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Author Topic: Reduce Focal Length & Crop to increase Dynamic Range with DOF restrictions  (Read 7235 times)

Guillermo Luijk

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Take a FF sensor and a situation where a minimum DOF requirement forces us to push ISO to achieve proper RAW exposure (it's then assumed we are already using the slowest possible speed to avoid trepidation). Now let's compare noise in the shadows (dynamic range) in two cases:

  • A: FF sensor at 24mm, f/4, ISO800
  • B: The same FF sensor but using it at 12mm, f/2, ISO200, and cropping it by 2x (1/4 of the original resolution)



Framing, DOF and RAW exposure are the same. But what about noise?

  • Assuming we have an ISOless sensor (leave Canon apart), pushing ISO by 2 stops in A makes us lose 2 whole stops of DR
  • On the other hand having 4 times as many pixels in A statistically halves noise when rescaling A to the B size, hence we gain 1 stop of DR (not 2!)

The combined effect is that the B image once both images are reescaled to the same output size will still hold 1 extra stop of DR over A, i.e. half the noise in the shadows. Of course we are losing a lot of resolution, but if noise becomes a problem this can be secondary.

The conclusion is that when a DOF requirement forces us to push ISO to achieve proper exposure, thanks to the statistical trick of noise using a lower focal length + crop (with the consequent wider aperture and lower ISO), can provide a noise improvement in the shadows. This can become of practical use with those new cameras having tons of Mpx.

This is also the explanation why noise advantage in larger sensors vanishes when pushing ISO is needed to achieve a minimum DOF.

Regards
« Last Edit: July 25, 2015, 12:28:10 PM by Guillermo Luijk »
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spidermike

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I'm struggling to see in what circumstances this is relevant.
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Guillermo Luijk

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Yes, usually when there is a strict DOF requirement a tripod is used. Night (or low light) street photography?.
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spidermike

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but given that DSOF depends in part on image size, where greater image size increases the DOF, the taking an image at f2 and blowing up twice the size will give DOF of about f4 or even more. You lose the narrow DOF.
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dwswager

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This is also the explanation why noise advantage in larger sensors vanishes when pushing ISO is needed to achieve a minimum DOF.

This is where I think it goes astray.  Key here is to determine the pixel pitch of the sensor which is likely going to impact noise the most.  Say two 24MP sensors (D750 and D7200) and the D750 wins merely because the pixels are bigger.  Even the 36MP D810 has bigger pixels than the D7200 which is why a 1.5x crop on the D810 results in a smaller 15MP image.
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TwistedShadow

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I'm struggling to see in what circumstances this is relevant.


Reunion Tower's Geodeck Dallas Texas. No tripods allowed...security even took my Joby gorillapod before even being allowed in the elevator  >:( Lincoln Memorial D.C. or the Ford museum would be a few more examples. I did okay with hand held bracketing for HDR but would be interested if this method works.
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hjulenissen

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0. I fail to understand the the mechanism that you are suggesting. Are the total number of photons hitting the (used) sensor area different or the same in the two examples?

1. Won't a wide-angle lens be more prone to glare, thus reducing the optical DR presented to the sensor?

2. Equivalent lenses may not be available or prohibitively expensive. Perhaps a better example may be 100mm f/2.8 vs 50mm f/1.4 (assuming that ~50mm is the sweet-spot for large-aperture FF lenses).
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Guillermo Luijk

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0. I fail to understand the the mechanism that you are suggesting. Are the total number of photons hitting the (used) sensor area different or the same in the two examples?

1. Won't a wide-angle lens be more prone to glare, thus reducing the optical DR presented to the sensor?

2. Equivalent lenses may not be available or prohibitively expensive. Perhaps a better example may be 100mm f/2.8 vs 50mm f/1.4 (assuming that ~50mm is the sweet-spot for large-aperture FF lenses).

Sorry for taking so long to answer :D

0. f/2 vs f/4 compensates for having 1/4 of sensor surface, thus in both cases the same amount of photons are collected

1 and 2. It's a theoretical exercise, I didn't care about real world implementations of lenses. Choose any pair of focal lengths where fA = 2 * fB

Regards
« Last Edit: October 15, 2015, 02:44:51 PM by Guillermo Luijk »
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EricV

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Hi, Guillermo.  I think your analysis is confusing dynamic range with shadow noise and coming to the wrong conclusion.  Theoretically your two scenarios are entirely equivalent, both in depth of field and in shadow noise.  There is no benefit to using a shorter focal length and cropping.

As you correctly note, both scenarios collect the same number of photons from the subject.  The simplest way to see this is to note that the physical lens aperture is the same (6mm in your example).  Exposure time is assumed to be the same, constrained by something (perhaps motion blur) other than subject brightness. 

Consider a small patch of dark shadow in the original scene.  That patch contributes the same number of photons to the image in both scenarios.  The photons are spread out over a larger sensor area and more pixels in one scenario, but that does not matter.  Since noise comes from photon statistics (neglecting sensor contributions), the total noise of the patch will be the same in both scenarios.

