1. Diffraction,
DOF and Crosstar Effects
The Irascible Iris
You probably think of these as three different
ideas to be parked on different levels in your photographic garage
of concepts. But they are so intimately connected that you may
slap your head in wonder when you find out how similar they are.
Careful now. No damaging the parking structure, and you don't
want to set off a bunch of alarms in your old four cylinder closely
held beliefs.
How come these topics are related? It's
all about that hole in the middle of your lens. The one that
lets in the photons. Don't look now, but it has a knife edge
to it, and as you alter the f-stop, it interacts with these photonic"wavicles"
in ways your mama never told you.
Consider this: for the moment, you're a
photon. You have a wavelength of around 600 nanometers (billionths
of a meter or millionths of a millimeter) so you are quite small
and reasonably orange. Your whole being is just a tiny spurt
of energy. If another photon of exactly your size were to happen
along, the two of you would find it hard to tell yourselves apart.
If that other guy were to slam into you--surprise--nothing would
happen. You would pass right through each other the way waves
in an ocean can move across each other, only in this photonic
case, more three-dimensional and without ever mussing each other's
coif.
You sail blithely along (at the speed of
yourself) and just happen to pass by a physical barrier some
hundreds of times your size off to your left.
What do you do about it? Most people would assume that since this distant chunk of matter is apart from you by hundreds of times your own size, you would merely keep on truckin' and continue on your way. That's the way it works out on the freeway, thank goodness, but in Ma Nature's cup of Physics, nothing is quite the way you might assume.
You are not a ball of physical matter; you are a single spurt of massless, fast moving energy with an electromagnetic personality. You have a size, front to back, but your sphere of influence allows you to detect and interact with things way off axis. You literally feel that chunk of matter way
over there, because it is made of atomic stuff that interacts
with your kind of folk. Its atoms exhibit an influence phenomenon
with your wavelength and it tugs at the outer edges of your magnetic
signature.
(All atoms exhibit extensive fields of
influence. It's those pesky electrons at their outer limits that
do the real work. Being electrons, they're all electric, all
the time, and being in motion causes them to give rise to electromagnetic
phenomena. Without that extended field of influence, they couldn't
get together and stick to each other, so I vote that Ma Nature
doesn't change this arrangement, even though it gets in the way
of my photons sometimes.)
We humans can detect which materials exhibit
this sort of interaction with photons by merely looking. Things
that snag onto passing photons this way are simply opaque to
some degree. The same phenomenon would cause you (the photon)
to be absorbed right smack into that physical, atomic stuff if
you hit it head on, but by being out here just off your starboard
bow as you pass by, it merely twists you a tad off axis.
If you had passed by that knife-edged barrier somewhat closer, you would have been diverted from your path even more, and if that barrier had been a hole only a few million of your wavelengths across, many of your kind would be scattered as they tried to pass through, and almost none of them would have stayed on their original vector (path).
The barrier is, of course, the aperture
mechanism in the middle of a camera lens, for this exercise.
It's a ring of six leaf-like petals of ultra thin metal far thinner
than a razor blade, which forms a variable hole appearing approximately
circular. It creates the f-stop that is expressed in numbers
derivative of multiples of the square root of 2 (which is 1.414213...
leading to such numbers as 2.8, 5.6, 11 and 22). Massive, heavy
blades and iris leafs a few molecules thick exhibit the same
influence over the passing photons. Photons have no mass, so
they are unimpressed with the weight of an iris blade, but they
are impressed with the opacity of the material it is made from,
and as they arc slightly from interacting with it, their wavelength
is changed ever so slightly and a sub-microscopic bit of energy
is imparted to the material in the blade.
(If a transparent iris were immersed in
a liquid that had the same refraction index, no iris-versus-photon
interaction would occur due to the difference between atoms of
liquid and atoms of transparent iris made of solid matter. But
float a molecule-thin opaque material out near a stream of photons,
and they will interact with that matter and scatter.) Opaque
materials (metals, dyes, molecular chains) are opaque because
of how they interact with those odd electromagnetic thingies
that are the photon. The nature of opacity can be seen to be
"interactivity with photons.".
The interaction we've been discussing has
a name; diffraction, and it shows up with sound waves
and water waves, too.
It's odd to think that materials can scatter
photons that zip past without apparently touching. But a photon
is not a BB sailing past the edge of a target. It has a wave
length and an extended field that interacts with opaque
atoms it sails past, too. Those atoms have their own field that
extends beyond their apparent surface and when fields collide,
the lights go out. Or photons swerve.
In a sense, a photon acts as if a magnetized
BB were fired past the edge of a piece of iron. That's a bad
analogy, but it gives you a mental image that may help.
For a camera lens, this diffraction effect
can become problematic as the iris in the center of the lens
grows smaller. A small diameter iris exerts influence over the
passing stream of photons for a greater percentage of its area
than does a large one. The larger one has a longer circumference,
and some diffraction does indeed happen because of it, but the
large expanse of clear passage allows many more photons to get
through unaffected than does an iris only a few millimeters in
diameter.
Numbers of the beast
Let's look at some math. On an 18mm lens,
an aperture of f/22 is only 0.81mm in diameter. Look into your
DR Kit lens at wide angle with the DOF preview button engaged
to see it. Its area is a scant 0.525 square millimeters. Its
iris circumference is 2.54 linear millimeters. At f/3.5, the
same lens has an iris that spans 5.14mm with an area of 20.1
square mm and a linear circumference of 16.1mm. In the f/22 position
it's a fight between 0.5 square mm ringed with 2.5 linear mm
of edge while in the f/3.5 example, 20 square mm are rubbing
shoulders with 16 linear mm of diffraction-causing perimeter.
