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Basics of Flash Photography
Four Fundamentals we must know

 Flash Photography Basics, an Introduction

The reason to use flash is of course that flash is very bright (and very fast) for easy camera exposure. In comparison, the brightest light bulbs are dim for photography, not nearly sunlight bright. Without flash, even well lighted rooms will suffer from long slow shutter speeds, or high ISO, or both. Light bulbs can be fine for still life photography, when a one second shutter is no problem, but which is unacceptable for pictures of people, who tend to move. Flash also allows us to create the lighting, to be like we want it, to place flash wherever we want them, and to be made soft as we might desire, etc.

Flash photography is many things. There is on-camera flash and off-camera flash, manual flash and automatic TTL flash, and direct flash and bounce flash. There is fill flash in bright sun, multiple flash units, studio and portrait and table top flash in umbrellas, high speed flash, and more. Lighting is a big and fun subject, but before anyone can get much into "lighting", there are a few more fundamental basics we need to know, about "light". In all of these cases, there are basic differences between flash and existing continuous ambient light. Unfortunately, one downside of automation today is that many photographers have not bothered to learn the actual basics. They can only get whatever their camera does (and cameras are much dumber than we might imagine). But knowing what to expect is the biggest part of knowing how to deal with it. When we know why, then we know how, and then it's easy. Flash is not difficult, it is just different than either sunlight or regular continuous room light, and we need to understand flash too.

In short summary, the major points, the really big deal about using flash, is:

This really is pretty easy stuff, but it can be new ideas too. So I suggest that it could obviously help to try just a little before letting your eyes glaze over. :) Photographers simply need to know. Many of us do just "want the picture" without any bother. But we are either interested in the photography or we're not (and there's much hope for those who are interested). It's about like learning to drive - we did have to learn to operate the car, and we did have to learn the rules of the road, and maybe a little about ice and snow too. So we learned a few easy things, and now we've got it for life, and can use it at will to great advantage, in any situation, with great results. So yes, there are a few extra details to know about flash too, and we may actually have to think a little about creating our picture now and then, but none of it is difficult. The rewards are great.

If you don't bother to learn anything about flash, then flash pictures may be among your worst results, and enthusiasm is surely diminished. :) But the opposite view is if you try just a little to understand how to use it, your very best pictures may be due to flash. Flash is how we make the light be great, to improve the scene. Being willing to give it a little thought will certainly always help.

"Lighting" is a skill to be developed (which is mostly about learning to actually "see" the results, to look, to notice, to think, to be aware of what happened). But the flash is just a light, and we can see exactly what it does (if we just bother to look at the result, carefully enough to actually "see"). Anything you cannot see should not matter in a picture, however, we do learn to observe more with experience. Much of the problem is that beginners probably have not yet learned to see much, and you should be aware that the ability to "see" is the main thing to be learned about lighting. There is a page about that too. Flash is just additional illumination, however we can aim and modify the light to be like we want it to be, and we can learn to control the shadows it makes. This concern is not so much speaking of the shadows behind the subject, because generally we try to eliminate those. This is speaking of learning to notice and see the shadows and soft gradient tones ON the subject's face, intentionally created by off-camera lighting (including bounce flash).

Flash can be necessary, and it can be a big help. The simplest tips for universally better hot shoe speedlight snapshots (the way we ought to be using our speedlights, but sadly, many don't know yet) are:

Which flash? The camera internal flash is a very small flash, extremely minimal, perhaps sometimes better than nothing, and convenient to carry, but it is very limited in use. A regular size hot shoe speedlight will have at least 4x power, at least 2x more Guide Number, and at least 2 stops more range. Other than power limitations, the internal flash won't zoom for longer lenses, it won't tilt for bounce flash, and it can't be used off-camera. Today, there are Chinese import flashes for less than $100 US, some of which are excellent, for example, Yongnuo flashes are very popular. See a Beginners Guide to Speedlights.

You should try these things, the results will be self-evident. There is a detail or two though, and if your experience level is comfortable working with aperture and shutter speed, and if you want to be able to manage your flash pictures, then the material here is what you need to know. If still a beginner, and not yet comfortable, you really do need to know, and there is a very useful book here. These first basics are the dividing line where we become knowledgeable, no longer clueless. We won't be able to go very far without fundamentals.

