CIH Radiation Reference: Ionizing and Nonionizing

At the Source: Activity Direct Measurement

The journey begins at the radioactive material itself. Activity measures how many atoms are disintegrating (decaying) every second within that source.

Imperial Unit: Curie (Ci), defined as 3.7 × 10¹⁰ disintegrations per second.
SI Unit: Becquerel (Bq), which is simply 1 disintegration per second.

How it's measured: instruments like a gas proportional counter or a Geiger-Müller (GM) meter detect these disintegration counts directly.

In the Air: Exposure Direct Measurement

Once radiation is emitted, it travels through the environment. For gamma and X-ray radiation, we measure the amount of ionization it produces in the surrounding dry air.

Unit: Roentgen (R). This represents the amount of charge produced in 1 cm³ of dry air.

How it's measured: typically with an ion chamber, which captures the voltage difference created by the positive and negative ions produced.

Key Note: This measures exposure only in the air and not in the body, and there is no direct SI equivalent to the Roentgen.

Striking the Target: Absorbed Dose Direct Measurement

When radiation hits a physical mass, such as human tissue, it is absorbed. The Dose measures the actual amount of energy deposited into that mass.

Imperial Unit: rad (radiation absorbed dose), where 1 rad equals 100 erg/g of mass.
SI Unit: Gray (Gy), where 1 Gray is equal to 100 rad.

How it's measured: devices like Thermoluminescent Dosimeters (TLDs) or calibrated detectors measure this energy deposition directly — for example, by measuring the light emitted when a TLD crystal is heated.

Limitation: this unit measures pure energy absorption but does not differentiate between the types of radiation or their specific biological impacts.

The Human Impact: Biological Dose Calculated

Bridge 3: absorbed dose to biological dose (rem). The quality factor sets the biological weight of that energy:

The final stage of the progression is determining the actual biological damage to a person. This is known as the dose equivalent, and unlike the first three categories, it isn't read directly off an instrument — it's calculated based on the Absorbed Dose, multiplied by the Quality Factor. Because different types of radiation (like alpha vs. gamma) cause different amounts of damage to human tissue even when the absorbed energy is the same, a Quality Factor (QF) must be applied.

Imperial Unit: rem (radiation equivalent). Calculation formula: $\text{rem}=\text{rads}\times QF$, where the rads are the Absorbed Dose.
SI Unit: Sievert (Sv), where 1 Sv equals 100 rem — calculated from Grays using the same biological weighting factors.

The "Why": if you have a direct measurement in rads, you multiply it by the QF (e.g., 1 for X-rays, 10 for high-speed neutrons) to determine the rem, the actual biological impact. X-rays have a QF of 1 while high-speed neutrons have a QF of 10 — meaning neutrons cause ten times the biological damage for the same absorbed dose.

Weighting factors by radiation type. The last step of the chain, absorbed dose to biological dose, works the same way for every type of radiation: only the weighting factor changes. Two systems are in use, and an exam question will name one.

How to use it: equivalent dose (Sv) = absorbed dose (Gy) × wR in the ICRP system; dose equivalent (rem) = absorbed dose (rad) × Q in the NRC system. The rem/Sv units follow the same 1 Sv = 100 rem relationship shown above.

Equation reference: dose equivalent and dose rate.

Know which system the question names. Canada’s Radiation Protection Regulations list the ICRP 103 weighting factors (Schedule 2). The NRC rule in 10 CFR 20.1004 still uses quality factors, which is why protons and neutrons differ between the two columns. Examples from the NRC neutron table: thermal neutrons Q = 2, 1 MeV neutrons Q = 11. Sources: ICRP Publication 103, Radiation Protection Regulations, Schedule 2, 10 CFR 20.1004.

