Hi! John Hess from Filmmaker IQ.com and in today’s lab we’re going to jump into the
underlying fundamentals of everyone’s favorite in camera shrinking effect: Forced Perspective
and put a woman inside a martini glass.
Forced Perspective is just an optical illusion to make an object appear larger or smaller,
or closer or farther than it actually is by carefully controlling distance and vantage
point. Today we’ll focus just on changing size, but forced perspective does have a lot
of application in set design.
The basic concept of forced perspective is pretty easy to grasp. The farther away something
is, the smaller it will appear. So you just have to carefully arrange align objects at
different distances to create the illusion that the objects are in the same space even
though they’re not - but how does it work scientifically? To understand it we have to
turn to some basic geometry.
Let’s imagine a viewpoint and work in 2 dimensions. We can draw a circle around the
viewpoint which represents the entire field view - all 360 degrees. Now let’s say we
have this box - how big will this box appear from the viewpoint? To define the size, let’s
draw tangent lines from each side of the box to the viewpoint. This resulting angle is
how many degrees the box fills up in our field of view - degrees is how we measure the apparent
size of an object from our vantage point. Notice that the closer the box is to the viewpoint,
the larger the angle, the more degrees of our field of view it will cover.
Now to figure out what this angle is, we’ll use a bit of basic trigonometry, we can split
this isosceles triangle created by our tangent lines into two right triangles and use the
arctan or inverse tangent to figure out the resulting angle. The equation breaks down
to 2 times inverse tangent of (the distance to the object divided by 2 times the width
of the object) This resulting number is in radians - a whole circle is 2 pi - so each
1 unit radian is about 57 degrees.
Using this equation we can determine the appearance of two objects of different distances and
sizes. Let’s use an extreme example from the film Apollo 13 where Jim Lovell played
by Tom Hanks covers the moon with his thumb. We know that the moon has a diameter of 2,159
miles and is about 238,900 miles from the Earth. Plug these values into our equation
and convert from radians and we get about ½ degree. My thumb is three quarters of inch
and my arm is about 28 inches long. So holding out my arm, My thumb is about 1.5 degrees
- almost three times wider than the moon!
Before moving on I want to point out that the angle of view equation be estimated pretty
accurately by a much simpler function: width divided by distance. As you can see in this
plot, the equations yield pretty much identical results for any distance greater than 2 times
the width - which is true in almost all practical applications.
So now can mathematically predict size relationships between two different objects at specific
distances. The next challenge is to capture that relationship with a lens and sensor.
The first concern is framing. We generally describe lenses by their focal length but
lenses can also be described by the field of view they cover - the total viewing angle.
There are two aspect that play into a lens’ field of view: Focal Length and the sensor
size.
The equation for finding the field of view is 2 inverse tangent of dimension of the sensor
along one axis divided by 2 times the focal length - looks very familiar doesn’t it?
Again this outputs radians so we have to convert that to degrees.
Now I need to make one really quick side note to dispel a very common myth when it comes
to lenses - that long focal lengths compress images while short focal lengths expand space.
The lens is doing no such thing. All the focal length does is determine the field of view
on the camera side, the compression you see in a high focal length shot is caused by distance
to the object! The greater the distance to the object, the less perspective plays a role
and hence the more compressed the image. In order to frame a far away shot we need to
use a higher focal length. The closer the object, the more exaggerated small distances
become. Because closer objects cover more of our field of view, we have to use a wide
angle lens. So that’s where the confusion comes in - it’s not the focal length, it’s
the distance that compresses perspective. This is of course fundamental to the Dolly
Zoom effect.
But back to forced perspective. Now we know how to mathematically determine the angle
our objects cover and we know how to match the framing using our focal length and sensor
size. Now we get to the most challenging aspect of creating forced perspective: and that’s
focus. We have to find a focus point and aperture setting that will create a depth of field
where both our near object and our far away object are both sharp.
Now if we are trying to create a forced perspective image with something large and far away - like
these Leaning Tower of Piza images - we could easily utilize the hyperfocal distance - which
if you’ve watched our Hyperfocal Distance lab, puts everything from half the hyperfocal
distance to infinity in focus.
But Hyperfocal distance won’t work on miniatures that you place close to the camera.
When it comes to finding the right mix of distance and lens settings there is one rule
of thumb. Wide angle lenses work better because they have a deeper depth of field than telephoto
lenses given the same aperture settings. For instance a 50mm shooting on Full Frame focusing
at 10 feet at F8 would only have a depth of field of 6.28 feet. But a 35mm on the same
sensor shooting 10 feet at F8 would have a depth of field of 18.1 feet - a huge difference.
So now we’re on kind of a balancing act. Wide angle lenses give us the depth of field
we need but the field of view may be too wide for our subject. In this case, we can control
the field of view by altering the crop - physically cropping in on an image or by using a smaller
sensor camera.
Now I’ve been purposely speaking in generalities to convey the concept as universally as possible.
Let’s walk through this forced perspective example to see the real challenges of getting
all this to work
On a film set, the Martini shot is the last shot setup of the day because the next shot
would be out of a glass at the bar. Well let’s make that a literal Martini shot.
The first step is to figure out the scale between the martini glass and the talent.