These flash basics here are about "light itself", and are obviously important even if you always use automatic TTL metered flash.

Some people avoid any math. Inverse Square Law and guide number concepts do have a little arithmetic, easy stuff. It will not do you any harm by simply reading it. We do need to understand the concepts, about what to expect. And relax, really only this page and the guide number page involve this arithmetic. So the following pages are better, but still, the first concern might be "how bright is my flash?"


1.  Inverse Square Law

Light intensity falls off rapidly with distance from its source. This is called the Inverse Square Law, which says the intensity varies with the square of the flash-to-subject distance, this way:

Inverse Square Law

Light at 2x the distance is 1/4 as bright.  Light at 1/2 the distance is 4x brighter (2 stops)

Light at 3x the distance is 1/9 as bright.  Light at 1/3 the distance is 9x brighter (3.17 stops)

Light at 4x the distance is 1/16 as bright.  Light at 1/4 the distance is 16x brighter (4 stops)

Light at 5x the distance is 1/25 as bright.  Light at 1/5 the distance is 25x brighter (4.64 stops)

Inverse Square Law is just a fancy name for a rather simple concept. Think of a flashlight - as the beam travels farther away from the source, the beam spreads out to illuminate a larger area, but becoming more dim with distance. All light spreads this way, your flashlight, the street light, your table lamp, and your photo flash, all weaken in this way too, with distance. We might imagine that if the light were twice as far away, it would be half as bright, but the correct answer is only 1/4 as bright. The drawing explains why it falls off so fast. At twice the distance, the coverage dimensions double, both width and height, so the lighted area becomes 4x larger, and the same light distribution is 1/4 as bright. The Inverse Square Law is only saying that the light spreads to cover a larger area as it travels, which dilutes it, so to speak.

Inverse Square Law

Our light remains the same as it travels (the photons it emits don't change), but as it spreads out, the light density per unit area is diluted.

This drawing is from the Wikipedia topic. It shows that when an angle spreads in space (a beam of light), and travels twice as far (2r vs. r in drawing), the Width and Height of its beam spreads to be twice as large (Similar Triangles). That 2W x 2H expands to 4x times the first Area, which still contains the same light, but which is therefore diluted to be only 1/4 as strong at 2x distance (same answer if we compute a circular beam). The illumination varies with the square of the distance (varies inversely - more distance is a weaker light).

We can suppose the red lines are the paths of a few photons of light traveling from the source. Photons don't become weaker with distance - the angle of the beam just spreads out. The greater area dilutes the light intensity - the same photons in a greater area, so less light per unit of area, simply because the light is the same energy distributed over a larger increasing area. Nine photons at 1x, distance dilutes density to about two per area at 2x, which is 1/4, and one per area at 3x, which is 1/9. Impressive little drawing!

It really is that simple, that's all there is to it. The Inverse Square Law is only about the spread of any angle, and is not about any property of light at all. The effect is the same on light, gravity, sound, and radio waves, because it is only about the angle and distance. Angles just spread out with distance, and any light just fills that larger area, and thus is weaker intensity (metered at any one spot). You already know this, a flashlight beam becomes dim with distance because it spreads out with distance, becoming more dim. We might imagine twice as far is half as bright, but the big deal is that in fact, it is only 1/4 as bright there, explained above. So the point is, light falls off fast with distance, more so up close, but the amount varies inversely with the square of the distance. Your photo flash is a light, and it does this too. A flash exposure can only be correct at one distance. Behind that distance will be underexposed, and in front of it will be overexposed. It is good to realize this.

The Inverse Square Law is NOT calculating the width of this light beam. A bare bulb spreads light in every direction. A typical speedlight flash may zoom from maybe 25 to 80 degrees. A flashlight or car headlight has a more narrow beam. A searchlight beam (spot light) might be very narrow, but it is not quite zero degrees. But whatever the angle, they all spread with distance. Even a coherent laser beam several mm diameter on Earth might be 7 km diameter on the moon, and if it traveled twice as far, it would spread twice as wide. They all lose intensity at distance, due to this spread. Whatever the angular beam might be, the Inverse Square Law is only calculating how much the intensity falls off as it spreads with distance (due to the greater area it will cover then). Twice as far is 1/4 the intensity, -2 EV.

