The first compensation principle uses the fact, that in a digital image contrast is nearly never independed of noise.
Compensation of reduced contrast by increased SNR
If optimization of contrast cannot be achieved, the noise must be reduced (i.e., increased SNR). If contrast can be increased, there is more tolerance for higher noise (moderate or lower SNR can be used)

Example: If the visibility of a 2-2T hole (Factor CNR/delta w -> difference of wallthickness ) is not given due to the limited contrast, there are several factors which could be used to get a sufficient image quality again.
The SNRITotal could be increased with
- longer exposure time (or more frames integrated in the PC),
- higher tube current (if possible and would not spoil the focal spot)
- higher keV (with the result in a lower µeff)
- better detector with higher efficiency
- better detector calibration.
The µeff can be influenced with
- lower kV setting (but mainly for the price of higher noise)
- scatter protection (diaphragms in front of the tube)
- screens and filters

In the upper post is a conflict:
increase the keV for a better SNR
and
reduce the keV for a better µeff.

What would be the optimum energy for an application?
Let us start with an example with an Aluminum stepwedge from 10 to 60mm - where the maximum power of the system is used (ISO-Watt: higher kV, lower mA - kV*mA=const.).
Hint: When the acceleration voltage is set to 120kV, the mean energy is 45keV only due to the distribution of energy by the tube.

For the three different acceleration voltages the system is set that in the free beam the signal is 100%.
At 10mm of AL with 90kV only 12.5% of the quants passes; at 120kV it is 30% and at 160kV 52.5%. The contrast at 90kV is much higher.
At 30mm of AL with 90kV only 0.2% of the quants passes - which is quite a dark image; at 120kV it is 2.7% and at 160kV 13.7%. The difference between 30mm and 31mm of AL would be hard to be detected when using 90kV.
At 60mm of AL nearly no quant passes with 90kV; with 120kV 0.075% and nearly 2% when using 160kV.
If 2% sensitivity is the requirement of your system you have to have in minimum 160kV if you have to inspect up to 60mm of AL.

The example with the signal or contrast of 1mm aditional Al on 30mm of AL is shown in the next graphs. The SNR will increase from 36 at 90kV to 250 at 160kV (+600%):

The specific contrast (signal difference from 30mm to 31mm) decreases from 5% with 90kV down to 3.8% with 160kV (-25%):

Finally the CNR of the 1mm material difference is important: It increases from 1.8 at 90kV up to 9.2 at 160kV:

Hint: In a lot of applications a minimum CNR of 2.5 is required.
It seems that higher energy is better always. But the two factors of reduced contrast and increased SNR will have an optimum (if you use a detector which is capable to do not saturate and resists the higher energies).
The amount of quants (intensity I) which passes the object of thickness w with the material constant µ in dependence of the energy E can be calculated by
where I(0) is the energy on tube side of the object and I(w,E) behind the object.
The required energy for the best CNR can be calculated for an object with thickness T and a flaw of length w in direction of the beam by

The relative contrast Crel is calculated for w small in respect to T as

and is nearly µ(E)*w.
With the noise [sigma] in the X-ray image which has a Poisson distribution
sigma=
the CNR results to

The optimal contrast to noise ratio depends on the energy which itself depends on the absorption coefficient µ

The optimum is when one of the terms become Zero - which could only happen for the last term inside the (). If µ(E) = 2/T this term is Zero and the maximum CNR is at this energy.
With other words: The optimal energy level is where the absorption coefficient is half of the penetrated thickness. The values of µ for different energies and materials can be taken of the .

As example an experiment from the BAM (with CR technology, but valid for DDA technology also), which can show the practical impact of the CP1:

The visibility of IQIs in dependence on exposure dose and tube voltage for steel with constant hole size is shown with the step wedge.
Looking on the step 0.2" (~5mm) at 80kV a dose of 10mA min was required to show the 2T hole. With 100kV the time could be just the half and with 150kV it is reduced to a fifth (2mA min) of the 80kV exposure.

Increasing tube voltage reduces the specific contrast µeff but increases the exposure dose on the detector. The increase of SNR by the improved quantum statistic compensates the loss of contrast.

By following the rule of the optimum energy there is a conflict with the European Guideline for max. tube voltage for given material and thickness, which came from film exposure with limited dose capacity and SNR with the message: To maintain a good flaw sensitivity, the X-ray tube voltage should be as low as possible.

These maximum values are best practice values for film radiography. DDAs provide sufficient image quality at significant higher voltages too. Highly sensitive imaging plates with high structure noise of plate crystals (coarse grained) should be applied with about 20 % less X-ray energy as indicated in fig. 20. High definition imaging plates, which are exposed similar to X-ray films and having low structure noise (fine grained) can be exposed with X-ray energies of the graph above or significantly higher if the SNR is sufficiently increased.