Greg's Photography Primer Copyright © 2008. ALL RIGHTS RESERVED.
Greg's Photography Primer
Overview / Focal Length / Aperture / Angle of View or Field of View / DOF - Depth of Field / Shutter Speed / Exposure / 35mm Film vs. Digital Camera CCD focal lengths
There are important specifications that photographers look for with respect to a camera lens. These include focal length and aperture, which are a few of the items covered in this paper. Also covered are other photographic information such as common photographic numerical relationships and camera settings.
In this primer, "Film" and "CCD" are used interchangeably. Film captures an image on photographic paper. A CCD, or Charged Coupled Device, is a small flat piece of semiconductor electronics that also captures images, just as film does, however the photographic concepts remain the same. It's just how the image is actually captured that changes (i.e.; film cameras vs. digital cameras).
Focal length is measured in millimeters. When the first lenses where used in cameras, a 50mm lens was actually 50mm long, a 1000mm lens was actually 1000mm long. Lenses where basically nothing more than a convex lens at the end of a tube. But as photography became more sophisticated, photographers became tired of lugging around huge lenses. Techniques were developed to use multiple optical elements in a lens to make the effective focal length much longer than its real length (example: a 1000mm lens can now be made 250mm long).
The magnification power of a lens is described by its focal length. From a numbers standpoint, focal length is the distance from the point of focus (the CCD), to the lens when the image is focused. You can draw this on paper, but it's easy to get the lines bending at the wrong angles through a convex lens. However, it does show how the image is actually turned upside down as it goes through the lens. Your eye is the same way, you have a lens and a CCD (your retina). You are actually seeing the world upside down, but your brain interprets it as right side up.
So another way to illustrate this (a picture is worth a thousand words), is to draw, from left to right, a CCD vertical line, then the lens, and finally the subject. Now, from right to left, draw two lines, from the top and bottom of the subject, and cross them in the center of the lens (in reality, light enters all parts of the lens), and connect them to the bottom and top of the CCD.
The picture below shows this, using an old-style camera, but the concept is the same. The tree in all three examples is the same distance from the camera (30 feet), but as the accordion becomes wider, the lens moves forward (zooming) This places the film (or CCD) further from the lens, increases focal length (6", 12", 18"), which results in magnification.
There are two ways of looking at this. If you use the black lines, you can see the images on the film in the box get larger with longer focal lengths. However, in real life, the CCD obviously does not change in size. It remains on the back of the box camera, and is shown in green. So now use the red lines, and it's easy to see how the a smaller portion of the tree falls on the CCD as focal length increases (often called 'zoom' or 'magnification')
When you cannot move the lens any further forward, you have the maximum focal length of the camera.
Now, if you really want to show maximum focal length by bending light through the lens, you could also show parallel lines (coming in from infinity), bending inward through the lens to the focal length, like in the below picture.
Generally, lenses with a focal length of around 50 to 55 mm are called "standard" lenses, shorter than 35 mm are called "wide angle", and lenses longer than 150 mm are called "telephoto". These are all approximate; there's no sudden cut-off.
Aperture is the opening that determines the amount of light a lens will let through. The amount of light let through is also dependent on the quality of the lens. It turns out that when the focal length gets larger, this opening also needs to get larger in order to let in enough light to expose the image. This is because the amount of light gathered by a telephoto lens is spread over a larger area (i.e.; magnification), thus making the brightness less.
The aperture or opening is a physical device that varies depending on the f-stop set. Sometimes manufactures use a ‘leaf’ type shutter that doubles as the aperture (since their size can be adjusted in addition to opening and closing). They can also use a leaf for the aperture only, and another leaf for the shutter. 'Focal plane’ shutters are also used, which are small metal curtains next to the CCD. It just depends on the camera. The Panasonic Lumix DMC-FZ20 uses a 6 piece leaf aperture and a separate leaf shutter.
To calibrate this light spread we use a calculation called f-stop. This number is equal to the focal length of the lens divided by the opening. This becomes f= FL / D, where FL=focal length and D=diameter of opening (aperture). It turns out that it is very difficult to make a lens that is as wide as its focal length, so you will not easily find a lens with a maximum f-stop of 1.0.
Here are two examples of an iris shutter, opened up at the left (f-stop = 4), and more closed on the right (f-stop = 8)
"f," means "fraction". We use a number like f2 but in reality this number is the inverse, or 1/2. An aperture of f16 is actually 1/16th and so on. Thus the larger the f-stop the smaller the actual opening on the lens, and vise versa.
Most camera lenses have a maximum f-stop of "2" which means the opening is half as large as the focal length. The nice thing about f-stop is that due to its equation (f=FL/D), the quantity of light hitting the CCD is the same, regardless of the focal length. The amount of light from a 50mm lens at f2 is the same as a 200 mm lens at f2. However, the opening for the 50mm camera is 25 mm and the opening for the 200 mm lens is 100mm. As said earlier, there is less light gathered at higher focal lengths, so more light must be let in. This is the reason we use the equation f-stop=FL/D; for a given f-stop, the camera's opening (D) adjusts itself automatically as the focal length (FL) increases or decreases.
