Resolution of digital SLR cameras, lens matching and film resolution

 

 

 

Bayer CCD

 

Sometimes, Bayer CCD can recognize spatial frequencies 1/(2*pixel size), but for near 0 phase shift only. For phase shift (relatively CCD sensors position) near½ or ¾ pixel, contrast tend to zero value. Then, recognizing of spatial frequencies 1/(2*pixes size) is not dynamically stable.

 

For spatial frequencies 1/(2*1.25*pixel size) lines recognized, but with contrast loss. Dynamical stability for this spatial frequency is not so good (MTF drop at some phase shifts, aliasing appeared).

 

For spatial frequencies 1/(2*1.5*pixel size) and less MTF tend to 100% (with adjacent pixel low contrast). Spatial frequencies less than 1/(2*1.5*pixel size) are dynamically stable for recognizing by CCD and digital cameras firmware.

 

 

SuperCCD, diagonal reading of the Bayer structure (white squares mean pixel that needed to spatial interpolation)

 

Like Bayer CCD, SuperCCD sometimes can reach 100% MTF at 1/(2*pixel size) spatial frequency (when phase shift near to 0 value). I have some pictures where this limit is reached really. For phase shift values near ½ or ¾ pixels, MTF value is equal to zero.

For spatial frequency 1/(2*1.25*pixel size) MTF value according to phase shift, fluctuate from 30% to 75%. All lines can be recognized, but MTF cannot be defined because of low dynamical stability (aliasing appear).

For spatial frequency 1/(2*1.5*pixel size) all lines are recognized with MTF tend to 100% value (average value is 87.5%).

 

5x scaled (by nearest neighbor algorithm) sample from S2Pro camera in 4288x2880 resolution. Spatial frequency 1/(2*p) is recognized (because little phase shift near 0 value by accident.

 

 

 

Then, we able to calculating maximum (CCD based) resolutions of the popular cameras

Nikon D100, CCD size 23.4x15.6mm, 3032x2016 pixels, 7.8 um

Dynamically stable resolution: 3032/23.4/2/1.5 = 43.2 lp/mm, 1011 line pairs/long side

Dynamically unstable resolution: 3032/23.4/2/1 = 64.8 lp/mm, 1516 line pairs/long side

 

Canon D60, CCD size 22.7x15.1mm, 3072x2048 pixels, 7.4um

Dynamically stable resolution: 3072/22.7/2/1.5 = 45.1 lp/mm, 1024 line pairs/long side

Dynamically unstable resolution: 3072/22.7/2/1 = 67.7 lp/mm, 1537 line pairs/long side

 

Fujifilm S2Pro, CCD size 23.0x15.5, read 4288x2880 pixels (with spatial approximation)

Dynamically stable resolution: 4288/23.0/2/1.5 = 62.0 lp/mm, 1426 line pairs/long side

Dynamically unstable resolution: 4288/23.0/2/1 = 93.2 lp/mm, 2144 line pairs/long side

 

Canon D1s, CCD size 35.8x23.8mm, 4064x2704 pixels

Dynamically stable resolution: 4064/35.8/2/1.5 = 37.8 lp/mm, 1353 line pairs/long side

Dynamically unstable resolution: 4064/35.8/2/1 = 56.8 lp/mm, 2033 line pairs/long side

 

Kodak DCS 14n, CCD size 36x24mm, 4536x3024 pixels

Dynamically stable resolution: 4536/36/2/1.5 = 42.0 lp/mm, 1512 line pairs/long side

Dynamically unstable resolution: 4536/36/2/1 = 63.0 lp/mm, 2268 line pairs/long side

 

What is strange resolution of S2Pro never was equal (moreover, never was better) per long side than resolutions of Canon -1Ds or Kodak DCS 14n in the objective tests. There is, at least, 2 reasons:

-         S2 Pro has more CCD resolution, that (as a rule) cannot reached by the most lens. If MTF of the lens at spatial frequency 93 lp/mm is about 3-5%, product of CCD MTF and lens MTF will be less than visible 2-3% contrast. Then, at testing must be used superior lens for comparable results. Second conclusion is that for S2Pro we must use excellent lens if we want to get Super CCD resolution advantage (50-60 lp/mm for 11-14Mp cameras can be derived from more cheap lens than lens that produce 90lp/mm with visible contrast).

