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Field of view crop/focal length multiplier


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#1 DeepDiscovery

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Posted 08 April 2003 - 10:49 AM

Does the view that one sees in the view finder of digital SLRs (Canon 10D and Nikon D100) equal the picture that the camera will take?

I think I understand the focal length multiplier of 1.5~1.6. That's simple math given the focal legth of the lens and the size of the sensor (well maybe not so simple for us english majors...but that's what calculators are for). At any rate, is what I will see in the view finder what the picture will look like or do people using these cameras have to do some mental approximation given the field of view crop?

I have been considering the E20/Titan but now considering the Canon 10D/Jonah housing but want to ensure I understand the above first. It would seem to me that if one has to make some sort of mental approximation when looking through the view finder, that it would defeat the whole purpose of having an SLR.

Thanks for your help.

Bill Spadie
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#2 craig

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Posted 08 April 2003 - 01:23 PM

dSLR viewfinders are adjusted for their cropping and I like your thinking, particularly the Canon/Jonah part!
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#3 james

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Posted 08 April 2003 - 01:30 PM

What you see in the viewfinder is what you get (or very nearly what you get).

There is no focal length multiplier. That is the incorrect term.

What you do have is a crop factor, since the sensor is not the same size as film. So your field of view is less. You get ~ 3,000 pixels width across the sensor and that's what matters.

This little ASCII dwg will help explain it.

If you are using a film camera with a film lens, you would capture the scene encompassed by "the big box"

With the digital sensor, you capture the scene in the little box with is approximagely 1/1.5 times the size.

______________
| .... ________.....| Film Size 36mm
| .... | Sensor.|......|
| .... | Size......|.....|
| .... |_24mm_|.....|
|_____________|

The focal length doesn't change, because that is a feature of the lens, NOT the camera. What changes is the field of view.

HTH
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#4 Stewart L. Sy

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Posted 08 April 2003 - 01:48 PM

For what it's worth, Subal is also coming out with a 10D housing in July. This was from an email from Mr. Stepanek himself. I don't know what the build quality is of the Jonah, but Subal's is beyond reproach....

I'm seriously considering the sale of my Subal CE5 housing and the Canon A2e body with it....

We shall see....

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#5 wetpixel

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Posted 08 April 2003 - 02:53 PM

There is no focal length multiplier.  That is the incorrect term.

Unfortunately, "focal length multiplier" has become the ubiquitous term for sensor cropping (or whatever you want to call it).

I had hoped the terminology problem would just GO AWAY, but with such low yields of perfect 35mm-sized sensors causing prices to stay high (and Nikon's introduction of dSLR-specific lenses), it looks like the term is here to stay.
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#6 craig

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Posted 08 April 2003 - 03:55 PM

...and it contributes to the belief that digital somehow has a depth of field advantage.
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#7 DeepDiscovery

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Posted 08 April 2003 - 08:09 PM

Thanks all for the answers...great to have all the help. Pretty much made up my mind to go with the canon 10d...what an awesome camera.

Another question...what does the dot on the envelope icon mean (colored envelope at the beginning of each post that denotes status of that post. The legend at the bottom of the forum page did not specify)

thanks

Bill Spadie
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Aquatica 5DIII, YS-90DX(2)
www.wespicsphotography.com


#8 james

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Posted 08 April 2003 - 08:30 PM

It means you have posted in that thread.

Welcome to Wetpixel!

Cheers
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#9 scorpio_fish

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Posted 08 April 2003 - 09:44 PM

The field of view crop because of the smaller than 35mm film sensor does not effect the viewfinder. The Canon 10D viewfinder shows 95% of the final image area. I believe the D100 is 92%. You can cheat this a little by looking around the edge of the viewfinder, but not if its in a housing.

...and it contributes to the belief that digital somehow has a depth of field advantage.