After sitting with the martini glass and doing some mental visualizations, I eventually decided
on 1/8th scale. I needed to make the glass eight times bigger or the talent eight times
smaller. This means whatever distance I have the martini glass, I had to have the talent
8 times further away.
Before I broke out the cameras, I created a handy spreadsheet to calculate angle of
view and mathematically prepare for the shoot. Object A is my Martini Glass with is 7.5 inches
tall. Object B would be how tall I wanted the martini glass after I blow it up. Since
I have a scale of 8, that value would be 60 inches or 5 feet. My studio has about a good
30 to 35 feet to work with so I set my talent at a distance of 20 feet from my lens - or
240 inches. Reversing the scale, one eighth of 240 inches is 30 inches and that’s where
I’ll put my martini glass.
At this distance the martini would cover about 15 degrees of my vertical field of view. Now
onto selecting the right lens -I found that a 70mm lens on my full frame Canon 5D mk II
would give me a 20 degrees of vertical angle - just enough to cover the subject with room
to spare.
But… and here’s the real frustrating thing: If I shot 70mm even at f22: if I focused at
11 feet - the talent would be in focus but my martini glass would be out of focus. If
I focused on the martini glass, then my deph of field would still only be half a foot even
at f22 - and that’s not to mention we lose sharpness at this really small apertures.
So the 70mm is out. Using my depth of field calculator I tried a bunch of focal lengths
until I found that a 30mm lens shooting f/18 and focusing to 4.5 feet would give me a near
depth of field limit of 2.5 feet and far limit of 26 feet - perfect. But my vertical field
of view with that lens would be 43 degrees - almost three times the field of view of
my martini glass and model - so I would have to crop in. If I crop in, I should use a smaller
circle of confusion - lets say I crop in 2x. My Circle of confusion is now 0.015 and now
my depth of field is shallower. So back to shooting a wider lens. Eventually I find that
a 20mm at f18 will do the trick. Cropping an image is acceptable for a photo with high
resolution to begin with but not so much for motion picture especially if I’m starting
with HD. But what if instead of cropping in, I used a crop sensor?
Redoing the numbers for my Blackmagic Cinema Camera values I find that 18mm at f/13 will
cover the distance. Now at 27 degrees vertical which would comfortably frame my martini glass
plus one extra stop which means less diffraction and less light needed on the set.
The numbers I gave you here are my final results - I did plug in a lot of different values
to see what worked… but the amazing thing is I could pretty much visualize everything
on paper and avoid the scary pitfall of not having the right lens combination on on set.
Keep in mind though that although we can calculate depth of field precisely, whether something
appears sharp or not is still rather subjective - there is some tolerance for error. Now it’s
a matter of executing the plan.
I measured the martini glass and scaled up the proportion to make a posing rig for the
model to rest on out of steel square pipe. At first I tried just putting this triangular
posing rig on the floor but I ran into a problem. In order to sell the effect, I have to have
the both front and back rims of the martini glass in line with the lens. I do have a cheater
martini glass which I was able to cut in half but that won’t hold liquid obviously. I
needed to raise my posing rig but by how much? Well the answer came from good old basic geometry
class again. If I know the height of my martini glass and I know the distance to the camera
- this is just a similar triangles problem - so I welded on an additional base with 14”
of height and micro adjusted with some square wood I had laying around. For padding on the
1 inch square pipe I went with pipe insulation which is pretty much the same thing as a pool
noodle but in black.
Now to light this monstrosity. Shooting at f11 and higher meant I needed a ton of light.
For the foreground martini glass, this wasn’t so hard. I just put a couple LEDs and a 500
watt tungsten fixture with CTB gel - I kept everything daylight balanced because I knew
I would use strobes for photos. By keeping the lights really close, by the distance rule
we can maximize their illumination effect. Lighting the talent in the background would
prove to be a little trickier. For shooting still images, I fired off two strobes. But
for motion picture I needed to bust out the big guns, a 2000 watt light with a daylight
blue gel. I kept this close and flagged them out of view using strips of material near
the camera.
And that is it, a martini shot created in camera with forced perspective based on some
simple mathematics.
Now what I just walked through took a lot of math and planning to get just right. Obviously
you can eyeball the effect and come away with pretty decent results. I shot these changing
up the perspective on the fly. But the math does matter if you’re working with miniatures
and want to stay consistent from shot to shot.
Of course all this work begs the question - wouldn’t it be easier to just greenscreen
the thing and do it in post? Well maybe- if you’re careful you can achieve results that
are as good or even better without having the challenges of shooting with deep focus.
For instance, because of the distance, we’re not seeing the talent inside the liquid, such
a thing would be a trivial fix if we shot it on greenscreen. Now I won’t say this
effect can’t be duplicated in a composite but there is something fun and exciting about
getting it in camera. Every special effect shot you encounter will need it’s own tailored
solution. So give forced perspective a serious try. Even if you never use it again, the discipline
of understanding perspective, lenses, and focus will prove to be a strong foundation
in your quest to making something great. Check out links in the description for more on this
subject, including a copy of my forced perspective spreadsheet - I’m John Hess, and I’ll
see you at Filmmaker IQ.com