We may not care exactly why, but it definitely matters to photographers that this does happen. All you really need to realize is that subject distance from the flash is a huge factor, like shown in the Inverse Square Law chart above. However, a confusion is that sunshine seems to be a major exception - direct bright sun appears to be constant brightness no matter where we stand, independent of distance to the subject.

Sunshine is quite special (due only to our own local situation). Sunshine does of course work exactly according to the Inverse Square Law too, there can be no exceptions. Yet sunshine seems very different, and actually appears NOT to work that way. However, it is the distance to the light source that matters, NOT the distance to the camera. Sunshine seems to have a constant brightness anywhere we look, which is only because we are 93 million miles from the Sun, and another few miles to yonder mountain we see here on Earth is a totally insignificant difference. Even the 240,000 miles to the Moon is insignificant (1/4 of 1%), so the astronauts could use the same Sunny 16 rule there that we use here. On Mars however (half again farther from the Sun than the Earth), they will have open up about one more full stop (Inverse Square Law). But since we cannot vary our distance from the sun source here on Earth, sunlight does in fact appear uniquely constant to us - only because the sun is always same distance from any subject here on Earth. This can give photographers false notions about how other light ought to work, but it is the Sun's distance that is the exception. The flash is in the same room with us, only a few feet from the subject, so we WILL see the Inverse Square Law in action. It is the overwhelmingly huge and major factor for our flash use. We might work with it without knowing exact details, but we absolutely must recognize it exists.

If you imagine your camera should always get the exposure right, you're in for occasional disappointment. Ways to deal with this include actually metering the Manual mode flash directly at the subjects location (incident metering), which should be accurate. Or TTL flash automation in the camera (reflected metering) often gets close, but can easily be fooled (just watch your results then, and use Flash Compensation as needed). Or the Guide Number method on the next page helps with Manual flash mode. Or even a few trial and error tries of proper exposure (Manual level or TTL Compensation) is not difficult if you have a minute. If you want it right, give it a little thought.

The exposure does not depend on where the camera is, or how far the camera is from the subject (unless the flash is on the camera). What matters is how far the flash is from the subject.

This is yet another confusion, another classic paradox, about how flash distance greatly affects exposure, but camera distance does not. It is enough to know it is true. Frankly, this topic may better be omitted for beginners, and instruction sources always do skip it. Yet, we may be puzzled about why camera distance does not affect exposure? Harder to explain, and it is covered here, if you must, but that explanation seems an advanced topic, not essential. Don't let it distract the pursuit of flash basics. What we need to know is that flash intensity falls off fast with distance, according to the Inverse Square Law.

Exposure variation due to flash-to-subject distance

Since intensity at the subject varies with distance from the light source, an implication is that any flash exposure can only be "correct" at one distance from the light source. Stop and think about that a second, it is an essential to know, a biggie. This Inverse Square Law (light falloff with the square of the distance) is true of all light, any light, a table lamp or a campfire at night, etc, but using flash for photos is commonly where this becomes more important to us to know. We cannot "fix" this Inverse Square Law situation, nor can we ignore it - we can only learn to work with it.

The Inverse Square law explains why the room is seen to be darker behind nearby people in a snapshot using direct flash. The distant background obviously has to be darker, it is farther from the flash (just how life is). There are ways to help this situation. Flash pictures are double exposures, of flash and ambient. Using a slow shutter speed will aid bringing the low room light level up, at risk of motion blurring the image. Or using high ISO will aid bringing the low room light level up to match the flash. Both methods are at risk of the incandescent light causing a strong orange cast (high ISO flash pictures often will require a CTO filter on the flash, so Incandescent white balance can be used with flash). Often far best, simply using ceiling bounce flash greatly helps to minimize this distance difference, since most parts of the (small) room are more equal-distant from the ceiling. Or in studio situations, another light is commonly used to illuminate the background area.