Consumer digicams do have a depth of field advantage, or rather a greate DOF for a given angle of view (not always an advantage). Digital SLR's using 35mm lenses actually have less DOF all things being equal because the diagonal of the sensor (or film frame) is part of the equation for the circle of confusion.
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#10 craig

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Posted 09 April 2003 - 06:18 AM

Consumer digicams do have a depth of field advantage, or rather a greate DOF for a given angle of view (not always an advantage).  Digital SLR's using 35mm lenses actually have less DOF all things being equal because the diagonal of the sensor (or film frame) is part of the equation for the circle of confusion.

DOF is limited by the wavelength of light and is a function of magnification and aperture. Sensor size effects magnification but also limits aperture in a proportional way. Thus, there is no DOF "advantage" to sensors of various sizes; the numbers simply change around. If the sensors have fewer pixels, then the circle of confusion can be larger. A single-pixel sensor has great DOF.

Looking at it another way, if I had a 1 megapixel sensor of a given size with optimized lenses but I wanted to improve the DOF field, what would I do? If I enlarged the sensor size, the pixels would become bigger and the circle of confusion would be larger. This would also allow me to use smaller apertures without fear of diffraction. Unfortunately, the magnification needed to capture the same image would have to increase as well, negating my gains. If I reduce the sensor size, the pixels would become smaller. The magnifcation needed would be reduced but the circle of confusion would be smaller and the best acceptable aperture would be reduced as well.

If you want to improve DOF, it turns out you need to shorten the wavelength of light or record phase information. The first is not an option for us and the second is apparently being worked on. You can also take multiple photos and splice them together.

Digital SLR's that use film lenses have DOF identical to film. If you don't believe me, take an identical image with each then crop the film result with a factor than matches the digital sensor. The perceived advantage that digital has comes from the misguided belief that its magnification is greater. That belief is fueled by the "focal length multiplier" myth. As to the claim that the DOF is actually worse, there is no technical justification for that claim. Everything that effects DOF has already occured with the cropping is performed. A 6MP cropping dSLR is really a 14MP with a non-removable matte on the sensor. If that same matte were applied at the film plane of the film SLR would its DOF suddenly become worse? I think not.

Consumer digicams are more difficult to compare since their lenses and sensors are both different, but any difference in DOF comes from optimization of the lens, not from any inherent superiority in the sensor size. There are currently no 6MP P&S cameras either, and lower pixel count cameras have better DOF. So which do you want, more detail or better DOF?
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#11 scorpio_fish

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Posted 10 April 2003 - 07:41 AM

Digital SLR's that use film lenses have DOF identical to film



I have read articles that compare depth of field for D-SLR's vs. 35mm film SLRs. They have included conclusions that:

1) DOF of DSLR is less. (Depends on how you look at it)
2) DOF is the same. (It is not)
3) DOF is greater. (Depends on how you look at it)

I'm going to do the math.

Depth of Field is calculated using variables; aperture (actual, not f/stop), focal length, circle of confusion and subject distance.

Circle of Confusion. I'll breeze over Circle of Confusion. The standard still used today is the Zeiss methodology, where the perceived depth of field is based upon viewing an 8"x10" from a distance of the diagonal of the print. Since the calculation includes the magnification from film/sensor size to 8"x10", it includes the diagonal of the film/sensor. The quick calculation is 1/1730th of the diagonal of the film/sensor.

I calculated the DOF for the following four examples based upon the following assumptions:

Focal length 35mm or equivalent for digicam
Aperture: f8 and f4.2 for the digicam (midrange)
Circle of Confusion: 35mm film = .025mm 35mm DSLR(1.5) = .016 Digicam = .0051
Subject distance: 1m or 1.5m

Example1: 35mm film
Circle of Confusion 0.025
Focal Length 35
Aperture f8
Subject Distance 1

Near 0.86m
Far 1.19m
DOF 0.32m


Example2: 35mm D-SLR 1.5
Circle of Confusion .016
Focal Length 35
Aperture f8
Subject Distance 1

Near 0.91m
Far 1.11m
DOF 0.2m

Based on this calculation, the DOF shooting the same lens on a 1.5 crop DSLR from the same subject distance would be less than that of a 35mm film camera. But wait, this isn't necessarily how we would shoot. If we compose the same subject, the DSLR will crop it. In order to get the same composition, I would move back to 1.5 meters. Now the subject distance has increased, which increases my DOF. How much would this backing off offset the smaller circle of confusion? Let's do the stupid math.



