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Author Topic: DoF, speed and format size  (Read 8324 times)

victoraberdeen

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DoF, speed and format size
« on: December 09, 2003, 04:17:21 am »

BJL, I’m sorry but I’m really not sure what you’re trying to say in this 1300 word essay.  From what I picked up, some of the items here are less than accurate and your conclusion while with merit is not clear. I hope I have understood you.  

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a) The relationship of DoF to f-stop within a format is roughly constant for fixed framing even if subject distance and hence perspective is changed.

- The term ‘Depth of Field’ describes the length of acceptable focus in-front of and behind the point of focus. It is increased or decreased by both the aperture (f-stop) of a lens, and the focal length of the lens.  Depth of field also increases the further the subject is away from the lens.
- Format describes the shape and size of the image and is inconsistently reported, for example a 35mm image has no dimension equal to 35mm it is 24x36mm.

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If choice of subject distance and perspective are also held the same but format (image size) is varied, keeping constant DoF involves changing f-stop and focal length in proportion to image size, so the aperture DIAMETER stays the same: equally large lens front elements, or equally "big glass" are needed regardless of format to get a given DoF and FoV.

- If you change the format but keep the focal length and aperture the same then the depth of field will be the same. Other optical factors may affect the actual results.
- The physical aperture is a fraction of the focal length and not that I am aware going to provide a set depth of field for a physical aperture size regardless of focal length! It is close but not the same.


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c) Aperture diameter for constant DOF varies in proportion with subject distance, regardless of format.

- Yes this is true; however the focal length of the lens will also have a significant effect, the longer the focal length the greater the impact.

There is a cool calculator http://dfleming.ameranet.com/dofjs.html

Quote
As noted above, one you choose the framing, you get the same DoF in a given format by using the same f-stop regardless of focal length and subject distance. However you play it, f/1.4 in APS format does about the same as f/2 in 35mm format, and 4/3 format would need about f/1 to match that..

If your saying that a portrait a taken on 35mm at f2 would need to be opened up to give the same Depth of Field on a smaller format. Then yes, the figures agree but there is only a small difference.

Format---1/1.8 "------------35mm
             (7.18 x 5.32 mm)--(36 x 24mm)
Lens-----35-------35-------104
f stop----1.4------2--------2
focus----2--------2--------2
nearc----1.97-----1.96-----1.988
far-------2.03-----2.04-----2.02

coc------0.006----0.006----0.03

So did I clarify or confuse
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BJL

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« Reply #1 on: December 09, 2003, 10:41:21 am »

Some replies to Victor.

I) Of course DoF depends both on focal length f and aperture ratio r, but it does so almost entirely through the combined quantity f/r, which is the diameter of the aperture opening! I will explain this and other points with all the relevant formulas in a subsequent post.

II)  About aspect ratio, I phrased everything in terms of achieving a given final framing of the image, with both width and height specified, and as fixing the aspect ratio, possibly requiring cropping from the full image formed in the camera.

   For those who cannot accept that, or just as a simplification, consider this discussion restricted to comparisons of cameras offering the same frame shape at different sizes, so that comparisons can be done purely in terms only of the diagonal length of the image. That is, either restrict to 3:2 and hence mostly 35mm and APS DSLR's, or restrict to 4:3 and consider only scanning backs for large format, 645 medium format and the larger digital backs for it, 4/3, and almost all smaller digicams.

   Actually, 645 MF (or even 35mm) seems a reasonable upper limit for the purposes of this discussion, since I am mainly concered about what will happen in future developments of the new smaller digital formats, not the potential glories of large format and view cameras.

III) About the claim that
"If you change the format but keep the focal length and aperture the same then the depth of field will be the same."
No: that conclusion assumes that you determine DoF on the basis of the same allowable circle of confusion size on the film or sensor.  You should no better since in your DoF calculator example, you adjuct the coc in proportion to sensor size. The reason for doing that is that with different formats, you enlarge a different amount to achieve a print of a given size, and the visual effect on prints of a given size will be less DoF when using the same focal length and aperture in a smaller format.

