Myth busted: larger sensors have thinner DOF.

[Daniel Browning]

Thank you for the response, David. Would you consider editing your post to remove the large quotations? Generally I think it's better to quote just one sentence or paragraph at a time.

For a fixed physical aperture and amount of light, a larger sensor with twice the area of a smaller sensor will be receiving only 1/4 of the light intensity per pixel.

One of the conditions above is "Sensors with the same total resolution and relative OLPF." This means the larger sensor has proportionately larger pixels. How does that affect your point of view on the matter?

(I chose the "same total resolution" condition to avoid discussion of what happens when the larger sensor has higher resolution. I believe this thread has enough complexities without adding that topic into the mix so I would really prefer to stick to the stated conditions for the sake of simplicity. I am working on posting a new thread soon where we can discuss the effect of varying pixel sizes.)

 

[David Rasberry]

One of the conditions above is "Sensors with the same total resolution and relative OLPF." This means the larger sensor has proportionately larger pixels. How does that affect your point of view on the matter?

The larger sensor would have to have two stops better ASA sensitivity or 6dB better signal to noise ratio to match the half size one at the same physical aperture. It is photon density per unit of exposed area that drops off with increase in coverage.

 

[Daniel Browning]

It is photon density per unit of exposed area that drops off with increase in coverage.

Agreed completely. My position seems to diverge from yours in that I think the area scales with the photon density/area (greater area and lower density per area comes out the same).

Say you have 10 drops of water per square millimeter and 50 total square millimeters. I have 1 drop of water/mm^2 and 500 total sq.mm. We both have the same total amount of water (500 drops), even though mine is spread out over a larger area. If we were to put them both on the same 100mm^2 surface evenly, they would both have 5 drops/mm^2 and look exactly the same.

[Given a large sensor with twice the area of a smaller sensor, but the same resolution.] The larger sensor would have to have two stops better ASA sensitivity or 6dB better signal to noise ratio to match the half size one at the same physical aperture.

My position is that the larger sensor only has to have the *same* sensitivity and S/N to match the smaller one. This is demonstrated in DSLR cameras that have been on the market for years. For example, if you shoot a D3 with 80mm f/4.0 ISO 530, then switch to "DX" mode (1.5X center crop) and shoot 50mm f/2.5 ISO 200, then display both images at the same size, they will look the same. You can do the same demonstration with any camera by just performing the crop manually.

That's the experimental verification, and here are the numbers to back it up (using your "twice the area" example):

Sensor C ("Fezzik") is 36x20.25mm, 1920x1080 pixels, each pixel is 18.8 microns and 352.6um^2.
Sensor D ("Vizzini") is 25.46x14.32mm, 1920x1080 pixels, each pixel is 13.3 microns and 175.8um^2.

Fezzik has 729mm^2 area, Vizzini has 365mm^2. That's a two-fold difference in total area. In linear dimensions, the difference is the square root of 2 (41.4%). Each pixel, also, has half the area (two times smaller) and 41.4% difference in linear dimensions.

A 50mm lens Fezzik has a 39.6 degree hAOV (horizontal angle of view).
A 35.35mm lens on Vizzini has the same 39.6 degree hAOV.

The difference in focal length is again sqrt(2). To get the same DOF on both requires 50mm f/2.8 and 35mm f/2.0. With both having the same AOV, perspective, focus distance, DOF, physical aperture, and scene, let's see what happens with sensitivity. Say that a 1/48 exposure causes 200 million photons to come out of the lens. With the same aperture, both will focus the same 200 million photons.

The 35mm f/2.0 on Vizzini will focus them into a smaller area with higher intensity: 548 photons/um^2. Since each pixel is 176 um^2, total photons falling per pixel in Vizzini is 96,000. If sensitivity (QE) is 50%, the pixel would record 48,000 photons.

The 50mm f/2.8 on Fezzik will focus the 200 million photons into a larger area with lower intensity: 274 photons/um^2. Since each pixel is 356um^2, total photons falling per pixel in Fezzik is 96,000. With the same sensitivity (QE) of 50%, the pixel would record 48,000 photons.

With the same number of photons per pixel, the output image will have the same brightness (sensitivity).

