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.