Focal length and crop factor

[Peter Ryan]

I am looking for some help to understand the focal length of a lens and the crop factor with smaller sensors. More particularly: -
Assuming a lens has a 200m focal length based on a full frame sensor and (for ease of maths) a digital sensor with a 1.5 x crop this would give the 200m length the same field of view as a 300m focal length lens.
1. While the field of view is akin to a 300m is the perspective of the lens changed from a 200m to 300m lens?
2. Without getting into discussion on vibration reduction lenses; to reduce camera shake the rule of thumb is that you choose a shutter speed being the reciprocal of the focal length so does that mean the rule of thumb is 1/250 second or 1/500 on the digital sensor?
Over to you guys now. I look forward to your feedback.

[Colin Southern]

Without getting into discussion on vibration reduction lenses; to reduce camera shake the rule of thumb is that you choose a shutter speed being the reciprocal of the focal length so does that mean the rule of thumb is 1/250 second or 1/500 on the digital sensor?

Hi Peter,

If you're shooting with a crop-factor camera then the minimum shutter speed for minimising camera shake is the reciprocal of the apparent focal length (ie you need to bump it up by whatever the crop-factor is).

Having just said that though, keep in mind that it's only a rule-of-thumb for MINIMISING camera shake, not eliminating it. If you want to ELIMINATE it then aim for about 5x higher.

[Dave Humphries]

While the field of view is akin to a 300m is the perspective of the lens changed from a 200m to 300m lens?

My belief is that perspective is set at the time of taking the image and is dependent upon camera to subject distance and (primarily for wider angle lenses) the relative distances of nearest and furthest parts of a subject to the camera.

The size of the sensor, crop factor, focal length, effective focal length, field of view and any PP cropping done do not affect this.

Hmmm, that sounds a bit of a statement, I hope I'm right

[Dave Humphries]

My belief is that perspective is set at the time of taking the image and is dependent upon camera to subject distance and (primarily for wider angle lenses) the relative distances of nearest and furthest parts of a subject to the camera.

The size of the sensor, crop factor, focal length, effective focal length, field of view and any PP cropping done do not affect this.

I'm pretty sure I am correct, but this isn't how it pans out in reality, here's what I meant:

If I stand on one side of a river and take a shot of a bird on its nest on the far bank with;
a) my 1.5 crop factor camera using a 200mm lens it will give a certain perspective of bird size in relation to say, a fence or bush behind, or a tree trunk in the river in front.
b) I shoot the same scene again with a FF body and the same 200mm lens
c) and d) Then I use say a 400mm lens and attach that to both cameras and take two more shots

Once the images are cropped to produce the same pleasing shot with a bit of tree trunk, all of the bird and some bush in shot, there will be no difference in the perspective between these picture elements in any of the images a) thru d).

In reality however, given a shorter lens, we usually attempt to get closer to the subject compared to a longer lens, it is changing the camera to subject distance that changes the perspective.
Conversely, given a very long lens, we may actually have to go back a bit to get the subject wholly into the frame; again, this will affect the perspective.

[arith]

I was a bit surprised by this; the first is 28 x 1.6 and the second 50 x 1.6 millimetres.





In the second the needle is clearly bigger; I shouldn't have been so surprised though.

[Peter Ryan]

Dave,

I am interested in your expanded comments above (i.e take 2) - yes I can see that and it makes sense, partcularly the last paragraph.

Thank you all for your time and input to this discussion.

[Dave Humphries]

Hi Peter,

You might want to look at the example on this tutorial on Focal Length, about half way down, where it discusses "Zoom lenses vs Prime lenses".

The image of the dog is actually 3 images, the default, plus;
if you hover mouse over "Change of Composition", it shows what happens if you zoom in, or increase focal length from same place. You'll also get the same result as this from a tighter crop in PP.
if you hover mouse over "Change of Perspective", it shows what happens if you move closer, but zoom out, or use a short focal length to maintain subject size.

Thanks,

[benm]

When you took these two photos you were standing in the exact same location? Is the 28mm photo cropped and enlarged so the gate appears to be the same size as in the 50mm photo? I am willing to bet you moved between shots.

