Camera Mathematics

Hey Everyone,

Tonight as I was driving home from the deep south in my city, I was pondering all the calculations when it comes to how F-stops affect shutter speed in the camera and how ISO when boosted how that changes shutter speed and aperture. Also I want to know when someone mentions well it 2 f-stops down when adding a polarizing filter what does that equate to in terms of shutter speeds and how to boost the ISO to make up for the 2 f-stops down. I hope this all makes sense. I would like to know how the camera calculates everything.

Thanks
Matt

Hey Matt,

Simply put, there are three factors that make up an EXPOSURE:

Light Sensitivity of the recording medium (Film or Digital)
The Hole Diameter through which the light must pass (Lens Aperture)
Time Light is Allowed to hit the Recording Medium (Shutter Speed)

Those basic components are ALWAYS at play... move one and you must usually have to move the others in respective relationship to maintain a particular exposure.

STOPS are the full measures you can change each component by. A stop is an old term from when controls used to have CLICK STOPS or DETENTS where the photographer would get a tactile feedback and the control would be reasonably selected and maintained through a shot. But more accurately, a STOPPING of light a control of the light...

[continued]

Let's go on... I am going to be simplistic on purpose.

STOPS used to be changeable in full increments. Stops are usually a halving of or a doubling of any of the three components. Say for example you go from f/8 to f/11, you just moved your lens diaphragm or aperture control ONE STOP. Meaning you cut the amount of light coming through the hole in half... you can also think of the hole being exactly half as small as the last aperture.

Same goes for Shutter speed. If you go from 1/200th of a second to 1/400th of a second, you just moved a whole stop and the shutter will allow exactly half the light through to the film/sensor.

ISO or what was once ASA is a standard measurement and description for a photographer to know how sensitive to light a particular recording medium is... B&W Film was made up of tiny particles of silver halide on top of a base of celluloid film. The silver would be literally burned by the light projected on to it and once "developed" it would leave an image behind on the celluloid. The more silver particles, the more sensitive the film hence a higher ASA (ISO) rating. Photographers could then select the right sensitivity for a particular application.

Digital is somewhat similar in that manufacturers have largely agreed to rate and calibrate a particular sensor in a particular camera with a sensitivity rating closely matching that of film. Each camera will vary slightly at each stated rating from another camera... this is normal. For all intents and purposes, ISO 200 is very similar from camera to camera to film.

[continued]

How this all relates...

So now let's put it all together.

A particular EXPOSURE is normally called an EV or an Exposure Value. This alone means nothing to you. It just means an exposure of some sort. How you get it depends on the combined settings of Shutter Speed, Aperture and Sensitivity. So a particular EV can be made up of totally different settings and still be the same EV. Confused yet? Don;t be, it is really quite simple... I'll explain in more detail with examples.

Say you have a proper EV at ISO 200, 1/1000th sec @ f/8. This is the Exposure Value. I can change two of the components and still achieve the SAME EV. To do so, you must move at least two of the underlying components to maintain the same exposure value. So I can get the same exposure by increasing the sensitivity to ISO 400 and then either the f/Stop or the Shutter Speed (or both, but let's keep it simple) so the same EV can be expressed as ISO 400, 1/2000th sec @ f/8 or ISO 400 1/1000th sec @ f/11.

OK, that above maintains the same EV. However, let's say you wanted a different exposure. You find your image is a little too dark. That means you need to increase your EXPOSURE VALUE somehow. This can be done any way you prefer or the best way for the particular situation or the results you're after. In this case, you can control any of the three components to get you the extra light you need. Each has advantages and disadvantages.

Let;s see them in the same example further developed (pun intended)

So let's take our first EV. ISO 200, 1/1000th sec @ f/8. You found the image a bit dark. This feels to you like a single EV or stop change. MEaning you need at least one more stop or EV of light. You can change one of the components to do so...

If ISO 200, 1/1000th sec @ f.8 is EV 0, you can achieve EV +1 any of the following ways:

ISO 400, 1/1000th sec @ f/8
ISO 200, 1/1000th sec @ f/5.6
ISO 200, 1/500th sec @ f/8

Each of the above has the same effect on the EV, they will all give you one stop more light or twice as much light as before.