IV) Your DOF calculator comparison is wrong because you change the focal length only by a factor of three instead of the factor of five ratio of sensor size and coc, getting a "closer crop". To correct that needs either a shorter focal length (about 21mm), or a greater subject distance, either of which increases DoF substantially for the 1/1.8" camera at f/1.4.
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BJL

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« Reply #2 on: December 09, 2003, 12:27:09 pm »

Ray,
  first some things that we agree on

a) extremely small format compact digital cameras as in your Minolta xt are very unlikey to ever offer extremely limited DoF; I said as much in my initial post in this thread.

 large formats will always have the ultimate image quality advantage in situations where enough light is available, since if long enough exposures can be used, larger formats can use the same low ISO sensor or film technology and get more resolution/tonal detail. Roughly, my guideline is that increasing format will increase possible image quality so long as one can operate at the optimal, smallest ISO, but once further increases in format size force one to use a higher ISO, due to limits on exposure duration, DoF or such, there is not much further gain with further size increases.

   In your scenario of combining multiple exposures, there seem to be no exposure time limits operating, so bigger is unequivocally better. My guess is that the mosaic of multiple images could give better quality than a single LF image, because the 35mm format lens could have higher resolution (lp/mm) than LF lenses.

c) Large formats can certainly handle shallow DoF. The question I am adressing is whether smallish formats, in particular the range from APS DSLR's down to high end 2/3" digicams, will also be able to handle shallow DOF reasonably well.


   One major disagreement: you have utterly misunderstood or misrepresented me when you say that
   "if I've understood what BJL is suggesting as a remedy, instead of increasing shutter speed with the the lower number F stops to maintain correct exposure, we instead lower the ISO rating, perhaps to ISO 12 or lower".
   I have tried to make it clear that this lower ISO strategy only works until one reaches the lowest available ISO, beyond which the smaller format is worse off; hence it main relevance to relatively low light situations. I never said anything about absurdly low values like ISO 12. Limiting the process to attainable ISO's and thus to relatively low light situations eliminates the next difficulty you mention, of constructing smaller sensors that can handle the extra light.


   Since I am mainly concerned with digital photography and the endless criticisms of digital formats smaller than 35mm, I will not comment on your 8"x10" LF example.
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Ray

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« Reply #3 on: December 09, 2003, 08:48:54 pm »

By the way, I have come across the odd lens advertised on the net, designed for large format, 360mm or longer with max aperture of F5.6. I image such lenses would need a centre filter when used at F5.6, which would increase exposure. But it seems clear, if you want really shallow DoF then LF is the answer.
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BJL

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« Reply #4 on: December 10, 2003, 10:42:55 am »

Quote
... it seems clear, if you want really shallow DoF then LF is the answer.
More specifically, if one wants shallow depth of field with roughly normal angular field of view, then 8"x10" large format is the answer, and for extreme wide angle on film, 4x5 LF can also do very well.
   Normal FOV only, because the f/5.6 lenses for focal lengths away from 300-360 (normal for 8x10) rarely or ever have enough image coverage for 8x10. And 8x10 only because down at 4x5, the typical fastest aperture of f/5.6 corresponds to about f/2.8 in MF, f/1.4 in 35mm.

   At extreme WA, LF does well for large apertures because one can get f/5.6 and up to f/4 all the way to very wide field of view (beyond 100 degrees). Eliminating the reflex mirror and so allowing the lens to be moved very close to the film plane gives LF great latitude for WA work.
   Unfortunately, this coincides with extreme angles of incidence of light on the focal plane at the corners of the frame, way beyond the 10-20 degrees that current sensors can accomodate. That might rule out more than slightly wide angle digital LF with traditional LF lenses, though the new digitally oriented LF lenses might help.
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BJL

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« Reply #5 on: December 10, 2003, 04:23:07 pm »

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I would also take issue with the idea that IS doesn't help wide open; I have shot wide open with a 300 and 500 many many times and been very thankful for the IS, even on a tripod. Shoot wildlife at dusk and you will quickly see what I mean.
Thanks for the info. on LF lenses; I recall now that only one or two of the longer "digitar's" cover 4x5, and they are not very wide angle then!

   About IS, I am sure you are right about the long prime lenses, and you have also confirmed my speculation that it might even help them on a tripod (to deal with shutter vibration?)