It is quite important to expect and plan on this distance variation for flash. Again, it does not matter to lighting where the camera is, but pay attention to distance between flash and subject. Arrange your subject, or look for a lighting angle for the flash, so that all parts of your subject are near the same distance from the flash.

I'm just saying, if your picture and subject has a camera angle something like this sketch, then a frontal flash will be different illumination levels at the three subject distances. If using only one flash, then consider a flash arrangement like shown here, to illuminate the subjects evenly. Off-camera flash will likely be better lighting than flat frontal on-camera flash anyway. And of course, bounce from the ceiling comes to mind too (or maybe bounce from the left wall, aimed at a spot about where this flash is shown now). The three subjects will be more evenly illuminated when equal distant from the flash, regardless of where the camera is. Or if multiple distances are necessarily involved, consider more flash units to illuminate each area - for example, another light on the background for portraits. Otherwise, that is why a white background half again farther than the subject will be underexposed about one stop, and will appear gray, not white. White backgrounds pretty much require their own light, to show as white.

If Manual flash, we just adjust the flash power level to produce what we want, for the best photo exposure result. For one flash, this can easily be trial and error, judged in the camera's rear LCD, or aided by the histogram. Or we can use a handheld flash meter to meter and set the power level of multiple lights, each set to known ratio values relative to each other. Metering is much faster for multiple lights, instead of guessing at trial and error multiple times. Each light can be set precisely, so we actually know what each light is doing, and then we can easily repeat the same setup exactly next time.

For TTL flash, exposure is automatically metered, but when we discover we need a bit more or less flash than the automation provides, then Flash Compensation is the way we control TTL flash. Which is very large part of any success, and is easily the best single tip about using flash - if you don't get the result you want, don't just bemoan your fate, that never helps. Do something - Fix it, then and there. Simply adjust it until you see what you want. Flash Compensation is the tool to adjust what TTL automation does. However, flash does have some different basic properties (discussed here), which are good to know to use it.

Inverse Square Law Calculator

This calculator computes the stops of light falloff between any two distances from direct flash or continuous light.

Enter two distances to compare light intensity in EV. Or one distance and an EV difference to compute the second distance. Distances can be any units (feet or meters, miles or cubits), but all distances must be the same units (it is a ratio).

Inverse Square Law Calculator

Distance:   to  units


Show range span within ±

Change distance for the light

to be EV  

EV format can be ± 1, 2.333, 1/3 or 1 1/2

The Inverse Square Law doesn't tell us a correct exposure at a specific distance. That exposure also depends on the light source intensity, which we could determine exposure with a light meter, or with guide number, or just trial and error. But based on that exposure at the first distance, the ISL calculator tells us the relative EV exposure at the second distance... the difference of the two, the effect of the distance on the light.

This intensity falloff with distance will happen, so it's good to be aware. The ± EV range is shown to emphasize this. The direct flash intensity can only be the "correct" exposure at one distance. If using flash on a subject with some depth, for example, the multiple rows of a large group portrait, it will be very important that you consider this. The Inverse Square Law discussion is speaking of direct bare lights, flash or light bulbs with only normal reflectors as modifiers (NOT bounce, NOT softboxes). Don't measure ISL from the fabric of a softbox or umbrella, a light meter will work better then (but see that section at bottom of this page).

My notion is that those with curiosity to play with the calculator a bit can learn a lot about Photography from the Inverse Square Law. It happens, regardless if we know or not.
For example, 4 feet (which is a f/stop number) with ± 1, 2, and 3 EV adjustment will see distance results numerically same as even f/stop number increments. Minus EV is 5.66, 8, 11.31, or plus EV is 2.83, 2, 1.41, which are distances here.
Works for 1/3 stops too, -1/3 EV with ± 1/3 EV span range (or -1 EV with ± 1 EV span range) will see tolerance exactly reach the original starting value (whatever it is).
This is the Handy Guide next. It's a lot to know, and is very easy, and predictable, and useful, and we already know f/stop numbers. Understanding can expect certain obvious things without using the ISL calculator. Like -2 EV will occur at 2x the distance (we know because two f/stops doubles the f/stop number). This is about the easiest, and the least that we ought to know to use flash. It is a major understanding of light that we can use without the calculator.

