Popping the Myth of the Focal Length Multiplier I

It seems that many otherwise intelligent and knowledgeable people on this board still “believe” in the myth of the Focal Length Multiplier (or FLM). It should be called the Cropping Factor and that is ALL that it is.

This is not to say that there is no benefit to the cropping factor - there is. It allows a Digital Camera to put ALL of its pixels on the smaller, cropped area of the image. Thus whatever a lens is capable of resolving will have greater clarity than on a full framed sensor where the crop is done later on your computer.

Belowand in part two of this post are excerpts from various sources, including this site. Follow the links if you wish to examine the full articles.

Those who think that their 45 mm lens is the equivalent of a 450mm telephoto, are the victims of marketing hype. NB. Just because you have x number of MP’s on the sensor, that has a ten times cropping factor only means you have the field of view of a telephoto and NOT the resolving power of a telephoto

Dave
*******************

Introduction

The terms crop factor and focal length multiplier were coined in recent years in an attempt to help SLR photographers understand how their existing ranges of lenses would perform on newly introduced DSLR cameras which had sensors smaller than the 35mm format. Using an FLM of 1.5, for example, a photographer might say that a 50mm lens on his DSLR "acts like" its focal length has been multiplied by 1.5, by which he means that it has the same field of view as a 75mm lens on the film camera that he is more familiar with. Of course, the actual focal length of a photographic lens is fixed by its optical construction, and does not change with the format of the sensor that is put behind it.

Magnification factor

The crop factor is sometimes referred to as "magnification factor." This usage commonly derives from the telephoto effect, in which lenses of a given focal length seem to produce greater magnification on crop-factor cameras than they do on full-frame cameras. It should be noted that the lens casts the same image no matter what camera it is attached to, and therefore produces the same magnification on all cameras. It is only because the image sensor is smaller in many DSLRs that a narrower FOV is achieved. The end result is that while the lens produces the same magnification it always did, the image produced on small-sensor DSLRs will be enlarged more to produce output (print or screen) that matches the output of a longer focal length lens on a full-frame camera. That is, the magnification as usually defined, from subject to focal plane, is unchanged, but the system magnification from subject to print is increased.

http://en.wikipedia.org/wiki/Crop_factor

Introduction

The advent of digital photography opened a completely new world for a lot of people. Just look around: there has never been a moment in photography’s long history that so many people actually had and used a photo camera. However, along with new technology always come misconceptions. One of these often heard and read delusions is the fact that “the focal length of lenses changes when used on a digital camera”, leading to strongly magnified images as indicated by a so-called digital magnification factor. The purpose of this article is to prove the above statement (and term digital magnification factor) to be incorrect by outlining the concepts of focal length and image sensor size as well as their combined effect on field of view.

http://209.85.165.104/search?q=cache:2tbPi0tPSAIJ:https://archive.ugent.be/retrieve/3673/Verhoeven%2B2007%2B-%2BDid%2Bthe%2BDigital%2B (R)Evolution%2BChange%2Bthe%2BConcept%2Bof%2BFocal%2BLength.pdf+%22focal+length+multiplier%22+%2B%22magnification%22&hl=en&ct=clnk&cd=10&gl=us

The sensor with FLM of 1.5X captures only part of the information projected by the 200mm lens into the 35mm film area. This results in a "cropped field of view", equivalent to the field of view of a 200 x 1.5 = 300mm lens on a 35mm film camera (see Case 2). The absolute size of the bird projected onto the sensor is the same as on the 35mm film because the focal length is still 200mm.

http://www.dpreview.com/learn/?/key=focal+length+multiplier

"Focal Length Multiplier" is a not-exactly-correct-but-helpful term that many like to use to describe the Field of View Crop Factor. Although the physical focal length of a lens is not actually changed on a FOVCF camera, the subject framing certainly is. By multiplying the lens focal length (or focal length range) by the FOVCF, you get the full-frame focal length lens subject framing equivalent when used at the same distance. For example, if you are looking for similar framing that a 50mm lens (the classic "normal" lens) provides on a full-frame (1.0x crop factor) SLR body, you probably want a 35mm lens on your 1.6x FOVCF body. 35mm x 1.6 = similar framing to a 56mm lens on a full-frame camera body. This focal length is often referred to as the "Effective Focal Length". The lens is still a 35mm lens, but your final image will only include a crop of the lens' complete image.

