Numbers don't mean anything on their own. To clarify everything above, all you need to do is put it all into context, and this is done by applying a little theory. First let's look at the paper LER. As with the film speed point, the 90% of D-max of the paper is just a point of measurement. Remember what I said about needing to define the limiting points of quality on the film curve? It's the same principle here. Loyd Jones found that after 90% of a paper's D-max perception of tonal separation drops off (it's never about density. It's about tonal separation). He never suggested that this is the usable range of the paper. In fact, the graph below is from the Theory of the Photographic Process and it illustrates this concept using a tone reproduction curve. The curve is generated by comparing the resulting print with the original subject.

Luminance Range.jpg

The average luminance range is 2.20 or 7 1/3 stops, but this doesn't represent the entire luminance range of the average subject. There usually are small areas of specular highlights and "cavity" shadows. The graph brings this out to a luminance range of 3.0 or 10 stops. So it's easy to understand how the ISO LER for a grade two paper is 1.05 even though a paper can handle a negative with a greater negative density range. The ISO LER of 1.05 only represents the 2.20 part of the luminance range.

Now if the paper can handle a 1.20 density range (paper D-max and D-min), and the film is processed so that the 2.20 range equals a density range of 1.20, then there's nothing left over for the specular highlights and cavity shadows. So how can Ralph suggest a negative density range of 1.20 for a 7 stop luminance range? The reason has to do with how the curves are measured.

Gradient is defined as rise over run. The luminance range is the run and the negative density range is the rise. 1.20 / 2.10 = 0.57. The standard model uses a luminance range of 2.20 and a negative density range of 1.05. The difference is that it factors in a flare factor. The subject luminance range is reduced at the film plane by veiling flare. Whatever the actual range of the subject might be, the determination of the degree of processing is based on the optical image at the film plane. Average flare is around 1 to 1 1/3 stops. Kodak uses 0.40 or 1 1/3 stops of flare in their calculations. 1.05 / (2.20 - 0.40) = 0.58.

Both methods produce almost identical gradients. The gradients of 0.57 and 0.58 are ideal for producing quality negatives printed on grade two glossy paper using a diffusion enlarger. As gradient is input to output, if the gradient values are the same, the same input will produce the same output. How then can the theoretical output numbers not be equal? Simple. One uses flare in it's calculation and one doesn't. Mathematically, In order for the no flare method to produce the target gradient, the rise must be higher. For a gradient of 0.57 / 0.58, a density range of 1.20 is where a seven stop illuminance range (note: not luminance range) will fall, but we are not processing the film for a 7 stop illuminance range but for around a 6 stop illuminance range. At around the 6 stop illuminance range, the negative density range falls around 1.05.

There is a chart in Photographic Materials and Processes that has the aim LERs for printing with a diffusion enlarger and a condenser enlarger. For printing on a grade two paper with a diffusion enlarger, it has the aim LER as 1.05. For a condenser enlarger it has it as around 0.80. Mind you this is for the same paper. As the aim numbers are for negatives printing with enlargers, we can reasonably conclude that the aims take into consideration some degree of flare. The reason why the diffusion enlarger LER aim is the same as that derived from a contacted test is because there is a slight Q-factor with the diffusion enlarger that tends to compensate for average enlarger flare.And I have not even thought much yet about the impact of enlarger flare.