Example3:
35mm D-SLR 1.5
Circle of Confusion 0.016
Focal Length 35
Aperture f8
Subject Distance 1.5

Near 1.3m
Far 1.77m
DOF 0.47m

This means that shooting the same composition (i.e. from a greater distance) more than offsets the reduced DOF caused by the smaller circle of confusion.

So it really depends on how you want to compare the shooting situation as to whether one has a greater DOF.

What about consumer digicams and their perceived greater depth of field? I used G1 specs because I could find them on the net. At 7mm focal length it is the equivalent of 35mm. Here is the result based on the same subject distance and the approximate midrange of the aperture range.

Example4:
Canon G1
Circle of Confusion 0.0051
Focal Length 7mm
Aperture f4.2
Subject Distance 1

Near 0.7m
Far 1.77m
DOF 1.07m


Looks like the digicam provides a greater DOF, just like we perceive.

Of course, I could be wrong.
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#12 craig

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Posted 10 April 2003 - 09:16 PM

Thanks for the reply, scorpio_fish. I found your reasoning to be sound, but after much struggle I've formulated a baffling response:

First, I'd only like to consider the case of the SLR and dSLR sharing the the same lens configuration. I think once you follow my reasoning, you can extend the results to include P&S cameras in your head. I'd like to add that I'm basing my explanation on information I'm getting from very good articles here and here. The assumption is that we shoot a subject using identical composition with a film camera and a digital camera with a cropping factor. This was scorpio_fish's second example. Here are some definitions:

x: cropping factor of dSLR
c: circle of confusion

M: magnification
D: total depth of field (sum of front and back depth of field)
Ne: effective f-number (bellows corrected)
N: the uncorrected f-number (that's the one you think you're shooting***)

For the following, I quote the lens FAQ I referenced above:

When the object distance is small with respect to the hyperfocal distance, the front and rear depth of field are almost equal and depend only on the magnification and effective f-stop and the following approximate formulas can be used.

frontdepth = reardepth = Ne*c/M^2


I'm just going to state that we satisify the criteria because we do. I also use the equation for computing effective f-number:

Ne = N * (1 + M)

yielding

D = 2 * N * (1 + M) * c / M^2

Calling the film camera 1 and the dSLR 2:

c2 = c1 / x
M2 = M1 /x

These are geometric relationships already defined by scorpio_fish.

What we are interested in is the ratio of depth of fields, or D2 / D1. That turns out with some chugging to be:

D2 / D1 = (x + M1) / (1 + M1)

What does that say? First off, a difference in DOF exists. It is independent of aperture or focal length, and as magnification increases, the DOF becomes nearly the same. Now I don't know about you, but for me DOF is most problematic at higher magnifications. That's not to say there's no difference. Shooting at a film equivalent of 1:1, a D100 or S2 has a 25% DOF advantage and the D60 has 30%. Not too shabby, or is it? Turns out there's more to it than that. So here's my second point.

Smaller sensors require a smaller circle of confusion, c, relative to larger sensors. Scorpio_fish points that out himself (itself?). This not only makes them more sensitive to focus but also to diffraction. We all know this because maximum apertures for P&S cameras are much bigger than for 35mm SLRs. The end result is the Lord giveth and the Lord taketh away. Sure you get a boost in DOF with the smaller sensor, but you have to give it back by opening your aperture. If you are running larger apertures than optimum, then you get more DOF but you obviously don't care or you have lighting issues.

This gets back to my original statement. DOF is dictated by the wavelength of light and mother nature is a firm governess. If you were tasked to design a system that maximized DOF, sensor size would not be a variable you would care much about. If it were me, I'd specify a 1-pixel sensor and be done, but then I'd probably be fired.

There are some real hardware ramifications. First, us cropped dSLR shooters may need to use a larger aperture than the equivalent film cameras would use. This is due to the expectation of greater critical focus. Second, there are real differences in specific cameras and lenses that lead to real, observable performance advantanges for some rigs. That shouldn't be suprising but it's also not proof. There is no such thing as f/16.935 on my lens even if the equations says that's what I should use.