What affect does the FOVCF have on lenses? None - physically. The lenses are the same and retain all of their same physical attributes. But, there are some differences in how these lenses are used that should be mentioned ...

http://www.the-digital-picture.com/Canon-Lenses/Field-of-View-Crop-Factor.aspx

It is really necessary to understand that the visible change of focal length is due to a crop, and absolutely not to any form of increase of the focal length. This one follows the optical laws : it is the distance which separates the optical center of the focal plane (in other words, the film or the sensor). If I cut my 35mm format to keep 1mm at the center, I won't have a 100mm lens transformed into 3000 mm ! We indeed speak about focal "equivalence".

http://www.withinlights.com/Labo/Articles/CropFactor/index_us.php

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. My Fuji S2 is built on a Nikon N80 body, 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.

If the full size of your lighted square is a 36x24mm rectangle, the full size of most digital camera CCDs is smaller. The S2 CCD is 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.

http://www.cimicorp.com/DI/DTipLenses.html

Early marketing literature, and the articles in the press based on them, described the chips in digital SLRs as 1.5x and 1.6x chips. The formula, said the marketing folks, was that you multiply the focal length of your lens by 1.5x or 1.6x (depending on the brand) to get the length of your lens when mounted onto one of their digital SLRs. The implication being that these chips provided some kind of magnification.

Image chips in digital SLRs crop the image provided by the lens. They don't offer any magnification. Is this really an advantage?

In the above example the image on the left was shot using a 300mm lens on a standard SLR. The image on the right shows the effect of mounting the same 300mm lens on a digital camera with a 1.5x chip. The result is the equivalent of a 450mm lens. This is a good thing right? This was a good thing said the marketing folks. What they didn't say was that it is more accurate to describe that 1.5x chip as a 2/3rds chip !

These chips are smaller than the area covered by a frame of 35mm film. There is no extra magnification, as is implied, and has been erroneously reported by journalists in any number of articles. These smaller chips crop the image rather than magnify it. So the "gain" is in fact no gain at all, it is a loss, and that loss occurs equally throughout the entire range of focal lengths from wide-angle to telephoto.

http://www.vividlight.com/Articles/3814.htm

Chato said:

Those who think that their 45 mm lens is the equivalent of a 450mm
telephoto, are the victims of marketing hype. NB. Just because you
have x number of MP’s on the sensor, that has a ten times cropping
factor only means you have the field of view of a telephoto and NOT
the resolving power of a telephoto

Click to expand...

You are a victim of false preises. There is no such thing as "resolving power of a telephoto". There is nothing particularly special about 45mm or 450mm, either one can be long, normal or wide depending on the camera that it's mounted to.

What counts isn't lens or sensor resolution, it's system resolution. i.e. results.

By your logic "FF" lenses are "crops" too. 645, 6x6, 6x7, 4x5, 8x10, etc.

--
Seen in a fortune cookie:
Fear is the darkroom where negatives are developed

Chato said:

It seems that many otherwise intelligent and knowledgeable people
on this board still “believe” in the myth of the Focal Length
Multiplier (or FLM). It should be called the Cropping Factor and
that is ALL that it is.

Click to expand...

I'm not sure it's a myth. For otherwise intelligent people, it's just a crutch manufacturers use to equate the FOV of a lens for the different sensors sizes of digital cameras to something familiar to most photographers coming from film, the 35mm equivalent. Nothing more to me and to other otherwise intelligent and knowledgeable people.

I think a direct FOV spec would be more direct, but seasoned photographers don't think in terms of FOV. Yet.

--mamallama

nickleback said:

Chato said:

Those who think that their 45 mm lens is the equivalent of a 450mm
telephoto, are the victims of marketing hype. NB. Just because you
have x number of MP’s on the sensor, that has a ten times cropping
factor only means you have the field of view of a telephoto and NOT
the resolving power of a telephoto

Click to expand...

You are a victim of false preises. There is no such thing as
"resolving power of a telephoto". There is nothing particularly
special about 45mm or 450mm, either one can be long, normal or wide
depending on the camera that it's mounted to.

What counts isn't lens or sensor resolution, it's system
resolution. i.e. results.

By your logic "FF" lenses are "crops" too. 645, 6x6, 6x7, 4x5,
8x10, etc.

Click to expand...

First, I have no idea what "preises" mean. I'm not being a spelling nanny here - I'm just ignorant of the meaning...

Second, here is what I mean by "Resolving Power"

American Heritage Stedman's Medical Dictionary - Cite This Source

resolving power
n.

The ability of a lens to distinguish small objects in close proximity.

So, my bad if I wasn't clear - In this thread I mean the above definition. And I mean that a 45mm lens on a sensor with a 10x cropping factor does NOT have the resolving power of a 450mm lens on a larger sensor - let us say, Full frame.