[Blazing fire]

I'm willing to bet you moved too. There is evident pespective difference. The background in the first shot looks distant.

[arith]

Yes I moved, the 50mm is taken much further back. I'm only showing the needle is bigger even though I'm further back, I couldn't get any further but still it illustrates an obvious difference.

[Djd3mo]

Hello !
I feel that, somehow, the discussion has moved away from the original question. So, more than 1 year later, I would like to retackle the title issue:

Focal length and crop factor

Somewhere in this CiC article you can read the following phrases:

"A common rule of thumb for estimating how fast the exposure needs to be for a given focal length is the one over focal length rule."

and

"For users of digital cameras with cropped sensors, one needs to convert into a 35 mm equivalent focal length."

Having these in mind let's consider the following example:
A Nikon D3x and a Nikon D80, both sharing the same nikon 50mm 1.8 AF-D lens. The smaller D80 sensor has approximately the same density of pixels as the wider D3x sensor. Taking the same picture from the same station point using both cameras and afterwards cropping the FX image to the size of the DX image (considering that we centered and focused both frames exactly) we should obtain the same field of view and the same 10MPixels size for both pictures, right ? Why, then, an angle shift would be more noticeable on the DX image than on the cropped FX image ?
Why do we have to multiply the focal length by crop factor in this rule of thumb as long as nothing is different between the DX image and the FX cropped image?

Thank you for your time and may the light be with you !

[William W]

Why do we have to multiply the focal length by crop factor in this rule of thumb as long as nothing is different between the DX image and the FX cropped image? Thank you for your time and may the light be with you !

There is a lot difference in regard to how much apparent blur will be seen, due to camera shake.

The 1/Focal Length "Rule of Thumb" to "arrest" camera shake is all about "an average print" when viewed at "an acceptable distance".

Although only a "Rule of Thumb" - the ENLARGEMENT SIZE of the final Print and the VIEWING DISTANCE of the final Print must be maintained "standard" when comparing: otherwise we have no basis for the comparison

With the APS-C camera the Full Frame Crop of the image viewed at arm’s length is a smaller area of the scene than the same Full Frame Crop of the image taken with the 135 Format Camera, viewed at arm's length . . . SO assuming the camera is shaken at the same rate for each photograph the RESULTANT BLUR from the camera shake will be more noticeable in the APS-C image.

Taking the same picture from the same station point using both cameras and afterwards cropping the FX image to the size of the DX image

What you want to do with your example is crop the larger image more than a FULL FRAME CROP – that is to say NOT use the Full Frame of it.

That means in effect for the FX image you are cropping to look at only the middle section which you made with a 50mm lens – and that would be like taking the same FULL FRAME CROP picture with an 80mm lens on your FX camera – so therefore the “Rule of Thumb” says 1/80s NOT 1/50s for that shot, which concurs with the 1/80s "rule" for a 50mm lens on an DX camera to make a picture of the same FULL FRAME CROP area in the scene.


The whole point is if you have a 24mm lens or a 300 mm lens and your hand wobbles the same rate for both shots; then BOTH images will be blurred the same amount across the same area of view inside the scene - it is just what is PERCEIVED in the final image (at FULL FRAME CROP) as a blur, that we are discussing and the 24mm lens has a larger area of view, than the 300mm lens.

WW

[William W]

While the field of view is akin to a 300m is the perspective of the lens changed from a 200m to 300m lens?

Answering the question above required reading this original post.
Therefore to answer this question - lenses do NOT have or make “Perspective”
PERSPECTIVE is determined by the CAMERA’S VIEWPOINT relative to the SUBJECT.
This CAMERA VIEWPOINT includes the DISTANCE from the SUBJECT and also the CAMERA’S ELEVATION in relation to the SUBJECT.

Once the PERSPECTIVE of the shot is determined by the CAMERA VIEWPOINT, the FOCAL LENGTH of lens chosen determines the FIELD OF VIEW.
Or another term, the FOCAL LENGTH of the lens determines “THE SHOT” (e.g. an Head Shot; an Half Shot; a Full Length Shot: a Wide Shot, etc . . .).

