The Math
Feel free to skip right over this part, this is the boring part, it’s so boring I thought of putting a picture of an artistic nude shot next to it just to keep people awake. Ok, so here we go. Before you can calculate the depth of field you first must know the circle of confusion for your camera.

Don’t get too lost on me yet, for most of us digital SLR users this is  one of two numbers. For most of us with APS/APS-C sized sensors this number is 0.019948, for full frame sensors (the big Pro cameras) and 35mm film the number is 0.02501. This represents the sensor size. Again, don’t get all lost on me yet, just remember the number for your particular camera.

The first thing we need to calculate is the Hyperfocal distance, for this calculation you will need to know the focal length of your lens. the aperture you are using and the CoC (circle of confusion) for your camera.

The math to calculate the hyperfocal distance is as follows:

HyperFocal = (FocalLength * FocalLength) / (Aperture * CoC)

Thus, the Hyperfocal distance of a 50mm lens at f/2.8 on an APS sensor (Canon 30D in my case) is 146.85 feet.

Next we need to calculate the near point which is the closest distance that will be in focus given the distance bdetween the camera and the subject. The math here (yes, it gets SO much worse) is as follows:

NearPoint = (HyperFocal * distance) / (HyperFocal + (distance – focal))

This is somewhat  complicated because the focal length is in millimeters and those of us in the US are better with feet and inches still so if you want the end value to be in feet you have to do some more conversions. If we are using the same 50mm lens, at f/2.8 on an APS sensor at a distance of 10 feet (3048mm) then our HyperFocal distance is 146.85 feet (44,749.23mm), giving us a near focus point of 9.37 feet (2,856.66mm). Are we following along still? Did I lose anyone?

Alrighty then, let’s now calculate the far point distance, this is almost the same as before but using slightly different math, so here we go.

FarPoint = (HyperFocal * distance) / (HyperFocal – (distance – focal))

Without changing our values that we used before, we now know that are rear point is 10.72 feet (3,266.81mm). Take note that the near point is actually closer to you than the subject is, typically the focus is 1/3 in front of the subject and 2/3 behind the subject.

The final step is to calculate the total amount of focal distance. This is one I can even do without a calculator, we simply subtract the far point distance from the near point distance.

TotalDof = FarPoint – NearPoint

Giving our example so far we have a total depth of field of 1.35 feet (411.48mm).

Let’s get practical
Why on earth would you want to know this? The simple answer is you may not, nor may you ever care to know it. When shooting portraits, weddings, events, and pretty much anything else it really isn’t going to matter much. However, if you are the type that wants to set up a shot and have it be EXACTLY what you want, there is simply no other way to know what the camera is going to do. This is important in macro, food, and product photography. By knowing exactly where you focus points begin and end you can more accurately design and execute precise shots.

Ok, how about the easy way?
This is kind of like taking a digital photography class and having to spend a semester cooking your own B&W film, its good to know the theory before taking on the practical application. So how can we do this easier than having to pull a scientific calculator each time you want to set up a shot?

• f/Calc Spreadsheet (download) – This is an Excel spreadsheet that will do all the math for you. This was development by me and is free to use.
• f/Calc Windows and Palm App (website) If you want a simple but powerful Windows or Palm based application, f/Calc does Field of View, Angle of View, Magnification, Spot Meter, f Numbers, Depth of Field and Hyperfocal distance
• PhotoCalc for iPhone (website) – Not only does it do everything for DoF, it also incorporates a sunrise/sunset function, flash exposure calculator, and Exposure Reciprocation calculator.
• CamCalc (Market) Android App for Depth of field, field of view, focal length equivalents, flash calculations, color temp. conversion, miniatures, and sunrise, sunset.
• PhoforPho (Market) Android App with Exposure calculator, Hyperfocal calculator, DoF calculator, Timer, and Exposure compensation calculation for multiple exposures.

I know this has been a doozy of an article to read through just to get to some free or almost free (PhotoCalc is $2.99) tools to make it dead simple to do these calculation. Hopefully this will help you perfect your images help you to use depth of field to its full extent.

What is this aperture thingy anyway?

