The Zone System

Adams Zone System was based on F/Stops at the time there was only Whole F/Stops, so he found there to be 11 Zones

O

I

II

III

IV

V

VI

VII

VIII

IX

X

the idea was if you take a picture at the same shutter speed but different F/Stop where would it put the zone or shade of black. I've found that you can use the zone system also as a way if you keep the same f/stop but change the whole shutter speed different. now a days we have 1/3 stops and 1/2 stops theory based on new photography hardware is there are more zones than the 11 Adams described, there are 44 zones. show I would give the zones like this

0	1	2	3	4	5	6	7	8	9	10
0.3	1.3	2.3	3.3	4.3	5.3	6.3	7.3	8.3	9.3	10.3
0.5	1.5	2.5	3.5	4.5	5.5	6.5	7.5	8.5	9.5	10.5
0.6	1.6	2.6	3.6	4.6	5.6	6.6	7.6	8.6	9.6	10.6

Now manually chart out the zones based on Adams Zone system we start with the middle being Zone V.
lets start with basic Adams System with a formula with the start of Zone V
Zone V = (whatever the light meter says)

Zone VI = V * (sqrt(2))

Zone VII = V * 2
Zone VIII = V * (sqrt(2))³
Zone IX = V * 4
Zone X = V * (sqrt(2))⁴

Zone IV = V / (sqrt(2))
Zone III = V / 2
Zone II = V / (sqrt(2))³
Zone I = V / 4
Zone O = V / (sqrt(2))⁴


We'll Say Zone V is f/16 so then we can calculate the rest of the f/stops

Zone VI = 22.6
Zone VII = 32
Zone VIII = 45.3
Zone IX = 64
Zone X = 90.5

Zone IV = 11.3
Zone III = 8
Zone II = 5.6
Zone I = 4
Zone O = 2.8


Based on the formula to calculate the different between F/Stops can find what zone different between F/Stops.

F/Stop different = (Log(f1) - Log(f2)) / (Log (sqrt(2)))

Here I've charted out starting at Zone V, then the difference between each zone from Zone V.

Depth of Field Version 2

OK I think I have it. Theory:
The bigger the Print the bigger the depth of field, and the smaller the film format (negative size) the larger the depth of field.
The Smaller the Print the smaller the depth of field, and the bigger the film format (negative size) the smaller the depth of field.

I've combined both my Circle of Confusion calculations with Depth of Field Calculator Applet and think I have something useful.

Circle of Confusion

The Circle of Confusion is defined as is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. The Circle of confusion is also effected by the magnification in size of the final print vs the original film( or digital scanner) size.

This is my theory on the Circle of Confusion, I have been unable to find a solid formula for the Circle of Confusion, and most information I have found states that the Circle of Confusion value is a set number with the assumption you are going to print an 8x10. Right there I say that's just crazy, Not all pictures I take end up as an 8x10, typically they end up as 4x5 proof prints for me, and they are also cropped in slightly which would increase the magnification of the film to print size. I'm going to keep it simple by not adding in the cropping assumptions, because not all pictures are cropped the same. Here is the follow formula I've come up with based that your enlargement be full frame.

1. calculate out the diagonal of the film format 35mm is 36mm X 24mm so the diagonal is is 43.26662mm.
2. calculate out the diagonal for an 8x10 print which is 12.8 inc or 325.2587mm.
3. Print diagonal divided by film diagonal divided by print resolution of 250 dots per mm, which comes to 0.03

Here is my magic formula for CoC:

C = (P / f) / 250

C = Circle of confusion
P = diagonal of print
f = diagonal of film focal plane

here is a table of some film sizes focal plane:

Format Size Diagonal
35mm 36x24 43.3
6x4.5 56x42 70
6x6 56x56 79.1
4x5 102x127 162.8
8x10 203x254 325.1

Here is a java applet to calculate out the different values.

Based on my experience, the larger the film size the smaller the depth of field, yet at the same time, the pictures seem sharper. We'll just keep with larger film size = smaller depth of field, with the depth of field formulas based off of Circle of Confusion it does make since. I'll next combine my theory on Circle of Confusion with Depth of field to see if my theory shows true.

Depth of Field

This document I'm pretty much going to take standard information on because I agree with it. This document does not include movements available in large format cameras. So to Start, the dictionary definition of depth of Field is: the distance between the nearest and furthest objects in focus. There is parts to calculating the depth of field and each part having it's own formula and set of rules the parts are Hyperfocal Distance, Near Distance , and Far distance.

Hyperfocal Distance:

The distance in front of a lens that is focused at infinity beyond which all objects are well defined and clear formula is: H = (F² / Fs*c) + F H = Hyperfocal Distance F = Focal length: the mm of the lens (such as I have a portrait lens of 80mm) Fs = F/Stop. The lens f/stop C = Circle of confusion (aka circle of least confusion) for film format. (For now I'm just going to chart out a few calculation values because this a whole subject in-itself, and will write a different document for that)

Format	CoC
35mm	0.029
6x4.5	0.047
4x5	0.11

Near Distance:

The Distance in front of the focused distance of the lens which all object are well defined and clear. formula is:

N = ( S * (H - F) ) / ( H + S - ( 2 * F ) ) N = Near distance

S = Focused distance (in mm) H = Hyperfocal distance F = Focal length

Far Distance:

The Distance behind of the focased distatnce of the lens which all object are well defined and clear.

formula is, however is the answer is less than 0 Far Distance is infinity.