A Picture taken with a Canon 5DMkII of a Man standing on an oval taken at 90ft SHOOTING DISTANCE with the Camera Elevation 5ft from the ground, has the SAME PERSPECTIVE if a 35mm lens is used or if a 500 mm lens is used.

The 35mm lens will give a Field of View of about 90ft wide (at the Man) - we would say that is a Very Wide Shot; the 500mm lens will give a field of view of about 6ft (at the man) and we would say that is a Full Length Shot (if we turned the camera vertical format) . . .

But BOTH pictures have the exactly the SAME Perspective.


WW

[MiniChris]

It is at this depth of discussion, I start wondering why everyone went to digital, and really, far more importantly, why did the digital folks attempt to emulate film. They are not the same except in a few instances. They look alike, but really don't need to; they make camera noises, but could just as easily be silent; they hold the same numerical references, though they have but little relationship to film media; they have formulae like those above which are only there because they chose to emulate another media in function, wheras it should have only been in name.

I have yet to figure out why one of the big boys doesn't just make a digital camera which is functionally, ergonomically, electronically, etc a digital media and quit trying to still be a filmic media. T'aint now, won't be tomorrow, either.

WW, you do understand this media as well as anyone I've read to date. Dave, Rob, and a lot of the others do as well...of course, Ian. But, if you've all noticed, it's always related to comparing it to a film medium...thus my little diatribe. I will assauge myself today by shooting my 5x7 view camera and spending some quality time in the darkroom...ahhhhh, fixer.

[rpcrowe]

I'm pretty sure I am correct, but this isn't how it pans out in reality, here's what I meant:

If I stand on one side of a river and take a shot of a bird on its nest on the far bank with;
a) my 1.5 crop factor camera using a 200mm lens it will give a certain perspective of bird size in relation to say, a fence or bush behind, or a tree trunk in the river in front.
b) I shoot the same scene again with a FF body and the same 200mm lens
c) and d) Then I use say a 400mm lens and attach that to both cameras and take two more shots

Once the images are cropped to produce the same pleasing shot with a bit of tree trunk, all of the bird and some bush in shot, there will be no difference in the perspective between these picture elements in any of the images a) thru d).

In reality however, given a shorter lens, we usually attempt to get closer to the subject compared to a longer lens, it is changing the camera to subject distance that changes the perspective.
Conversely, given a very long lens, we may actually have to go back a bit to get the subject wholly into the frame; again, this will affect the perspective.

Absolutely... Perspective is controlled by camera to subject distance. However focal length often controls the distance from which we shoot or the distance will control the focal length we choose.

Going even further along this line of thought... If I shot a scene using my 400mm lens and then stood in the same place and shot the same scene with my 12mm lens and then cropped the shot so that the 12mm image covered the same field as the 400mm lens, the perspective would be the same.

However, in truth; I would never do that because the image quality from the highly cropped image would be terrible. Given that set of circumstances; I would either zoom with my feet to get closer to a subject or slap on the 400mm lens.

If I had framed a shot using my 12mm lens and then wanted to use a 400mm lens, I would need to move back to get the same field of view. The perspective would then be changed.

[Djd3mo]

First of all I would like to thank all of you for your answers.

@William W. - I really tried to understand your explanations but, and I am not being rude, I didn't quite get it. It is probably because you have been continuously using the term “full frame crop”, which doesn't make any sense. It's either full frame or it's crop, full frame crop is confusing. If you are willing to explain it again in a different manner I'll be thankful.

Meanwhile I will try to build a different and more compelling view of my theoretical experiment:

Step 1 – I take one picture of a subject situated in point station A using D3x and 50mm lens from point station B. Afterwards I take another picture of the same subject situated in point station A using D80 and 50mm lens from the same point station B. No distance or elevation changes, so perspective doesn’t change. The outcome: a wider 24.5MPixels image and a narrower 10.2MPixels image of the same subject.

