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)

Flash Test Circles

Flashes have a shape and that shape is expanded by distance we know that the amount of light is diminished by the distance, and by observation I know that the size of the shape gets larger the further away.. Alien Bees 800 light I have, I have a reflector ring of 80degrees, I'll measure the diameter of the reflector, place the flash on a stand and then measure diameter of the circle as I move the flash backwards. Pictures is taken at an angle because I couldn't take it straight on because the light was to close to the wall. There is clearly different zones, so I took out my which is a Polaris light meter, used incidental light metering, and reflective light metering, and actually got the same values when metering the same zones. The value I left out of the picture is ISO 200 at shutter speed 30.

I took another picture with a tape measure put on the wall where the light circle was located found that each zone was smaller in the size at the one before by one inc, I'm going to name the zones 5 for the middle (funny how there is 5 zones here) anyways.. in inch. zone V (the middle one) is 7inc, zone IV is 6 inc, zone III is 5 inc, zone II is 3 inc, zone I is 1inc. Zone V: 7inc Zone IV: 6inc Zone III: 5inc Zone II: 3inc Zone I: 1inc now I move back the light to 2feet from the wall. I think that zone one will be half as bright and will be 2x bigger in size. wrong again. it actually went down 2 stops

the zones are bigger, but the power went down by 2 stops not just one. Zone V: 16 inc Zone IV: 13 inc Zone III: 12 inc Zone II: 10 inc Zone I: 8 inc moving to 3 feet back from wall.

fstops are 2.8 2, 1.4, 1 zone sizes: Zone V: 31inc Zone IV: 25inc Zone III: 20inc can't measure the other to hard to tell difference between wall and light. move back to 4 feet. fist all I realize I need a bigger test area, and I'll need to test at night. can't do that right now.. so I tried to use the flash itself, more light, and smaller fstops.. maybe will work better, because it's not very bright day today. light in the room without flash is at shutter 30 fstp 1.4.. that is a problem with low light test. redoing testing with flash... first I set flash to lowest power, because that metered at 125/f32 problem i have here is I don't have f/32.. oh well.. I take picture anyways at 125/f22

basically same values just higher flash power... see how zone V looks like it blasted it's way into the middle only other problem now is I can't measure ... oh well. now going to shot at 2 feet it meters at f11... just for fun I'm going to keep my fstp at 22... so to keep the picture the same.. only change is the distance from the wall. I see there is a ring in the middle for the 2foot mark, I think that is a reflection from the wall to the ring on the flash, and then reflecting back. also I see that each zone seems to have a brighter ring around it.

now I'm going to move back to 3feet middle meters at 125/f8 but still taking the pictures at 125/f22

then at 4 feet

now going back to 1 foot but using a 12inc umbrella I'm placing the rim of the umbrella at 1 foot. the max fstp is f11 so that is where I'll place my fstp.

now at 2 feet

3 feet

what I'm seeing, is not much that using an umbrella defusses the light, it actaully makes the light bigger. what my theory light and more on, strobe lights, is that I would decript the way the light reaches the subject is more like in the shape of an ice cream cone which would explain why in the middle of the light circle it's brighter, and furter away from the middle the less light there is.

I think I have a formula down now to calculate the size of the circle. center Zone 5 say = f11.. so now at 4ft and the guide number for the flash is 32. (yes crummy flash)... f11 is gn / feet. and we know gn = 32.. so 32/ft = 11, what is feet? so it would be 32/11 which is about 3ft.... however the flash unit itself is 4ft away from the wall in this case... so now we take the next formula size = sqrt(3 ² + 4 ² ) ... size = 5ft. so f11 would be 5 feet from the center of the flash circle.

I've perfected the formula (I think anyways) because we already have the Guide Number / feet. so really all we need to know if the Guide Number and distance to subject. so formula is simply. S = ( Sqrt ( (Gn / Ft) ² + (Ft / Ft) ² ) ) * 2 S = size Gn = Guide Number of Flash Ft = feet then to get to the next f stop down you take first part of the formula and add in ((Gn/Ft) / 1.4) here is a java applet that I programed to calculate the Size of the zones of the flash. I've based it off my Studio lighting, I've found that yes there is set - F/stops for power, however I still can set the value in between... one more thing I realized after making the java applet, was that while my testing seems correct, and my formula seems correct based on my theory, one thing I didn't test is that I has tilt or turn on the flash, I only had the flash square with the wall (being my subject). So there is not any tilt or turn values into the formula. I'll find those equations and add those into my formula. My guess is, I can use the same formula as used for large format camera.

F/Stop Difference

F/Stop Difference.

There is basically 3 types of F/stops, Whole Stops, 3rd Stops, and Half Stops. F/Stops are based on the Power of the Square Root of 2. which is rounded to 1.4

There is a formula to calculate the difference between F/Stops.
The formula is
( log(fstp1) - (log(fstp2) ) / (log(sqrt(2) )

I've made a simple java applet to help calculate the difference.

Flash power to Fstop

Flash power has a calculation based on the formula of: F = (Gn/Ft) * Ia

F = f/stop
Gn = Guide Number of the Flash
Ft = distance in feet from the flash to the subject.
Ia = ISO adjustment based on iso selected (values are powers of the square root of 2)
ISO 100 = 1
ISO 200 = 1.4142135623730950488016887242097
ISO 400 = 2
ISO 800 = 2.8284271247461900976033774484194
ISO 1600 = 4

then chart out each power the flash can give out be dividing the previous f/stop by the square root of 2.

calculated out using

Gn = 131
Ft = 7
ISO = 200

(131 / 7) * 1.4142135623730950488016887242097 = F
F = 26.46599666726792162757446041021
closes fstop would be 22

Power fstop
Full = 26.46599666726792162757446041021
1/2 = 18.714285714285714285714285714286
1/4 = 13.232998333633960813787230205105
1/8 = 9.3571428571428571428571428571428
1/16 = 6.6164991668169804068936151025525
1/32 = 4.6785714285714285714285714285714
1/64 = 3.3082495834084902034468075512762
1/128 = 2.3392857142857142857142857142857
1/256 = 1.6541247917042451017234037756381

Here is a java applet I've programed to help with the rounding of the calculation. This java applet does round the numbers to the first decimal point. Also I've added in rounding for Whole Stops, 1/3rd Stops, and 1/2 Stops.