   My comment about IS not helping so much wide open referred to the IS zooms, which are typically about a stop slower wide open (f/5.6 at the tele. end) than comparable non-IS zooms, so that the longer usable exposure times and smaller apertures somewhat balance out.
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Jeff Donald

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« Reply #6 on: December 11, 2003, 10:34:43 pm »

Olympus made a 250mm F2 and 350mm F2.8 for the OM series.  When NASA tested them for certification on shuttle flights they reported that those two lenses where the sharpest lenses they had ever tested.  Olympus certainly has the know how, if they choose to apply it.
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Ray

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« Reply #7 on: December 12, 2003, 12:28:48 am »

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 When NASA tested them for certification on shuttle flights they reported that those two lenses where the sharpest lenses they had ever tested.  
I never knew that. I hope Olympus and others in the consortium persevere with the format.
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BJL

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« Reply #8 on: December 12, 2003, 09:40:41 am »

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I'm not aware of any independent tests of the Olympus lenses but that MTF chart of the 300mm F2.8 on the dpreview site is sure impressive.  Could this be the best lens in the world?   If one can trust the accuracy of those charts (a big if) this lens has about the same performance at 60 lp/mm as the finest lens Photodo has ever tested at 40 lp/mm (the Canon 200/1.8L).
This might be largely a beneficial effect of the smaller image circle; since MTF at a given resolution falls off with radius, and apparently also falls off roughly as a power law with respect to lp/mm, a good 35mm lens might look comparable if one measures at about 50lp/mm but only on an "APS" radius of about 15mm. I say 50lp/mm not 60 because this is about proportionate for the "APS" formats.

   It would be interesting if someone were to do 50lp/mm MTF tests of various Canon (or Nikon, or Pentax) lenses just over the smaller radius.

   As far as independent testing, the one thing I have heard consistently is that the 50/2 E system macro is extemely sharp and impressive; macro photography has long been a strength for the rather scientifically oriented Olympus, and to go with this, they have just announced an array of specialized macro flash equipment for the E system.

   Certainly, the MTF graphs fit with Kodak's comment that the current 4/3 lenses are good enough for pixel sizes down to somewhat below 5 microns, and hence somewhat over 10MP. (Noise at that pixel size is a debate that I am not trying to re-open!)

   One interesting technical point; we seem to be agreeing that the lenses have better MTF than the current sensor, and yet it is also clear that increasing lens MTF even more by changing from zoom to macro produces very noticable imnprovements in image quality. Beware the fallacy that the worst of lens and sensor MTF determines system resolution; the MTF percentages from the two sources multiply, so improving the lens res. beyond the sensor, or vice verca, still brings some improvement.
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BJL

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« Reply #9 on: December 12, 2003, 09:49:00 am »

Quote
The Olypus E-1 has a lot going for it, but first indications are the sensor is simply not good enough to do justice to the fine lenses.
Which indications are you thinking of? Prints of inadequate quality, fuzzy on-screen 100% pixel views, lab test numbers, or something else?
   If you simply mean that the lenses have MTF performance good enough to support significant future development in sensors, this sems to be true across the board; even the zooms have quite good MTF curves at 60lp/mm. One would certainly hope that Olympus has heeded Michael R.'s warning about good sensors pushing the limits of all but top quality lenses, and so has produced lenses that can "outlive" the first generation sensor! (As I said above, Kodak has indicated a bit beyond 5 microns and 10MP as what the current lenses are good for.)
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Ray

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« Reply #10 on: December 12, 2003, 09:58:41 pm »

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Which indications are you thinking of? Prints of inadequate quality, fuzzy on-screen 100% pixel views, lab test numbers, or something else?
  
All the reviews and lab test numbers I've seen seems to indicate that E-1 images are not quite at the level of quality of 10D images. But I'm not one to split hairs. The advantages of a significantly smaller, lighter system easily justify a 'slight' sacrifice in absolute image quality.

However, you have probably thought about such issues more than I have. I'm locked into the Canon system ..... but the great thing is, I'm not even trying to get out.  :)

I suspect if it were possible to fit an Olympus 4/3rds lens to a 10D and crop the image to E-1 proportions, the 10D image quality would also improve. Whatever the advantages of the E-1 system, the sensor size will ultimately limit the 'absolute' quality achievable by this system. With a Canon system, one feels there's room to grow. For example, it's quite conceivable that Canon could at some time in the future increase the format size of 22.7x15.1mm to accommodate a greater number of pixels. What about a true APS size format, or even slightly larger, with 9M pixels?  :)

And of course, there's always the option to buy a 1Ds if one wins the lottery.  :)
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Ray

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« Reply #11 on: December 13, 2003, 07:25:06 pm »

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suggests that DSLR makers other than Canon and Nikon are aiming at using "sensor stabilization" to mitigate the effects of camera motion, instead of doing it in the lenses. That is, what Minolta does in the 2/3" (11mm) format A1, but with the challenge of doing it with far larger sensors.
  
