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Lenses on Digital

In the good old days, everybody shot 35mm, and everybody knew pretty much what any given lens would do when mounted on their camera.  If you wanted "normal" perspective and magnification, you shot with a 50mm lens.  If you wanted telephoto, you picked one 100mm or longer, and wide angle was 35mm or shorter.  You felt so darn secure in this world it was hard to leave it.

Medium-format photography changed that for some people.  Anyone who shot in the old two-and-a-quarter (6 cm) size knew that "normal" for them wasn't 50 mm at all, it was more like 85mm, and that telephoto and wide angle were similarly different ranges.  But medium-format stuff is expensive and heavy, so most of us managed to avoid the confusion it caused.

Now digital SLRs come along, and there's all sorts of new problems.  Most people who have read about digital SLRs have read about the so-called "focal length multiplier" applied to digital.  In shorthand, this is described simply enough; digital cameras multiply the focal length of a lens by some factor, usually between 1.4 and 1.6.  Like most shorthand explanations, this one isn't completely true.

A lens is a projector, creating the image of the real world inside the camera at what is called the film or focal plane.  In standard 35mm cameras, the size of a single film frame is 36mm long and 24mm high.  The diagonal measurement of that frame is 43mm, and when the diagonal of the image is about the same as the focal length of the lens, you get roughly "normal" size and perspective.  The camera sees pretty much what the eye sees.  Great.  A 50mm lens is thus roughly "normal" for that film size.

Snap that same lens onto a digital camera and what happens?  Classical wisdom says that the 50mm gets multiplied by the focal length multiplier, giving you 75mm or something close.  But what really happens?

To the lens, nothing.  All of the digital cameras I have or had (Fuji D2X, D2X, D200) were built on Nikon bodies, and the CCD (charge-coupled device) that digitizes the image is placed at the focal plane, the same place that the film would usually be.  This lens, remember, acts as a projector.  Project a light from your own slide projector on the wall and get it focused.  Correctly focused, the size of the square of light will be constant for a given setting of your projector's zoom lens.  Lens size impacts image size.

This lighted square is a good way of understanding what happens with a digital camera.  If the full size of your lighted square is a 36x24mm rectangle, the full size of most digital camera CCDs is smaller.  The CCD on my Nikons is about 23x15.5mm.  The diagonal of this is 27.7mm, so the 43mm diagonal of a 35mm camera is 1.5 times that, which is where this focal multiplier stuff comes from.  But go back to the image on your wall for a moment.  Suppose we drew the lighted rectangle of a 35mm slide on the wall (lightly in pencil of course).  Now, turn off the projector a moment and draw a smaller rectangle whose size is related to your original slide image as 36x24 is to 23x15.5.  You now have a little rectangle inside, centered.  Put a slide in your projector and without moving anything, project it on the wall.  See how much of the image is contained inside the smaller rectangle representing the CCD?  Imagine now that this smaller piece of image was the actual slide.  What you'd then see is this smaller crop of the image expanded to fill the original lighted rectangle.  Since the field of view was smaller, this process would make the image look like it was taken with a telephoto lens!  In fact, it would make it look like it was taken with a telephoto lens with a focal length of about 75mm.

So why can't we just say that the focal length was multiplied?  Are we being a bit too much of a purist here?  No we are not, and here's why.

First, did you ever see one of those pictures that showed a coyote baying on a hilltop with a moon the size of a Buick behind him?  Clearly nobody can move the moon to the coyote, and you similarly can't get howls out of a coyote three-quarters of the way between earth and moon.  What happened was that a photographer was sitting down at the base of the hill with a telephoto lens, and shooting the picture.  The telephoto lens changes the perspective of the scene; far objects seem magnified more relative to near objects than we'd see with the eye.  You may also have taken a picture of someone lying on the beach, using a wide-angle lens, and found their feet looked about three times as big as their head.  Wide-angle lenses also change perspective; the near objects are magnified more than the distant ones relative to what the eye sees.

How does this apply to our digital camera?  Well, the perspective of a lens is based the position of the subject relative to the photographer.  Wide-angle lenses make close stuff appear big relative to far stuff because "close" stuff is really close to the camera, so it's relative size is large.  A coyote baying at the moon taken with a wide-angle lens with the coyote filling a third of the horizontal frame would show a really little moon, because it would be taken close to the coyote and the moon's size relative to the coyote's size would be small.  The same combination shot with the same coyote size taken with a 500mm lens would show the moon larger relative to the coyote, because from the position of the photographer (now farther away), the moon is larger relative to the coyote and the lens magnifies the angel of each equally.  Throw that lens on a digital camera, again keeping the same in-frame size of the coyote, and you'll be moving farther from the subject again, so now the moon looks larger compared to the coyote.

