Sensor exposure equivalency

[mjperini]

Bob,
I read something today that I don't quite understand, so I thought I'd come to the source of 'good explanation of complicated stuff'

In a review of the Nikon 18.5mm f/1.8 for the Nikon 1 system (1"  2.7 crop factor) Thom Hogan made the following statement:
But you have to remember that from a light gathering standpoint (how many photons get recorded), the 1” sensor is 2.7x worse than full frame. So we actually have a “system” that’s closer to an FX f/5 one when used in really low light. That’s not terrible, but don’t think you’re going to solve the Nikon 1 small sensor problem with just an f/1.8 lens. As the light goes down this lens is not going to suddenly turn the V3 or other Nikon 1 into a low-light master. The photosite size is just too small, and the random nature of photons is going to definitely produce noise (quantum shot noise).

In thinking about it, I realized that if Thom is correct (which he probably is) then there was something I didn't quite understand about how digital 'works'.
With F/ ratios being mathematical f/1.8 is f/1.8. It's a simple modern lens so it's T/Stop would be very close to it's F/stop.  ISO values of sensors should also be a standardized measurement where ISO 200 should be within a small range of tolerance from sensor to sensor, manufacturer to manufacturer.   
Thom mentions that the smaller "System" (18.5mm f/1.8 lens on a 1" sensor) would be the equivalent of an f/5 on a FX 'System' (50mm f/1.8 on a FF sensor), in "really low light"

If we took a silicon sensor wafer and cut it into FF and 1" sensors so there was complete equivalency between the pixels/semsels other than Area, would this f/1,8 on 1" = f/5 on FF still apply?
Or is Thom saying FF has bigger better pixels?  I'm having trouble seeing where f/1.8 = f/5
Wouldn't an f/1.8 normal lens project the same amount of light   per unit of sensor area  regardless of focal length.?

If he is just saying 2.7x more photons fall on a FF sensor than a 1" sensor, I get that, but can't quite understand where the f/5 equivalency comes in.
If I took a hand held exposure meter reading that indicated proper exposure was f/1.8 @ 1 second at any iso that was within both camera's normal range, wouldn't both exposures (1" and FF) be correct.??   Isn't exposure based on Light per unit of area?
Or was Thom saying something else entirely that I've missed?

Thanks for any help you can offer.
Michael

[Frank Kolwicz]

Michael,
Perhaps this website will be of help:
http://www.clarkvision.com/articles/index.html, see especially Part 1b: Exposure and Digital Cameras: Understanding Exposure.

I have found Dr. Clark's highly technical (for a photographer) explanation of things digital in photography to be very useful in trying to understand what's really going on and where many internet/media ideas about digital camera/lens functions fail.

[mjperini]

Frank,
Thank You very much. It's a Great site with a wealth of information, that I hadn't seen before.
I just spent an hour there and I'm certain I'll refer to it often . A great resource.
ISO is too often presented as an equal third variable along with Aperture & shutter speed.
Even though modern cameras have done a great job of minimizing the effects of electronic 'push processing'
I have been a 'base iso whenever possible' guy since I moved to digital.
His explanation of that is extremely clear.

He makes a distinction between light density (light per unit area which determines exposure) and "Total Light"

"Constant f/ratio, changing sensor size. Another common situation is using cameras with different sensor sizes. For example, consider two lenses: 100 mm f/4 and 200 mm f/4. Regardless of sensor size, both f/4 lenses deliver the same light density to the sensor. Light meters read the same exposure time at the same ISO. The 100 mm f/4 lens has a lens diameter (technically the entrance pupil) of 25 mm. The 200 mm f/4 lens has an entrance pupil of 50 mm, so twice the diameter and 4 times the area of the 100 mm f/4 lens. Therefore, the 200 mm f/4 lens collect 4 times the light from a subject as the 100 mm f/4 lens."

If I understand it correctly then, All other things being equal, (small and large sensors cut from the same wafer, Aperture & shutter speed) the exposure density will be the same on both cameras, but total light will be proportional to sensor size---the bigger sensor will have more pixels describing any given image.

I guess that's the same as it was for film, if I shot 4x5 & 8x10 Tri X with  normal lenses on both cameras  my exposure would be the same but I'd have more film grains describing the same subject with 8x10.
I always understood that as having more detail on larger film, just as I understood a larger sensor gave me more detail.
Where I think I'm still having trouble is equating detail or descriptive ability with thom's f/1.8  1" = f/5 FF.......... I'll have to go back and read more I guess.

Thanks for the reference.
Michael

[Bob Atkins]

I'll have to look at the article in question more closely, but off the top of my head I'm guessing he might be saying that because an AP-C sensor is 2.7x smaller (in area) than a full frame sensor, any image recorded on it (using the same lens at the same aperture) will be made by 2.7x fewer photons. Now that doesn't affect exposure in any way because exposure is determined by the number of photons per area and that's the same for both sensors.