The Easiest Handy Guide to estimate the light falloff

For reference, we know that one stop of exposure is a 2x brightness difference, and two stops is 4x. We already know the lens f/stop numbers (f/2, f/2.8, f/4, f/5.6, f/8, f11, f/16). Anyone seriously thinking about their photography for awhile probably can recite all the third stop numbers too. Notice that if we double f/stop number (like f/4 to f/8), that's two stops, so the light falls off two stops. Inverse Square Law numbers coincidentally also use the same square root of 2 numbering, so the "numbers" work similarly. Inverse Square Law says that if we double the distance, the light is reduced two stops, which is -2.0 EV difference. And f/4 to f/8 is also a -2 EV difference too. Very different concepts, but coincidentally, the numbers work out similarly due to both using square root. We can use that.

So suppose the subject is at 8 feet from the direct flash, and the picture is setup to be correctly exposed there. Then we can be certain that background objects at 11 feet will be underexposed 1 stop, and objects at 16 feet will be underexposed 2 stops. Foreground objects at 5.6 feet will be one stop overexposed, and objects at 4 feet will be 2 stops overexposed. Use feet or meters. I'm talking feet, but it's exactly the same for meters. You recognize those example distance numbers (1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16) as being f/stop numbers that we already know. And very coincidentally (simply due to both definitions using square roots), this aperture scale we have memorized provides a good quickie guide to estimate this distance falloff of direct light. It's an easy way to "be aware".

When setting up lighting for portraits, it's not enough to just get the exposure right. That's important, but it's just the easy part. Lighting is about controlling the ratio of the Main and Fill lights, called the lighting ratio. This purpose is to create and control the gradient shaded tones on the face, which shows curves and shapes (adds interest and looks real and natural). It's not hard, and lighting choices make all the difference. Frankly, a light meter for flash makes it easier, especially for quick and easy setup repeating the same result next time (setting each lights power to be exactly the illumination you want it to be).

There are many ideas about lighting. Equal lights just placed on either side of camera is flat lighting (dull, uninteresting), which is Not the best for portraits. There are different goals, but common to many of the best plans, an overall basic general concept for good portrait lighting is this: Main light high and wide, meaning about 45 degrees around to the side of subjects face, and 30 to 45 degrees higher. Fill light is back near camera, and it's very frontal, as close to the lens axis as possible (to NOT create more shadows itself). Off axis Main light intentionally causes shading on face to show features, and the fill light fills exactly what the lens sees to reduce harsh shadow contrast (without causing more shadows). A decent lighting ratio is the Fill light about one stop weaker at subject (than Main). See more detail about portrait lighting setup. Pay particular attention to the gradient shading tones you want to create on the face, that's what the job is about. Learning to actually look and see it is the trick. Learn to notice it in all the portraits you see. Watch gradient shading on faces in movies and TV, news anchors and commercials too, all of this lighting is carefully planned. As photographers, we should learn to see the lighting.

An example, about setting up lights for portraits without a light meter. It is all about the Inverse Square Law (ISL). If using two Equal lights (flash or light bulbs, and Equal reflectors, everything the same), with a main light at 4 feet, then a fill light placed at 5.6 feet (from subject) will be one stop less light than the main light (normally a desirable lighting situation). Or it could be 1.41 and 2 meters, same ratio of light, one stop difference. Or the fill at 8 feet will be two stops less than the equal main light at 4 feet (same as f/stop numbers, get it?) This is one way to control lighting ratio without a light meter. Again, this assumes equal lights (identical, both power and reflectors the same). For either equal continuous light bulbs, or for equal flashes too, with distances as mentioned.

