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Let's take a step back and look at the problem starting with the goals.
Back in the days of B&W film you didn't need flash because the film could be manipulated to record any scene like you saw it with detail very where.
So why is flash even necessary outdoors when there is lots of light? Because scene contrast exceeds the film/print or sensor's ability to record it as you would normally expect to see it. But in some photographic scenarios, like shooting in open shade or on an overcast day there's so little contrast in the natural modeling that the results look abnormally flat.
So seen in that context what is the goal of the exercise when flash is employed? To try to "normalize" the lighting ratio illuminating the scene overall or at least it's most important focal point such as the face and front of the subject. How the sunlight and flash are used together will dictate whether adding flash decreases the lighting ratio on a face or decreases it.
Scenario 1: Sun as key light
If we choose or are forced to use the sun as key light the ratio between sunny highlights and shaded eye sockets will be 3 stops, an 8:1 incident ratio.
We choose to expose for detail on the cheeks. With camera in M mode we set ambient exposure at 1/200th @ F/11 @ ISO100. That's Sunny 16 adjusted by 1-stop to anticipate the sync limit when flash is added next. The highlights are recorded accurately on the cheeks but the range of the sensor will render the shadows in the 8:1 incident ratio lighting much darker than you want. It's natural light, but it's not flattering natural light.
We add flash to lighten the shadow. But if it's near the axis it hits the entire face including those correctly exposed cheekbones. As the shadows are lifted the highlights are too. How does that change the lighting ratio?
We started with 8:1 in highlight and shadows. If we match the power of the sun with the flash (8 units) as fill this is what happens:
H:S
8:1 Ratio created by sun and skylight
8:8 Even fill matching sun added
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16:9
The combined ratio is 16:9 or roughly 2:1. That's the same ratio you'd get with key and fill in a studio setting when the key and fill are equal incident strength:
H:S
1:1 Even fill
1:0 Same incident intensity key light
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2:1 reflected ratio seen and recorded by the camera. Light open shadows.
What happens in the outdoor sun as key light scenario if the flash fill is 1/2 the power if the sun?
H:S
8:1
4:4
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12:5 = 2.4:1
1/4 the strength of the sun?
H:S
8:1
2:2
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10:3 = 3.3:1
Exposure must be pegged to the highlights on the cheeks. As more or less flash is added to change the ratio the camera settings, set for correct ambient exposure must be adjusted using aperture or ND filters on lens to compensate for the added flash BECAUSE IT OVERLAPS THE SUNNY HIGHLIGHTS ON THE FACE. The amount of FILL flash added affects the ratio on the face. The more flash, the lower the ratio to the point where flash exceeds the power of the sun and it looks totally flat like an indoor flash on camera shot.
Scenario 2: Sun as rim light
Here the sun is used as hair /accent light. The first decision for exposure is whether or not to let the hair, skin and clothing the sun hits clip or not in the photo. Let's assume the goal is detail so that will require a Sunny 16 exposure, again adjusted to keep shutter at sync speed: 1/200th @ F/11 @ ISO 100.
Taking a shot with ambient only we find the hair and white shirt the subject is wearing is rendered with detail but the shaded face is much too dark. We open the lens to f/4 @ 1/200th and now the cheeks highlighted by the brighter downward skylight are correctly exposed, but looking at the eyes we see the brow shading them. What is creating the shading? The ratio between the brighter downward component of the skylight and the skylight hitting from shallower angles. The skylight isn't "flat" it just has a very low lighting ratio.
Backlight, open shade, and light by a window create similar highlight modeling via the stronger downward component. What differs is the amount of omni-directional fill.
By window light the fill varies depending on how much light bounces off the walls and ceiling and any other windows contributing light. WIth the same size window you'd get darker shadows if the room is painted black than if they are white.
In open shade the amount of fill will vary depending on the surrounding. Anything that blocks the fill from the side will increase the ratio by making the shadows darker relative to the highlight exposure adjusted for accurate detail.
In backlight there tends to be even more fill because the sun that is hitting the back of the subject is also hitting the ground around and in front of them. We'd get lots of more or less neutral fill on a beach, less fill with a greenish bias if the subject is surrounded by grass.
The point is that the natural lighting ratio created by any of those situations isn't a constant. We need to evaluate what the natural light is doing in terms of pattern and ratio on the side shaded from the sun then base the flash strategy around it.
In the case of open shade without any sun hitting the background there's no need for flash to reduce contrast. The range in the shadows will fit the sensor. But the lighting ratio on the face will tend to look flat. So in that scenario we'd want to use flash to INCREASE the lighting ratio on the face. The way to do that is to use the flash not as "fill" as in the first scenario, but as a secondary "key" light.
The primary "key" light in an open shade or back-lit scenario is the modeling created by the skylight on the face. If we look at the face and see the cheeks highlighted but the eyes shaded by the brow darker if we find a higher POV for the camera then have the subject look up at it that will get the natural soft "key" light from the sky in the eyes (assuming you want light in the eyes). Likewise changing the orientation of the face to the sky as we would to model it with a key light in the studio will create the desired pattern on the face naturally. The modeling will be very subtle because the ratio of downward:sideways light is so low, but it will be there. The modeling will be more difficult to see in backlight because there tends to be more bounced fill and your eye sight is affecting by facing into the sun while looking at the face.
Once the face is aligned to the direction of the skylight to create the desired pattern, similar to how we'd do it next to a window the light is flattering in terms of pattern but the ratio may be too low and look to "flat". It's not flat because of the light direction but because of the low lighting ratio of the skylight.