Special Case: Gamma and X-Rays Have the Full Chain, from Activity to Biological Dose Calculated

The table above applies to every radiation type, but it starts from absorbed dose. Only gamma rays and X-rays let you calculate all the way from a source’s activity, because only they have an exposure (roentgen) and a gamma constant. The whole chain, Activity → Exposure → Absorbed Dose → Biological Dose, has four stages and therefore three bridges. Time, distance and the source strength go in; rem comes out.

Bridge 1: activity to exposure (R). The air exposure from a point source is

Bridge 2: exposure to absorbed dose (rad). Each roentgen of gamma or X-ray exposure deposits about 1 rad in tissue (the usual exam simplification):

Bridge 3: absorbed dose to biological dose (rem). The quality factor sets the biological weight of that energy:

All three bridges together:

Worked example: a 5 mCi Co-60 source, Γ = 13.07 R·cm²/(mCi·h), a worker 50 cm away for 4 hours.
Bridge 1 (activity to exposure): $\frac{13.07\times 5\times 4}{50^{2}}=\frac{261.4}{2{,}500}=0.105\ \text{R}$.
Bridge 2 (exposure to absorbed dose): $0.105\ \text{R}\times 1\ \text{rad/R}=0.105\ \text{rad}$.
Bridge 3 (absorbed dose to biological dose): $0.105\ \text{rad}\times QF\ 1=\mathbf{0.105\ rem}$ (about 105 mrem).

When it applies: gamma and X-rays from an unshielded point source, ignoring decay during the exposure and attenuation in the air. Adding shielding is a separate step (HVLs, below). If a question gives you Γ, use the value given.

When it does not apply: alpha, beta and neutron radiation have no roentgen and no Γ, so there is no Bridge 1. You cannot go from activity to dose with this formula. Bridges 1 and 2 are not available, so you start at the third stage, the absorbed dose (rad or Gy), and cross only Bridge 3 using the weighting factor in the table above. Source for Γ: NRC gamma constants; tabulated values vary slightly between compilations.

Time

Dose = dose rate × time. Halve the time, halve the dose. Plan the job, rehearse it away from the source, and rotate workers.

Distance: the inverse square law

For a point source, intensity falls with the square of distance: $I_1 d_1^{2}=I_2 d_2^{2}$. Doubling the distance cuts the rate to one quarter. Example: 100 mR/h at 2 ft → 25 mR/h at 4 ft. Tongs and remote handling tools use this directly. Equation reference: inverse square law.

Shielding and the half-value layer

A half-value layer (HVL) is the thickness of a material that halves the intensity of a photon beam. Each extra HVL halves it again: after n HVLs, 1/2ⁿ remains (3 HVLs → 1/8). Match the shield to the radiation: paper for alpha, plastic or aluminum for beta, lead or concrete for gamma and X-rays, hydrogen-rich material for neutrons.

Shield Material Shielding

Six materials, six different jobs. A shield is good only for the radiation it actually stops, and the wrong material in the first layer can make a new, more penetrating hazard. Look at the marks next to each name first.

Lead ✔ Good: gamma and X-rays✖ Bad: first layer for beta or neutrons

✔ Good for gamma and X-rays — why

Lead is both very dense (about 11 g/cm³) and high in atomic number (Z = 82). A photon is absorbed or scattered by interacting with atoms’ electrons, and a dense, high-Z material packs far more electrons into each centimetre, and the chance of absorbing the photon rises steeply with atomic number. So a thin layer of lead removes a large share of the photons.

✖ Bad as the first layer for beta or neutrons — why

The same property is what makes lead a trap for two other radiations:

Water (and other hydrogen-rich materials) ✔ Good: neutrons✖ Bad: gamma and X-rays

✔ Good for neutrons — why

Moderate. Water, paraffin and polyethylene are rich in hydrogen, and a hydrogen nucleus has almost the same mass as a neutron. Like a cue ball hitting another billiard ball, a head-on collision can hand over most of the neutron’s energy, so fast neutrons are slowed to thermal speed in few collisions. This slowing is called moderation.