Powerf/ Value
1.41401
1.41411.414
1.41422
1.41432.828
1.41444
1.41455.657
1.41468
1.414711.314
1.414816
1.414922.627
1.4141032

Why the numbers like f/11.314? Shutter speed and ISO values increment EV in powers of 2 (double is one stop), but f/stop and distance values increment EV in powers of √2 (double is two stops). Because, √2 is 1.414, and area of a circle is Pi r2, so multiplying radius by 1.414 gets squared to 2 which doubles the area of a circle, which is one EV stop of aperture. The numeric values f/1, f/2, f/4, f/8, f/16 are nice even precise values, but the alternating values are odd powers. The chart at right better shows this (5.657 x 2 = 11.314, double is still two stops). We say these rounded for convenience (nominal values), but the camera knows to use the precise values - see more about these precise values. F/stops are each exactly 2x exposure, but the f/stop Numbers are powers of √2 (which is 1.414).

The Inverse Square Law is of course NOT related to f/stops, except that both systems use the powers of √2. So the numbers just happen to be the same, and we already know f/stop numbers - which is a lot to know. This numeric sequence of precise f/stop progressions, when arranged into rows of every other doubled aperture values, are:

f/  12481632
f/1.4142.8285.65711.31422.627

The initial ISL calculator default example above is 4 to 11 distance (feet or meters). We said that if the distance numbers are thought of as f/4 to f/11, that's -3 EV. The calculator says -2.919 EV, only because the actual value of nominal f/11 is instead the precise value f/11.314. The calculator defaults try to show this. 4 to 11 feet is -2.919 EV, but 4 to 11.314 feet is -3.0 EV. Likewise, in the second default there, 8 feet - 1.0 EV is 11.314 feet, but 8 feet - 0.919 EV is 11 feet. Easy and obvious when expected.
f/stops of 1, 2, 4, 8, 16, 32 are even powers of 2 and are precise even numbers, but f/stops of 1.4, 2.8, 5.6, 11, 22 are powers of √2, and are usually rounded or approximated.

The method to measure the portrait light setup placements without a light meter involves the Inverse Square Law. You can use a short rope with paint or knots at 1, 1.414, 2, 2.828, 4, 5.657, 8, 11.314, 16 (feet or meters, whichever you use). Mark the 0 end too. More than 12 feet or 4 meters seems not likely needed for studio portraits. Use the rope to measure the location of lights with equal intensities placed at these distances from subject. Each mark is one stop less light. Main light distance is measured at one mark, and then fill light at the next mark is a -1 EV ratio, which is a very good general fill value for color portraits (maybe sometimes a bit more ratio for grayscale).

A flash meter to actually meter each flash intensity (at the subject) will of course be the most help, but otherwise for example, if using the ISL calculator, if the portrait main light is at 5.0 feet, and if we want a fill light to be -1.2 EV for ratio, then the calculator's computed distance for an equal fill light is 7.6 feet (located back very near the camera lens). Which is also enough camera distance for proper portrait perspective.

Or, if two equal flashes are at Same Distance, then the Fill set to half of the power level of the Main will be one stop down, for example, two of same flash set at 1/2 and 1/4 power are one stop different. But if using flash, it is also convenient to meter flash level, to adjust individual flash power levels for fill light to actually meter one stop lower at the subject (the meter is certainly useful in any non-equal situations).

There is additional we can know about the "depth" of the light field. Direct flash light has a small distance range around the subject where exposure might be usable. This is not unlike depth of field, except it is light intensity instead of focus. The ISL calculator can show this range.

You can already know in your head that a distance corresponding to a f/stop third stop number will see a 1/3 EV light change (use the top of the two ISL calculators to show and verify this). Example, distances corresponding to 4 and 4.5 feet correspond to f/stop third stop numbers, so if we just stop to think, we already know in our head that the light difference is -1/3 EV. And we know f/5 is 2/3 stop from f/4, and of course, f/5.6 is 1 EV. This is not hard. We might be concerned to know if it's a suitable range for our subject size extent. We know that if the light is right at 4 feet, then it's a full stop wrong at 2.8 or 5.6 feet. In that case (4 feet), you might want to backup some and zoom in, to increase this zone. If your subject moves (kids or dancing or a dog running), then this gives a good clue how much movement range you might tolerate around the median distance.