 

[Paris Remillard]

To get the same DOF on both requires 50mm f/2.8 and 35mm f/2.0. With both having the same AOV, perspective, focus distance, DOF, physical aperture, and scene

At the risk of entering into to water that is way over my head, and diverging slightly off topic, I think I'm going to disagree on perspective. People seem to focus on how much or how little DOF a particular format has. But to me, in terms of photography or cinematography, the perspective shifts caused by using longer focal lengths for a given field of view on larger formats contributes more to the image characteristics of the format than DOF. Particularly the magnification of background elements. So while a 50mm at f/2.8 on sensor 1 has the same DOF and FOV of the 35mm f/2.0 on sensor 2, the images are not going to look exactly the same. The background elements on the 50mm image are going to be more magnified than the background elements on the 35mm causing the appearance of less depth or more compression.

Sorry to diverge, but I think that how the final image actually looks, as opposed to the math of DOF calculations, is often overlooked.

The shooting at different f/stops but getting the same exposure on the same sensor thing has me scratching my head a bit, too. But I'm sure that Daniel will eventually sort things out in my brain.

EDIT: Oh. Nevermind. I missed the part about switching the ISO from 530 to 200. All sorted.

 

[Daniel Browning]

The background elements on the 50mm image are going to be more magnified than the background elements on the 35mm causing the appearance of less depth or more compression.

If you keep sensor size constant and change the lens, that's true, but my experience is changing the lens and sensor at the same time results in the same magnification of background elements.

EDIT: One important part is the display size. The larger sensor with a longer lens *does* result in a larger image recorded on the sensor (that is, a 6-foot tall person will be 24mm high on FF35, but only 6mm high on 2/3"). In that sense, magnification is higher. But the difference is equalized in the display size: the larger sensor is magnified less than the smaller sensor, so they end up the same.

In that sense, the higher magnification caused by focal length is counteracted by the lower magnification to reproduce the same display size.

Sorry to diverge, but I think that how the final image actually looks, as opposed to the math of DOF calculations, is often overlooked.

Agreed. If observations and experiments don't support the math/theory/science, then one of them is wrong and should be fixed.

 

[Chris Pickle]

.......
On the other hand, the RED seems practically to be a 320 ASA camera and most people shooting on S35 film are used to 500 ASA levels, so the question is whether the FF35 EPIC will look good at ratings higher than 500 ASA in order for it to be relatively easy to stop down a little. If the FF35 EPIC ends up having to be shot at 320 or 400 ASA just to look good, then more people are going to complain about having to light to a little higher levels just to maintain a workable depth of field. So there are still some unknowns here about this FF35 system.

I hope that even the Scarlet S35 will shoot at ASA500 with less noise than the Red. From an Indie film perspective, a faster camera would be more valuable then more resolution or larger format. In my mind, that is the weak link. Finding a stop or 3 through the ASA would have a major impact against thin lighting budgets and fast (read: expensive) lenses.

Chris

 

[Paris Remillard]

If you keep sensor size constant and change the lens, that's true, but my experience is changing the lens and sensor at the same time results in the same magnification of background elements.

As always, you're right. I just did a little quick test comparing 1/3" all the way up to 4x5 and it appears that the magnification is the same. I suppose that since the distance from the subject doesn't change, the compression of depth wouldn't change. And in my mind I was assuming that the AOV was narrower on longer lenses, as it is for a given format size, but as the format gets larger the AOV evens out with the shorter lens, smaller format combo. Seems so basic now that I think about. Damn, Daniel, you make my brain itch sometimes. I'm getting out of this pool before I drown!

Keep talking, though. I always think that I have something figured out completely and then you explain something on a level just below, or above depending on how you look at, where I understand it, and I have to get out the calculator and protractor and etch a sketch and re-evaluate the whole structure with the extra variables. It's good. Keeps me from thinking I know too much... or anything, for that matter.

 

[David Rasberry]

My position is that the larger sensor only has to have the *same* sensitivity and S/N to match the smaller one. This is demonstrated in DSLR cameras that have been on the market for years. For example, if you shoot a D3 with 80mm f/4.0 ISO 530, then switch to "DX" mode (1.5X center crop) and shoot 50mm f/2.5 ISO 200, then display both images at the same size, they will look the same.

.