-         S2Pro produce more noisy images at high spatial frequencies because of spatial interpolation.

 

Some comments about the film technology.

Fujifilm developers estimated resolution of Velvia film (G=9) about 30 millions of effective elements (in 3 layers, that mean 10 Mpixels image) and about 50 millions for Provia 100F.

 

I calculated another way by the same results:

(1) Granularity = 100/M,

where M = minimum magnification scale, when granularity become visible.

(2) Human eye dot resolution is 0.1mm = 100microns

 

Then, for known Granularity factor (G), size of the grain (S) will be

S = G/10^6

Fuji Provia 100 (old) with G=10 have visible grain size about 10microns = effective pixel size

Resolution = 36mm/10um x 24mm/10um x 3 layers = 3600x2400x3 = 26 Mp (or color 9Mp)

Fuji Velvia 50 with G=9 have visible grain size about 9 microns

Resolution = 36mm/9um x 24mm/9um x 3 layers = 4000x2467x3 = 32 Mp (or color 10.6Mp)

Fuji Provia 100F with G=8 have visible grain size about 8 microns

Resolution = 36mm/8um x 24mm/8um x 3 layers = 4500x3000x3 = 40.5 Mp (or color 13.5Mp)

I dont know, why Fuji developers estimated 50 millions of elements may be, they calculated this value for 4 layers film?

 

This estimating made for visible grain size, we can recognize some details that made by little b/w grains with sizes less than 1 microns (but in this case S/N ratio will be very small, about 1).

 

Film resolution (135 lp/mm for Provia 100F etc.) calculated for MTF about 7% and for alone black&white grains (with S/N=1) is not dynamically stable. I think that for film/sensor compare we should using low-contrast (grayscale) resolution value that is 63 lp/mm for Provia 100F.

Another way is using 20% MTF threshold, which reached at the same 63 lp/mm like dynamical stability threshold. (from spatial frequency 20-30 lp/mm, contrast cannot derived from biggest grains (its are exposed by less spatial frequencies) and derived from less grains (in the background of big grain) that lead to contrast drop.

 

 

MTF of the Fujifilm Provia 100F (derived from official pdf document, extrapolated for spatial frequencies 60-135 lp/mm).

 

Moreover, I think, I can explicate, why scanning with 8000dpi instead of 4000 dpi can produce only a bit of additional details.

4000 dpi scanning can resolve dynamically stable 4000/25.4/3lpmm = 52.5 lp/mm or dynamically unstable 4000/25.4/2lpmm = 78 lp/mm

8000 dpi scanning can resolve dynamically stable 8000/25.4/3lpmm = 103 lp/mm or dynamically unstable 8000/25.4/2lpmm = 156 lp/mm

Because of better of non-special films can reached (at 1000:1 test target and S/N=1) dynamically unstable 135-145 lp/mm (with 5-7% MTF, best lens can resolve about 100 lp/mm (with 3-5% MTF), then united lens-film resolution with MTF>3-5% will be about 60 lp/mm (that required 60*3 lpmm*25.4 = 4572 dpi scanner resolution for non-aliased scanning).

This resolution mostly can be recognized by 4000dpi scanners. 8000 dpi scanner with the same lens like 4000dpi scanner can add about 60-52.5/52.5 = 14% extra information about object and as a rule, 8000 dpi scanners have more complicated lens with better MTF, that lead to 20-25% extra recognized details of image (not about of film grain, which will recognized more better).

Using of 8000 dpi scanner is needed for high-resolution microcopies/microfiches films with more than excellent (in terms of resolution) special high-contrast lens for microcopies production.

 

TeddyBear http://digicam.narod.ru

20/10/2002

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