Sounds like the logical way to go. I've got no idea how successful trying to do this in software could be, but prevention is usually better than cure.

Image Stabilisation in the lens seems the best option to me because that leaves the sensor free for other uses - for example, what about a sensor that can move around the image circle, allowing multiple shots that can be seamlessly and flawlessly stitched together in camera?  :D

Turn the camera vertically and that 'relatively cheap to manufacture' 22.7x15.1mm 300D sensor could produce a panorama 36mmx22mm consisting of 14MP. From starting position, the sensor would have to move twice, a mere 10mm each time at AEB speeds. Of course, the subject would have to be reasonably static since the operation might take a whole second.

One could also have another option consisting of 5 moves and 6 images to produce a 36x36mm square format consisting of 22MP. There'd probably be a bit of vignetting in the corners though, especially with Sigma lenses, so we could have a third option, 32x32mm which would produce an 18MP image with no more vignetting than we're used to.

Since it's already been established that a 6MP 10D image is slightly sharper and more detailed than the same size crop of a 1Ds image (4.2MP versus 6MP) and that pixel for pixel the 10D is less noisy than the 1Ds, such images I have described above would be a significant improvement on the 1Ds in terms of both resolution and noise - and all done with a cheap, small sensor.

Now, if Canon were to put me in charge of their R&D department, I could steer them in this direction.  :D
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Jonathan Wienke

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« Reply #12 on: December 15, 2003, 07:30:32 pm »

The only problem with a moving sensor would be accurately depicting the sensor position in the viewfinder (unless using an LCD in lieu of an optical viewfinder). Perhaps a "sports finder" with a mask that shifts around in sync with the sensor?
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BJL

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« Reply #13 on: December 18, 2003, 10:22:05 am »

Returning to the potential and limitations of smaller sensors, I have come across an argument that might set a speed limit for smaller sensors, at about f/1.4. If so,
(a) the current small interchangable lens formats can about match the f/2.8 speed limit of professional zooms and most primes, but not the extreme speed and limited DoF of a few lenses like an 85/1.5 "portrait lens".
( the current one-piece digicam formats (2/3" and below) might be within one stop of their potential, and might never go "faster" or "shallower" than the equivalent of about f/5.6 in 35mm format.

    The argument for this is that light comes to each point of the focal plane from a cone with base at the back of the lens, and the cone's "shape" is dictated by the aperture ratio. At f/1.4, some light from the outer edge of this cone is striking the sensor at about 20 degrees or more off perpendicular, and most sensor chips have sensitivity that falls of severely at about this angle and beyond. With sensors that use microlenses to increase sensitivity, the angle limit is stricter, so even f/1.4 is probably pushing it.
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BJL

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« Reply #14 on: December 08, 2003, 05:20:03 pm »

[If you do not share my previously expressed optimism about being able to do almost everything as well in smaller formats as larger, read on for a few ideas you might agree with!]


When one compares the high speed, low light ability of cameras in different formats, and the latitude to choose extremely limited depth of field, there is an apparent paradox.

    On one hand, the new smaller digital formats, and in particular one-piece "digicams" with sensor format 2/3" or smaller, seem distinctly more limited than 35mm format, and theoretical comparisons based on assuming similar sensor speed ("ISO equivalence") or similar aperture RATIO (f-stop) support this.

  On the other hand, amongst serious film formats, the highest speed and most extreme shallow DOF options available and regularly used are in the smallest such format, 35mm, and the options get slowly but steadily more limited as one works up through the various medium formats and into LF.

   Here is an attempt to reconcile this, with a few predictions for what might happen as the new formats mature and acquire a greater range of lens choices.

