Radiation Quantities and Units

Author: Dr. Wilhelm Buttler
Issue: 30 September 2011

This discussion shall supply you with information on radiation quantities and units, particularly on German regulations that were decisive for the design of our instruments. We already mentioned various measuring quantities in the General Notes on our Products, however without explaining details. Now we try to catch up on this subject.

This is anything but a thorough and comprehensive treatise on radiation quantities, nor will it be scientifically accurate down to the last detail. It is the attempt of a clear explanation of an admittedly complex subject. Moreover, we shall restrict ourselves to the application of our instruments.

We shall discuss photon radiation only. Photon radiation is a generic term covering both X-radiation and gamma radiation. X and gamma radiation are electromagnetic radiation, like radio waves and visible light are, but with much shorter wavelengths (traditionally X and gamma rays are characterized by energy in keV or MeV, not by wavelength, although this would equally be possible). X rays are created when fast electrons are stopped in matter like, for example, an electron beam in an X-ray tube or in a CRT (cathode ray tube). The maximum X-ray energy is equal to the energy of the electrons that were stopped. For example, an X-ray tube operated at a voltage of 100 kV accelerates the electrons to an energy of 100 keV. The X-radiation generated by that tube covers an energy spectrum ranging from zero to 100 keV (continuously, but with varying intensity). On the other hand, gamma rays originate from the decay of atomic nuclei. Gamma radiation does not form a continuous spectrum, but consists of one ore more »lines« that are characteristic for the decaying nucleus. For example, the gamma radiation following the decay of Cs-137 has an energy of 662 keV. Apart from their origin, X and gamma rays are the same, and therefore are joined by the term »photon radiation«.

Background information: What has wavelength to do with energy? Wavelength »L« (visible light as an example: L = 400 to 700 nm) and frequency »F« (FM radio as an example: F ~ 100 MHz) of electromagnetic radiation are linked to each other through »c«, the velocity of light: c = L x F. Max Planck discovered that the energy of electromagnetic radiation is not distributed evenly but divided into small packages of energy E = h x F, where the Planck constant »h« is a fundamental physical constant. These packages are called photons (»light particles«). Their energy is E = h x F = (h x c) / L. This means that wavelength, frequency and energy are equivalent quantities to specify electromagnetic radiation.

Furthermore, we shall focus on »strongly penetrating« photon radiation, that is photon radiation with energies not lower than 15 keV.

Remark on notation: We avoid subscripts because they disturb line spacing. For example, we use Hx and Ka instead of Hx and Ka.

Exposure Dose

Back in 1928 the second ICRU (International Commission on Radiation Units and Measurements) congress defined the »Roentgen« to measure the »quantity of X-radiation«. The definition of that quantity, also known as »exposure« or »exposure dose«, is based upon the X-radiation's ability to produce electric charge in air. That definition was extended to gamma radiation in 1937, that is to photon radiation in general. In 1928 the symbol for the Roentgen unit was defined as »r«, and was changed to »R« in 1962 (surprisingly enough, you can still meet the »r«). The SI unit of exposure is C/kg of air, which converts to R as follows:

1 R = 2.58 E-4 C/kg (Coulomb per kilogram of air, that is charge per mass of air).

The SI unit C/kg is hardly used in practice. Instead, the SI system prefers a quantity called »air kerma«, see the comments on absorbed dose now to follow.

Absorbed Dose

In 1957 ICRU defined: »Absorbed dose of any ionizing radiation is the energy imparted to matter by ionizing particles per unit mass of irradiated material at the place of interest«. Note that, unlike the definition of exposure dose, this definition is neither restricted to a particular radiation type nor to a particular absorbing material. The traditional unit is »rad« (Radiation Absorbed Dose), and the SI unit is »Gy« (Gray):

100 rad = 1 Gy = 1 J/kg (Joule per kilogram, that is energy per mass)

For photon radiation in air you can easily convert Exposure to Absorbed Dose by applying the appropriate factor:

Absorbed Dose [rad] = C x Exposure [R], where C = 0.877 rad/R (in air)

In water or tissue, C is within the range of 0.94 to 0.98 rad/R for photon energies ranging from 100 keV to 3 MeV. In other materials other values for C apply. If you further wish to convert absorbed dose from rad to Gy, simply divide by 100:

Absorbed Dose [Gy] = Absorbed Dose [rad] / 100.

