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#28
 Fred_76 Registered User Join Date: Dec 2014 Location: Le Havre Posts: 16
Hi Joe,

You are absolutely right. Both formulas are based on the same theory, and both of us found the "14" factor. The only difference is that I took into account the Airy disk size (hence the 17xA term in the "full NPF formula"). I agree with you that the seeing has a minor effect (f/10).

If we neglect the Airy ans seeing contribution, we both arrive to the same formula :

t = 14*N*p(µm) / [ F(mm)*cos(dec) ]

(my formula is with n=1)

Assume that the original picture (full size, out of the DSLR) has a width of Wo pixels. It is then reduced (for Internet) to a width of Wi pixels. We can calculate the coefficient n = Wo/Wi and use that in the formulas.

Example :
- photo shot with a 1000D, pixel size = 5.7 µm, images are 3888 px witdh
- published image is 1000 px wide
- lens is a Canon 17 F/4 has a focal length of 17 mm, aperture of 4

Exposure time (declination = 0°)
- Fred : t=[17*4+14*5.7+17/10]/17=8.8 s => rounded to 9 s
- Joe : t=[14*5.7*3888/1000]/17=18.3 s => rounded to 18 s

If we combine our works, we can derive a better formula :

t = [17*A+7*(1+n)*p(µm)]/ [ F(mm)*cos(dec) ]

where :
A is the aperture
F is the focal length in mm
p is the pixel physical size on the sensor, in µm
n, two cases :
- photo to be published on screen : N=nb pixels width original / nb pixels width on screen
- photo to be printed with a resolution of nDPI : N=nb pixels width original / (width of print in inches x nDPI)

and the example becomes :
- Fred+Joe : t=[17*4+7*(1+3888/1000)*5.7]/17=15.5 s => rounded to 16 s

Note that in the case one uses a real B&W sensor the "1+n" factor shall be replaced by n only as there is no more CFA matrix.

Concerning my statement (in french), I agree with you that I did'nt invent anything. However, I did an extended survey, 5 years ago when I first publish my formula (here), to find out what kind of "rule of the thumb" was used. The most used was the "500 or 600 rule" and many photographers were claiming they had problems with these rules with their DSLRs. They were proposing some modifications by taking the crop factor into account, or by adding more parameters. These solutions were OK for their equipment, but not for all cases. That is why I tried to understand the physics behind and derived my solution.

In fact I discovered the 500 rule was already used in the film epoch and was working pretty well. But at that time, the films had to be used a high ISO grade for night shoots, with a quite poor resolution (600 to 1000 dpi on the film) and today, the DSLRs have a far better resolution (more than 4 times).

But as you explained me in PM, these formulas are too complex for most photographers. I therefore propose a simplier formulation assuming the following :
- allowable drift of about 1.5 pixels (n=1.5)

Therefore the formula becomes :

t = 25 x (N + p) / F, rounded to the highest available speed

where :
- N is the aperture
- p is the pixel width in µm
- F is the focal length in mm

again, in the above example, we get :

t = 25 x (4 + 5.7) / 17 = 14.3 s, rounded to 15 s

Last edited by Fred_76; 20-12-2014 at 12:27 AM.