However photon (Poisson) statistics dictate that the image made with fewer photons will show more noise, i.e. a larger sensor - which sees more photons - will give you a cleaner image in low light. It's called "Shot Noise" or "Poisson noise". It really only shows up at lower light levels. Actually rather than sensor size, it's pixel size, but that pretty much scales with sensor size since most sensors are now in the 20MP range. You could have a small low noise sensor with large pixels, but it would have lower resolution.

I don't think the aperture comparison is useful, and indeed may be (and obviously is!) misleading. He's probably trying to say that you get the same number of photos on the sensor with full frame and f5 as you do with a 1" sensor and f1.8. while that may be true, I'm not sure what its practical significance is. Maybe he's saying that the ISO you'd need at f5 and FF gives you about the same image noise as the ISO you'd need at f1.8 with a 1" sensor - assuming the same shutter speed in both cases. I don't think that's a very useful comparison, other than to point out smaller sensors give noisier images. In this case he's saying that the FF sensor has about a 3 stop advantage (f1.8 to f5) in terms of noise, or that the FF sensor at ISO 800 might be expected to show the same amount of noise as the 1" sensor at ISO 100.

So what he may be saying is that small sensors (with small pixels) are noisier - and that's really nothing new. You can't really get around that with faster lenses (which project more photons onto the sensor), because there's a practical (and theoretical) limit on just how fast a lens can be.

[mjperini]

Thanks Bob,
I'd be interested in your thoughts after reading Thom's post.
He says '1" is 2.7 times worse than FF'  I'm still not getting that part.  Does he mean ANY FF sensor,  one with exactly the same size pixels as the 1",  or one with larger pixels than the 1" sensor.

If exposure is determined by light per unit of area (and thus f/1.8 will produce the same exposure on a small or large sensor) I'm not getting where the "Extra Light" comes from on the larger sensor.
I also assume he is talking about terrestrial photography and not astro photography where the point source nature of stars is different.

He does say "in really low light"  as though the 1" sensor might not be "2.7 times worse" in normal light with full exposure.
In any event I remain confused ;-))
Michael

[Bob Atkins]

Well...he says "But you have to remember that from a light gathering standpoint (how many photons get recorded), the 1” sensor is 2.7x worse than full frame".

For a start that's not true. A 1" sensor has a 2.7x crop factor. It's 13.2 x 8.8mm which gives an area of 116 sq.mm. A full frame sensor is 24 x 36mm which gives an area of 863 sq. mm or 7.4x the area. Therefore, for a given illumination, a FF sensor will collect 7.4x as many photons as a 1" sensor, not 2.7x. in fact 2.7 is the linear multiplication factor (lens focal length multiplier), but 7.4 is the area multiplier (2.7 squared is 7.3)

So I really don't know what he's trying to say in numerical terms. I'm not quite sure what 2.7x worse means without defining all the other parameters. What's the measure of "worse"? Is it signal to noise ratio? If so, at what illumination level? If we're talking about photons per pixel if each sensor has the same number of pixels, then the 1" sensor is 7.4x "worse", i.e. it collects 7.4x fewer photons.

The low light comes in because signal to noise ration is determined by Shot noise (based on photon arrival statistics) when few photons are collected. When a lot of photons are collected the overall noise is mainly a function of thermal noise and amplifier noise. In addition there is always some level of quantization noise, "salt and pepper" noise and possibly row and/or column noise thrown in.

Sensor noise is a rather complicated subject. Bottom line is that smaller sensors (smaller pixels) generate more noise, but the source of that noise can vary with exposure time and illumination level.

[mjperini]

Bob,
Thanks very much.
It just didn't make sense to me. and when I tried to do more 'homework' , it became less clear.
So if it doesn't make sense to you either, I just won't worry about it.

Thanks Again,
Michael

[KeithB]

Did you try asking Thom?

He might just be wrong.

It especially is unclear since he is reviewing a fixed lens, not a sensor. While the crop sensor "uses" less photons than FF, those photons are just lost outside the chip. If you would change the focal length to an equivalent FOV, you would not "waste" any of the photons.

[Bob Atkins]

I'm not sure about the concept of "wasted" photons. All lenses and all formats "waste" photons since sensors are rectangular and lenses produce a circular image circle which is larger in diameter than the diagonal of the sensor.

It really all boils down to "the bigger the pixels the lower the noise" (at the same ISO, Aperture, and exposure time, sensor structure and electronics) and that's really all that's important.

I suppose he's commenting on the fact that some of the smaller sensor camera makers may push the availability of fast lenses as a selling point. While that's true, the fast lenses still don't compensate for the smaller sensor and smaller pixels. The fast lenses for small formats also don't provide the shallow depth of field that they do on larger formats either.

