Digital BW, The Print

Paul Roark wrote:



> If the sensors are inefficient, capturing less than 100% of the photons,
> wouldn't increasing sensor efficiency be the same as enlarging a cell of the
> same efficiency? 

> How efficient are our sensors?

Paul, here's some stuff, much of which is pasted from lecture outlines 
for an introductory class I teach. Much regarding responsivity, noise, 
and dynamic range, but very long:

Quantum efficiency is the metric that specifies what proportion of 
photons reaching the photoelectric sensor surface are converted to 
electrons and captured by the potential well. The only measurement of 
quantum efficiency I know of for a Canon camera was made by Christian 
Buil of a 300D (Digital Rebel); IIRC he figured around a 0.25 QE. This 
seems plausible on other grounds; a few years ago, a CMOS sensor with a 
QE of 0.4 was considered very highly efficient, and was sold at a large 
premium. As far as I know, Canon doesn't specify the QE of their sensors 
except for medical and industrial imagers.

CCD sensors are available in a range of QE from say 0.5 to around 0.95 
(for very expensive science chips). Nikon users with CCD cameras can get 
the QE from the sensor manufacturer in many cases.

Most of these sensors are Bayer filtered, and that cuts a lot of light 
prior to detection. But on the other hand, many of them have 
microlenses, which direct light that would have otherwise missed it into 
the photosite (perhaps this light would have struck circuitry adjacent 
to the photosite instead). These considerations affect the responsivity 
of the sensor - how responsive it is to the scene.

So tricks like microlensing increase the responsivity of the sensor (you 
capture more photons than an otherwise identical sensor without 
microlenses), but do not increase the quantum efficiency. Filtering 
reduces responsivity but does not reduce quantum efficiency.

If you increase the effective photosite size, you will increase the 
responsivity of the sensor, because you are letting it scoop up photons 
from a bigger area. Putting a microlens in front of the photosite has 
the same effect. This is a really good thing to do, because it also 
reduces photon noise.

Photon noise is a result of photons arriving at the sensor in a 
disorganized way. They don't come as though they were all neatly and 
evenly lined up on a factory conveyor; instead, picture water spurting 
from a garden hose half full of air: photons arrive in bursts (arrivals 
follow a Poisson distribution). If two adjacent photosites are looking 
at something with exactly the same tone, photon noise will almost always 
insure these two photosites end up with different values in the 
resulting picture.

Increasing the area of the photosite (through microlensing or otherwise) 
gives you a bigger net to catch photons with; this tends to average out 
the burstiness of their arrival time. Hence you get less noise in the 
image. Most digital cameras today are not limited by bias and dark noise 
in normal photography; the bulk of the visible noise in an image is the 
result of photon noise. This is a prime source of many photographers' 
obsessions with large photosites (and hence large sensors, which are 
needed to regain the lost spatial resolution of large photosites).

So the sensor is a balance of considerations that include photosite 
size, QE, and responsivity modifiers. These only affect detection, 
though. If you can't read out the sensor, it is all to naught.

A photosite responding to a photon produces an electron through the 
photoelectric effect. This electron typically gets captured in a 
potential well. (NB: When I say "potential," I mean voltage; when Normal 
Koren says it on that page that was quoted, he refers to that which is 
mathematically possible - this isn't apples and oranges, it is more like 
apples and duckbill platypuses.) The electrons get stored in what 
amounts to a little capacitor right on the sensor. Electrons sitting 
around in this potential well, which do not belong there because they 
came from somewhere other than photons, constitutes noise.

So the dynamic range of the sensor is defined at the low end by noise - 
spurious electrons hanging out in the potential well (plus amplifier 
static contributed during readout). You have to pick a statistical 
significance that constitutes non-black - "real" black might be defined 
as (say) anything below 25 sigma in the image that gets read out.

At the high end, the dynamic range of the sensor is defined by clipping. 
A certain number of electrons can be stored in the potential well. If 
you go above that number, the potential (=voltage) gets high enough that 
some electrons find other ways off the sensor than through the readout 
circuits. A capacitor can only hold so much juice.

If the maximum number of electrons the well can hold is 1,000 (we'll use 
a conveniently small, entirely made-up number), then if you put 1,000 
electrons in the well you read out white. If you try to put 1,001 
electrons in it, you read out white. If you try to fill it with 2,000 
electrons you still get white. The useful dynamic range is between the 
noise floor and the potential well's clipping point.

Big photosites have big wells. They can store more electrons than a 
small photosite with a small well. But they don't generate any 
additional noise. So the white point gets brighter; the black point 
stays the same. If you are saying to yourself that it sounds like this 
is one way to increase dynamic range, you are right.

(You can also clip in other ways - amplifiers can clip before the well 
is filled, for example. It doesn't matter much to the end result - it 
simply means that you can only *measure* so many electrons from the 
well, which is not much different from only being able to *store* so 
many in the well.)

Once the exposure is over, the signal is read out. The potential 
(=voltage) in the well is amplified; the amplifier output is sent to an 
analog-to-digital converter. Most ADCs on digital cameras output 12 
bits. So the ADC outputs 4096 analog-to-digital units (ADUs). This gets 
recorded in your raw file.

The big myth in dynamic range discussions is that somehow, if only you 
could change those ADUs to give you more bits, you'd have more dynamic 
range. Unfortunately the ADUs operate after image capture - they can 
have no effect on the white clipping point of the photosite well.

Now to be fair, there is a reason for the irrational conclusion that 
bits equals dynamic range: A camera with a larger dynamic range 
*requires* more ADUs to properly sample the signal. Therefore cameras 
with higher dynamic range tend to, on average, output more bits.

Think of it this way. If you are sampling a brightness ratio of ten, and 
you have 4096 ADUs to do it with, the difference between two adjacent 
ADUs is a ratio of 1.0024. In other words, a part of the scene producing 
an ADU of 100 is 1.002 times brighter than a part of the scene producing 
an ADU of 101. Let's consider this a "small" difference. You can take a 
picture full of subtle tonal differences, and really define a texture 
(like an egg, say) with such a camera.

If, however, you are sampling a brightness ratio of 100 with 4096 ADUs, 
then the step ratio is (predictably) 1.024. In this new situation there 
is a big real-world brightness difference between a pixel value of 100 
and a pixel value of 101. This leads to posterization; you aren't 
recording enough brightness differences to define a surface. Therefore, 
(most) makers of sensors that have a big dynamic range (usually) provide 
more ADUs in output. Photographers tend to reduce this to the formula 
that the more bits a camera outputs, the more dynamic range it has. 
Unfortunately, using that formula to choose a camera can burn you badly, 
because there are a number of exceptions to the rule. Some cameras 
merely sample a poor dynamic range with excessive precision.

Now, is all this merely theoretical? No. Much of it can lead to better 
decisions at exposure time and camera-purchase time, just as knowledge 
of tone curves and spectral response of film helps the analog 
photographer at exposure time and film-purchase time. Tone curves and 
spectral response are pretty arcane topics in themselves - many 
beginners succumb to mistaken thinking on these topics. The digital 
medium is different, but no more arcane. Perhaps it is true that 
awareness of its technical underpinnings has not penetrated the 
conventional photographic world very effectively as yet.

--
Jeff Medkeff
Eagle River, Alaska