[continued]

How do you or your camera select this? Well, Magic :tongue: Seriously though, our preferred device for this is a Light Meter. External Light Meters were the only type for a number of years before compact cameras were made. Modern light meters use a special Selenium or Cadmium Sulfide elements that are sensitive to light and can generate electricity or change the resistance of an electrical circuit in relation to how much light it senses. Another common Semi conductor is Silicon and they are also widely used. Selenium meters are great when you go hiking or camping because they do not need batteries :-)

Anyway, the meter either has a computer or a scale by whcih you the photographer can see the measured light in reference to your medium in terms of f/Stops and Shutter Speeds and film/sensor sensitivity.

Modern Cameras now have very sophisticated computers in them and very simple meters integrated in some very fancy ways.

The simplest forms or built in light meters were simply mechanical needles inside the viewfinder that would let you see the scale while looking through the viewfinder and you had to make all adjustments manually yourself. More recently, the meter is now connected directly to a computer in your camera that helps [it] control shutter speed, sensitivity and aperture automatically following a strict set of rules built in by the manufacturer.

Even more sophisticated are the Evaluative or Matrix Meters found in Canon and Nikon cameras (respectively) and also found in similar form (different trade names) in most other cameras. These combine many meters into a complex light measuring computer with a database of comparative image light values to which it compares the current scene against and the selects an appropriate exposure for you.

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Various modes...

OK, so you ave Aperture Priority, Shutter Priority, Auto, Programmed Auto, and Manual. These are most common but you will find cameras with many more types, so called Picture Modes in some cases like Sports, Sunset, Landscape, Portrait etc. etc. They are all closely related programs... they all work on the same basic principles:

-An intelligent built in light meter or light meters
-A computer
-A Database of pre-recorded image values for comparison.
-A set of rules

The Database is a collection of exposure values for hundreds or thousands of images previously recorded and analyzed to be good exposures. These values are stored (not the actual images) and the computer calculates the exposure the built in meter just measured, compares it to the database values and the closest match is selected and its recorded Exposure Values set in to the camera automatically and the camera exposes the image properly for you (most of the time) The computer has no idea of the shooting conditions, the time of day, the date, the location on earth, the sun position etc. etc. It simply does an empirical comparison.

The rest of the modes are there to give the photographer control over one component or two and allow the camera to select the remaining ones.

Aperture Priority. The camera will automatically input the calculated Shutter Speed and sometimes the sensitivity and the photographer selects the Aperture he /she desires. The camera will not change the aperture but instead will use the measured exposure calculation and then change the Shutter speed for you given the calculated EV from its computer.

Shutter Priority works the same but in this case you select the shutter and the camera will input the aperture for you. The EV calculation mechanism is the same.

Programmed Auto or Auto or Program are all usually very similar. In these modes the camera selects everything except the ISO sensitivity, but in some cameras even the sensitivity can be changed on the fly by the camera given some rules the photographer selects.

Some cameras allow the photographer an AUTO mode that can be shifted or biased towards a particular set of selection criteria. For example an SPORTS AUTO mode will tell the camera that no matter what it calculates, to select HIGH SHUTTER SPEEDS to stop the action. A PORTRAIT Auto mode will tell the computer to select very large apertures (smaller f/stops) in order to reduce depth of field and enhance the photo with out of focus backgrounds. LANDSCAPE mode will select very small apertures (larger f/stops) in order to keep more of the picture in focus through increased depth of field.

That's it for now... it should cover you as far as the basic components are concerned. To dive deeper, go ahead and ask some questions. I will do my best to answer or seek the help of those in the forums with much deeper knowledge of exposure and cameras than I have. My knowledge is very limited unfortunately to the very basics of old photography. I am just beginning to grasp Digital Photography and the much more advanced digital cameras and all they are capable of doing. Things like Matrix Metering is an incredible tool we did not have 5 or 6 years ago. Now every camera has some form of it. The fact that you can trust the meter to expose white shirts as white and black suits as black is incredible. :cool:

Excellent work Manny and crystal clear (at least to me). Just remember the triangle and the each of the 3 points of the triangle (ISO, Shutter, Aperture). This indicates all 3 are related in order to achieve a proper exposure. Next lesson by Manny will be on Depth of Field (DOF). :P

Excellent read Manny. Very clear explanation and not confusing in the slightest.

