# Exposure Calculations

Properly exposing a radiograph is often a trial and error process, as there are many variables that affect the final radiograph.  Some of the variables that affect the density of the radiograph include:

• The spectrum of radiation produced by the x-ray generator.
• The voltage potential used to generate the x-rays (KeV).
• The amperage used to generate the x-rays (mA).
• The exposure time.
• The distance between the radiation source and the film.
• The material of the component being radiographed.
• The thickness of the material that the radiation must travel through.
• The amount of scattered radiation reaching the film.
• The film being used.
• The concentration of the film processing chemicals and the contact time.

The current industrial practice is to develop a procedure that produces an acceptable density by trail for each specific x-ray generator.  This process may begin using published exposure charts to determine a starting exposure, which usually requires some refinement.

However, it is possible to calculate the density of a radiograph to a fair degree accuracy when the spectrum of an x-ray generator has been characterized.  The calculation cannot completely account for scattering but, otherwise, the relationship between many of the variables and their effect on film density is known.  Therefore, the change in film density can be estimated for any given variable change.  For example, from Newton's Inverse Square Law, it is known that the intensity of the radiation varies inversely with distance from the source.  It is also known that the intensity of the radiation transmitted through a material varies exponentially with the linear attenuation coefficient (μ) and the thickness of the material.

A number of radiographic modeling program are available that make this calculation.  These programs can provide a fair representation of the radiograph that will be produce with a specific setup and parameters.  The applet below is a very simple radiographic density calculator.  The applet allows the density of a radiograph to be estimated based on material, thickness, geometry, energy (voltage), current, and time. The effect of the energy and the physical setup are shown by looking at the film density after exposure. Since the calculation uses a generic (and fixed characteristic) x-ray source, fixed film type and development, the applet results will differ considerably from industrial x-ray configurations.  The applet is design simply to demonstrate the affects of the variable on the resulting film density.

## How To Use This Applet

First choose a material. Each material has a mass attenuation constant, mu. Next, the voltage to the x-ray source needs to be set. Continue to fill in numbers for the rest of the variables. The current is the number of milliamps that flow to the source. After the Distance, Time, and Thickness have been set, press the "Calculate" button.

Note, the Io field has a number in it. This is the initial intensity of the x-ray beam. For large numbers, it may be necessary to use the mouse to see the entire number. Click on the number and move the mouse as if selecting it. The cyan pointer indicates the density on the resultant radiograph. The two other pointers represent under- and over-exposure by a factor of four. These may be used to judge the degree of contrast in the resultant radiograph.

Try the following examples: material: aluminum, kV: 120, mA: 5, distance: 0.5 meter, time: 90 seconds, thickness: 6.5 cm. The resultant density will be 2.959. As can be noted on the stepwedge, reducing the exposure by a factor of four will change the density to a value of 1.0, and increasing the exposure by a factor of four will result in a density of 5.0. Reduce the time from 90 seconds to 22.5 seconds (factor of four) and note the results.

Change the material to iron and press "Calculate". Note that not enough radiation is received to generate an image. Change the following: kV: 320, mA: 10, time: 900 seconds, thickness: 1.25 cm, and then click "Calculate". Note the resulting center density of 0.561. With aluminum, the time was altered by a factor of four to change the density. With the iron, current (mA) must be increased by a factor of four to produce an increase in density. Change the current from 10 to 40 and calculate the results.

Caution: This applet does not have knowledge of the characteristics of any particular real-life x-ray source and should NOT be used other than as a theoretical tool for making predictions of exposure and contrast.

First choose a material. Each material has a mass attenuation constant, Mu. Next, the Voltage to the x-ray source needs to be set. Continue to fill in numbers for the rest of the variables. The current is the number of milli-Amps that flow to the source. After the Distance, Time, and Thickness have been set, press the Calculate button.

Note: Io is the initial number of x-ray photons, it is a dimensionless whole number. It is often 1E+10 or more.

Film Density is a dimensionless number that goes from 0 to 6.

The over and under exposure levels may be used to judge the degree of contrast in the resultant radiograph. Under-expose and over-exposure are unitless factors of 4 over and 4 under the user’s first guess of (time * mA).

Caution: This app should be used for educational purposes ONLY and is NOT valid for scientific, medical or industrial purposes.