Apart from cost and convenience, there's no getting around the fact that bigger is better when it comes to pixel and sensor size from the point of view of image quality. This shows up more in low light situations.

[mjperini]

Keith, others,
I did ask Thom, and he was kind enough to reply, but it was not as helpful as I might have hoped.
I think we all understand that bigger sensors with bigger pixels are 'better ' --especially in low light,
but he seems to stick to this f/1.8 Cx = f/5 Fx equivalency, but doesn't choose to 'show the work' as to how he arrived at that conclusion.

I started this thread because I thought there was some principle that I didn't understand.
Now I think he is just referring to the lower light gathering and descriptive ability of smaller vs larger sensors, and quantifying it as a certain number.
He chose not to answer my question about if pixel size was the same on each sensor, or different resolution FF sensors.
I still don't feel as though I really understand what he is saying or to what degree it is correct or not.

I'm feeling that if he had a solid technical argument he would have made it, but nor do I feel that I understand exactly what he is saying. (more than that bigger sensors with bigger pixels are better)
It seems odd to put a single concrete number on the difference between the Nikon 1 sensor and any number of different resolution FF sensors and have it always be correct???

For those that care here is my email to him and his answer: (Both in their entirety)
Thom,
Thanks for an informative site, I read it regularly.
In the 18mm review I came across a statement that I'm having great
difficulty understanding.
" the 1" sensor is 2.7x worse than full frame. So we actually have a
³system" that¹s closer to an FX f/5 one when used in really low light"
Seeming to equate f/1.8 normal CX with F/5 normal Fx ?? (despite the fact
that f/1.8 is the correct exposure in both cases)
Is this just another way of saying bigger sensors are better in low light?
If the CX &FX sensors were both cut from the same wafer so pixels were the
same would this still be true??    In the real world we have Fx sensors
from
36 to 16MP, would both be f/5 equivalents??
By saying "in really Low Light" implies that it might not be true for
brighter light.
If it involves 'Total light falling on the sensors would that not be
proportional to sensor area whic is different by a factor of 7+ rather
than the crop factor which is a ratio of diagonals 2.7
I'm really confused here and I might not be alone.
Thanks for any light you can shed on this

Thom's Answer:
Exposure is one thing, equivalence is another. In this case, even if we
shot in bright light with a Nikon 1 with the 18.5mm at f/1.8 and shot an
FX camera from the same spot with a 50mm lens, to get equivalent images
we¹d be at f/5.

Low light would add to the woes because of quantum shot noise. A larger
photosite is going to collect more photons and produce less random results
(less noise).

--
Thom Hogan, writer/photographer

[Frank Kolwicz]

http://www.sansmirror.com/lenses/lens-reviews/lenses-for-nikon-1-cx/nikon-1-185mm-f18-lens.html is the site that is being discussed.

The quote in the original message of this thread comes from this, the second paragraph in the Hogan review:
"But you have to remember that from a light gathering standpoint (how many photons get recorded), the 1” sensor is 2.7x worse than full frame. So we actually have a “system” that’s closer to an FX f/5 one when used in really low light. That’s not terrible, but don’t think you’re going to solve the Nikon 1 small sensor problem with just an f/1.8 lens. As the light goes down this lens is not going to suddenly turn the V3 or other Nikon 1 into a low-light master. The photosite size is just too small, and the random nature of photons is going to definitely produce noise (quantum shot noise)."

Note the last line, all of this is about noise in the images and the part about it being a problem in low light is the first clue. As to why he uses an aperture value as the metric for noise level comparison, I don't know, it's a source of unnecessary confusion, as witnessed here. I think he's confused, too.

There is a standard way of reporting this metric with various levels of technical detail, but a standard deviation number should do for simple comparisons like this. See: http://www.cambridgeincolour.com/forums/thread95.htm for example.

I've tried to think of the things that aperture can affect and come up with these:  exposure, depth of field, noise, diffraction blur and, possibly, the angle of light on sensor (related to microlens design(?)). I bet there are others that I am unaware of, but even this is an unnecessary level of confusion to bring into a discussion of sensor noise effects.

[mjperini]

All,
I think Frank is correct and the real mystery is why Thom chose to attempt to quantify the difference between a 1" Sensor and a FF sensor in STOPS.
It doesn't make sense to offer a fixed difference when the FF sensor could be anywhere from 36mp to 16mp.

We all understand that larger sensors and larger pixels gather more light
But if we took the same properly exposed picture on 1" & FF sensors with Normal f/1.8 lenses, and we printed a 4x6 or 6x9" print of each, I really don't thing one would look '2.7 times worse'  than the other. With bigger prints we'd see differentiation.
I don't know how you turn that into stops.
Thom publishes a lot of helpful information which even a Canon guy like me can find helpful. My aim wasn't to find fault but to understand.
I don't think we'll get to understand exactly what he meant, but nrither do I think it matters any more.
Thanks to all
Michael