Dear Antoine,

yes, Gerhard is right.

A small problem is the linear attenuation coefficient µ for water, which you can for example get from NIST's XCOM database. You will see, that µ values are, of course, energy dependent. As X-ray sources are polychromatic, you need to calculate µ values according to the photon energy spectrum of your X-ray source. This spectrum mainly depends on the accelleration voltage, the anode material (e.g. tungsten) and anode angle as well as the filtration (e.g. X-ray exit window [beryllium], addition filtration [Al, Cu,...]). Measuring the spectrum is challenging, therefore calculation is mainly done using Monte-Carlo-Code or other softwares such as SpekCalc or XOP (there are also some x-ray spectrum databases available, e.g. SRS-78). Having the spectrum you can get the µ values according to the energies and then calculate the attenutation using Lambert-Beer law (for point sources).

Best regards

Dear Antoine Nauleau ,

the penetration of x-rays obeys the Lambert-Beer law:

I=Io*exp(-µ*d).

Here Io is the primary x-ray intensity and I the intensity at depth d. µ is the linear attenuation coefficient and depends on the photon energy E ( or wave length λ) : µ=µ(E) .

According to the exponential law the penetration depth dmean is defined as:

dmean = 1/µ

For calculating the µ you have to go via the mass attenuation coefficient µ/rho (with rho being the density).

µ=(µ/rho)*rho and the Lamber Beer law now is I = Io*exp[-(µ/rho)*rho*d]

The mass attenuation µ/rho is provided by:

https://physics.nist.gov/PhysRefData/Xcom/html/xcom1.html

Please enter the necessary data and press the 'Submit Information' button.

You may enter special photon energy values but you also may skip the standard energy grid .

From the calculated table*) please take the 'Total Attenuation' column 'with coherent scatter'.

Fortunately the density of water is 1g/cm³. So the numerical value of the data will not change but the unit will change into 1/cm when multiplying the µ/rho value (in cm²/g) by 1g/cm³.

Please play around with this nice page.

For any question please do not hesitate to contact me here.

Good luck

*) please scroll down the result page. The table is below the chart.

Dear Antoine,

yes, Gerhard is right.

A small problem is the linear attenuation coefficient µ for water, which you can for example get from NIST's XCOM database. You will see, that µ values are, of course, energy dependent. As X-ray sources are polychromatic, you need to calculate µ values according to the photon energy spectrum of your X-ray source. This spectrum mainly depends on the accelleration voltage, the anode material (e.g. tungsten) and anode angle as well as the filtration (e.g. X-ray exit window [beryllium], addition filtration [Al, Cu,...]). Measuring the spectrum is challenging, therefore calculation is mainly done using Monte-Carlo-Code or other softwares such as SpekCalc or XOP (there are also some x-ray spectrum databases available, e.g. SRS-78). Having the spectrum you can get the µ values according to the energies and then calculate the attenutation using Lambert-Beer law (for point sources).

Best regards

To calculate the linear attenuation coefficient (see GM answer] , you will need to determine the mass attenuation coefficient (MAC) of H2O for the wavelength of radiation being used.

MAC (H2O) =(weight fraction of H) x MAC (H) + (weight fraction (O) x MAC (O)

Then apply to the attenuation formula,

I = Io x exp [-MAC (H2O) x distance / density (H2O)]

Two remarks:

a) The above equation should read:

I = Io x exp [-MAC (H2O) x distance x density (H2O)]

b) please be carefull when doing the calculations by your own:

in the weight fractions the atomic weight of H (=1) and of O (=16) as well as the molecular weight of water (=18) are involved:

(weight fraction of H)= 2*1/18 and (weight fraction of O)= 1*16/18

Fortunately the calculator in the NIST/XCOM database is doing all that automatically for you when asking for the H2O attenuation data.

Besides what is already uploaded by colleagues, you may also easily use the Website of the centre of x-ray optics, www.cxro.lbl.gov, and then follow to "x-ray database" , and the choose the proper sub-menu. Good luck, Dirk

I agree with Gerhard's correction to the attenuation formula.

I think you need know what energy of x-ray meter

because behavior photon in different energy is difference