D300 characteristic curve

I don't have very much new to report this week. My first week at my new job went well, the commute on the RER-B train is pretty easy, and I have a nice walk through Parc Montsouris to get to the local train station, and a 10 minute hike up the side of a hill to get to the lab at the other end, so it seems I will be staying fit even despite myself.

Over the last few weeks I've been reading The Negative, the second of Ansel Adam's series on photography. It's a really well written book, that describes how he went about bringing the vision he had for his photographs into reality. It details how he meters the scene, decides on exposure for the shot and what processing he will do to during development to enhance or contract the contrast. I was amazed at the laborious care he put into each photograph, far more than I put into mine... but then of course, his photos are far far superior than any of mine :-)

The other thing that is obvious from the book is that he had a complete understanding and mastery of all the technical aspects of photography. His book is full of scientific explanations of how film works, the nature of light, and how intensities in a scene relate to density on the film (and ultimately on paper), which he describes as the characteristic curve of the film. He devotes a large part of a chapter and a full appendix explaining these curves and how he and his assistant determined them for each combination of film type and development regime he used. It made me realize that there are large gaps in my knowledge of how my camera responds to light intensities, and that I really have no idea how well the monitor on my laptop renders intensities, except that I think it is not very good when I compare it by eye to other laptops. This post explores the first part of the problem, determining the relationship between exposure and the mean value in the RAW and JPEG output of my D300.

Actually it's pretty easy to determine the characteristic curve with a digital camera, you just have to take a bunch of photos of a uniformly illuminated screen, ranging from severely under-exposed to severely over-exposed, and determine the mean of the values in the image file. The D300 makes it easy to take both a RAW and JPEG files at once, which means you can work out the characteristic curve for both types of files with one set of shots. Alternatively if you have a different workflow, converting from RAW to JPEG using external software, you can use that also. To remove any headaches, it is probably best to set the white-balance to PREdefined and take a WB measurement off the screen before starting.

The plot shows the response of the RAW images (mean value in the image) over a 10-stop range. It is clear that the log of the mean signal in the RAW image increases linearly with the exposure in stops. A "zero" stop exposure, i.e. the exposure that the D300 metered as correct, and which should correspond to a middle gray exposure, creates a mean signal of approximately 300 in the RAW image. The sensor maxes out at 4096 (evidently a 14-bit sensor) about 4-stops over middle gray and reaches about 8 at 5-stops under middle gray.

The RAW data can be shown in a more useful form by plotting the y-axis as a base-2 logarithm relative to its "middle gray" value of 300, as above. In this form an increase in one unit on the y-axis corresponds to a doubling of the mean value in the RAW file, just as the exposure on the x-axis increases by a factor of two for each 1-stop increase. In this form it is clear that doubling (or halving) the exposure corresponds to a doubling (halving) of the mean value in the RAW file. The response is linear over an impressive 8-stop range, and possibly more.

The characteristic curve of the JPEGs produced by the camera is shown above. This curve has a 4-stop region around middle gray in which the response is roughly linear from an approximate value of 50 to 225. At lower values the response curves over, with the darker exposures being compressed into values below 50. At exposures 3-stops above middle gray, the curve saturates abruptly at a value of 255, unlike film which has a graceful rollover and some continued response even at high levels of over-exposures.

Another interesting thing that can easily be measured is the response of the camera to a middle gray exposure under different ISO settings. In the JPEG, the response is roughly constant, with the exposure being decreased as the ISO is increased, to maintain the middle gray level in the JPEG. The interesting thing (perhaps) is that it also remains roughly constant in the RAW file, as shown below, which means that the high ISO mode is implemented on the camera using a variable gain amplifier in the analog section of the CMOS sensor, rather than the camera digitally amplifying the value produced by the ADC.

Well that's it for now. Hopefully by next week I'll be able to measure the response of my laptop screen to fixed intensity images. That should be easy enough to do by photographing the screen of the laptop, since it's clear that the RAW file is very linear in its response to light.