   Firstly, I will assert without formulas some optical facts that I believe have been agreed in numerous previous discussions on this site: once one has chosen a given framing for the final cropped image, meaning a certain angular width and height for the image of the subject formed in the camera, the aperture ratio (f-stop) giving a certain DoF depends only on the in-camera image size, changing in proportion to image size. Thus
a) The relationship of DoF to f-stop within a format is roughly constant for fixed framing even if subject distance and hence perspective is changed.
 If choice of subject distance and perspective are also held the same but format (image size) is varied, keeping constant DoF involves changing f-stop and focal length in proportion to image size, so the aperture DIAMETER stays the same: equally large lens front elements, or equally "big glass" are needed regardless of format to get a given DoF and FoV.
c) Aperture diameter for constant DOF varies in proportion with subject distance, regardless of format.

    Interestingly, in all cases giving the same DoF, the lens gathers light from the subject at the same rate (but delivers it to the sensor at higher intensity when the image size is smaller), so in this sense, DoF and "light gathering speed" are tightly tied together. Also, diffraction spot size as a fraction of image size is also fixed for given subject framing, regardless of format or subject distance!
   Thus I will refer to the various aperture options giving the same DoF as "light gathering speed".

   The main question for me, as one changes camera format and image size, is how do the available, appropriate choices of "light gathering speed"/DoF vary? If a smaller format has greater limits on shallow DoF and "speed", this would involve being pushed to use some combination of a smaller aperture diameter or a greater subject distance.

   It seems that in the film world (35mm and up), nothing has limited the options for smaller formats and shorter focal lengths any more than the larger formats; shallow DOF options are there, and regularly used. On the other hand, larger formats typically have the potential for more resolution at a given print size, and to fully realise this requires reducing diffraction spot size relative to image size, which leads to choosing larger aperture diameters and hence accepting less DoF; perhaps compensating with view camera motions to keep all the important scene elements sharp.

   But might this change when formats gets smaller than 35mm? Are there some design, performance, or market limits that will make it distinctly harder to get good zooms that go sufficiently beyond about f/2.8, or normal to mild telephoto primes going far enough below the current lowest f-stops at various FoV levels?

   Optimistically, I have seen no optical design argument yet that would rule out making and using new lenses for smaller formats with the same aperture diameter as their 35mm counterparts; one crude idea is to add a "focal reducer" to the back of an existing 35mm lens design. That is, a teleconverter, except with magnification less than one, which also nicely increases resolution in lp/mm roughly in proportion to the demagnification factor, so roughly maintaining "lp per picture height." Also, neither Ray nor anyone else has persuaded me that small format cameras  equipped with an adequate lens selection will systematically force photographers to stand further from their subjects, and hence increase DoF!

   However, there are some market factors that might limit the options of "big glass for small formats".

   Firstly, the mass market for digital cameras is very enthusiastic about "compact digicams", and being compact sets a size and weigh limit that precludes the big aperture diameters and large front elements needed to match fast 35mm format lenses. Combined with the fact that the compact lenses on such cameras can already provide a lot more speed than most of their users ever experienced with consumer film cameras (like f/2.4 at moderate telephoto and ISO 200+), I see little pressure in digicam mass market for significantly "bigger glass".

   (The category of big lens 2/3" format digicam with EVF's cares far less about being compact; Sony in particular has offered a series of cameras that look like big lenses with a tiny control and recording device at the back end. Who knows how big apertures will get in this category?)

   Secondly, I suspect that the desire for "big, fast glass" is overall driven by speed more than DoF, with some obvious exceptions like portrait lenses. (By the way, the portrait market has apparently just drawn the DoF line at 85/1.4 by not sufficiently embracing the now discontinued Canon 85/1.2.) Recently, overall speed has been helped by increases of several stops in usable ISO ratings of DLSR's over film, and some speed improvements in film too, and also in some situations by image stabilization technologies.

   One apparent consequence is somewhat reduced supply of and demand for exteme large apertures; zooms are being used more often instead of primes, and a number of new, rather high end lenses from Canon, Nikon and Pentax that are f/4 or slower where their precessors would have been f/2.8. Traditionalists complain, but the SLR market overall seems to be opting for using these technological improvements partly to achieve less cost and weight, rather than using the gains entirely to get more speed (and less DoF).
[Examples: Canon 17-40 f/4L, 70-200 f/4L (?), 100-400 f/4.5-5.6L IS, Nikon 12-24 f/4 DX, 80-400 f/4.5-5.6 VR, Pentax 16-45 f/4 DA for *-ist D.]