In scorpio_fish's examples, he used parameters that produced effective magnifications modest enough to show significant differences. I believe he's right although I didn't get out the calculator. His numbers didn't include the effects of diffraction. At f/8 diffraction isn't the issue, but he was also producing pretty good DOF numbers for subjects a meter away. When was the last time you heard people complaining that 1 foot of DOF for a subject 3 feet away wasn't good enough but they couldn't go to f/11? This is just not the range where it matters. In scorpio_fish's defense, he never said it did.

I hope this is helpful and I hope I'm right! Scorpio-fish was right, I'm right, I'm King of the Hill, so come knock me off!
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#13 craig

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Posted 11 April 2003 - 03:56 PM

I've done a little more thinking and want to make a little bolder statement.

For macro, there are times when we want to achieve the maximum possible DOF without destroying detail. To do that, we choose the highest aperture possible that doesn't create excessive detail-killing diffraction. For this argument, I'll define a factor, Q, which is the best possible compromise between DOF and diffraction. To define what Q is, we have to accept a circle of confusion, c, and a diffraction threshold. For traditional digital cameras, three diffraction thresholds come to mind: the single pixel size (luma resolution), the double pixel size (chroma resolution due to Bayer pattern), and the circle of confusion itself. Regardless of which threshold you choose, a maximum aperture will be dictated.

So here are some terms:

Q : optimum depth of field
c : circle of confusion
Nm : maximum diffraction-limited f-number
M : magnification
x : cropping factor (ratio of sensor sizes)

For subjects close to the lens, the optimum depth of field will be:

Q = 2 * Nm * (1 + M) * c / M ^ 2

So when comparing a cropped sensor camera to a full frame sensor one, the following is true:

c2 = c1 / x
Nm2 = Nm1 / x
M2 = M1 / x

So how does the cropped sensor camera Q compare? That would be:

Q2 = Q1 * (x + M1) / [x * (1 + M1)]

So as magnification approachs zero, the optimum depth of field will be the same. As magnifcation grows large, Q2 = Q1 / x. Ha! A small sensor camera produces, at best, DOF parity with a large sensor camera in macro mode. At high magnifications, its DOF is INFERIOR, not superior, by the ratio of sizes. For a given megapixel resolution, a larger sensor is preferable to a smaller one for macro, exactly the opposite of commonly accepted folklore. Eric's 1Ds will be the macro setup to have provided he can get a lens that works and enough light on his subject.

So how does a P&S like the 5050 compare to a D100? That depends on how you choose to define the diffraction threshold. If you define it as equal to the circle of confusion, then it compares poorly as above. If you define it in terms of luma or chroma resolving power, then it does a little better up to 1:4 and worse after that. That's solely because the 5050 has a lower resolution sensor. The maximum f-number of the 5050 (f/8) is chosen to allow diffraction greater than 1 pixel but less than the circle of confusion for all wavelengths.

For a D100, 1-pixel thresholds produce f-numbers of 11 for red and 14 for green. A circle-of-confusion threshold is 24 for red. If you are used to shooting f/32 with film, then don't shoot a D100 beyond f/22 for comparable results. The full frame numbers are f/36 - f/63 for red to blue light, thus justifying the limit of f/32 on the lenses.

The right way to compare the 5050 with the D100 is 21mm f/8 vs 105mm f/22. At a D100 1:1 magnification, the D100 has a DOF of 1.5mm compared to the 5050's DOF of 1.0mm.

There is another element not considered and that's the ability to build a high resolution lens at the greater magnifications necessary for large sensor sizes. That doesn't alter the conclusions above, but it means that there are practical considerations and ultimately it is specific sensor and lens combinations that matter.
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#14 marriard

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Posted 11 April 2003 - 07:20 PM

I've done a little more thinking and want to make a little bolder statement.
... long technical discussion from scorpio and craig deleted...

Que??

Math hurts my brain. :)

I think I'll go diving and take some pics....

M