Within the SI system, absorbed dose in air measured in Gy is called air kerma (Ka). The word kerma means »kinetic energy released per unit mass« or »kinetic energy released in matter«. Air kerma is the common SI replacement for exposure because these two quantities only differ by a constant factor over a very wide range of photon energies:

Ka [Gy] = 0.00877 Gy/R x exposure [R].

Air kerma can be regarded as the basic SI quantity. If conversion factors for other SI quantities such as dose equivalents are reported, those conversion factors usually refer to air kerma.

Dose Equivalent

Exposure and Absorbed Dose are general scientific quantities; they are not primarily related to protection of persons against radiation. With regard to radiological protection, we need a quantity that measures the biological effect on tissue. One might suppose that the absorbed dose in tissue could serve that purpose. In fact, it does in the case of photons and electrons (beta particles). For other radiation types, however, the same amount of absorbed dose has a different biological effect. Therefore, RBE Dose (Relative Biological Effectiveness Dose) was introduced in the 1950s. The RBE Dose is the Absorbed Dose in tissue measured in rad multiplied by a quality factor Q (formerly called RBE factor) accounting for the biological effect of different types of radiation. The corresponding traditional unit is »rem«.

RBE Dose [rem] = Q x Absorbed Dose in tissue [rad], where Q = 1 for photons and electrons.

For neutrons or alphas Q may range up to 20. Both rem and rad represent energy per mass, so Q has no unit. Rem means »Rad Equivalent Man« indicating that one rem is the amount of any type of radiation that has a biological effect on human tissue equivalent to the effect of one rad of photon radiation. In other words, one rem of any type of radiation causes the same biological damage as one rad of photon radiation. If we use that equation for photon radiation (Q = 1) and replace Absorbed Dose in tissue with Exposure, we obtain

RBE Dose [rem] = C x Exposure [R] (C <= 0.98 rad/R)

Since C is close to 1, Exposure Dose is a good estimate for RBE Dose originating from photons. It even slightly overestimates RBE Dose. This reflects many years' practice to take the reading of instruments indicating Exposure in R as the RBE Dose of photons in rem.

The advantage of an »equivalent« dose is obvious: If a person is exposed to different radiation types, you may add the equivalent dose values of those radiations to get the total amount of biological effect. This total amount, the »effective« dose, decides whether permissible limits are exceeded or not. It took a long time for the Dose Equivalent to be widely accepted. In 1957 ICRU mentioned the RBE Dose and the rem as »recognized symbols«, however did not define them as recommended quantity and unit. In the time thereafter a lot of work (and, unfortunately, a lot of modifications) on the dose equivalent concept was performed as documented in many publications of ICRU and ICRP (International Commission on Radiological Protection). One of the results is the SI unit »Sv« (Sievert) to replace the rem as unit for the Dose Equivalent:

1 Sv = 100 rem = 1 J/kg

Now we have to confuse you a little bit. We just learned that 1 Sv = 1 J/kg. When discussing Absorbed Dose (see above), we mentioned that also 1 Gy = 1 J/kg. This means that 1 Sv = 1 Gy. From this equation one might conclude that Dose Equivalent is equal to Absorbed Dose. However, that conclusion is not correct at all. You cannot conclude that two quantities are equal just from the fact that they are measured with the same unit.

Background information: A quantity and its unit are different things. For example, think of the distance between two cities. That distance depends on the type of transportation (air, road, rail). The type of transportation is the measuring quantity, and the unit is, for example, miles. When specifying a distance in miles, the type of transportation (the quantity) needs to be specified, too, if the specification shall be unambiguous. A common way to manage this problem is to »invent« new units clearly allowing to conclude the quantity from. Such new units would be »air miles« or »road miles« in our example. Electrical engineering makes full use of this method. In order to specify various voltages such as direct, alternating or peak-to-peak voltage, units such as VDC, VAC, Vpp have been created although the official unit is just V like Volt.

The distinction between a quantity and its unit was not always clearly observed in the radiation business (in the early days even by experts), and we feel that among users a lot of confusion arose from neglecting this distinction.

A good example for confusing a quantity and its unit is the popular equation »Sv/Gy = 1.20 (for Cs-137)«. Since we just learned that 1 Sv = 1 Gy, how can then be Sv/Gy = 1.20? The answer is that »Sv/Gy = 1.20« is a short - but incorrect - notation for the following fact:
H*(10) [Sv] = 1.20 x Ka [Gy] (for Cs-137).
Correctly the popular equation reads »H*(10)/Ka = 1.20 (for Cs-137)«, because 1.2 is the ratio of the quantities, not the ratio of their units. Ka is air kerma, and H*(10) is a dose equivalent quantity that will be discussed later.