Check out the Exposure Triangle:

http://www.capturingthecoolness.com/..._Triangle2.jpg

My next question and I just would like further clarification is about STOPS. You mentioned about moving from f8 to f11 and that would cut the light coming in my half or from 1/200 to 1/400 in shutter speed. What about moving from f8 to f7.1 or f8 to f9,f10. Or f8 to f3.5. Everything else you explained very well and I learned some new things today. Just the STOPS thing is still a bit confusing with the light coming in on apertures. Thanks

Matt

two clicks of aperture is a stop
so
f1.8 to 2.0 is 1/2 of a stop
F1.8 to 2.2 is 1 stop
F1.8 to 2.5 is 1.5 stops
F 1.8 to 2.8 is 2 stops

one click on the Aperture is 1/2 stop
two clicks is 1 stop....and so on

Quote:

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Originally Posted by Derf

two clicks of aperture is a stop
so
f1.8 to 2.0 is 1/2 of a stop
F1.8 to 2.2 is 1 stop
F1.8 to 2.5 is 1.5 stops
F 1.8 to 2.8 is 2 stops

one click on the Aperture is 1/2 stop
two clicks is 1 stop....and so on

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Fred explained it but I want to add a bit of clarity.. it depends on how YOUR camera can be set to deal with the stops.

For example, Nikon pro cameras have selectable stop clicks meaning you can program how many stops the dial will move for each component. You can set it to FULL STOPS, 1/2 stop increment/decrement or 1/3 stop clicks...

So when you go from f/5.6 to f/6.3 and then f/7.1 and then f/8, that is 1/3 stop increment... whcih is what I prefer. Sometiems FULL STOPS are too much to adjust one way or the other. I prefer small amounts. So in my head I already have memorized that three clicks are basically a full stop. I don;t even look at the viewfinder or my LCD screens. I also will switch to FULL STOP increments in bad weather like today when I need to quickly dial in + 2 or + 3 stops compensation. It would be the difference of 9 clicks or three clicks :-) So it is really up to you or up to the camera.

In the old days of MANUAL aperture controls, it was up to the manufacturer of the lens to give you IN BETWEEN stops... some old lenses only had full stops... newer lenses had more stops available.

Now to really confuse you, the electronic computers in most modern cameras will select the closest aperture or shutter they need to achie an exposure so don;t be surprised to see numbers that don't fit a nice click-stop scale in the EXIF data. My Nikon D70 would pick apertures like f/6.5 and f/10 and f11.5 etc. Too funny.

So to add to my crazyness, I keep my finger on the rear control dial on my Nikon and have override compensation turned on. So, I will HARD SET an exposure compensation value but I can still override this by simply spinning my dials... I then compensate on the fly as I pan from left to right or right to left depending on the light. Remember that when the sun is high in the sky, the ligth is even all around you... but when the sun is low in the horizon, facing SOUTH EAST is different light than facing EAST and then further different facing NORTH EAST. So I change compensation on the fly as I feel the need. I d keep an eye on my shutter speed and aperture inside the viewfinder

I will KILL for a live histogram in the viewfinder like some SOny cameras have... LIVE HISTOGRAM is the next big thing in exposure boys and girls... :cool: That will be so sweet... no more chimping after each shot ... lol

Oh you had to go there?!?!?!? LIVE HISTOGRAM...YOUR A TEASE!

Thanks. I will go play around with my camera settings and see how it works.

Matt

Quote:

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Originally Posted by Derf

Oh you had to go there?!?!?!? LIVE HISTOGRAM...YOUR A TEASE!

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Fred, when I first saw this feature, I think it was a Sony P&S not sure, I was just FLOORED ... I mean, wow... I really don;t need to look at the rear LCD any more... it woudl be so incredible. Unfortunately it would mean semi-transparent mirrors or no mirrors which I still can;t get over ( they were pulling it off the sensor directly) as I do not want to affect the light on the sensor in any way.

But if they could somehow READ the scene with a sensor similar to Matrix but with many many more zones, say 1000 zones or 10000 zones, we could get a pseudo histogram straight from the light meter like we do today for Matrix/Evaluative meters without sacrificing the light path to the sensor or better yet, giving up a mechanical shutter (I still hate electronic shutters as my D70 suffered tremendously from blooming and other side effects of digital shutters)