Capture. Once slow, the neutron is absorbed. Boron (boron-10, for example in borated polyethylene or borated water) has a very high capture probability for thermal neutrons and gives off only a low-energy gamma (about 0.48 MeV) in most captures. Capture in hydrogen alone releases a much more penetrating gamma (about 2.2 MeV). So a neutron shield is built in order: moderator, absorber, then a gamma layer if the capture gammas matter.

Layer order and the moderator-plus-absorber approach: UTK NE 406, shielding lesson. Treat the gamma energies as typical values; confirm the isotope data in your reference when a calculation depends on them.

✖ Bad for gamma and X-rays — why

Water is made of light atoms (hydrogen and oxygen) at only 1 g/cm³, so it holds far fewer electrons per centimetre than lead and the photons mostly pass through it. It can attenuate gamma, but only with a very large thickness, so it is not the material to choose for photons.

Concrete ✔ Good: neutrons and gamma/X-rays together

✔ Good for neutrons and gamma/X-rays together — why

Concrete is the usual bulk structural shield because it stops two different radiations in one material:

Ordinary concrete already does both jobs; heavyweight aggregate raises the gamma attenuation for a given thickness.

Acrylic plastic (Plexiglas, Lucite) ✔ Good: beta particles✖ Bad: gamma and X-rays

✔ Good for beta particles — why

Acrylic is made of light atoms (carbon, hydrogen, oxygen), so beta particles are stopped with very little bremsstrahlung. In Health Physics data for phosphorus-32, about 0.5% of the beta energy becomes X-rays in Lucite, against about 4.8% in lead. It is also clear, so the worker can see the source. A layer of about 1 cm stops all P-32 betas (the maximum range is about 0.6 cm). If X-rays from stronger sources still matter, add lead on the outside of the acrylic, never in front of it.

✖ Bad for gamma and X-rays — why

Acrylic is low in density and low in atomic number, so photons mostly pass through it. It contains hydrogen, but far less than polyethylene and no boron, so it is not a designed neutron shield either.

Sources: University of Michigan, phosphorus-32 data sheet; Harvard EHS, P-32 shielding. Local guidance quotes thicknesses from about 1/4 inch to 1 cm.

Aluminum ✔ Good: beta particles✖ Bad: gamma and X-rays

✔ Good for beta particles — why

A thin aluminum sheet stops beta particles, and aluminum is light, rigid and does not burn, so it suits holders, covers and guards where a plastic would soften or crack.

✖ Bad for gamma and X-rays, and as the first layer for strong betas — why

Aluminum is only moderately dense (about 2.7 g/cm³) and has a low atomic number (Z = 13), so it is a poor photon shield. Its atomic number is also higher than plastic’s, so it turns more of a strong beta’s energy into bremsstrahlung X-rays than acrylic does. For high-energy betas, put plastic first and aluminum or lead behind it.

Polyethylene and borated polyethylene ✔ Good: neutrons✖ Bad: gamma and X-rays

✔ Good for neutrons — why

Polyethylene is almost all hydrogen and carbon (CH₂), so it packs even more hydrogen into each cubic centimetre than water does, and it comes as a solid sheet that is easy to machine. Hydrogen slows fast neutrons by elastic collisions (moderation). Borated polyethylene, commonly sold at about 5% boron, adds the capture step: once the neutrons are slow, boron absorbs them with only a low-energy gamma (about 0.48 MeV in most captures). Plain polyethylene slows neutrons but leaves them to be captured in hydrogen, which releases the more penetrating 2.2 MeV gamma.

✖ Bad for gamma and X-rays — why

Polyethylene has a low density and a low atomic number, so it does little against photons, and neutron capture in it makes gamma rays. A gamma layer (lead or concrete) is usually needed behind it. Polyethylene is also combustible, so check the fire rating where it is installed.

Source for the borated grade and its boron content: borated polyethylene sheet supplier (a manufacturer description, not a standard).

