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--------------------------------------------------------- By Bill Claff

Estimating DX Crop Mode Photographic Dynamic Range (PDR) is not so simple as adjusting the FX PDR for the crop factor

Before explaining why let's review how PDR is measured.

What follow is only a brief explanation; my main PDR article is more complete.

The Photon Transfer Curve (PTC) is constructed and searched for the
intersection with the PDR target SNR.

The PDR target SNR is always 16000/(height of image). This is the normalization
for print size and viewing distance.

Log_{2} of the intersection x-value is subtracted from the number of
bits of the Analog to Digital Converter (ADC) and this value is the PDR.

The diagram below uses idealized values for the D800 at ISO 400; but they are based on best available information at the time of writing.

The thin blue line is the FX PTC.

The dotted blue line is the FX PDR target.

In this case they intersect at about 24.9 ADU for an FX PDR of 9.36

If we naively subtract log_{2}(1.5^{2}) from
9.36 we get 8.19 but this approach is flawed and the value shown at the red
diamond is wrong.

The correct value can be obtained in one of two mathematically identical ways.

The first way is to follow the dotted cyan up to a new stricter DX PDR target and then across to the FX PTC.

The second way is to follow the dotted magenta line down to the DX PTC and locate the intersection with the original FX PDR target.

In this case both methods arrive at 45.3 ADU for a DX PDR of 8.50

In retrospect, the flaw in the usual reasoning is treating
the PCT curves as if they are straight lines starting at the origin.

But read noise is never zero and photon noise goes up with the square root of
signal; so these are never straight lines.

Technically, depending on where you are on the PTC the naive
method will either overestimate or underestimate the DX Crop Mode PDR.

However, as it turns out, for the region that interests us, the correct value
is always better than we might quickly estimate; good news!

My hope is that this article will help people understand why DX Crop Mode PDR curves are closer to their corresponding FX PDR curves than one might expect.

I certainly advise that if you're choosing a camera and you're comparing a DX body to an FX body in DX Crop Mode, to examine the PDR curves rather than simply making a quick estimate.