And yes, if the tiny sensor has a Gig of pixels it still will not be able to resolve two close objects that it is not presented with enough light to even see. A clear blur is still a blur.

Dave

nickleback said:

--
Seen in a fortune cookie:
Fear is the darkroom where negatives are developed

Click to expand...

You haven't bought the myth? Watch the replies that this post gets.

Dave

Chato said:

First, I have no idea what "preises" mean. I'm not being a spelling
nanny here - I'm just ignorant of the meaning...

Click to expand...

It's a type. premises.

Chato said:

resolving power
n.

The ability of a lens to distinguish small objects in close proximity.

Click to expand...

Fine.

Chato said:

So, my bad if I wasn't clear - In this thread I mean the above
definition.

Click to expand...

Not all lenses are created equal. The smaller the film/sensor, the easier (and more necessary!) it is to create a lens with high resolving power.

Just one example. The Canon G7 is a 10mp 1/1.8" sensor. The sensor is 7.18x5.32mm. According to tests on this site, this camera can resolve 1850 LPH vertically and 1775 LPH horizontally. To get 1850 LPH into 5.32mm the lens must resolve about 175 lpm.

35mm system lenses are typically in the 80 to 100 lpm ballpark.

--
Seen in a fortune cookie:
Fear is the darkroom where negatives are developed

nickleback said:

Just one example. The Canon G7 is a 10mp 1/1.8" sensor. The
sensor is 7.18x5.32mm. According to tests on this site

Click to expand...

link:

http://www.dpreview.com/reviews/canong7/page16.asp

--
Seen in a fortune cookie:
Fear is the darkroom where negatives are developed

nickleback said:

You are a victim of false preises. There is no such thing as
"resolving power of a telephoto". There is nothing particularly
special about 45mm or 450mm, either one can be long, normal or wide
depending on the camera that it's mounted to.

Click to expand...

There is a difference - aperture!

A 45mm at f/5.6 will have an 8mm aperture. A 450mm at f/5.6 will have a 80mm aperture.

Try looking through a small pocket peer of binoculars like a 10x20. (10 is the magnification, 20 is the aperture) Then try a larger 10x50 set. While the magnification remains the same, the extra aperture will resolve finer details that were not visible in the pocket binoculars.

The same reason larger telescopes resolve finer details than smaller telescopes.

This is a very basic principle of optics.

--
If stupidity got us into this mess, why can't it get us out?

kiwi2 said:

nickleback said:

You are a victim of false preises. There is no such thing as
"resolving power of a telephoto". There is nothing particularly
special about 45mm or 450mm, either one can be long, normal or wide
depending on the camera that it's mounted to.

Click to expand...

There is a difference - aperture!

Click to expand...

I'm well aware of that. There still isn't anything special about 45mm or 450mm. What matters is the whole system.

kiwi2 said:

A 45mm at f/5.6 will have an 8mm aperture. A 450mm at f/5.6 will
have a 80mm aperture.

Click to expand...

Aperture has little to do with detail, other than when you hit diffraction limits. That isn't in play in any of the typical camera examples at max aperture.

kiwi2 said:

Try looking through a small pocket peer of binoculars like a 10x20.
(10 is the magnification, 20 is the aperture) Then try a larger
10x50 set. While the magnification remains the same, the extra
aperture will resolve finer details that were not visible in the
pocket binoculars.

Click to expand...

Bad example, your eyes haven't changed size. With the camera example, for a 450mm and 45 mm lens to give equivalent FOV the film/sensor in the "45mm" example must be 1/10th the size of the "450mm" camera.

--
Seen in a fortune cookie:
Fear is the darkroom where negatives are developed

Chato said:

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.

Click to expand...

Lenses don't change perspective. They only change magnification. The perspective is a function of the distance between the photographer and the subject(s).

Telephoto and wide angle lenses just make it easier to "fill the frame" in specific situations. That's all.

kiwi2 said:

The same reason larger telescopes resolve finer details than
smaller telescopes.

Click to expand...

Missed this part. Telescopes, especially cheaper ones, are designed to "go long". At the apertures used, diffraction limits are very much in play. As I wrote in the previous reply, this is not typically the case with camera lenses at max aperture.

--
Seen in a fortune cookie:
Fear is the darkroom where negatives are developed

Personally, I like to call it Field Of View Equivalent.