Fr = ( S * (H - F) ) / ( H - S )

Fr = Far distance

S = Focused distance (in mm) H = Hyperfocal distanceExample: 35mm camera, lens is 55m, F/stop 11, focus distance is 3048mm (10 feet)

	mm	Feet
Hyperfocal	9286.004	30.46589
Near Distance	2301.709	7.551539
Far Distatnce	4510.433	14.79807

Lighting Radiation V2

I've added more features to my Flash Circle Java applet to help chart out the light radiation.
If my theory on the lighting is correct, the angle and size of the light is the same, the formulas I had in my first attempts to calculate out the size of the light circles were backwards..
they were somewhat correct but something isn't good enough.

This new java applet shows the distance from the center to the different whole stops down.
Formula is first start at the center formula being:
Gn / Ft = F

Gn = Guide Number
Ft = Feet from flash to subject.
F = F/stop

After you have the base F/Stop, then I would calculate the size of the F/stop Zone, from the center out.

D = Sqrt( ( Gn / ( F / 1.4 ) ) ² - ( Gn / Ft )²)

D = distance from center
Gn = Guide Number

Ft = Feet from flash to subject.

F = F/stop

For example:
Gn = 310
Ft = 10
F = 31

D = sqrt( (310/ (31/1.4))² - (310/31)² )
D = sqrt((310 / 22.1)² - (10)²)
D = sqrt((14.1)² - 100 )
D = sqrt( 198.81 - 100)
D = sqrt( 98.81 )
D = 9.94 (basically rounded to 10 because there are allot of rounded numbers in each step of the calculations)
Then to get the next distance basically use the formula over again just take the previous F/stop and divide by 1.4
F = 31 / 1.4 = 22.1
now we start the formula over again.
D = sqrt( (310 / (22.1 / 1.4)² - ( 310 / 31 ) ² )
D = sqrt( (310 / 15.8)² - (10)² )
D = sqrt( (19.6) ² - (100) )
D = sqrt( 384.16 - 100 )
D = sqrt( 284.16 )
D = 16.8 (this calculated out to the 10th decimal place makes the Distance to 17.3)

Flash Radiation Circles

Strobe Radiation

After a lot of thinking and evaluations of pictures and formula of GN / Feet = F/Stop

I come to realize that lighting can be better defined as radiation of energy in all directions from the centralized source that diminishes in volume the further the radiation travels.

Studio lighting or strobe lighting is a fast discharge of energy that causes an explosion that crates a bright light (and a lot of heat as well but we don't care to much about that for this document). I've discovered though experimenting a few days back discovered a formula of S = ( Sqrt ( (Gn / Ft) ² + (Ft / Ft) ² ) ) * 2

this works but it's off by 1 stop, but I can adjust for that.... new formula

S = ( Sqrt ( ( ( Gn / Ft ) ² ) / 1.4 + ( ( Ft / Ft ) ² ) / 1.4

I first tried to manually draw out the flash circles by using drafting paper, but I don't have a drafting compass, and I don't have a protractor. I went to Wal-Mart but also there wasn't one, so I ended up making a java applet for this. I know this isn't the best, but I made it to draw out each whole steps for the flash circles based on the Guide Number. Then there is a line to show how the flash circle would actually display depending how close the wall is to the flash. I marked on the wall line 5 feet markers. I'll work on making the markers actually find the 5 zones down and the size of the..... maybe.. but for now here is what I have.

Manual Fill Flash

I first have to say, I don't like TTL flash system in my cameras.

I cannot consistently have a correctly exposed fill flash and even exposed picture correctly. That is very not good enough for me a working people photographer, maybe for other types of photography where you need to take pictures very quickly TTL flash might work but I very rarely have that type of photography work, so I throw TTL flash out the window.

Think about this one... why doesn't a race car driver use auto transmission?? The theory of Fill Flash is my friend, which is the use of a flash to lessen the shadows of your picture. The more flash you use in the picture the less difference in f/stop for the shadows. Here is how it works.

1. Use a spot light meter, and meter the general exposure of the person I'm taking a picture of, ISO 200 shutter 250 f/stop 16. (yes sunny day rule).
2. Next I use my spot meter and meter the shadows around the my subject, typically is located on either the left or right side of the person. We'll say, ISO 200 shutter 250 f/stop 8.
3. Calculate the f/stops difference. this example is 2 stops.. shows are -2 stops.
4. Next I measure the distance from my flash to the subject and find based on what power setting would match the f/stop of the shadows.
5. Next I would chart out based on how much flash power I used, how would that change the f/stop of the shadows. Note I am not going to use a flash/power that is more than then main subject f/stop.
6. I calculate out the difference the fill flash makes for the shadows to main f/stop.
7. Select what type of contrast I'm looking for, and based on that I select which flash power setting to use.

One thing to look at is, typically you do not want to set the fill flash to be the same value as the main subject because this causes the picture to be flat, it removes most if not all the shadows, causing the picture to have little to no contrast. This is known as a dull picture.

I will take example pictures as soon as I can take day time pictures outside, which will not be for awhile.. stupid day light savings.... and having to go to work. (Darn day jobs)