Another lens issue, depth of field, is more complicated.  It's generally (or at least often) said that depth of field is a function of the lens.  Since a digital camera crops the image, which is the same whatever film or CCD is at the focal point, why wouldn't the depth of field be the same for that lens?  If that were true, wouldn't it be true that the The D200 or D2X had the same depth of field at 500mm that the 35mm camera had at that lens size, but achieved the equivalent of 750mm magnification?  The best of both worlds?  It would seem logical but it's not quite true.

The concept of depth of field, meaning a zone in which objects are in focus instead of a precise narrow focus point, is based on the fact that the human eye cannot judge detail below a certain level, so focus imprecision below that same level can't be detected.  The generally accepted standard is that five lines per millimeter is the resolution of the eye at normal reading/viewing distance (10 inches).  Light can be scattered in a small circle and still appear sharp, and this (roughly speaking) is the "circle of confusion".  From this, you can probably begin to grasp why that 500mm lens won't have the same depth of field on my D2X as on a 35mm camera.  The detail required to create a viewable image with the D2X must be created by magnifying the smaller CCD image more than would be needed with the larger 35mm image.  The circle of confusion on the D2X is thus smaller than on a 35mm frame, and depth of field is narrower.

How much narrower?  Using Don Fleming's online calculator of depth of field (http://dfleming.ameranet.com/dofjs.html), you'll find that a 500mm lens on a D2X or other digital camera with the same size CCD focused at 250 feet at f8.0 would have a depth of field from about 238 to 262 feet.  That same lens on a 35mm camera would be in focus at these same settings between 233 and 270 feet.  The reason is that the digital image is expanded for viewing and the "circle of confusion" is smaller than for 35mm as a result.

But the good news is this.  To get the same image size, the 750mm lens on a 35mm camera would have a depth of field of from 242 to 259 feet!  So while the depth of field for a digital camera and a given lens is slightly smaller than that of a 35mm with the same lens, that same lens has an effective telephoto value of 1.5 times when mounted on a digital camera.  Getting that same telephoto effect with 35mm would require a longer lens that would have significantly less depth of field.  In short, the telephoto expansion effect for digital cameras makes the depth of field of a given lens less, but its magnifying power is increased by a greater factor as compared to 35mm.  For the same relative image size, the D2X will have greater depth of field.

Next point; macrophotography.  You put a Nikon or Sigma 105mm macro lens on both an F5 and an D2X (or on any Nikon DSLR with the 1.5x multiplier effect) and skootch down to get a closeup picture of an insect; say, the praying mantis on the collage of shots that's part of our digital imaging lead-in page.  What happens?  We know that that lens will let you get a 1:1 image at about a foot.  Is that true with digital?

No, and you probably know why by now.  The image of the mantis at the film plane is exactly the same in both cameras, but the CCD only makes a picture out of that smaller inner rectangle.  When the D2X image is compared, the smaller inner rectangle is blown up to full frame, so the D2X gives you something like a 1.5:1, or an image that's larger than life-sized.

Now let's look at another issue; sharpness.  Up to now, you may be seeing all the advantages stacking up for digital (which, of course, is why I bought one), but here we start finding things that cut the other direction.  Sharpness is our transition point, because here digital wins some and film wins others.

Most reviews of lenses talk about "edge sharpness" and note that the sharpness of the image falls off toward the edge of the picture.  That's because it's harder to get the lens to focus cleanly across the whole image plane and the edges sometimes suffer.  Digital cameras crop off the edges because of the smaller CCD, and often exhibit much better edge sharpness with a given lens than a 35mm body would.  This may be particularly true when the lens is shot at a large f-stop-"wide open" is the phrase used.

But the smaller CCD also hurts sharpness.  Because the image is "multiplied" in virtual size, any movement, shake, or lack of precision in focusing is all the more visible.  Many of the forums on digital cameras are populated with postings that moan about lost pictures due to this effect.  Some of the problem can be alleviated by treating the focal multiplier as a real multiplier; a 500mm lens would normally be thought to require 1/500th second shutter speed or better, but on a digital camera 1/750th is best.  For the rest, the photographer will have to be very careful to get precise focusing.

It's possible now to get digital cameras with a CCD that's the same size as a 35mm frame (some of Canon's high-end models and the upcoming D3X from Nikon).  For these cameras, there's no "focal multiplier" so none of these factors matter.  For those interested in wide-angle photography, the larger CCD is a boon because it's nearly impossible to get a digital camera with its small CCD to perform well for wide-angle shots.  The multiplier means that to get a 30mm lens effect, you'd need a 20mm lens, which will exhibit considerable perspective distortion.  For my own photo-mission, which is primarily wildlife and adventure photography, I bless the unique lens-to-camera relationship that digital brings with every trip I make.  I'd never be able to carry a lens large enough to give me the same impact with a standard 35mm.  If you're in the same boat, give digital serious thought.


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