It isn't really a multiplier until you print an image or view it on screen to make it larger; it is when you make a print from a smaller sensor that is the same size you would have printed with a larger sensor that the "multiplier" happens. You are enlarging more than you would have with the larger sensor and that enlarging is the multiplier. The smaller format itself does not create a multiplier.

It isn't a crop factor if you are using a lens that was made for the smaller sensor size because then you are using pretty much the whole usable part of the image circle--nothing is actually being cropped. Cropping necessarily cuts away chunks that were usable, and that is not happening.

To my thinking, FOV Equiv. describes this best. The smaller sensor is capturing a subset of the horizontal field of view in comparison to a larger format. There is always an equivalent focal length from a different size format that would have captured the same field of view. Just specify what that focal length is and what format you are referencing. This usage captures the concept rather nicely, it seems to me.

Thanks for your interesting thoughts.

A lot of posters refer to FOV when talking about a cropped shot. This is not strictly correct, as what the sensor sees is the cropped AOV . The FOV iis not quite accurate because the viewfinder is slightly higher than the sensor.

the pixel density governs the whole concept. Thats what
creates the "FLM" or the "crop factor". If the 30D and 20D
had the same pixel density as the 5D per square, then this
so called crop factor would totally vanish.

--
Logic is superior to emotion
BUT
Emotion is much more fun!

Watch out for the exposure police.
They will tell you that its wrong even
though they weren't there to witness it.

Come visit me at:
http://www.pbase.com/keithallenlaw
See my profile for what i shoot with.

stan walker said:

A lot of posters refer to FOV when talking about a cropped shot.
This is not strictly correct, as what the sensor sees is the
cropped AOV . The FOV iis not quite accurate because the viewfinder
is slightly higher than the sensor.

Click to expand...

Your viewfinder statement confuses me since I don't see what the viewfinder has to do with it. I'm thinking about the property of the lens with respect to a particular size sensor.

To me FOV and AOV are somewhat equivalent. Field (F) is an area and Angle (A) is angle in one linear dimension (horizontal, vertical or diagonally). Some think if AOV is to be chosen for specification the horizontal dimension make more sense since we tend to think of that dimension when deciding on a lens.

Anyway all we have now is some crutch to bring it down to 35 mm equivalent.

--mamallama

This post comes up every few months - someone is all excited to bust the big focal length multiplier myth. Unfortunately, it's just a battle of words. You can call it crop factor, you can call it focal length multiplier, or you can call it by the correct name, the field of view multiplier, or you can make up your own name. the end result is exactly the same. It's not even worth discussing. Everything else being the same, changing the crop length changes the field of view, and changing the field of view changes the crop factor.

Bottom line is, a 100 mm lens on a 2.0 crop factor camera will take a picture identical to a 200 mm lens on a 1.0 crop factor camera (ignoring pixel noise, and perhaps a slight change in sharpness due to using the lens center) Whether calling it a focal length multiplier is correct terminology is hardly important. True the optically defined focal length of the lesn hasn't changed, but for every practical photographic aspect you can't tell the difference.

So, if it makes you happy to proudly point out (for the millionth time) that the focal length, in the optical sense of the word, hasn't changed, consider us told. Just remember that you can't tell the difference (perspective, depth of field, composition, distance to subject, etc.) between a FZ50 at 84MM and a 5D at 420MM, and for that reason I doubt that the term "focal length multiplier" will ever go away.

Chato said:

Second, here is what I mean by "Resolving Power"

American Heritage Stedman's Medical Dictionary - Cite This Source

resolving power
n.

The ability of a lens to distinguish small objects in close proximity.

Click to expand...

I see you should be shopping for a macro lens then. (or a macro-capable digicam. And bugger the crop factor!)

tko said:

This post comes up every few months - someone is all excited to
bust the big focal length multiplier myth.

Click to expand...

But I do believe he wins the award for making the longest post on this topic

tko said:

Bottom line is, a 100 mm lens on a 2.0 crop factor camera will take
a picture identical to a 200 mm lens on a 1.0 crop factor camera
(ignoring pixel noise, and perhaps a slight change in sharpness due
to using the lens center)

Click to expand...

There is a real difference in DOF - at the same aperture the 100mm lens on a 2.0 crop factor camera will yield a larger DOF compared to the 200mm lens on a 1.0 crop factor camera. The "built in" shallower DOF of larger format sensors and film cameras comes in handy sometimes (example: good headshot of star in cramped hotel room needs shallow DOF); and the "built in" larger DOF of compact P&S with their tiny sensors makes AF accuracy less demanding for the manufacturers - and customers happy with their cheap but sharp digicams!
--
Phil

GMT +1