Question about density and log measurement

<p>Hello,<br>

I'm currently slogging through "The Perfect Exposure" by Roger Hicks and Frances Schultz and on page 22, under Density, it's mentioned that 8 stops = 512. "The important thing about logs is that they make it easy to deal with the way that we actually work in photography. Each 1 stop change in exposure means doubling or halving the exposure, so an 8 stop change means 512x". Starting from 1, I get to 512 after 10 stops. What am I missing?</p>

<p>Thanks</p>

<p>Hmm I think 8 stops is going to give you 256 not 512, below is how it should go.<br>

1 stop = 2<br>

2 stops 4<br>

3 stops 8<br>

4 stops 16<br>

5 stops 32<br>

6 stops 64<br>

7 stop2 128<br>

8 stop2 256</p>

<p>2^0=1<br /> 2^1=2 [probably the starting point, since f/2 is a common wide aperture.]<br /> 2^2=4 [one increment of change between 2^1 and 2^2]<br /> 2^3=8 [two increments of change]<br /> 2^4=16 [three increments]<br /> 2^5=32 [four]<br /> 2^6=64 [five]<br /> 2^7=128 [six]<br /> 2^8=256 [seven]<br /> 2^9=512 [eight increments of change to get you here.]</p>

<p>I don't know about what he was talking about, but if you count up the changes from the starting point of 2^1 to 2^9, and count only the changes (the intervals between the powers of two), then there are eight increments of change between 2^1 and 2^9.</p>

<p>Since every increment of change is a doubling, a power of two, they would each be called a stop. Since there are eight of them, it could be said that there are eight stops between a value of two and a value of 512.</p>

<p>What's happening in the scheme above is that we're counting the increments of change between powers of two. The word "stop" identifies the progression of powers of two. We know that f/2 is a common starting point, because it was mechanically difficult for anyone to build a lens which actually had an f/1 (there are a few out there which are below f/1.5, but these are rare). So, f/1 has been largely hypothetical; therefore, eliminated from discussions about density because density on a negative will be based on observed reactions; they have to be caused by physical phenomena. Therefore, the scale begins at f/2.</p>

<p>From there, use a counting number set to count the changes. Not the bulk amounts achieved, but, rather, the changes it takes to get you to the goal.</p>

<p>That'd be eight stops to get you to 512.</p>

<p>Hey, 9-1 = 8.<br /> Maximum observation - observation baseline = difference observed.<br /> 9-1 = 8.</p>

<p>This would be similar to counting how many clicks on the aperture dial it takes to get from one f/stop to another. Just counting the clicks.<br /> 9-1 = 8.</p>

<p>First understand I have not read the book. Historically cameras used a simple block or stop to control the volume of light allowed to stream through and play on the film. John Waterhouse in 1858, devised a system using sheet metal plates. Each had a different size hole. These slid into the barrel of the camera lens. These were called Waterhouse Stops. This system consisted of a series of hole sizes. This system evolved into the current aperture adjustment mechanism. The industry settled on a series of hole sizes based on a multiplier of 1.414. In other words the next larger hole is its smaller neighbor's diameter multiplied by 1.4 (rounding is OK).<br>

A number set emerges: The f/numbers in whole (full or 2x changes) 1 - 1.4 - 2 - 2.8 - 4 - 5.6 - 8 - 11 - 16 -22 - 32 -45 -64. Note: Each number going right is its neighbor to the left multiplied by 1.4. Each number going left is its neighbor on the right divided by 1.4. The value 1.414 is the square root of 2. If you desire to double the surface area of a circle, simply multiply its diameter by 1.4. The result of this multiplication is a revised diameter with twice the surface area.<br>

The number set 2 - 4 - 8 - 16 - 32 - 64 - 128 - 256 - 512 - 1025 is linear; thus it is not a logarithmic progression. Early photographers (and current old photographers) use this number set to deal with filter factors, bellows factors, f/stop adjustments etc. We count on our fingers in powers of 2. As an example, a filter has a filter factor of 8. The scene calls for an exposure of 1/60 sec. @ f/22. We count on our fingers 2 - 4 - 8 -- that is three fingers or three f/stops, we open up to f/8. If the filter factor was 512, that's 8 fingers or 8 f/stops, we open up to f/1.4<br>

Now way back in 1890 Messieurs Ferdinand Hurter and V.C. Driffield began using the scientific method to expose and measure film as to their response to light (blackening or density). They assigned numerical values to the blackening. As was the custom of engineers of that period, they worked using the slide rule and math tables to take the drudgery out of math. Tables of logarithms and the slide rule were used to speed things along in the pre-calculator pre-computer era. Graphs of the response of films were made. To this day, they are called H&D curves in their honor.<br>

Table of exposure f/stops using logs:<br>

1 f/stop = 2x change = 0.30 (log base 10)<br>

2 f/stop= 4x change=0.60<br>

3 f/stop= 8x change=0.90<br>

4 f/stop=16x = 1.20<br>

5 f/stop =32x=1.50<br>

6 f/stop=64x=1.80<br>

7 f/stop=128x=2.10<br>

8 f/stop=256x=2.40<br>

9 f/stop=512=2.70<br>

10 f/stop=1024=3.00</p>

<p>Film and paper response are graphed using the log values. The graph looks elegant this way. Additionally early engineers believed the human senses of sight and sound respond logarithmically. As a sidebar sound is measured in decibels. A 3 db change translates to a doubling of the sound level</p>