Summary: when you set the f-stop, the aperture will open up as the focal length increases (to make up for less light gathered), and the aperture will decrease for shorter focal lengths (to compensate for the increased light).
My Lumix DMC-FZ20 lens opening is f2.8 through-out the complete focal length. So the aperture gets pretty large at long focal lengths (72mm/2.8 = 25.7mm, or about an inch), as the aperture must increase as the focal length increases to maintain the f-stop. The aperture on my camera gets so large that it cannot do super-fast shutter speeds when at it's lowest f-stop, due to the mechanical limitations of the shutter having to move so much (shutters often double as the aperture, as mentioned above).
A “stop of light” (stops) is halving or doubling the amount of light reaching the film. The amount of light will be halved (-1 stop) when the f-stop number is increased (a smaller aperture) by one full f-stop; for example, going from f/2 to f/2.8. Conversely, the amount of light passing through a lens is doubled (+1 stop) when the f-stop number is decreased (a larger aperture) by one full f-stop; for example, going from f/5.6 to f/4. They used empirical testing to get the standard f-stops.
Standard f-stop settings are:
1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32
... each increase in f-stop is half the light reaching the film.
Field of View
Field of view (FOV) is directly related to focal length. The longer the focal length, the less the angle of view (makes sense- you are magnifying the subject to fill the frame ).
Here are some other angle of views for various focal lengths. They are all referenced to 35mm cameras, and are total angles:
7.5mm lens gives FOV of 180 degrees*
28mm = 75 degrees (these you can calculate)
35mm = 63 degrees (shown in picture)
50mm = 47 degrees
100mm = 24 degrees (shown in picture)
135mm = 18 degrees
300mm = 8 degrees
500mm = 5 degrees
1000mm = 2.5 degrees
Here is the formula for calculating the viewing angle:
Angle of View (FOV) in degrees = 2 * (INVtan (d/2f))
or if you want focal length:
Focal Length = d / (2xtan(FOV/2))
Where d = image diagonal (diagonal of film or the CCD) and f=focal length
Note: the diagonal of 35mm film is 43.3mm. This comes from knowing the sides of 35mm film is 24mm high and 36m wide. The diagonal dimension of the film comes from Pythagoras' theorem A^2 + B^2 = C^2, or C=(A^2 + B^2)^0.5 = (24^2+36^2)^0.5 = 43.3mm.
*Note it is impossible to calculate a 180 degree FOV, since tan 90 degrees = infinity, but it's still correct
Depth of field (DOF) is a term which refers to the areas of the photograph both in front and behind the subject which remain "sharp" (in focus).
When the opening is small (higher f-stop) the DOF is higher. When the opening is larger (smaller f-stop), the DOF is smaller. You can see this for yourself. Cut a hole in a piece of cardboard and look through it. Everything appears in focus (high DOF, high f-stop). That’s why most point and shoot cameras use a small aperture, so they do not need any focusing mechanisms. (just like a 'pin-hole' camera, which offers good focus at all distances).
These cameras also benefit from their wide-angle lens. Not only can you get more in the picture, but the wide angle lens also contributes to greater DOF. Why is this? Read on.
Focal length also has an affect on DOF. We now already know that to maintain a constant f-stop, the aperture must get larger with the focal length. We know larger apertures result in lower DOF. So you can also conclude that longer focal lengths have less DOF. Likewise, a lower focal length which provides more wide angle has a smaller aperture since more light is available.
Lastly, if you keep the f-stop and focal length the same, the DOF will decrease as the subject distance is decreased. This is why using macro mode has a very small DOF. Taking a close-up of something as small as a coin at an angle, and the depth of field can be so small only the front of rear of the coin will be in focus. Keep in mind this is not related to focal length, but how close the coin is to the lens. Closer = less DOF.
Summary:
1. Lower f-stop = larger opening = lower DOF (depth of field)
2. Higher f-stop = smaller opening = higher DOF (depth of field)
3. For a given f-stop, the aperture (D) will increase as the focal length (FL) increases, to maintain the ratio f=
FL/D, resulting in even less DOF.
4. For a given f-stop, the aperture (D) will decrease as the focal length (FL) decreases, to maintain the ratio f=
FL/D, resulting in even more DOF.
5. Closer subject = less DOF
So the lowest (or most ‘shallow’) DOF will be found when you fully zoom (max focal length) and set the camera to it’s lowest f-stop, and move as close as possible to the subject. The highest DOF will occur when the camera is set to its widest angle (lowest focal length) and highest f-stop, and the subject is far away.
You can 'trick' the camera to reduce DOF. One way is to simply use a higher shutter speed (in shutter priority mode), and the camera compensates for the lower light by lowering the f-stop.... or just force a lower f-stop using aperture priority. Another way is to use a threaded filters in front of the lens to reduce the amount of light that enters the camera, resulting in the camera using a lower f-stop. Neutral Density (ND) filters are dark glass and reduce the amount of light reaching the CCD without otherwise affecting it. They are also sometimes used for slower shutter times to show smooth action, such as a waterfall. Manufacturers mainly use two ND nomenclatures:
Tiffen ND 0.6 = 2 f-stop
reduction (same for Heliopan filters)
Hoya and Tokina ND4 = also 2 f-stop reduction (same for Cokin, Sunpak and Nikon
filters)
ND-2 absorbs 1 f-stop of light, ND-4 absorbs 2 f-stops, and ND-8 absorbs 3 f-stops
or in other words...