   So quite likely, most new lenses for formats APS and smaller will likewise offer a stop or two less lens speed than somewhat older fast 35mm film lens designs, and primes specifically for the smaller formats will be rare. For example, no company seems to be planning to offer a "fast normal prime" for APS or 4/3 format. For APS format, f/2.8 already seems to be the speed limit (except fr ner normal primes), and for 4/3 it is perhaps f/2; both are equivalent to about f/4 in 35mm format.


    To be controversial, f/4 in 35mm format is probably "shallow" enough for most photography, but not all, so this leaves as my final open question what will be done, or needs to be done, about lenses specifically desired for extremely shallow DOF rather than speed, such as portait lenses?

   As noted above, one you choose the framing, you get the same DoF in a given format by using the same f-stop regardless of focal length and subject distance. However you play it, f/1.4 in APS format does about the same as f/2 in 35mm format, and 4/3 format would need about f/1 to match that.
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Ray

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« Reply #15 on: December 09, 2003, 07:56:50 am »

In a way, it's fun to see what combination of lens focal length and f stop on different format cameras will give similar DoF. I'm concerned using simple mathematics (the only sort I can handle  :)  )  might give only approximate results, but the implications seem clear.

I like comparing 35mm to 8x10 field cameras because I have a project in the back of my mind to stitch together about 100 35mm images and achieve a level of resolution and detail that I anticipate would greatly exceed that of a single image from an 8x10 camera. Unfortunately I've not found an economical way of handling such large images (18MBx100=1.8GB). Photoshop CS is going to help, but still restricts me to 30,000 pixels in both dimensions for printing purposes.

Anyway, I've applied my simple formulas to 3 formats, slightly modified to keep the proportions the same; 12"x8", 35mm and 7.5mmx5mm, the last one being about the same size as the smaller digicams such as Pentax Optio S and Minolta xt. I've calculated standard lenses for the 3 formats as 360mm, 44mm and 9mm, the exact diagonals of the rectangles (give or take a couple of points).

Now, according to my calculations for DoF, I get the following. 360mm f8 = 44mm f1 = 9mm f 0.2.

I've used the basic formula F stop=Focal length/aperture diameter. All 3 lenses at the f stops quoted, have the same physical aperture ( ie. about 44 or 45mm).

There are a number of interesting points that flow on from these results (assuming they're correct).

(1) Not a snowball chance in #### of ever getting a Minolta xt with an F 0.2 lens, I would think.

(2) If it's a shallow DoF you want, I think large format can handle it. I don't know if there are any 360mm F5.6 lenses available, but if there are, you've got a 35mm equivalent of F0.7.

(3) If one keeps the ISO rating constant and the lighting on the subject constant, then each lens will throw the same amount of light on a unit area of film or sensor for 'correct' exposure. However, [/I]the total amount of light falling on the entire surface of each frame will be different - vastly different.

The 12x8" frame will receive about 64x the light the 35mm frame will receive and the 35mm frame about 25x the light falling on the digicam sensor.

Now, if I've understood what BJL is suggesting as a remedy,  instead of increasing shutter speed with the the lower number F stops to maintain correct exposure, we instead lower the ISO rating, perhaps to ISO 12 or lower, the smaller sensor can then receive the same amount of light as the larger sensor or film. In other words, we keep the shutter speed constant but vary the ISO.

If we then devise a way of constructing small sensors to handle that extra light, we will then have removed two of the main objections to small sensors - high noise and low dynamic range. But we've still got the problem of low resolution.
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BJL

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« Reply #16 on: December 09, 2003, 11:47:09 am »

I tried to avoid it, but we seem to need formulas! Here they are, put into a form that I find more useful when comparing different formats. As noted above, I will ignore aspect ratio differences and so measure sizes entirely in terms of diagonal lengths.

   The bottom line is that the aperture diameter alone determines the DoF close enough for most situations, though in practice you will often compute it from the focal length and aperture ratio, so formulas often are stated in terms of those quantities.


A) Measurements that go into DoF formulas

sc = camera format size: diagonal length of the image formed in the camera

cc = camera CoC limit: maximum allowable diameter of circle of confusion in the image in the camera in order for the subject to be considered in focus

sp = print size: diagonal length of the image on the print on which DoF is to be assessed

cp = cc*sp/sc = print CoC limit: maximum allowable diameter of circle of confusion as it appears on the printed image

f = focal length of lens

A = aperture diameter

r = f/A = aperture ratio (f-stop)

D = subject distance from camera

S = subject size: the diagonal length of rectangular region at the subject distance that ends up in the print.