Step 2 – Considering that the D3x sensor size is 864 mm2 and the D80 sensor size is 370 mm2, I know then that the D3x sensor is ~2.33 times bigger than the D80 size. Therefore I do a 2.33 postprocess crop of the 24.5MP image framing the subject exactly as in the D80 image and I get a 10.5MP image (slightly bigger than the D80 image).

Step 3 – Comparison. How much is each of the pictures affected by a one degree angle shift of lens (caused by whatever you want, let’s say hand shiver for the sake of discussion) ?

Those being said, I am still trying to figure out WHY are we multiplying the focal length by the crop factor in the empiric rule of thumb time=1/focal, since there's NO magnification involved ?

[Dave Humphries]

Those being said, I am still trying to figure out WHY are we multiplying the focal length by the crop factor in the empiric rule of thumb time=1/focal, since there's NO magnification involved ?

Hi Nick,

The one degree of movement relates to the lens as held and the effect on the full image from either camera.

That is 1 in 40 degrees (across the sensor) of the full frame view, or because of the magnification caused by the crop sensor, it is about 1 in 27 degrees for the crop factor camera. So the blur amount is 1/40th of the frame width against 1/27th of the frame width, i.e. more on the crop sensor.

If you crop the full frame image to match the angle of view of the crop camera, then yes, you have removed that factor and it makes no difference

Cheers,

[Djd3mo]

Hi Nick,

The one degree of movement relates to the lens as held and the effect on the full image from either camera.

That is 1 in 40 degrees (across the sensor) of the full frame view, or because of the magnification caused by the crop sensor, it is about 1 in 27 degrees for the crop factor camera. So the blur amount is 1/40th of the frame width against 1/27th of the frame width, i.e. more on the crop sensor.

If you crop the full frame image to match the angle of view of the crop camera, then yes, you have removed that factor and it makes no difference

Cheers,

FF - D3x sensor width = 35.9mm and 6048 pixels. Divided by 40 degrees, we have ~0.89mm and ~151 pixels per degree

ASP-C - D80 sensor width = 23.6mm and 3872 pixels. Divided by 27 degrees, we have ~0.87mm and ~143pixels per degree.

I believe the difference is insignificant so that you can safely say that the blur amount is the same and no crop factor multiplication is involved, what do you say ?

[William W]

I really tried to understand your explanations but, and I am not being rude, I didn't quite get it. It is probably because you have been continuously using the term “full frame crop”, which doesn't make any sense.

I would not assume rudeness.

“Full Frame Crop” is referring to the FINAL PRINT which we will scrutinize to look for blur due to camera movement.

The Final Print is a “Full Frame Crop” if it is (for example) a 5 x 7½ inch print, which shows the WHOLE sensor area – and NOTHING cropped out.

As mentioned this “1/Focal Length Rule” is RELATIVE and therefore for any COMPARISON there MUST be a standard reference – and for that to be a reference, we MUST look at the FULL FRAME IMAGE of any cameras’ sensor.


***


Another answer written differently:

I read your number two experiment and would love to go into the trigonometry to calculate 1° of camera movement, that is right up my pedantic nature so to do – but it is unnecessary, I think.

Meanwhile, what I would like you to do is forget about pixels and also quantifying amounts of movement in degrees (at the moment), but rather just consider the images if we PRINTED the whole sensor's pictures of each camera to a 5” x 7½” photograph.

We take this picture with a 5DMkII (a “full frame camera”) and a 50mm lens:

In this photo we see about 18ft width, across the Garden.


And we then stand in the same spot and take this picture with a 30D camera (a “crop camera”) and the same 50mm lens:

In this Photo we see about 14ft width, across the Garden.

The bald tree stump, in the middle of each picture is 25ft from the camera.

Obviously, in the picture taken with the 5DMkII we see more width across the garden, either side of the tree stump in the middle.

Now let’s print each of those images to a 5 x 7½inch print (i.e. print a “full frame crop” of each image).

Let’s assume the camera shake is only sideways (horizontal), and makes the scene “blurred” to the extent that we can measure this blur by the sideways movement (soft edge) of that bald tree stump in the middle of the picture.