You have proven my point here. You had to increase ISO rating (sensitivity) to get the same exposure results on the larger field. What happens if you use ISO 200 for both exposures? With digital media change in ISO, whether done in camera or in post, means changing the gain applied to the original signal output by the sensor. Increased gain always means increased noise. Within the usable dynamic range of the sensor, this may be an acceptable trade off.

 

[Daniel Browning]

What happens if you use ISO 200 for both exposures?

The larger sensor will appear darker until gain is corrected in the raw conversion.

With digital media change in ISO, whether done in camera or in post, means changing the gain applied to the original signal output by the sensor.

Correct.

Increased gain always means increased noise.

This is where we disagree. Increased gain means increased noise relative to itself or relative to sensors of the same size. But it does not mean increased noise relative to smaller sensors. ISO 530 on a DSLR has less total noise than ISO 200 on a digicam, unless you take away the size advantage by using the same aperture on both, in which case the noise is the same, AOTBE.

The noise is the same after the brightness is equalized through hardware gain or software gain.

Let's discuss points that we agree on, you correct me if I'm wrong:

• 50mm f/2.5 ISO 200 in DX mode has a certain level of noise in the final image, "n".
• 80mm f/2.5 ISO 200 in FX mode has less noise in the final image thanks to its much larger physical aperture and sensor size; so noise is about "n/2.6". (Smaller is better.) It also has thinner DOF.
• 80mm f/4.0 ISO 530 in FX mode has a certain level of noise which is worse than "n/2.6".

Here is the part where we appear to disagree:

• 80mm f/4.0 ISO 530 in FX mode also has a level of noise "n", the same as 50mm f/2.8 ISO 200 in DX mode.

If the images are ranked from cleanest to noisiest, they are, cleanest image with the least noise would be the 80mm f/2.8 ISO 200 in FX mode. After that, 50mm f/2.5 ISO 200 in DX mode and 80mm f/4.0 ISO 530 in FX mode would come in equal.

Within the usable dynamic range of the sensor, this may be an acceptable trade off.

My point is that this isn't a trade off. It's just a natural consequence of the larger sensor having more light gathering area. It all comes down to physical aperture, and physical aperture is what determines the total amount of light.

It's the light that matters; not ISO, f-number, focal length, or any of that.

 

[Pawel Achtel]

Thanks for the posting, Daniel. Good reading, as usual.

 

[Joel Kaye]

Thanks for the posting, Daniel. Good reading, as usual.

A picture will be worth a thousand posts when these cameras arrive.

 

[David Rasberry]

The larger sensor at the same physical aperture and the same ISO speed looks darker because the intensity of the light striking the sensor is 1/2 as much. This is a property of light and the result is the pixels of the sensor put out less voltage than for the same physical aperture covering a smaller area. This is true regardless of the size of individual pixels if ISO rating and sensitivity are the same. The larger sensor may have better signal to noise ratio with larger pixels, and greater dynamic range. But it still responds linearly to intensity of light per unit of area striking the surface. For the same conversion efficiency it will put out half the voltage compared to the smaller image size, so you have to compensate by increasing gain for a higher ISO rating.

Other than this I think your observations are spot on.
The advantage of a larger sensor with greater dynamic range is that you have more creative latitude to depart from the optimum native ISO sensitivity without negatively impacting image quality to an unacceptable degree.

 

[Eddie]

Daniel you seem to be forgetting the greatetst advantage of using larger sensors... you get to use longerfocal lenghts! wide lenses has all kinds of perspectival distortions and compromises when especially when used for close-ups. 49mm looks better than 14mm in terms of avoiding balloon-head effects. Secondly you also forget that bigger sensors in general are more forgiving when you to crop-down in post to smaller fields of view. So in spite of the math, it really is apples and oranges

 

[Paris Remillard]

Daniel you seem to be forgetting the greatetst advantage of using larger sensors... you get to use longerfocal lenghts! wide lenses has all kinds of perspectival distortions and compromises when especially when used for close-ups. 49mm looks better than 14mm in terms of avoiding balloon-head effects.

See, that's what I had in my mind as well. But from Daniel's comment about it and then from some quick tests that I did with several formats from 1/3" up to 4x5", the perspective is the same on all formats. So long as your lens to subject distance remains the same and you increase/decrease the focal length of the lens in direct proportion to the size of the sensor/format, AOV and magnification remain the same, since they are calculated based on format size. Assuming that the shorter focal lengths on the smaller formats are of the same design as the longer focal lengths on the larger, etc...All other things being equal, I should say.