ND-2 reduces amount of light to 50%, ND-4 to 25%, and ND-8 to 12.5%
The main purpose of the shutter is to control how long film is exposed to light. Shutter speed is the length of time the shutter is open in fractions of a second. Shutter speed has a great effect on stopping motion. If the subject is moving, a faster shutter speed is needed to eliminate or reduce blurring (if that's what’s desired).
Concerning shutter speed and light exposure, here is yet another relationship. The amount of light will be halved (-1 stop) when the shutter speed is increased by one full speed; for example, going from 1/60" to 1/125" (" means seconds). Conversely, the amount of light will be doubled (+1 stop) when the shutter speed is decreased by one full speed; for example, going from 1/250" to 1/125". They used empirical testing to get the standard shutter speeds.
Standard shutter speeds in seconds:
B, 4, 2, 1, 1/2, 1/4, 1/8, 1/30, 1/60, 1/125, 1/250, 1/500, 1/1000
... each increase in shutter speed is half the light reaching the film.
It should be noted that 1/60 or 1/30 second is about the slowest speed possible if the camera is hand held (without internal stabilization). Use a tripod to overcome the lower shutter speeds. B is for Bulb which allows the shutter to stay open for as long as you hold the shutter release down. Bulb can also be used with flash for interesting effects.
Aperture (f-stop) and shutter speed come together to create exposure. Exposure is the amount of light that reaches the film. How much light passes through the lens is controlled by the lens aperture. How long the film is exposed is controlled by the camera’s shutter speed.
Reciprocity is the relationship between shutter speed and f-stop that allows the same exposure to be achieved when one is changed to increase the amount of light and the other is changed to decrease the light by the same amount. For example, the same exposure will result if the shutter speed is changed +1 stop and the f-stop is changed -1 stop. The amount, or quantity, of light striking the film will be identical.
"Time" shown below is shutter speed. You can see that a shutter speed of 1/30 seconds at an f-stop of 16 is equal to a shutter speed of 1/500 seconds at an f-stop of 4.
Film Speeds (back to the 35mm days for a moment!)
As film speed increase, the amount of light needed to properly expose the film is reduced. Higher film speeds have thinner photosensitive emulsion, and require less light (higher speed and/or smaller aperture), but are grainer. Conversely, as film speed decreases, the amount of light needed is increased. They have thicker emulsion, require more light (slower speed and/or larger aperture), and produce good large prints.
Film speed is set by the manufacturer and cannot be changed. They range from 24-1200.
Examples
Situation: The camera meters the subject using 100-speed film and f-stop 22 at 1/30 sec., but I can’t hold the camera steady at 1/30 sec.!
WHAT ARE MY OPTIONS?
1) Change to 200-speed film
+1 stop = 1/60 sec
2) Use flash (1/60 sec)
3) Change the f-stop to 16
+1 stop = 1/60 sec
4) Use a tripod & you can shoot at any shutter speed.
What if I change the f-stop to 5.6?
(22;16;11;8;5.6) = +4 stops
(1/30;1/60;1/125;1/250;1/500 sec.) = -4 stops
Summary of exposure (relationships and tradeoffs)
To get the right exposure level:
- higher speed = less light = so need larger aperture
(lower f-stop)
- slower speed = more light = so need smaller aperture (higher f-stop)
35mm Film vs. Digital Camera CCD focal lengths
The CCD image sensor in digital cameras is much smaller than 35mm film. In the example in the Focal Length section, draw from left to right, a CCD vertical line, then the lens, and finally the subject. Now, from right to left, draw two lines, from the top and bottom of the subject, and cross them in the center of the lens and connect them to the bottom and top of the CCD. Film would sit further to the left for the lines to cross on the bottom and top of it. A CCD is much smaller, and needs to be moved towards the lens to have the lines hit the top and bottom of it. That's equivalent to a smaller focal length for a CCD (as compared to film).
On a digital camera, 6mm gives about the same angle as 35mm lens using a 35mm camera, since the CCD sensor is about 1/6th the size of 35mm film (i.e. about 4mm x 6mm).
Examples:
For my 3.4MP Sony DSC-S75, the CCD f = 7 - 21mm.
The 35mm equivalent focal length is 34 - 102mm. (this is a 34/7 = 4.86X focal length multiplier. 34mm is fairly wide-angle.
For my 5MP Panasonic Lumix DMC-FZ20, the CCD f = 6 - 7mm.
The 35mm equivalent focal length is 36 - 432mm (all at f2.8!) This is a 36/6 = 6X focal length multiplier.
The higher the multiplier, the smaller the CCD. So the Panasonic actually has a SMALLER CCD than the 3.4MP Sony. This is primarily due to the use of optical stabilizers (which the Panasonic has). It's must easier to stabilize the picture using smaller CCD.