    When considering a print of a given size, what counts for appearing in focus is the "print CoC", so I will consider cp as fixed, so that the image CoC limit cc varies in proportion to the format size sc.


 Hyperfocal distance.

   The easiest case for measuring DoF is when the camera is focused at infinity; the hyperfocal distance H is the distance to the closest object that is in focus:

H = f*f/(cc*r) = A*f/cc = A * (D/S) * (sp/cp)
= aperture diameter * (subject distance/subject size) *(print size/print CoC limit)

Note: everything on the right except aperture diameter will in general stay the same if you aim for prints of a given size and sharpness of the same subject taken from the same position, so when focusing at infinity, the aperture diameter alone determines depth of field exactly.

   If instread you change subject distance but keep the same framing (subject size S), hyperfocal distance H varies in proportion to D.


C) Focusing at a finite subject distance, D

When focused at subject distance D, the formulas quoted by Leon Vick from the Van Nostrand's Scientific Encyclopedia simplify to
near focus = D^2/(H+D)
far focus =  D^2/(H-D)
   These are actually slight approximations which break down in close focus situations but are close enough otherwise. The exact formulas, derived from www.normankoren.com, are
near focus = D(D-f)/(H+(D-f))
far focus =  D(D-f)/(H-(D-f))
which show that in close-up situations, smaller formats (smaller focal lengths) gain a bit more DoF.

   What the formulas show is that under the circumstances described that give equal hyperfocal distance H, one also has almost the same range of in-focus distances when exact focus is set at the subject distance D, but with a slight increase in DoF for smaller formats, only noticable in close-up situations.


D) Main practical conclusions

   When the subject distance is far less than hyperfocal, the DoF (the difference between these distances) can be described as
DoF = D^3/H^2 approximately. Thus,

I) DoF varies about inversely with the square of aperture diameter.

   If you vary subject distance, D and H vary in proportion, so

II) near focus, far focus and DoF all vary in proportion to subject distance D.

III) Once you know these two numbers, D and A, almost nothing else has any significant effect on DoF, except in close-ups, where DoF is a bit greater for smaller formats.
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Ray

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DoF, speed and format size
« Reply #17 on: December 09, 2003, 08:12:51 pm »

Quote
  One major disagreement: you have utterly misunderstood or misrepresented me when you say that
   "if I've understood what BJL is suggesting as a remedy, instead of increasing shutter speed with the the lower number F stops to maintain correct exposure, we instead lower the ISO rating, perhaps to ISO 12 or lower".
   I have tried to make it clear that this lower ISO strategy only works until one reaches the lowest available ISO, beyond which the smaller format is worse off; hence it main relevance to relatively low light situations. I never said anything about absurdly low values like ISO 12. Limiting the process to attainable ISO's and thus to relatively low light situations eliminates the next difficulty you mention, of constructing smaller sensors that can handle the extra light.
BJL,
If I've misunderstood you completely then we're back to square one. I haven't got the foggiest idea what you're talking about. The 3 disadvantages of the small digicam are very apparent; high noise, low dynamic range and low resolution. In order to boost the performance of such a camera, it seems to me one has to takle one or more of those areas without in the process making the other parameters worse. No point, for example, increasing the number of pixels, if doing so makes the camera even noisier. I think there are a few examples on the market already where a later 5 megapixel version of a 4 megapixel model produces an over all slightly worse picture quality.

I think one can get a broad idea of the sorts of problems that have to be solved even though the solutions are not technically (currently) feasible.

I chose 3 extreme examples in the previous thread in oder to highlight the consequent differences of changing format. If you want to narrow the gap, fine. But I think the principles are the same.

Lowering ISO instead of increasing shutter speed might well result in absurdly low ISO settings. So what! Increasing shutter speeds, by the same token, results in absurdly high shutter speeds. A 250th sec at F 8 and ISO 100 on one format becomes 1/4000th sec at F2 on a small digicam. Or, a 250th sec at F2 at ISO 6. The latter approach is simply a process of sacrificing one advantage of the smaller format in order to claw back another disadvantage.

Has it not already been discussed extensively on this forum that ISO changes on digital cameras are not 'real' in the sense that a film might have a fixed ISO rating, but rather instructions to the camera software that a particular image is going to be under or over exposed?