So, a 150mm lens on 4x5, 3 feet from the subject will distort facial features just as much as a 7mm lens 3 feet from the subject on a 1/3" video camera(These lenses have essentially the same angle of view on their given formats). You'll just have much shallower depth of field for the same light levels on the larger format.

It seems like common sense now that I think about it, but I just had it wrong in my head for some reason. Even having shot many different still formats.

 

[Daniel Browning]

(I chose the "same total resolution" condition to avoid discussion of what happens when the larger sensor has higher resolution. I believe this thread has enough complexities without adding that topic into the mix so I would really prefer to stick to the stated conditions for the sake of simplicity. I am working on posting a new thread soon where we can discuss the effect of varying pixel sizes.)

OK, four months have passed, but I finally got around to creating a thread to discuss the effect of varying pixel sizes:

May I add that larger pixels are;
1/ inherently less noisy than small pixels.
2/ collect more electrons so for practical purposes said to be "more sensitive"

Myth busted: small pixels have worse performance than large pixels.

 

[Michael Brennan]

OK, four months have passed, but I finally got around to creating a thread to discuss the effect of varying pixel sizes:

Originally Posted by Michael Brennan
May I add that larger pixels are;
1/ inherently less noisy than small pixels.
2/ collect more electrons so for practical purposes said to be "more sensitive"

Myth busted: small pixels have worse performance than large pixels.

Not sure why you quoted my post Daniel as larger pixels are inherently less noisy than smaller pixels and they do produce better pictures under low light.

Michael Brennan

 

[Michael Brennan]

As I have been writing for years, for a given amount of light and field of view, smaller sensors have greater depth of field than larger sensors.

or

For a given amount of light larger sensors have shallower depth of field than smaller sensors.



Neither of the above statements are myths in context of discussions between DPs cameramen and producers who assume that such comparisons have two constants that of field of view (not focal length) and light level.


Those keen to promote HD in the early days said that you need less lights to shoot HD.
The statement that for a given depth of field a 2/3 inch sensor require less light than 35mm is a better way of communicating the point that lighting levels can be lower on a f900 shoot compared to a 35mm shoot, something that is attractive to producers when budgeting very large bluescreen shoots.

Mike Brennan

 

[Pawel Achtel]

As I have been writing for years, for a given amount of light and field of view, smaller sensors have greater depth of field than larger sensors.

or

For a given amount of light larger sensors have shallower depth of field than smaller sensors.

I think the point that Daniel was trying to make is that larger sensors CAN have shallower DOF, but you can can underexpose a larger sensor by stepping down and achieve equivalent DOF and noise levels as with a smaller sensor. In this respect Daniel is right. The devil is, as usual, in the detail. :crazy:

 

[Pawel Achtel]

Those keen to promote HD in the early days said that you need less lights to shoot HD.
The statement that for a given depth of field a 2/3 inch sensor require less light than 35mm is a better way of communicating the point that lighting levels can be lower on a f900 shoot compared to a 35mm shoot, something that is attractive to producers when budgeting very large bluescreen shoots.

This statement is plainly wrong, Michael. It doesn't suprise me because producers rarely have the technical background and, at times, have been misled by the myths floating around.

You can (and should) shoot with 35mm at the same lighting levels. You can either open up the aperture and achieve lower noise and shalower DOF, or you can step down, underexpose the sensor and achieve equivalent DOF and equivalent noise as with a smaller sensor. That's the whole point you've been missing.

Michael, it will serve you well if you read Daniel's post carefuly because, I think, you are spreading the myth.:001_rolleyes:

 

[morgan_moore]

I did a test with some stills cameras

the D80 is red size, the D3 is FF 5d2 size and the hasselblad 645 is not available in digital movie aquisition..

www.sammorganmoore.com/smmcom/format_test/index.html

IMO small sensors have more DOF !

645 at f11 seems about the same as d80/90/red at 2.8 for the same FOV - that difference is unlikely to be 'lightable' or gained by use of a higher ISO even if the larger sensor is cleaner at higher ISO

S