Having listened to many reports about the good and bad characteristics of this
and that digital camera, it seems to me that a test method is much needed.
There is a standard method used to rate astronomical CCD cameras that will work
for those digital cameras that allow manual setting of exposure and yield a raw
(uncompressed) image file. The method, the Photon-Transfer Curve, while fairly
technical, is considered one of the best diagnostics of digital camera
performance.
Googling on "photon transfer curve" will yield libraries full of articles on
the method, and on its application to this and that astronomical camera.
Anyway, this method is something an ordinary user can use on an ordinary
digital camera, and could help clear up some of the various mysteries. (In
theory, one can also use this method on a digital film scanner, but the
mechanics seem far more difficult, as one will need a set of very well made
test strips. One may also need to disable the automatic gain control.)
The basic approach is to point the camera body (without lens) into an
integrating sphere (for absolute flatness of illumination) and take a series of
images with varying exposure, starting at zero (darkness).
The first is taken with the shortest exposure time in total darkness, and
generates the "bias" frame, which consists of camera electronic self-noise
only. (If necessary, one can take a bias frame at each shutter speed.)
Then, one takes pairs of images at each of a number of exposures, by varying
the integration time (shutter speed), and perhaps the intensity of the light
illuminating the integrating sphere.
The image pairs are subtracted pixel-by-pixel from each other, yielding a
series of difference images, one to an exposure level. Each difference is
squared, the squares are summed, and the sum is divided by twice the number of
squares summed. This yields the variance of the original flat field at the
specified exposure level. The square root of this is the standard deviation of
variation about the average illumination at the image sensor, for the specified
exposure level.
The same image pairs are summed pixel-by-pixel, the sums divided by two, the
bias frame subtracted pixel-by-pixel, the results being summed, and the
resulting sum divided by the number of pixels. This results in the mean output
level for that exposure level.
The photon transfer curve is the plot of the logarithm of the standard
deviations (y-axis) versus the logarithm of the mean output levels (x-axis).
If there are bad areas in the image, one can compute the photon transfer curve
on less than the full image. A typical approach would be to use a uniform
20x20 pixel patch somewhere.
There are three regions of interest: Toe, slope, and cliff.
The toe of the curve, where at low exposure levels the curve becomes
horizontal, shows the intrinsic read noise of the camera. When the curve
becomes horizontal, the camera is blinded by its own noise, and cannot see the
(very faint) image for the noise.
The slope of the curve is the normal operating region, where the noise is only
that due to the discrete nature of light, which comes in photons. Basically,
this noise is mathematically the same as the noise of rain on the roof. Each
drop makes a little noise upon impact, and the heavier the rain the louder the
noise. In the optical case, it's the photons that arrive randomly, and the
more photons the more noise. It's a long story, but photons and raindrops
follow Poisson statistics, so the standard deviation will equal the square root
of the mean in this regime. (As the mean grows, the relative prevalence of the
noise will fall, so the overall picture becomes less noisy looking, but the
absolute amount of noise has in fact increased.) So, in the slope region, the
slope on log-log plots will be one half, the signature of that square root.
This is inherent to the physics of light, and cannot be evaded, no matter how
clever the camera design.
The cliff is where the sensor saturates, and the noise falls off abruptly, as
the output is clamped by saturation, preventing the underlying random-arrival
noise from being seen. If one cannot see the intrinsic noise, one cannot see
the information carried on those photons either.
Anyway, from this plot one can tell many things. First, the true dynamic range
is the range from toe to cliff. This allows one to see past such marketing
bafflegab as reporting the dynamic range of the analog-digital converter (ADC),
but neglecting to mention that the image sensor and electronics are so noisy
that the least significant couple of bits are rendered useless, or that the
image sensor saturate at half the ADC maximum, reducing the effective dynamic
range to a fraction of the claimed value. If the slope isn't one half, then
there is a source of noise that is proportional to exposure and overwhelming
the random-arrival noise. One can also see how linear the camera is:
deviations from linearity in the slope region are deviations from linearity in
the camera.
Joe
Some references:
<http://www.kodak.com/global/plugins/acrobat/en/digital/ccd/applicationNotes/noiseSources.pdf>
J.R. Janesick, P.K. Klassen, Tom Elliot, "Charge-Coupled-Device
Charge-Collection Efficiency and the Photon-Transfer Technique," Opt. Eng.
26(10), 972-989 (1987).
E.C. Reichenbach, S.K. Park, R. Narayanswamy, "Characterizing digital image
acquisition devices," Opt. Eng. 30(2), 170-177 (1991). This article describes
how to measure the optical modulation transfer function using only a slightly
skewed knife-edge, thus eliminating the effects of aliasing on the measurement.
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