As nanotechnology develops, I forsee that eventually we'll have multilayered sensors that go far beyong what Foveon has attempted. Each tiny 1 micron (or smaller) photodetector will handle just a narrow band of the light spectrum.

A major point I was also making in my previous post is that, despite keeping the FoV the same, the lighting conditions the same and the exposure equally 'correct', the smaller format sensor or film receives less[/i] light in total. This might not be intuitive, but is a crucial factor in attempting to overcome the inherent disadvantages of the smaller format.
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Ray

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DoF, speed and format size
« Reply #18 on: December 10, 2003, 06:59:00 am »

Okay! Perhaps what you're proposing is merely using the existing ISO settings on a small camera to better use. With the Olympus E-1, for example, there would be situations where you could get by with ISO 100 whereas the 1Ds with equivalent FL lens and 1.5  stops smaller aperture for same DoF might require ISO 300. Not sure if there's going to be much benefit there. Do the Olympus lenses have image stabilisation?

I always try to use ISO 100 with my D60 and IS was the main reason I switched to Canon from Minolta a few years ago.

If you're comparing the E1 with the 300D and crop the 300D to 4/3rds proportions, the difference is insignificant - less than1/3rd of a stop.
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BJL

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DoF, speed and format size
« Reply #19 on: December 10, 2003, 10:25:49 am »

Quote
Okay! Perhaps what you're proposing is merely using the existing ISO settings on a small camera to better use. With the Olympus E-1, for example, there would be situations where you could get by with ISO 100 whereas the 1Ds with equivalent FL lens and 1.5  stops smaller aperture for same DoF might require ISO 300. Not sure if there's going to be much benefit there. Do the Olympus lenses have image stabilisation?
That is roughly right; I am talking about low light situations where the smaller camera is already either struggling to get away with its base ISO (often 100), or is forced to use a higher ISO, where the noise starts to become more noticable.  (I thin we agree that higher ISO is really underexposing the sensor and then "push processing", and probably is not a lot different than using the base ISO, underexposing, and then adjusting the levels up afterwards.)

   the comparison I had in mind is "The current best available digital camera in a given format size struggles to get good image quality in some situations because one has to use an elevated ISO setting that leads to visible noise in prints; how much could moving to a larger format help in this situation?" (My answer roughly is that a larger format camera could help to reduce the noise, if an appropriate lens is available for that format of larger maximum aperture diameter than anything usable with the smaller format camera, and if I prefer the trade-off of lower noise, lower DoF.)

   In your example of E-1 vs a Canon in 1.6x format, the Canon does slightly better in ISO choice than you gave it credit for. Shifting to lower light levels where one is forced to choose ISO 400 on the E-1 (the level at which noise starts to be a significant issue in prints from the E-1, according to user comments) it would be about ISO 600 for the 1.6x crop cameras, ISO 700 for Nikon, Fuji, Pentax, ISO 1600 for 35mm format. Looking at noise level graphs at DPReview, comparing at these matched ISO levels, the E-1, 300D, 10D and D100 are not much different; the S2 noise is distinctly lower. The 1Ds and 14N seem definitely worse off in this sort of comparison, though this might well be because more professionally oriented cameras like those do less in camera noise filtering, leaving it to "PP" with NeatImage, NoiseNinja or whatever.

   The E-1 has a strange dichotomy of either no in-camera noise filtering, or a thorough filtering option that takes a second or so per shot; most others like the 10D seem to have a quick noise filtering always applied. These variations complicate comparisons unless the differences are very substantial, like the far lower noise levels of the Fuji S2; but even it has been accused of achieving its good test numbers with heavy in-camera processing: noise filtering and then edge sharpening to get high test pattern resolution numbers.


    I am not sure that IS has much place in what started as a general discussion of some effects of format size differences; since I started by talking about 5MP 2/3" format fixed lens EVF camera, perhaps I need to also consider a Minolta A1 now, for its IS?

   Unfortunately, as with most IS lenses other than a few super-telephoto primes, the A-1 lens is a stop or so slower than the non-IS alternatives, so IS is mostly used to reduce camera motion blur at intermediate f-stops and to reduce lens bulk; IS lenses typically do far less to improve maximum wide-open speed, and of course IS does nothing about freezing subject motion. (I like to think of IS as an invisible monopod.)
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