Quote
Great work!

I'm just trying to figure out what you're saying here.

So, first of all, do your results for f-stop and diffraction relate to focal length at all? I mean, f/32 at 33mm (33-55mm lens) results in a 1mm aperture. However, f/32 on a 300mm lens results in a 9.4mm aperture. A 1mm is like a pinhole and that would seem to result in greater diffraction than a hole that's almost 3/8" wide (9.4mm). Am I right?

Regarding these results:

12.3 MP DX sensor: f/5.6;
35mm film: f/10;
25.4 MP FX sensor: f/16;
40 MP MF sensor: f/20;
645 film: f/25; and
67 film: f/35.

Are you saying that an image with 645 film @ f/25 will look the same as 40 MP MF sensor @ f/20?

So, if I'm shooting my 645NII at f/22 to f/32 most of the time, that's the equivalent of f/18 to f/25 on the 645D (based on the crop factor). Since I'll be at these small apertures most of the time, does digital in any way "magnifiy" the effects of diffraction over what you'd see with film? I remember talking to an engineer at Schneider who said that diffraction becomes a big problem after f/8. And, I'm thinking, huh? If that's the case, then I'm screwed!

Thanks for your help and the great work.
01-07-2011, 11:45 AM   #4
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Alan, thanks. That helps! Again, I appreciate you efforts.

01-07-2011, 12:51 PM   #5
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Your figure from pixel spacing to MTF 50 is too optimistic for digital sensor even no color demosiacing is involved. On film silver halide crystal distribution is random but he sensor pattern is regular and how it affects MTF measurement is highly depending on methodological details. The presence of AA filter complicates the matter even much further and depending to the real characteristics of such filters.

Yes to resolve a line pair you only need two pixels, one dark and one bright. However there are equal chance the lines on the target are right centered to the pixels or right in between, in later cases the both pixels would be equal and gray. Statistically therefore an approximate factor to use is 3db reduction, or devide by square root of two. Thus, for example the 6um 645 sensor can only reliably resolve (1/0.006)/2/1.414 = 59 lpr/mm, which is the realistic requirement for lens resolution. This is in line with the old MF lens MTF measurements where they found the best lens can reach around 65-75 lpr/mm at the center. Usually the Hasselblad and Mamiya ones are the highest at the center but fall down fast towards the edges, while the Pentax lenses tend to be more even, 65 center and 50 edges, for example. Evidences so far do show these best lenses resolve to the 645D 40MP sensor limit.

Last edited by leping; 01-07-2011 at 01:02 PM.
01-07-2011, 07:09 PM   #6
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Hi Leping,

Thank you for your comments. I too struggled over the issue of how many pixels are required to resolve a line pair to MTF50 with a digital sensor. Many people routinely use 2 pixels per line pair and ignore the issue of alignment. But as you point out, depending on alignment, this results in the MTF ranging from 0 (no contrast) to 1 (perfect contrast). However, a statistical average would result in an average MTF of 50%.

With 3 pixel resolution, the lp/mm count is about 59 lp/mm for the three sensors considered, not taking into account aliasing. Depending on alignment, the resulting MTF would range from 33% to 66%, with the statistical average again at an MTF of 50%. One would think that the results of MTF tests would show much less variance in the results if 3 pixels per lp was the more accurate assumption.

As for the effect of aliasing, I have seen photo comparisons between sensors with and without a low pass filter installed to remove the effect of aliasing. The photos shown without the filter installed were indeed sharper, but in some photos, Moire patterns were evident. But strictly speaking, application of alias filtering in accordance with the Nyquist criteria would reduce the resolution of the sensor by 1/2. Perhaps implimentation of low pass filters on modern sensors is not so strict and some compromise is accepted, but I do not have this type of information.

For comparison, I recalculated some results given below assuming 3 pixels per lp, but not taking into account anti aliasing. These assumptions correspond to a digital resolution round about 59 lp/mm at MTF50, as you have suggested.

RESULTS FOR MAXIMUM COLOUR PHOTO SIZE - 3 pixel per lp digital resolution

Results are given at f/8, 1m setback, and limit of visual acuity, rounded to the nearest inch:
12.3 MP DX sensor: 12in x 18in;
35mm film: 17in x 25in;
25.4 MP FX sensor: 18in x 27in;
40 MP MF sensor: 23in x 30in;
645 film: 27in x 37in; and
67 film: 37in x 45in.

My problem with these results is that they indicate that modern 25MP FX digital sensors resolve to about that of 35mm film, and that the 645D has significantly less resolution than the 645 film camera. I believe that these results run against the preponderance of current opinion.

As for lens defocussing, most of the resolution tests performed that I have seen test the lens together with the camera, so one gets the combined resolution of the sensor/film and lens. If we assume such a test yields 34lp/mm for MF film, and 54lp/mm for modern digital, common values, we can back out what would be the lens only resolution, which with my initial assumptions (but ignoring diffraction) would correspond to a 105lp/mm MF lens and a 150lp/mm 35mm lens.

Best, Alan

QuoteOriginally posted by leping Quote
Your figure from pixel spacing to MTF 50 is too optimistic for digital sensor even no color demosiacing is involved. On film silver halide crystal distribution is random but he sensor pattern is regular and how it affects MTF measurement is highly depending on methodological details. The presence of AA filter complicates the matter even much further and depending to the real characteristics of such filters.

Yes to resolve a line pair you only need two pixels, one dark and one bright. However there are equal chance the lines on the target are right centered to the pixels or right in between, in later cases the both pixels would be equal and gray. Statistically therefore an approximate factor to use is 3db reduction, or devide by square root of two. Thus, for example the 6um 645 sensor can only reliably resolve (1/0.006)/2/1.414 = 59 lpr/mm, which is the realistic requirement for lens resolution. This is in line with the old MF lens MTF measurements where they found the best lens can reach around 65-75 lpr/mm at the center. Usually the Hasselblad and Mamiya ones are the highest at the center but fall down fast towards the edges, while the Pentax lenses tend to be more even, 65 center and 50 edges, for example. Evidences so far do show these best lenses resolve to the 645D 40MP sensor limit.
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