Given that we are not opting to change the amount of natural fill by using flags (i.e., subtractive lighting) we need to increase the ratio by adding more key light with the flash. Where do we need it? In the same place the highlights are being created on the face posed to the skylight. Where do we need to place it? So it hits the face at the same angle as the natural lighting.
Here we have a scenario where we start with a very low ratio on the face and try to increase it:
H:S
1.5:1 Skylight modeling is very low ratio. About 1.5:1
1.5:0 Key flash equal to the natural key light added
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3:1
We add flash, not overall, but just in the highlights because it is off axis, overlapping the natural highlights from the sky. The flash doesn't hit the sky-lit shadows so they don't change.
The difference between doing that in open shade vs. backlight is:
In open shade, assuming we started with correct ambient exposure on the cheeks, we'd need to adjust ambient exposure to compensate for the flash we add to keep them the same tonal value below clipping. Since the amount of sky fill doesn't change the net effect is that the ratio increases and the shadows wind up looking darker and the lighting on the face more normal, not flatter than normal. Again it's the lighting ratio changing the illusion of flat vs angular with the tone of the shadows.
In backlight we started by pegging exposure at f/11 @ 1/200th to keep the sunlit parts under clipping and start with a face that is modeled nicely by the skylight but is several stops underexposed overall. We don't change the camera settings when adding flash we simply increase the flash power coming from the same direction as the natural sky key lighting until the shaded side of the white shirt looks perceptually correct—not an exact match to the sunny parts which still retain detail (Zone 9), but a "zone" darker (Zone 8) in Zone System parlance.
It sounds very complicated but in practice it's a no-brainer if you use the camera clipping warning:
1) Set shutter to sync speed. Adjust aperture until sunlit highlights are 1/3 stop below clipping (assuming you want detail in them when you convert the RAW file to JPG).
2) Turn on the flash. Raise it's power until you see the flash start to clip the shaded front side of the same objects. Lower flash by 2/3 stops. It's just as easy to do this with flash in M mode as it is in ETTL. You wind up moving the same dial the same number of clicks. The differences is that in M mode once set the flash exposure will not vary if the subject changes pose and reflects light differently.
The result? A full range of detail with balance of sun and flash that looks natural. The modeling on the face is made to look natural by first posing the face up into the skylight as with any key light, then adding the flash at the same angle:
http://super.nova.org/MP/BelenBacklitEyes.jpg
That's a single flash shot with flash and DIY diffuser on a bracket. My wife was standing below me on a river bank looking up which got the natural light into the eyes and allowed me to match that angle with angle of the flash to blend the two as seamlessly and transparently as possible.
The fill for the shadows came entirely from the skylight hitting from the sides and from the light bouncing up from the white jacket. Had she been wearing a black jacket the shadows would have been darker. The shadows are dark where both skylight and flash were shaded, such as under the chin but that occurs naturally outdoors because the light nearly always has a downward key component.
When I want to control the lighting ratio and get lighter shadows than the skylight alone will produce I add a second flash for fill just as I would indoors in a dark room. For full face shots I stack the flashes vertically:
http://super.nova.org/MP/ButterflyCanon2.jpg
The higher flash on my bracket becomes acts as secondary "key" light as in the single flash shot above, with the second slave placed lower adding supplemental flat fill as in the sun as key light scenario or and indoor key/fill centered scenario to control the lighting ratio and create lighter shadows. I used that scenario for these action shots of a neighbor's kid using the afternoon sun as backlight and shooting from a ladder to surround her with the grass (shot in the front yard):
http://super.nova.org/MP/ButterflyCanonExample.jpg
http://super.nova.org/MP/ButterflyCanonExample2.jpg
I'll use the same dual flash centered scenario with sun as backlight for group shots, again shooting from a ladder to get the faces and eyes up into the skylight, adding my "key" flash to the faces from the flash on bracket above the camera, and then placing my slave fill about chin level with the subjects in front of me to control the ratio and keep the shadows on the face lighter and more flattering than the sky fill alone does in a single flash shot.
The goal in all the scenarios? In essence it distills down to changing the range of the scene via lighting ratio to match the DR of the sensor and allow it to record the same amount of detail, everywhere in the foreground, that you'd expect to see if standing there looking at the same scene in person. That's what makes a photo seem "normal" or not.
Indoors its a matter of using key and fill flashes to control the ratio.
Outdoors its a matter of how the sun is used. Using the sun as key light on the face requires different placement and exposure strategies that when the sun is kept out of the shot entirely (open shade) or used as backlight.
Indoors and out environmental variables affect the amount of fill. Indoors with flash it varies depending on how much light the flashes spill onto walls and ceiling and how reflective those surfaces are. Much of the "wrap" effect seen with big modifiers used in small rooms comes from the spill fill. Take the same lights outdoors at night and duplicate the same set-up and there will be darker "harder" looking shadow because there is no spill fill.
Outdoors during the day the sun and skylight hit and bounce off the environment around the subject affect the lighting ratio on the subject before any flash is added.
Outdoor lighting so situational it's impossible to reduce the techniques needed into a single all encompassing generalization. Start by grasping the goal of the exercise — fitting range of scene to sensor range to "normalize" it's appearance — and learn what different flash techniques are needed achieve that goal in different situations based around how the sun is used.
You might not always want to match the sensor range, or be able to do it, but learning how to do it better equips you skill-wise to deal with those other situations.
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