Imaging

Professional slide film has a grain size of between 8 and 11 microns (Fuji Velvia 100F has an RMS grain size of 9 microns)
A 24 x 36 mm slide will be 24/9= 2667 grains by 36/9 = 4000 grains or a total of 4000 x 2667 = 10.7 M grains.
You need to scan at 25,400 microns/in. / 9 microns/grain = 2822 dpi.
Hence the common wisdom has it that a scan of somewhere between 3000 and 4000 dpi will capture just about all of the information there is on ISO 100 transparency film.

Notes:
1. A Micron (um) and micro-meter are the same thing 1/1,000,000 m.
1" = 25,400 um (microns)
2. RMS Granularity Ð Measures the noise in film, because it measures variation in an area of uniform density (usually 1.0D). RMS Granularity is not a measure of Ògraininess,Ó even though several publications have made this mistake.

Something called Nyquist's Theorem states that you would need to scan at at least twice the resolution to get the information in the original. That works out to about 5600 dpi and scanning at this would yield a file with over 40 megapixels. And it gets worse than that potentially for scanning film since grain is both irregularly sized and irregularly spaced.

Color print film A typical colour negative film (such as consumer 35 mm film) has silver-halide crystals to sense the light. These are (depending on the speed of the film - faster = bigger), in the range of 0.5 to 3 microns in diameter.

The term Òfilm grainÓ is often incorrectly used to describe the ÒfundamentalÓ particles in a chemical-based photographic image. Fundamental image particles are the smallest particles that form an image: (a) silver particles (0.2- 2.0 um) or (b) color dye clouds (10- 15 um), while grain is 10-30 um.
Film Grain in a color film is the accumulation of tens, to hundreds, of dye clouds in each of the nine dye layers found in modern color film.

Prints are formed of tiny dye-clouds, centred on the position of a silver-halide crystal that was exposed and developed. These dye clouds are formed from many very tiny (sub-micron) oil droplets which were coated with the silver halide, and each contains a chemical which reacts with oxidised developer to form dye. Dye clouds vary in size and can be generated from a number of silver halide crystals, depending on how much exposure there was in an area; they can overlap with each other, and of course the packing density of the silver-halide grains themselves has an impact on the granularity.

Transparency films are said to be grainless because there are no silver particles in the final emulsion, and the dye clouds have indistinct edges. While silver particle are present in color film before, and during, the many stages of the development process. At a point, the silver particles are bleached out.

See: Film Grain, Resolution and Fundamental Film Particles

A digital camera records only red, green or blue at each photosite in a Bayer mosaic pattern and interpolates the remaining values to the true resolution possible is dependent on the quality of the interpolation algorithm used. Each photosite can typically register 256 levels (8-bit) of luminance. A 10.1 MP Cannon EOS XTi produces about a 10-12 MB RAW12 file.

The human eye can resolve at best about 1 minute of arc, 1/3440. You can see things smaller than this, but you can't distinguish between two objects closer together than this. 300mm (12")/3400 yields 87 microns ; 300 dpi is 84 microns per dot. 2 dots are required for one period if we want to speak in terms of line pairs. Young human eyes may be able to resolve 60 microns.

It can distinguish about 100 levels of brightness and very early in our neural pathway, connecting eye to brain, we split the signals into colour and brightness (or in jargon - chrominance and luminance). We have three chrominance receptors, roughly sensitive to blue, red and green light. Our sense of luminance is derived about 60% from our green receptors, 30% from the red and only 10% from the blue. We can see luminance detail about 0.2mm wide in an image about 350mm or 14 inches away (normal viewing distance). We cannot see small details in chrominance.
So in a 4 x 6 print we can detect only 387 K (pixels).

Printing:
Dots per inch (DPI) and pixels per inch (PPI) are used interchangeably a lot of the time, but are not the same thing. For example, you can print an image on your 300dpi printer at 72ppi, 100ppi, or 300ppi.

Some HP documents say:
A photo printer needs at least 600 x 600 dpi.
Some offer up to 4800 x 1200 dpi color prints.
6 ink printers up to 73 Million colors.

Is this more hype to sell new printers, since the human eye can only detect 300 dpi at 12"? I guess if you want to look at your pictures thru a magnifying glass it might be necessary. I've got to look into the basis for this statement.

Bibliography:
Campbell, F.W. & Gubisch, R.W., Optical Quality of the Human Eye, Journal of Physiology, Vol. 186, pp. 558-578, 1966.

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