Now that we are aware of distinguishing quantities and units, we may discuss different dose equivalent quantities (unfortunately there are more than one) which are all measured in Sv.

Photon Dose Equivalent Hx

Photon dose equivalent Hx (measured in Sv) is a quantity introduced in Germany in 1980. It became the legal quantity in Germany on 01 January 1986. Hx was an interim solution because at that time no international agreement on dose equivalent quantities had been achieved. In Germany Hx was replaced by SI quantities such as H*(10) on 01 August 2001. Hx was not accepted internationally. Nevertheless, we have to discuss Hx because it affected the design of our instruments.

Most instruments available up to the early 1980s were designed for Exposure (rate) and calibrated in R(/h). The question arose whether we could still use them to measure dose equivalent. The answer was: Yes, we can, because Exposure is a good estimate for the dose equivalent of photons in tissue. Therefore Hx was defined as

Hx [Sv] = 0.01 Sv/R x Exposure [R].

Since this conversion does not depend on photon energy, Hx and Exposure are strongly related quantities; they just differ by the factor 100. This is why some of our instruments (some 6150AD models) allow the user to select either R or Sv as the unit. Basically Hx was not really a new quantity. It was more the old quantity Exposure in a new wrapping.

Why the denomination Hx? Probably because the letter H was already internationally designated for the Dose Equivalent quantities, however there was not yet agreement which suffixes or indexes to append to that letter (H*(10), Hp(10), ...). Consequently the magic »unknown x« had to serve as the index.

»New« Dose Equivalent Quantities

The new quantities distinguish, in all combinations, area and personal monitoring, as well as strongly and weakly penetrating radiation. This makes a total of four quantities:

Table 1
The four new Quantities
  Strongly penetrating radiation (e.g., gamma) Weakly penetrating radiation (e.g., beta)
Area monitoring Ambient Dose Equivalent
Directional Dose Equivalent
H'(0.07, Omega)
Personal monitoring (Deep) Personal Dose Equivalent
(Shallow) Personal Dose Equivalent

A new feature of all these quantities is that they are defined in or on a phantom simulating the effect of the human body on the radiation field.

Ambient Dose Equivalent H*(10)

Ambient Dose Equivalent H*(10) is a quantity now widely accepted. In case of photons, it is similar to Hx except that it accounts for absorption and scattering of radiation by the human body. The definition of H*(10) simulates the human body through a phantom (the ICRU sphere, a sphere of 300 mm in diameter made of tissue equivalent material). H*(10) is the dose equivalent at a depth of 10 mm inside that sphere, that is at the place of an assumed inner organ. An instrument measuring dose (rate) free in air must simulate by design the effect of the ICRU sphere if it shall measure H*(10). Then this instrument will provide a good estimate for the dose a person would receive if he/she finally went to that place.

The effect of the ICRU sphere depends on photon energy. The factor converting some classical quantity to H*(10) is not a single number, but depends on energy. For example, the German quantity Hx converts to H*(10) as follows:

H*(10) = f1(E) x Hx

If we substitute air kerma Ka for Hx, we obtain the internationally more common equation using Ka as reference:

H*(10) = f2(E) x Ka, where f2(E) = f1(E) / 0.877

Table 2 below shows values for f1 and f2 as a function of photon energy. If you are not familiar with the German quantity Hx, f1 will be new for you. Nevertheless we recommend to have a look at f1 because it reflects the effect of the ICRU sphere phantom (as opposed to f2, which additionally includes the factor 0.877). You will notice that f1 is lower than 1 at the lowest energies. This comes from absorption of the 10 mm tissue layer that covers the place of interest inside the ICRU sphere. At higher energies f1 is greater than 1. This comes from radiation scattered by the ICRU sphere towards the place of interest. With increasing energy, f1 approaches 1. This means that at very high energies the effect of the ICRU sphere phantom almost vanishes.

Table 2
Conversion of Hx or Ka to H*(10)
Radiation quality (X or gamma radiaiton) Average photon energy in keV f1 =
f2 =
N-20 17 0.28 0.32
N-30 25 0.71 0.81
N-40 33 1.05 1.20
N-60 48 1.39 1.59
N-80 65 1.53 1.74
N-100 84 1.50 1.71
N-120 101 1.45 1.65
N-150 118 1.39 1.58
N-200 165 1.28 1.46
N-250 207 1.22 1.39
N-300 248 1.18 1.35
Cs-137 662 1.05 1.20
Co-60 1250 1.02 1.16

The radiation qualities N-xxx in the first column represent narrow spectrum filtered X radiations as defined by ISO 4037-1. We chose these because they are commonly used for measuring energy response of radiation meters.