Calculating attenuation with the half-value layer

The half-value layer tells you how much a shield of any thickness lets through, not only whole numbers of HVLs. Two relationships do all the work.

Worked example (a different case). A shield material has an HVL of 20 mm for a gamma source. What is the attenuation of a 50 mm layer?
Number of HVLs: $\frac{50}{20}=2.5$.
Transmission: $\left(\frac{1}{2}\right)^{2.5}=0.177$, or about 17.7%.
Attenuation: $100\%-17.7\%=\mathbf{82.3\%}$.

Working backwards. To cut the intensity to a chosen fraction, solve for thickness: $x=\mathrm{HVL}\times\log_{2}\frac{I_0}{I}$. For 1% transmission, $\frac{I_0}{I}=100$ and $\log_{2}100=6.64$, so $x=6.64\times 20\ \text{mm}\approx 133\ \text{mm}$. Equation reference: half-value layer and attenuation coefficient.

The HVL belongs to one material and one photon energy: the same material has a different HVL for a different source. These relationships assume a narrow beam of a single energy; in practice buildup from scattered radiation means real shields are made somewhat thicker. Use the HVL value given for the material and source.

ALARA and internal exposure

Keep doses As Low As Reasonably Achievable, not just under the limit. For unsealed sources, the main job is preventing intake: contamination control, ventilation, gloves and protective clothing, no eating or drinking in the area, and surveys before leaving.

The 5 classes of radiation detection instruments

Class 1: Gas-filled detectors

The principle: radiation passes through a gas-filled chamber and strips electrons from the gas atoms, making ion pairs (positive ions and free electrons). A voltage across the chamber pulls the electrons to an anode wire, which creates an electrical pulse you can count.

What it detects: depending on the voltage applied, there are three sub-types:

1. Ionization chambers: measure the total exposure rate. Excellent for gamma and X-rays.
2. Proportional counters: can tell particle types apart (pulse size is proportional to the energy deposited). Excellent for alpha and beta; also wipe and contamination counting.
3. Geiger-Müller (GM) tubes: the high voltage makes a large avalanche of ions from a single interaction. Highly sensitive for detecting the presence of beta and gamma, but with no energy discrimination.

Alpha hook A standard GM tube cannot detect alpha because its metal wall is too thick. To detect alpha, a gas detector needs a paper-thin, fragile mica window that lets the weak alpha particle into the gas.

Limits GM counts events and gives no energy information, and it can saturate in high fields. Ion chambers are less sensitive at low levels. Proportional counters are usually laboratory or bench instruments.

Class 2: Photographic film (passive dosimeters)

The principle: silver halide crystals in the film emulsion react photochemically when radiation hits them. When the film is developed in a lab, the areas struck by radiation turn dark, and the darkness (optical density) shows how much dose was received.

What it detects: highly penetrating gamma and X-rays, and moderately penetrating beta particles.

Alpha hook Cannot detect alpha: the film is wrapped and the alpha particle cannot get through the wrapper.

Limits Read afterwards, not in real time. Affected by heat and light. Largely replaced by TLD and OSL.

Class 3: Luminescent solid-state dosimeters (TLD and OSL)

The principle: specialised crystals (lithium fluoride for TLD, aluminum oxide for OSL). When radiation hits the crystal, electrons are knocked loose and become trapped in flaws in the crystal. The badge stores this energy until it is read:

• TLD (thermoluminescent dosimeter): the lab heats the crystal, which releases the trapped electrons as measurable light.
• OSL (optically stimulated luminescence): the lab shines a green light or laser on the crystal, which releases the electrons as blue light.

What it detects: gamma, X-ray and beta.

Alpha hook Cannot detect alpha unless the badge is made with a specialised, uncovered element, because the standard plastic badge case blocks alpha completely.

Limits Personal dosimetry: gives the worker’s cumulative dose, read afterwards, not in real time.