Now when we compare the two 5” x 7½” Prints and hold them each at arms’ length, we will likely notice more blur in the shot taken by the 30D and the 50mm lens – because the “blurred distance” is spread across a larger linear distance of the 7½” width of that photograph.

A simple diagram of the plan view of the shoot is here:


Obviously, if we crop the image made with the larger format camera and then print that CROPPED image to 5” x 7½”, there will be the same appreciable increase in the PERCEIVED BLUR:


Now, let’s not argue about the numbers regarding my example of sideways movement
being a factor of 18/14 increase in the Blur, and the "1.6 factor of the 30D" - as I suggested at the beginning, please forget about quantifying this into numbers (at the moment) for this example: because mathematics and numbers are precise and it is not suitable to attempt to quantify this “rule” into any numbers for one portion of movement (at this stage) - as is it a “Rule of Thumb” in the first place.


Hopefully this text, image samples and plan view of the shoot, will explain the fact that there is a difference in the Blur we will notice, for any given SAME AMOUNT of camera shake if we use the any lens on a 5DMkII and then take the same shot with the same lens on a 30D and make a print of the FULL FRAME of each sensor; and then view each print at the same viewing distance.


***


The History:

This 1/Focal Length Rule seemed to sprout up and be “applied” around the end of 1950: certainly I have many references to it, in Photography Magazines and Journals published in the 1970’s.

We must realize that by the 1970’s the 35mm Film SLR Camera and the amount of INTERCHANGEABLE lenses available to the “amateur” and fast Film Speeds had revolutionized Photography . . . and Tripods were becoming unnecessary for many applications - so “rules” for hand holding were required.

And moreover this “1/Focal Length Rule of Thumb for Hand Holding” really only came about when “Miniature Format” (*1) came into a Popular standing and more so, when SLRs were becoming more common place, from 1950 to 1970.

Side note:
[(*1) “Miniature Format” is the precise, yet now little used technical term, to reference the camera format which uses 35mmfilm or a camera such as a 5DMkII. The APS-C format (such as a 30D) is “Sub-Miniature Format” and a camera such as an Hasselblad 6x6cm is: “Medium Format”]


***


Why does this 1/Focal Length Rule work? (now a little Mathematics)

Let’s talk about a 5DMkII and a 50mm lens on it and the shaky hands using it, because that’s the base upon which this 1/Focal Length Rule was initiated.

(A simple answer follows)

When holding a camera, we have several movements we can make:

1. Yaw: Swinging to the left / right.
2. Pitch: Tilting up / down.
3. Roll: Rotates.
4. Vertical: Moves up / down parallel to the scene
5. Horizontal: Moves left / right parallel to the scene
6. Axial: Moves back / forth parallel to the horizontal


I will discuss only the first three – they are the most relevant for “camera shake”, in most shooting scenarios.

In really simple terms, the amount of “average shake” a human has holding a camera is about 0.6°/sec to 0.9°/sec.(*2) (you are going to have to trust me on that, please).


Now it is obvious that the amount of movement we will notice in the final print will depend on the focal length of the lens we use: if we use a 500mm lens, or if we use a 35mm lens: we know that we will see more movement in the final 5” x 7½” (Full Frame Crop) print from the 500mm lens than the print from the 35mm lens, if we have the same shaky hands holding the camera and we use the same shutter speed.

Now, for a lens FL = 50mm lens, a 0.75° swing will move the image through about 0.75 mm, which will cause noticeable blurring.

If we want no significant blurring, we need to reduce the linear blur to the order of about 12 to 20 microns in the sensors’ frame: 12 to 20 microns is about one HALF the value of the range of the circle of confusion (*3) used for 35mm format cameras.

Now think about the “image” projected onto the sensor of our 5DMkII.
We are using a 50mm lens.
Our hand is shaking at the SPEED of 0.75°/sec.
The IMAGE projected onto the sensor will move though 16 microns . . . in about 1/50s.

Therefore we need to shoot at about 1/50s, or faster, such that we will not see any "noticeable" or "perceived" image blur in or "standard" full frame crop print, which we view at arms length.