Inside each lens is a diaphragm that can open and close, the size of the opening at any given setting is what we refer to as the aperture setting. On our cameras we refer to specific size settings as f-stops such as f/2.8, f/5.6, f/11, etc. While the obvious value of adjusting the aperture is to control how much light enters the camera, there is a secret hidden world beneath the hood that we will need to get a grasp of as well, but let’s start at the basics first.

For a given ISO setting and shutter speed we can adjust the amount of light entering the camera by adjusting the aperture, a smaller diameter (higher f-stop value) will allow less light in, while a larger aperture (smaller f-stop number) will allow more light it. If we refer to the Sunny 16 rule, we know that on a bright sunny day, if we are using ISO 200 and a shutter speed of 1/200^th then we will get a good exposure at f/16. As the sun goes down and there is less light, we need to allow more light into the camera, we can do this by opening the aperture up (again, using a smaller number) to allow more light in. This sounds easy enough right?

Image showing relative sizes of aperture

If that is all there is to it, then this whole aperture thingy would be a piece of cake and life would be good. It is enough to get you going into how aperture plays a role in getting a good exposure, so it is certainly a lesson worth learning and understanding well.

Have you collimated your rays lately?

The opening of the diaphragm also will control cone angle of light coming into the camera and this is why adjusting the aperture can affect the depth of field. To see how this works use your thumb and pointer finger to make a big circle, with one eye closed look through that at a finger on your other hand held about 12″ away. This is going to simulate a large aperture, you will be able to focus on the finger but you will have far less focus on something across the room. Next, make the circle very small and look through it again (now simulating a small aperture), you will be able to focus on both your finger and something across the room equally well. The reason for this has to do with the angle of light coming into your eye, with the large circle, light is able to come in very straight which creates a shorter focal plane, with a smaller aperture opening the light comes in as a cone shape giving a longer focal plane. While this simple experiment has a very subtle effect (not everyone may even notice it working) in your camera it can have a dramatic effect on how your images look.

Factors that determine depth of field

There are three factors that will determine the amount of depth of field you will have in your image, and taking from a comment post from Photo Larry, this points out the different factors:

In a comment from an earlier post, Photo Larry provided this very simple guide:

• Distance from the subject (Close=shallow, Far=Deep)
• Focal Length (Short=Deep, Long=Shallow)
• Aperture (Small=Deep, Open=Shallow)

Aperture Setting
We have already covered this one, the larger the opening (smaller f-stop number) the shorter the depth of field will be.

Focal Length
The longer the focal length the shorter the depth of field will be. This is why you will get more blurring effect on telephoto lenses than you will with wide angle lenses. The most popular portrait lens is the 70-200 f /2.8 because as you back up from the subject and use the longer focal length with a large aperture the more the background will get blurred out.

Distance to Subject
The further you are away from the subject, the more depth of field you will have as well. This is much easier to see with a long telephoto lens, if you focus on something very close to you, much of the background will be blurry, as you focus on things further away less of the foreground and background will be blurry.

Two images with different aperture settings

Summary

Hopefully this will help you understand the basics of what your aperture setting can do for you and how to begin to use it to your advantage both in getting enough light into your camera and by being able to add some extra flair to your images using the depth of field.

Author: Kerry Garrison

Press Release:

Canon brings HD moviemaking and 4fps shooting to its PowerShot super zoom series

United Kingdom / Republic of Ireland, 17 September 2008: Canon today supercharges its PowerShot digital compact camera range with two powerful new models: the 10 Megapixel PowerShot SX1 IS and PowerShot SX10 IS, which jointly replace the PowerShot S5 IS.

Both raise the benchmark for compact zooms with an outstanding 20x wide-angle (28mm) optical zoom, with USM and VCM for fast, silent, zooming. The  PowerShot SX1 IS offers a revolutionary series of features never seen before on a Canon compact camera – a 10 Megapixel Canon CMOS sensor, 4 frames per second continuous shooting, and full HD movie capture – while both cameras use Canon’s new DIGIC 4 processor for fast performance and richly detailed, clean images in a wide range of shooting situations.