TTL flash is very good for measuring such moving targets, since it keeps remetering the current situation, but its Inverse Square Law range is still the same depth. Bounce flash (where practical) is very good about increasing the direct flash zonal range (very good at home, but not in large gyms, auditoriums, etc). And bounce flash also typically creates very desirable lighting.

Effective Flash power

Quick notes about the relative scale of things related to flash power. Some random facts, cute facts even, but which ought to become obvious to your understanding.

Stopping the aperture down one stop (like from f/4 to f/5.6) requires double flash power (one stop). Two stops is 4x power, and three stops is 8x power. Speedlights often don't have enough power to do low ISO bounce at much more than about f/4. With a regular full powered speedlight, ISO 400 f/4 is generally a safe try for TTL bounce flash standing under up to 12 foot high regular white ceilings (but 12 feet is pushing f/4).

Changing manual flash power level to half or double the previous power level is a one stop difference. The marked manual power levels of Full, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64 are full stop steps. So increasing the flash power by one stop simply means to double the previous power level (like from 1/8 power to 1/4 power is double power). If you reduce your flash power to half of any previous level (like from 1/16 to 1/32 power), you can open one stop of aperture to compensate (from f/5.6 to f/4).

Increasing ISO to double value (like ISO 200 to ISO 400) requires only half of the flash power (one stop). Doing that ISO double twice (ISO 200 to ISO 800) requires only 1/4 the power (2 stops). One implication when buying lights is that this means that a 160 watt second flash at ISO 200 is exactly the same lighting situation as 320 watt seconds at ISO 100 - both at same power level setting will use the same f/stop for same exposure at same distance.

Increasing flash-to-subject distance by 1.414 (square root of 2) times more distance requires double flash power (one stop). Two times the distance needs 4x power (Inverse Square Law), which is two stops.

The Guide Number (next page) of multiple equal flashes used in combination as one, is
  (GN of one) times sqrt(number of flashes).
Two equal flashes are one stop more power than one flash. Four flashes is two stops. Eight flashes is three stops, etc.

About adjusting settings for TTL flash: Note that when using automatic TTL flash, the automatic flash metering will simply respond to any changes with a different level of flash power, trying to keep the same correct exposure.

For TTL flash, changing aperture, or ISO, or distance, or adding a diffuser, or bounce, or an umbrella, just changes power level, NOT exposure.
TTL compensates the exposure with power, tries to keep exposure right. That's what TTL does.

So - Flash Compensation is instead the tool we use to control what automatic TTL does, to adjust the automatic flash exposure. Flash Compensation changes the goal of the TTL exposure.

However, for Manual flash mode, changing aperture or distance or ISO or modifier changes flash exposure of course, unless we manually compensate the power level ourself.

White Balance with Flash:

Flash White Balance is very nearly the same as Daylight White Balance, however the color temperature of the flash varies a little with flash power level - Color is NOT a constant. Ionization spectrum in flash tubes depends on the level of electrical current through the flash tube (power). Speedlights adjust power by truncating the duration, to be shorter, but necessarily more reddish at high power level (full low level trailing discharge tail is retained), and more bluish at low power level (red tail chopped off). Here is obvious evidence of that, which you can repeat yourself. Most studio lights are the opposite, most adjusting power with voltage level, becoming reddish at low power levels. Flash tube color simply varies with adjusted power level (just how it is). However, the Paul Buff Einstein lights are an exception, which combine these two methods in a calibrated way, so that one trait offsets the other, for a more constant color at all power levels (but you still have to match that one color to your cameras White Balance). It is extremely convenient in studio sessions to include a White Balance Card in the first test pictures, to easily and trivially correct the color of the pictures later (also suggesting Raw is very helpful).

Exposure when adding multiple lights:

Combining two equal flashes directed at the same subject area from same distance is double power level, and twice more powerful is one stop. Four equal flashes doubles again, to two stops. Eight flashes is three stops. Each double is one stop.

Combining two flashes of unequal power will still add, and two will be brighter than the brightest alone, but two (even if equal) are never more than 2x brighter than one (all else the same, distance, etc). Your Main/Fill light situation for portraits will meter 1/3 or 2/3 stop more (depending on lighting ratio) than just the Main light alone (so if you set camera aperture to what just the main light meters, you will overexpose a little). So meter both main and fill together, to set the camera aperture. FWIW, the math is that if we have main at f/8, and fill at f/5.6, they add to be sqrt(8² + 5.6²) = f/9.76 (but just meter them together). Calculators are on the next page (Guide Numbers).