Class 4: Scintillation detectors

The principle: a material (a phosphor, crystal or liquid) gives off a tiny flash of visible light the moment it absorbs radiation. A photocathode captures the flash and a photomultiplier tube (PMT) multiplies it into a measurable electrical signal.

What it detects:

• Solid crystals (sodium iodide, NaI): exceptional for gamma and X-ray spectroscopy, which means identifying the exact isotope.
• Liquid scintillation: the sample is dissolved directly in the fluid. Suited to low-energy beta (such as tritium) and alpha, because the particle is completely surrounded by the detector fluid.

Limits The crystal is fragile and temperature sensitive.

Class 5: Semiconductor (solid-state) detectors

The principle: works like a digital camera sensor made of very pure silicon or germanium. Radiation excites electrons across a narrow bandgap to make electron-hole pairs, which show up as a precise electrical current.

What it detects: alpha, beta, gamma and X-rays. It is the gold standard for high-resolution laboratory isotope analysis.

Limits The equipment is delicate, and germanium detectors often need liquid-nitrogen cooling.

The five classes side by side

Radioactive decay and half-life

A radioactive source does not stay at the same strength. Each nucleus decays at random, but a large group follows a fixed pattern: the activity falls by half in every half-life (T_½), a constant for each isotope. A reading taken today will be lower next week, so allow for decay when you plan a job, compare readings or store a source. In alpha decay the nucleus loses 2 protons and 2 neutrons, so its mass number falls by 4 and its atomic number by 2 (for example radium-226 becomes radon-222).

Worked examples. (1) A Co-60 source (T_½ ≈ 5.27 years) starts at 10 mCi. After about 10.5 years, which is two half-lives, it holds $10\times\left(\frac{1}{2}\right)^{2}=2.5\ \text{mCi}$. (2) An I-131 dose (T_½ ≈ 8 days) of 80 mCi has to fall to 10 mCi. $\frac{10}{80}=\frac{1}{8}=\left(\frac{1}{2}\right)^{3}$, so it takes 3 half-lives, about 24 days.

The dose rate from an unshielded source falls in step with its activity, so the Direct Dose formula above uses the activity at the time of the exposure. Half-lives come from nuclide data tables. Equation reference: radioactive decay, initial activity and effective half-life.

Radon

Radon is a naturally occurring radioactive gas from uranium in soil and rock, and the second leading cause of lung cancer after smoking. EPA recommends fixing a building at 4 pCi/L (150 Bq/m³) or more, and considering it between 2 and 4 pCi/L (EPA). The harm comes mainly from radon’s short-lived decay products, which lodge in the lung and emit alpha particles; the high-LET alpha energy deposited in the airway cells is the damage mechanism.

Photochemical damage vs thermal damage

The same eye can be hurt in two different ways, and the wavelength band tells you which one to expect.

UV safety time: how long before the daily limit is reached Calculated

With a laser you find a safe distance. With ultraviolet light you usually cannot move away, so you find a safe time: how many seconds of exposure use up the day’s allowance. The idea is the same: keep what reaches the tissue below a limit.

1. Why time matters: irradiance is the rate, radiant exposure is the total

Irradiance says how fast energy arrives on each unit of area. Radiant exposure says how much has built up. At a constant irradiance:

$$H_{\mathrm{eff}}=E_{\mathrm{eff}}\times t$$

Think of filling a container: irradiance is how fast you pour, and radiant exposure is how much is in it. A faster pour reaches the brim sooner.

2. What “effective” means

Different UV wavelengths harm tissue by different amounts. Effective irradiance has already been weighted with the UV hazard action spectrum, so it is not simply the lamp’s total UV output. A question that says “effective irradiance” has done that weighting for you.

3. The daily limit

For the weighted UV exposure of unprotected skin or eye over an 8-hour day, the guideline limit is:

$$H_{\mathrm{limit}}=3\ \text{mJ/cm}^{2}=3{,}000\ \mu\text{J/cm}^{2}\ (=30\ \text{J/m}^{2})$$

This is the ACGIH TLV and the ICNIRP limit, which are the same dose in different units. Because 1 µW = 1 µJ/s, a rate in µW/cm² is already µJ per second per cm².