Unbeatable reach
With a Canon 20x wide-angle (28mm) optical zoom lens, the PowerShot SX1 IS and PowerShot SX10 IS tackle everything from long-range telephoto shots to sweeping landscapes. Canon’s Ultrasonic Motor (USM) combines with Voice Coil Motor (VCM) technology for near-silent operation and the speed for sports or wildlife subjects. And thanks to Canon’s optical Image Stabilizer – which now offers a 4-stop advantage – camera shake blur is avoided even with the zoom fully extended.

10 Megapixel power
The PowerShot SX1 IS and PowerShot SX10 IS feature resolutions of 10 Megapixels, capturing all the necessary detail for poster-size prints or creative cropping in post processing. A Canon CMOS sensor allows the PowerShot SX1 IS to shoot full-resolution JPEGs at speeds of up to 4fps – making it a powerful, pocket-sized tool ideal for capturing fast-paced action sequences.

High Definition moviemaking
For the ultimate in visual quality, the PowerShot SX1 IS delivers 1080p (30fps) High Definition video – ready for instant playback on any HDTV via a built-in HDMI connection. The PowerShot SX10 IS offers fun, spontaneous VGA movie shooting. Movies on both cameras are enhanced with CD quality stereo sound, optical zooming and Face Detection Technology; and if extra reach is required, the PowerShot SX1 IS includes Canon’s Advanced Tele-Converter for an extra 2x zoom with no loss in movie quality.

DIGIC 4: intelligent processing for better photos
The PowerShot SX1 IS and PowerShot SX10 IS both feature Canon’s new DIGIC 4 image processor. As well as ensuring ultra-fast operation and superb, low-noise images, DIGIC 4 drives several intelligent technologies that make great photos easier than ever.

People shots benefit from improved Face Detection Technology, which even detects faces positioned at an angle to the camera, or in profile. Face Select & Track tracks a specific subject even more accurately, while a new FaceSelf-timer function – which automatically triggers the shutter shortly after a new face enters the frame – makes group shots and self-portraits easy.

Canon’s improved Motion Detection Technology delivers fantastic, sharp results by registering camera and subject movement, then automatically adjusting ISO to prevent image blur. Blur is further guarded against by new Servo AF, which continuously adjusts focus on subjects moving towards or away from the camera.

DIGIC 4 also powers Canon’s new i-Contrast feature, which brings out great, natural-looking detail in dark areas of pictures – without blowing out lighter areas.

Total Control
For the ultimate creative precision, the PowerShot SX1 IS and PowerShot SX10 IS offer full manual control over both aperture and shutter speed. A Multi Control Dial offers fingertip access to all key settings. Plus, compatibility with a range of accessories – including Canon’s professional Speedlite EX flash units – extends creative potential even further.

Also included with the PowerShot SX1 IS is Canon’s WC-DC300 controller, which allows wireless control of shooting and playback. This is ideal for tripod shots at slow shutter speeds, or any situation where keeping a distance from the camera is preferable.

“Both of these cameras offer exceptional imaging possibilities,” said Mogens Jensen, Head of Canon Consumer Imaging, Europe. “In particular, the PowerShot SX1 IS genuinely redefines what a compact digital camera can do. This kind of power and versatility must be experienced to be believed.”

Pricing & Availability
The PowerShot SX1 IS is available from December priced at £519.99 / €679.99 RRP inc VAT
The PowerShot SX10 IS is available from October priced at £359.99 / €469.99 RRP inc VAT

Features at a glance:

• 20x wide-angle (28mm, f/2.8) optical zoom with optical Image Stabilizer
• 10.0 Megapixels
• Canon CMOS sensor for full resolution continuous 4fps shooting (PowerShot SX1 IS)
• Full HD (1080p, 30fps) movies plus HDMI output (PowerShot SX1 IS)
• DIGIC 4 for outstanding images and fast response times
• Shooting modes include full manual control
• Great people shots with Face Detection AF/AE/FE/WB plus Face Select & Track and FaceSelf-Timer
• Targets every possible cause of blur with High ISO Auto, optical Image Stabilizer, Motion Detection Technology and Servo AF
• Auto Red-Eye Correction in shooting and playback
• i-Contrast boosts brightness and retains detail in dark areas
• 2.5” vari-angle LCD II with wide viewing angle plus electronic viewfinder (PowerShot SX10 IS)
• 2.8” widescreen vari-angle LCD II with wide viewing angle (PowerShot SX1 IS)
• Multi Control Dial and customizable My Menu
• Smooth, 30fps VGA movies (PowerShot SX10 IS)

Do I need to know this?
If you are always using your flash in automatic modes, you may never need to know much about guide numbers but in manual modes, if you don’t have a flash meter, understanding how guide numbers work can be a powerful tool in helping you to get your lighting setup faster. Many older flashes even have built-in guides to help you calculate the aperture setting for a given distance.

