Relationship Between Constants

[Stephen Benskin]

On page 190 of D. Connelly's paper Calibration Levels of Films and Exposure Devices,here, there is an equation (circled) where Connelly defines a value of K as 8/0.65. What's interesting is that 8 and 0.65 are also constants: P and q respectively. That makes the equation K = P/q. This illustrates the interconnection between the different constants in the process of exposure. K is connected to the exposure meter, q to the camera exposure, and P to the film exposure. If any two constants are known, the third can be determined.

Connelly's equation has K = 12.3. According to the ISO exposure meter standard, the "ideal" value of K should equal 12.5. Contrary to what most people seem to believe, this isn't about reflectance. 12.5 isn't 12.5%, but cd/m2. If you plug 12.5 into the equation P = 8.11 and not 8. This makes a small difference in the exposure value but it helps will the math. I believe the difference comes from rounding differences. 125 film speed is rounded down from 128.

Here are the breakdowns of the constants. Notice how many of the variables are in both the q and K equations, and how the value of P is K1 in the K equation. I think this is definite evidence of the interconnection between the exposure meter, camera exposure, and exposure placement on the film. It also proves that the the value of K is not an arbitrary value chosen by exposure meter manufacturers.

P


q


K

 

[snapguy]

Well, ah....

Huh?

 

[Stephen Benskin]

The post is a little advanced, but the three constants comprise the core of exposure theory. K is connected to the exposure meter. The K equation has three parts: light loss in an optical system, aim exposure, and the meter's physical response. The light loss of an optical system is basically the equation for q. The aim exposure in the K equation, K1, is the constant P. P is also the same as E for the statistically average scene in the basic exposure equation Eg * t = Hg.

With P equaling Eg, you can determine the value for the metered exposure, Hg, for a given film speed. As Eg is for the statistical average conditions, it can be considered part of the Sunny 16 rule. So, P * 1/ISO = Hg. It can also be written as P/ISO = Hg. So for 125 speed film, Hg = 8/125 = 0.064 lxs. 100 speed = 8/100 = 0.08 lxs, 400 speed = 8/400 = 0.02 lxs.

 

[Stephen Benskin]

The following example might help illustrate how P and Eg are basically the same. Lg comes from the exposure meter, and q is part of the the exposure equation that together with Lg equals Eg or P. The rest of the variables are f/16 at 1/ISO (for 125 speed film) or in other words, the Sunny 16 rule.



Exposure meters are "hardwired" to produce P (8 lxs). Setting the meter's calculator to the film's ISO gives Hg. f/stop and shutter speed are reciprocal.

 

[RalphLambrecht]

I need to drink a lot more first.

 

[RalphLambrecht]

there must be a simpler way

 

[Stephen Benskin]

there must be a simpler way

Of course there is, but this isn't about making exposures. This is exposure theory. Understanding the principles of exposure sill answer once and for such questions as what the exposure meter "sees," exposure placement, and film speed.

All the exposure values might be a little abstract, but if they are used in a relative way, you don't have to own a calibrated sensitometer in order for them to be useful. It's already been established that P = 8 and that the metered exposure value is Hg = P/ISO. For a 125 speed film, Hg is 0.064 lxs. That doesn't mean much by itself. The b&w film speed equation is 0.80/Hm = S. To find what the value Hm should be for any speed film simply change the equation to 0.80/S = Hm. For a 125 speed film that would be 0.80/125 = 0.0064.

Now we have reference points. The difference between Hg and Hm is 0.064/.0064 = 10. Hg is 10 times greater than Hm, or Δ1.0 log-H, or 3 1/3 stops. This means that the b&w speed point is 3 1/3 stops below the metered exposure. For those who do Zone System testing, Zone I is 4 stops below the metered exposure point or Δ1.3 log-H. That's a difference of 2/3 of a stop. So even without dealing with lxs, we can conclude without question that the Zone System's speed testing is not in agreement with the ISO standard. BTW, in Connelly's paper he uses the variable k1 to represent the difference between Hm and Hg.

 

[Stephen Benskin]

Quick correction to the previous post. The difference between the metered exposure point and Zone I is four stops or Δ1.20 log-H, not Δ1.30 log-H which is the difference between the metered exposure point and the shadow exposure for the statistically average scene luminance range of 2.20 logs.

 

[Old-N-Feeble]

This is too cerebral for me... returning to my comic books and pron now.

 

[Stephen Benskin]

Connelly writes in section 4.3 Exposure Meter, "An exposure meter separate from a camera is designed to measure only scene luminance, it cannot directly control any of the camera parameters. In consequence it cannot allow for the particular value of q or any one camera but must assume that a value of q can be found which will be satisfactory for all cameras."

And in section 6 Conclusion, "Initially, before the advent of the automatically controlled camera, exposure was determined by an exposure meter separate from a camera and in consequence it was necessary to assume a specific value for the constant q, and that this could reasonably be considered as applicable to all cameras...For automatically controlled cameras the quantity q need not be assumed to have one specific value, it can be measured, and its actual value applied individually to each camera, in which case the constant K2 is derived from the basic constant P and the actual value of q."

Exactly what does q do in the exposure equation? q is a light loss factor. As q = 0.65, that means 45% of the light striking the lens doesn't make it to the film plane. So for Lg, 3196 nits enter into the camera's optical system and only 2077 lux emerges (if you don't factor in the aperture setting). That's just a touch less than 2/3 of a stop loss.