See Part 4 for more about fill flash in bright sun.

Inverse square law with umbrellas and softboxes:

Note that for any Inverse Square Law distance computation (where half the distance is expected to give two stops more intensity), we cannot measure distance from the fabric. The distance should be measured from the real light source, which is from the flash tube or bulb to the subject. For a softbox or shoot-through umbrella, the distance is from the flash tube through the fabric to the subject (distance of subject to light stand pole is close). For a reflected umbrella, this is the distance from the flash tube to the umbrella fabric, and then back to the subject (includes two trips along the umbrella shaft). The fabric is not the source of light, it is merely an intensity bump in the path that looks that way. Out in front of the fabric (where it affects all distances), this bump is just a constant power step, as if we just turned the light down.

And yes, I do know this is not what is taught in school (engineers feel a compulsion to measure from an infinite luminous panel, a fun calculus problem - been there, done that). But the softbox fabric is not luminous, nor is it the source of a softbox or umbrella. So sure, there are plenty of doubters (who apparently never actually tried this). Yes, I do understand that when up close, all the points out towards the edge of the large panel also contribute added light inwards to the center line. Yes, actually measuring from the fabric certainly is a big problem up fairly close. Yes, the center path is attenuated by the fabric (but it is just a constant step function there, it does change guide number).

Yes, there are major ifs and buts and exceptions. So do NOT measure from the fabric. Instead do measure from the actual light source instead. A softbox is not a luminous panel - the light from behind it is attenuated by the fabric. There are no great new scientific principles revealed here, just that if you insist on using Inverse Square Law from a wide diffuser, you'll do much better measuring from the actual light source than from the fabric. Anyway, Inverse Square Law obviously does hold pretty close if simply measured from the (actual) flash tube source. Try it.

Yes, that is a major awkward measuring inconvenience, and a flash meter certainly does have much to be said for it. But we can easily verify the truth of it. For example, an Alienbees B400 flash at 1/2 power in a 40x32 inch Alienbees softbox (double baffled, internal nylon panel), metered at ISO 100 with a Sekonic L308S meter. Flash tube is 17 inches behind front fabric (the 2 foot below was measured 7 inches in front of fabric). Metered using a makeshift plumb bob string held in metering hand, over a long measuring tape on the floor (with its zero end directly under the flash tube).

Softbox Evidence: Inverse Square Law at doubled distance should be 2 stops down, and it is. FWIW, the closest reading here (24 inches from flash tube) was seven inches in front of the fabric. But, we are NOT measuring from the fabric.

From flash tube
Feet,   Inches
Meter
f/ + tenths
Step
Stops
224f16 + 0.7-
448f8 + 0.72
896f4 + 0.72
16192f2 + 0.81.9
32384f1 + 0.72.1

The 16 foot reading was unfortunately 0.1 stop off, which was repeatable. The chart sure would look beautiful if that one were 0.1 different. But which is only 0.1 stop, and ALL of the others were right on, within 0.1 stop (and 16 feet is extremely close to precise, no more than 0.1 stop). I think that I caused the issue, there was a large glass cabinet at the side there, at about the right angle in front of that 16 foot point, probably it added a little extra added wall reflection? The stated accuracy of this Sekonic meter is ± 0.1 stop, and I was otherwise careful, but I'd suppose my procedure might cause another bit of error now and then. Switching to less precise third-stop metering would hide or smooth tiny variations.

It sure does appear that metering from the flash tube obviously does follow Inverse Square Law (from the actual light source), as it should. This also works for a reflected umbrella, if of course that light path includes distance back to the flash tube too. I've checked this several times, it always works for me, certainly close enough (has to, there is a law). There is no noticeable discrepancy. Try it yourself.

Of course, it is much easier to meter the lights, than to worry with this. But do we need to know the concept of the Inverse Square Law, it explains so much that we see.

Continued

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