Using the guide number to determine aperture
At the end of this article is a link to an Excel preadsheet that will do much of the work for you as well as containing the guide numbers for a handful of popular flash heads. First off you should understand the math behind it and how to read the guide number information for your own equipment.

Some flash devices will simply have a single guide number value while others may have different numbers at different ranges and even ISO settings so you need to pay attention when reading the guide number. Let’s take a look at a typical flash setup. A Canon 580 EX II flash has a listed guide number of 191, if we divide the guide number by the distance in feet we should get a good estimate of the aperture to use. In this example we will use a distance to the subject of 30 feet.

Guide Number / Distance = Aperture
191/ 30 = 6.3

The closest aperture setting on my Canon 30D to that is f5.6 so that would be an appropriate aperture to use if I was using ISO 100. If I was using a higher ISO number then I could use a smaller aperture. The following chart shows the multiple factor for common ISO speeds:

ISO Multiplier Table
ISO 100: 1.0
ISO 200: 1.44
ISO 400: 2.07
ISO 800: 2.99
ISO 1600: 4.30
ISO 3200: 6.19

To expand on the previous calculation, we can add in the ISO to give us more aperture options. Using the same guide number and distance while adding the ISO, let’s see how this affects our aperture setting:

(Guide Number / Distance) * ISO Multiplier = Aperture
(191/ 30) * 1.0 = 6.3
(191/ 30) * 1.44 = 9.1
(191 / 30) * 2.07 = 13.1
(191 / 30) * 2.99 =19.0

The most common question now is how to determine the distance to your subject without measuring it with a tape. Most lenses will have a distance readout that will show you the distance to your subject once you focus on it. Just press your shutter half way down while aiming at the subject, take your finger off the shutter, and then look at the distance readout. We aren’t aiming at hyper-accuracy here since the aperture settings in your camera aren’t going to exactly match the calculations but we are trying to get as close as possible and avoid a lot of trial and error. Using this information you should be able to get your light dialed in much faster than just by guessing.

Determining Maximum Flash Distance
Using a similar method we can also determine the maximum distance your flash can be effective at, this is extremely useful when trying to determine if you can light up a person on a stage from the back of an auditorium for example. The calculation for this is the guide number divided by the f/stop, and again the ISO value can be used here as well. In this example we will use the guide number of a Canon 580 EX II (58) and an f/stop of 5.6.

(Guide Number / f/stop) * ISO = Max Distance
(191/ 5.6) * 1.0 = 34′
(191 / 5.6) * 1.44 = 49′
(191 / 5.6) * 2.07= 70′
(191 / 5.6) * 2.99 = 102′

Since the f/stop and the ISO determine how much light enters the camera, you see how using a larger aperture (lower number) and a higher ISO can really affect the range of your flash. Let’s compare the difference between f/5.6 and f/2.8 as an example:

GN 191@ f/5.6 100 ISO = 34′
GN 191 @ f/5.6 200 ISO = 49′

GN 191 @ f/2.8 100 ISO = 68′
GN 191 @ f/2.8 200 ISO = 98′

These calculations will help you determine if a long distance shot is even possible or if you need to bring in additional light. If you are too far from the subject for your light to be effective, you could place your light closer to the subject and fire it with a wireless trigger, this would allow you to shoot from a distance but get the desired light effect.

Summary
I know this can seem a little intimidating at first but understanding these concepts will help you get your lighting technique under control much faster and help make sure you can get the shots you want. You can even use the calculations to build a custom “cheat sheet” for your particular flash that can print out and keep as a handy reference. The spreadsheet that we have made available for you has both the f/stop and maximum distance calculators but has a second worksheet that will create the cheat sheet for you by simply changing the guide number on the first line to match your flash device’s output.

Calculation Spreadsheet [ Download ]

Author: Kerry Garrison