This corresponds to the 1/Focal Length Rule – And it is very important to understand that the rate at which the camera moves around will vary but that “average shake” a human rated at about 0.6°/sec to 0.9°/sec. is an average based on the experience of many people.

Sometimes 1/50s will be fast enough to give a sharp image, sometimes it won't . . . it is just a “Rule of Thumb” – and it is a rule of thumb based upon the 35mm format because it grew out of the growth of 35mm film cameras and the need for “guidelines” for their use.

Side Notes:
[(*2) Note that this is a SPEED - i.e. degrees per second, the SPEED of the shake is important, if we want to talk even superficially about the Mathematics, we must speak of the SPEED of the shake, because we are discussing the SPEED of the shutter which will arrest same]


[(*3) Also note we have now introduced the Circle of Confusion.
Because the CoC is the basis upon which we establish if the image is sharp.
So what does sharp mean: it means NOT Blurred.
The CoC is another bit of the relevant Mathematics and as we know, the CoC changes when there is a change in Sensor Size.
Also as we know, CoC is sort of arbitrary measure within a range of what is "accepted".
Also the CoC is based upon a "standard print viewed at a standard distance" - and also the "average" ability of the human eye to see and differentiate really small lines - i.e. the "average" persons eye's resolving power]


***

It is at this depth of discussion, I start wondering why everyone went to digital . . . if you've all noticed, it's always related to comparing it to a film medium...thus my little diatribe. I will [assuage] myself today by shooting my 5x7 view camera and spending some quality time in the darkroom...ahhhhh, fixer.

Haha – I love what you wrote.

I know that smell of fixer very well.

I do understand that your post was somewhat tongue in check: and again I note my appreciation of it.

But it is important to also note (seriously) that the 1/Focal Length Rule of Thumb is related to Film ONLY because it is related to 135 Format SLR cameras and the Rule was born because of those SLR cameras.

Possibly this rule has no relevance to your 5x4 View Camera, but maybe some relevance to a 5x4 Field Camera.


***


Just concluding:


Sorry about the “Full Frame Crop” confusion: this happens when some of us write with older style formal or technical words: the fact is Photography is as much a craft or trade as it is an art form and it is in that trade where many technically precise words reside.

But as the internet spreads words many have become diluted or polluted in their meaning and it is important to be pedantic when it is important so to be – to hopefully explain something more clearly, but precise words and meaning are required for precise explanations – especially when we are dealing with only the written word.

So often my hobby horses for pedantic responses are subjects like the misuse of the word, “perspective” leading to misunderstanding of “perspective”; and the phrase “crop factor camera” . . .

So with absolutely no disrespect - I will mention another phrase which may create a false impression and thus can lead to confusion “zooming with my feet” – we cannot do that.

Zooming is the act of a lens changing its Focal Length – moving with the feet, moves the camera and thus changes the Perspective.


***

The very bottom line:

If you want to be really conscientious about arresting camera shake whilst hand holding:
Then use a tripod – and make sure it is a bloody good, solid tripod.


WW

[Djd3mo]

we MUST look at the FULL FRAME IMAGE of any cameras’ sensor

I totally agree, but look at it on the screen of your computer at 100% magnification. Don't do it while printed at full frame crop, whereas your entire demonstration is based on that. Better yet, compare the image shift to the fixed elements in your picture. Don't compare it to the image size.
A lot of changes may occur between computer and print (cropping, resizing up or down, sharpening or blurring etc.).
The rule was established when little or no crop was done between taking the photo and printing. Nowadays you can do a lot of post process that could change the perceived blur. Should I change my rule of thumb for each one of them or only for the DX crop ?

When I use burst mode to avoid camera shake, I compare my pictures at 100% magnification on my monitor, I choose the sharpest one and afterwards I continue my workflow. I don't carry on with my post processing and printing for all the pictures within that series and choose the best one from the prints. I am pretty sure you do the same.

So let's NOT compare print perceived blur and then "establish" how optics work. Because one lens angle shift doesn't care about the print size. A 1 (one) degree lens angle shift translates into the same pixel shift amount, no matter the sensor size !

May the light be with you !