Megapixel Equivalence of Film

Resolution of digital cameras is often given in megapixels (MP). In order to compare film resolution with digital capture resolution we use the diffraction limited resolution of the lens at a particular f-stop as well as the resolution of the film given by the film's MTF and derive a comparative estimate.

The Rayleigh limit determines the maximum aerial resolution of a lens having f-number f and light wavelength of λ, with units of line pairs per mm when λ is in mm:

rayleigh[f_,λ_] := (1/(1.22 f λ))

For recording media with MTF of r2 in line pairs per mm, recording image having rayleigh limit r1 in line pairs per mm, R is defined as:

R[r1_,r2_] := (1/r1)+(1/r2)

Where the recording media has dimensions x and y (mm), and equating a line pair as 2 pixels, we can estimate the equivalent resolution of film in megapixels as:

mp[f_,λ_,mtf_,x_,y_] := ((4 x y)/((10^6)(((R[rayleigh[f,λ],mtf]))^2)));

In the following panel use the sliders to adjust mtf value to the MTF of the recording media of interest, then adjust the x and y sliders to the width and height of the recording media. The resolution estimate is plotted as a function of the f number, e.g. at the default values of mtf = 40 line pairs per mm, x = 100 mm and y = 200 mm, f/45 produces a MP equivalence of approximately 30 MP whereas at f/16 the resolution is approaching 50 MP.

Manipulate[Plot[mp[f,.00055,mtf,x,y],{f,1,64},PlotRange->{0,250},Filling->Bottom,GridLines -> {{2,2.8,4,5.6,8,11,16,22,32,45,64},Automatic},AxesLabel->{Style["f",16],Style["MP",16]},Ticks->{{5.6,8,11,16,22,32,45,64},Automatic}],{{mtf,40},10,100,10,Appearance->"Labeled"},{{x,100},24,200,1,Appearance->"Labeled"},{{y,125},36,250,1,Appearance->"Labeled"},SaveDefinitions->True]

Copyright © 2009 Jim Michael
Please email comments and corrections to jm@10squaredcorp.com