Background information: These conversion factors have been calculated, not measured. This is partly because tissue equivalent material for manufacturing an ICRU sphere is just not availabe. The ICRU sphere is a phantom in the true sense of the word. Moreover, a sphere would be quite incomfortable to handle. All this is not really a drawback because instruments for H*(10) do not need to be calibrated on a phantom, contrarily to personal dosimeters, see the remarks on the Personal Dose Equivalent Hp(10) below.

For many applications f1 is quite close to 1, which means that the effect of the ICRU sphere is quite small. The factors f1 in Table 3 were taken from the PTB report PTB-Dos-23 published in July 1994 (PTB = Physikalisch-Technische Bundesanstalt, the German national institute for standardization). We later added the factors f2 according to f2 = f1 / 0.877:

Table 3
Conversion of Hx or Ka to H*(10)
for some typical photon radiation fields
Radiation field f1 =
f2 =
Natural background 1.07 1.22
Radiation field originating from contamination following a reactor accident 1.06 to 1.10 1.21 to 1.25
Radiation field in a nuclear power reactor 1.03 1.17
N-16 radiation (6 MeV gamma radiation) 0.97 1.11
Radiation having passed the housing of an X-ray unit up to 1.5 up to 1.7
Radiation of Ir-192 behind a 5 cm lead shielding 1.06 1.21
20 MeV bremsstrahlung behind 1.7 m of concrete 0.98 1.12

For those applications where f1 is very close to 1, H*(10) is very close to Hx and therefore very close to Exposure. For such applications there is almost no difference between exposure as defined in 1928 and the very modern quantity H*(10). Amazing, isn't it?

Directional Dose Equivalent H´(0,07, Omega)

Directional dose equivalent H'(0.07, Omega) is the dose equivalent produced in the ICRU sphere at a depth of 0.07 mm, that is skin dose. In case of strongly penetrating radiation, skin dose will not significantly contribute to effective dose. Therefore, directional dose equivalent is only important in case of weakly penetrating radiation, such as alphas, betas with energies lower than 2 MeV, and photons with energies lower than 15 keV. Since we do not offer instruments for this quantity, we shall not further discuss it.

(Deep) Personal Dose Equivalent Hp(10)

Personal dose equivalent Hp(10) is the dose equivalent in tissue at a depth of 10 mm in the body (not in the ICRU sphere) at the location where the personal dosimeter is worn. Of course it is impossible to measure at that place, but one can calculate what a personal dosimeter placed on a phantom must indicate if it shall properly register Hp(10). This has been done for the ISO slab phantom (a square slab dimensioned 300 x 300 x 150 mm³, PMMA walls, filled with water). There are tables with conversion factors for the slab phantom, however we would like not to confuse you with all these numbers.

Dosimeters are irradiated on the ISO slab phantom to check whether they are suited for Hp(10). Dosimeters may also be irradiated on the phantom for calibration purposes. However, the ISO slab phantom is no longer required during routine calibration. For that purpose a correction factor accounting for the effect of the phantom is determined for a particular dosimeter type and a particular radiation quality (Cs-137 in most cases). After that, dosimeters of that type can be irradiated free in air, and applying the correction factor to their reading results in the value they would have indicated on the phantom.

Since personal dosimeters are worn on the body, they have always been exposed to radiation scattered from the body. At photon energies not too low, the radiation field at the place of the dosimeter is quite similar to the field 10 mm inside the body. One might suppose that personal dosimeters measured Hp(10) from the very beginning, even before Hp(10) was introduced. In fact, this is true to some extent. It can be assumed that many classical personal dosimeters, calibrated in R, will measure Hp(10) quite well; just multiply their reading by 0.01 Sv/R. Maybe energy and angular range would have to be specified newly. We confirmed this when examining our old Hx dosimeter ALADOS for response to Hp(10). Of course, its successor ALADOX was nevertheless optimized for Hp(10).

(Shallow) Personal Dose Equivalent Hp(0.07)

Personal dose equivalent Hp(0.07) is the same as Hp(10) except that it refers to weakly penetrating radiation (skin dose). Hp(0.07) dosimeters are calibrated on rod phantoms simulating fingers, arms, or legs. Since we do not offer instruments for this quantity, we shall not further discuss it.

to top of page © 1998-2012 Automess GmbH