The small aperture has a 5:1 ratio of edge to surface while the
wide aperture example has a 0.8:1 ratio. Comparatively, that
smaller aperture has 6.25 times as much lip per square unit of
clear portal.
Given all this background you're probably
predicting the inevitable: More border and less hole equals more
diffraction. And you would be right. How does it affect things
in your photographic world?
Here's an animation that says it better,
and with more practical, real-world visualization than anything
else:
As the aperture closes from f/5.6 to f/8,
the image gains detail. F/11 looks good, too. This is because
the more optimum center of the lens elements are being used to
focus the image and at wide apertures more of the total glass
is involved in forming the image. Lens design is a practice of
minimizing compromises, but no design has zero compromises. Apertures
that allow more light in also show slightly less perfection in
focus.
With f/16 and beyond diffraction softens
the fine detail and by f/32, notable softness has blurred even
the intermediate detail. With smaller apertures like these, a
more optimum portion of the glass is being asked to focus the
image, but diffraction overpowers the image, softening details.
Wait, there's more...
Something else is happening as the iris
closes down. The limit on the detail may be deteriorating, but
the depth of focus is increasing dramatically. DOF stands for
depth of field, and the field here is the field of sharp focus.
The dark line across the lower part of the image is a telephone
wire a hundred feet from the lens. It gets sharper by a small
margin from f/5.6 to f/11, then gets lost in the diffraction
effect from there on. Just off the ISO lettering a nearby leaf
tip (silhouetted) just begins to make its presence visible at
f/22. It's mere inches away from the lens and as the lens encounters
f/32 it's much closer to being in focus, even though the lens
is parked at infinity.
Round it goes...
Other things are happening, too. The crosstar
filter effect grows off of specular highlights (actual lights)
and it rotates. Huh? Rotates?
As the iris closes two phenomena appear
in parallel. The ever-shrinking hole becomes saturated with diffraction
effects and the geometry of the iris blades cause that hole to
become a more straight sided, hexagonal figure than a continuously
circular aperture. The straight lines of the iris blades at small
apertures diffract light as a straight streak. No crosstar filter
is needed. A five bladed iris would cast no less than ten ! spokes
and lenses with more blades will cast fancier stars. In odd-numbered
iris blade configurations, the points will most often be seen
as a major and minor point 180 degrees opposite each other.
As the iris mechanism stops down, the angle
of the hexagonal hole appears to rotate, but that is just a product
of the geometry of the mechanism pivoting the thin blades from
a point outside the diameter of the maximum aperture.
Notice that the spoke graphic--the crosstar
effect--spreads out at smaller apertures, and at f/5.6 (full
tele) there is no star effect at all. That's because the iris
mechanism has fully retracted out of the optical path and a perfectly
circular mask inside the lens has defined the aperture.
Reflection?
Some in the past have attributed the stars
to "reflection" off the depth cut of the iris blade.
I doubt it. Blades are micro thin and finished with exceptionally
non-reflective surfaces--even the tiny edge. In photon count
alone, these edges are not thick enough to glint significantly.
And there is no guarantee that they are vertical surfaces at
all. How much reflection would you get off the edge of a razor
blade that had been treated to be black matte and non-reflective?
Diffraction alone can be counted on to produce this sort of effect.
Plus...
Yet another phenomenon can be seen in these
images due to the fact that the Rebel kit lens has an iris with
an even number of blades. Notice at high f-numbers that the points
are broken up by regularly spaced bands? It's a result you won't
see on images made with odd-numbered irises. But odd-numbered
irises will put out twice as many points--a major and minor point
for each blade. It's because diffraction cuts in both directions.
Diffracted photons don't simply swerve behind the nearest iris
blade and spread out, they smear in both directions perpendicular
to the blade edge. And when they cross over into the same image
area diffracted photons from the blade 180 degrees across the
iris gap are landing on, the two sprays of diffracted photons
do a subtraction/reinforcement trick as their waves cancel or
double up on top of each other. Here it shows up as the slight
banding of the points. Light is weird.
So...
Bottom line to all this is that as photons
sail past things, they scatter due to a phenomenon called diffraction,
which owes its presence to interactions between the opaque materials
making the iris and the nature of electromagnetic photons. Irises
give rise to this phenomenon, and when the iris portal shrinks,
diffraction phenomena overpower the ability of a lens to form
a tightly focused image. At the same time, the smaller apertures
that are destructive to sharpness in general become constructive
to evening out sharpness seen as depth of field.
This means that when you want an easy to
implement cross star effect, head for f/22. And while you're
at it, shoot that f/22 image at the Rebel's Medium size, because
the diffraction effect has jumped on the image definition hard
enough to lose any detail edge one might think they're getting
from the larger file format. To catch the full importance of
that last declaration check out the challenge
on this page.
All because of Ma Natures marvelous, mysterious,
but consistent, cup of Physics.
It'sCanon
For your Canon Digital Rebel- DSLR: Canon Digital Rebel EOS 300D eBook and DSLR: Canon Digital Rebel XT are on the shelf. These are great cameras with a great deal inside them, so we put a great deal of information into their eBooks. You'll find things here that nobody else ever told you about and not even Canon knew or could discuss.