The Dynamic Range

There are many ways how the dynamic range of digital cameras are being specified and evaluated, naturally giving much different readings. It is important to understand that dynamic range results can be compared only when the measurement method and the evaluation criteria are exactly the same and that usable dynamic range is not the same as the technical dynamic range.

The sensor and digicam manufacturers do not take the photon-shot-noise (Poisson noise) into account at all. Even if this is the one of the most detrimental source of image noise (speckle). Poisson noise is the property of light so in that sense one could consider it admissible to simply remove if from the equations. However the the sensors parameters (the size of the active photon collecting area of the individual "pixels" and the quantum efficiency) plays a major role in regards how the Poisson noise affects to the image quality.

Evaluation of the Finepix F30 Dynamic Range

I used Stouffer's calibrated 41-step density wedge T4110C, it was placed on a light table (that has 5000K fluorescent tubes that are driven at high frequency), the rest of the light table surface was covered and the room was darkened, not dimmed but fully darkened without any light, except what passed the Stouffer target. The calibration documentation (by Stouffer) of the target is shown on the right. The aim value for the steps of this target is 0.1D, so three steps approximately equals 1 f/stop.

The unedited F30 shot (ISO == 100) of the step wedge target is here. In this imaging situation the F30 does not provide enough freedom to adjust the exposure in such way that the most luminous patches would not overexpose. So in this shot the steps 1 to 7 of the wedge are overexposed. However this does not affect to the dynamic range evaluation at all, since the target still has enough range to cover the whole dynamic range of the F30. But for normal pictures this is somewhat an alarming finding.

Evaluation of the zero point at the light end

I have used a very simple, but still very accurate, method in evaluating the dynamic range, simply using Photoshop. Because the target steps have know densities there is no need to apply color-management, what only needs to be evaluated is the range of steps that got registered by the digicam.

The limit of the dynamic range at the light end is very easy to assess from a step wedge, it is the first step that is properly exposed (not overexposed). In this shot it is the step 8, it will be the relative zero point for the calculations. Or if you want to split the hair, then the average of the steps 7 and 8.

The below image shows that arrangement in Photoshop for searching the most light step that is not overexposed (not clipped). Note that the green channel is being used, another way would be to convert the image to grayscale first. There is no significant difference between these.

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Evaluation of the light end from the target using Photoshop, on step 8.

Note that the Mean and StDev values that the Histogram tool provides could be used to calculated the Signal to Noise ratio but not from an unedited digicam image, the image data must be linear for such calculation (S/N == Mean/StDev) to be correct.

The criteria for the dark end of the range is much more interesting. If you'd run this shot through a dedicated software that is designed to evaluate the dynamic range mathematically then very likely it would claim that the dynamic range does extend down to the patch 41 because that is where the mathematical Signal to Noise ratio of 1:1 approximately is in this shot. But let's take visual a look at that region at the dark end:

The dark end of the target boosted visible using the Levels command. Shown at 100% zoom.
Does not look very nice, but the mathematical S/N ratio of 1:1 really appears to be at about step 41. This is so of course only because of the noise reduction that is applied by the digicam.
In fact it is possible to discern the left end of the film (or the edge of the back frame that holds the film).

In case we do accept the image quality at the step 41 (3.97D), then the dynamic range of the F30 would be:

Log2(10^(3.97-0.75)) == 10.7 f/stops. (The relative white is at step 8 == 0.75D)

But for me, the image quality at S/N = 1:1 is not useful at all, so some other criteria than the mathematical S/N = 1:1 has to be used. This then leads to the discussion about usefuldynamic range. And further to the discussion about the very nature of usefulness, what is not useful for someone could easily be very useful for somebody else.

But if a specification is laid out then at least the evaluation will be repeatable and comparable. One such specification is resolution bandwidth. Not spatial resolution but detection resolution on the tonal curve. With this particular Stouffer step wedge a resolution of 0.1D is smallest possible criteria that can be used. Verbally this criteria could be formulated as: At what step in the dark end of the range the digicam is still able to resolve a 0.1D step (or 1/3 EV). This kind of specification quite fairy takes the strength of the noise reduction into account also. And is very easy to evaluate using Photoshop.

Preparation of resolution bandwidth evaluation with Photoshop

1. The image data has to be boosted up quite strongly using the Levels command (using the right input slider), so that the Histogram tool is able to show the result accurately.
2. In case of 8-bit/c image data, Gaussian Burr == 1.0 has to be applied, this helps in evaluating the Histogram and does not significantly affect to the the result.
3. A two region selection has to be created, both regions must have same pixel size. The two regions must map over the adjacent steps, but not on any of the the borders. Note that the border between the adjacent steps are very visible in all step wedges, this is (mainly) an imperfection of the target itself. So, with step wedges, never draw any conclusions based on the visual separation.
4. With the selection active, move it towards the dark end, step by step, searching those two steps that give a histogram that shows two peaks and a valley in between the two peaks that is about half the height of the average height of the the two peaks.
5. The darker of these two patches sets the limit for the 0.1D resolution bandwidth. If you inspect even more dark patch-pairs you will notice that the histogram only shows one peak, meaning that the 0.1D difference can not anymore be resolved.

Illustration of the 0.1D resolution bandwidth evaluation with Photoshop

From this shot the 0.1D resolution bandwidth limit appears at the step 30 (2.97D). Since the reference white is at step 8 (0.75) then the Dynamic Range where 0.1D can be resolved by the F30 is:

Log2(10^(2.97-0.75)) == 7.4 f/stops.

My feeling indeed is that the F30 seems to perform about 2 stops worse than my D60 that gives about 9.5 f/stops in this same test.