In the long focal length image, the photons from the patch are spread out over 4x as many pixels.  Each pixel will therefore have 1/4 signal and 1/2 noise.  To make the brightness the same, the signal in each pixel must be amplified 4x (by raising ISO in your example).  The end result is that each pixel will have 2x noise.  However, to make a print of the same size, those pixels will require 4x less area magnification.  In effect, the pixels get averaged 4:1 in the final print.  This averaging reduces image noise by 2x, exactly compensating for the extra noise per pixel.

I think the confusion in your analysis comes from equating dynamic range with shadow noise.  You note that increasing ISO by a factor of 4 reduces dynamic range by 2 stops.  That is true because of highlight clipping, not shadow noise.  In your two scenarios, pixels will have the same final brightness (f/stop reduction compensates for ISO multiplication), so highlight clipping will be the same. 

If shutter speed was not constrained, then the large focal length scenario would actually win.  Just lower ISO to the original level and increase exposure time 4x.  Shadow noise will improve because of the increased photon statistics, with no change in image brightness or highlight clipping.  This is the fundamental DR advantage of large sensors.
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Herbc

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I'm with Eric V on this one.  It is sort of like LF vs MF.  Edward Weston never shot anything larger than 8x10, and never enlarged, but his stuff was good.  Enlarging it would be a problem. 8)
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Guillermo Luijk

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Re: Reduce Focal Length & Crop to increase Dynamic Range with DOF restrictions
« Reply #10 on: October 16, 2015, 03:45:07 PM »

The photons are spread out over a larger sensor area and more pixels in one scenario, but that does not matter. Since noise comes from photon statistics (neglecting sensor contributions), the total noise of the patch will be the same in both scenarios.

I don't agree with this Eric. Photon noise in the deep shadows (the whole exercise is aimed to maximise SNR in the deep shadows, i.e. captured dynamic range), is negligible because of the low signal (light) captured, being read noise from the sensor the dominant contribution to SNR.

What you say takes place away from the shadows, in correctly exposed areas where photon noise prevails. In those areas there would be no advantage in either of the two scenarios. The improvement only comes in the more challenging areas.

Regards
« Last Edit: October 16, 2015, 03:51:07 PM by Guillermo Luijk »
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EricV

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Re: Reduce Focal Length & Crop to increase Dynamic Range with DOF restrictions
« Reply #11 on: October 16, 2015, 06:22:11 PM »

Sorry, I was assuming the noise of concern was in moderately dark areas, still dominated by photon statistics.  As the patch gets darker, photon noise does get lower, but the signal/noise ratio also gets lower, so the noise becomes move visible.  In most practical situations where shadows are visibly noisy, I think this is the primary noise source.  That is, photon noise becomes objectionable before sensor read noise starts to dominate.

For the extremely dark areas where the photon signal is not much larger than the electronic read noise (around 5 electrons on many modern sensors), you are correct -- the signal/noise ratio can be improved by concentrating the limited light onto fewer pixels.  This is basically what your short focal length scenario does.  Sorry I missed this point from the original post.

Some cameras have an internal pixel binning mode to accomplish the same function.  This allows light to be summed from multiple physical pixels, before paying the read noise penalty for just one pixel.  Using this function gives the DR benefit of the full sensor area, while achieving read noise reduction from the reduced pixel count.  Of course this incurs a sensor resolution penalty, just like in the short focal length scenario.
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EricV

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Re: Reduce Focal Length & Crop to increase Dynamic Range with DOF restrictions
« Reply #12 on: October 16, 2015, 07:57:25 PM »

Here is a little simulation to illustrate the dark image noise we are considering.  The average signal is just 16 electrons per pixel, with corresponding shot noise.  In one case, additional read noise of 5e per pixel has been included.  To make the signal visible, overall brightness has been raised quite a bit, as might be done when lifting the shadows in post-processing, or by setting very high ISO.  Noise is visible in the dark image, and the inclusion of read noise is visually quite significant.  Pixel binning or the short focal length trick would bring the read noise image close to the image with only shot noise.
« Last Edit: October 16, 2015, 08:11:51 PM by EricV »
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Guillermo Luijk

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Re: Reduce Focal Length & Crop to increase Dynamic Range with DOF restrictions
« Reply #13 on: October 17, 2015, 03:18:37 AM »

Exactly. In practice, the usefulness of the trick would depend on how far from saturation the crossover between the photon and read noise dominance takes place for isoless sensors. But I found the theoretical exercise interesting since it may sound as magic!.

Regards.
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Guillermo Luijk

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Re: Reduce Focal Length & Crop to increase Dynamic Range with DOF restrictions
« Reply #14 on: October 24, 2016, 07:31:40 PM »

I did a test to demonstrate what was explained here. In an application where ISO3200 was needed to achieve a good exposure with certain DOF requirement, using half the focal length with a 2 stops wider aperture at ISO800, and cropping by 2X the resulting image provides the following improvement in noise in the final image (the ISO3200 image has fairly been rescaled 50% to model the statistical SNR improvement for having twice as many Mpx):


(upper half in correctly exposed areas, lower half in the shadows -3EV, Sony A7 II over a uniform colour wall)

Greater improvement in the deep shadows (dynamic range) was totally expected since SNR improves much quicker in those areas when increasing exposure (photons) than in good exposure areas. Nevertheless there is improvement in the whole range.

Regards
« Last Edit: October 24, 2016, 07:34:47 PM by Guillermo Luijk »
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