4. The maximum time

Divide the exposure allowance by the exposure rate:

$$t_{\max}=\frac{H_{\mathrm{limit}}}{E_{\mathrm{eff}}}$$

Equation reference: permissible exposure time.

5. The allowance is shared across the day

“During an 8-hour day” means all the exposures of the day add up to the limit. A break does not reset it. At the same effective irradiance, these all use exactly the same allowance:

6. Worked example

A welding inspection booth exposes a worker only while the arc is struck. The effective irradiance at the worker’s position is 12 µW/cm². What is the maximum cumulative exposure time in a day?

$$t_{\max}=\frac{3{,}000\ \mu\text{J/cm}^{2}}{12\ \mu\text{J/(s}\cdot\text{cm}^{2}\text{)}}=250\ \text{s}$$

Answer: 250 seconds, which is 4 minutes 10 seconds of cumulative exposure in the whole day.

Does distance help? If the source behaves as a point source and the worker stands twice as far away, the irradiance falls to a quarter (inverse square law): $12/4=3\ \mu\text{W/cm}^{2}$. Then $t_{\max}=3{,}000/3=1{,}000\ \text{s}$, which is 16 minutes 40 seconds. Shorter time lowers the accumulated exposure, and more distance (or a shield) lowers the rate.

7. What this calculation does not cover

• Other limits still apply: a full assessment also checks the UV-A eye limit (315–400 nm), and the allowance assumes no other UV source adds to the day.
• No warning: UV is invisible, so you cannot rely on the blink response or on feeling anything while the exposure builds up.
• Keep the controls: shielding and appropriate eye and skin protection stay in place during the exposure. The time limit is not a reason to drop them.

Limit and method: ACGIH TLV for ultraviolet radiation and ICNIRP, Protection of Workers against Ultraviolet Radiation (2010). The TLVs are recommendations, and OSHA has no UV limit of its own (OSHA letter of interpretation). Confirm the value against the current edition and your jurisdiction.

Near field vs far field

Close to an antenna (within a few wavelengths) the electric (E) and magnetic (H) fields vary independently, so each must be measured separately. In the far field they are locked in a fixed ratio, so one measurement gives power density (mW/cm²), and the field falls off with distance like any point source.

Step 1: why do we assess electric and magnetic fields? Both fields can produce electrical effects inside the body and contribute to energy absorption.

From about 10 MHz up to 6 GHz, Safety Code 6 builds its reference levels on limiting whole-body heating (SAR). Below 10 MHz, limits that prevent nerve stimulation also apply. E and H are external exposure indicators; neither directly measures absorbed dose. Sources: Health Canada, Technical Guide for Safety Code 6, §4.2.2; Safety Code 6 (2015).

Step 2: compare with where the worker stands. Two distances from the antenna mark the three zones. D is the largest dimension of the antenna and λ is the wavelength, in the same units. Use E in V/m and H in A/m to get power density in W/m² (1 mW/cm² = 10 W/m²); keep P and the area (or distance) in matching units.

Step 3: combine the readings using the appropriate average. The table above assumes a heating-based RF assessment and equally weighted spatial sampling points. n is the number of sampling points and the subscript i is each reading.

The boundaries are approximate, not sharp edges, and they assume an antenna larger than the wavelength. Sources differ slightly on the inner coefficient (0.62 or 0.5), and for very small antennas the reactive zone is commonly taken as $\lambda/2\pi$. The 377 Ω ratio holds in the far field only. Equation reference: power density. Sources: field regions around an antenna; MVG, antenna measurement fields.

Limits and the body

Exposure limits are built on heating, expressed as the specific absorption rate (SAR, W/kg) and as measurable field strength or power density. Tissues with poor blood flow to carry heat away, such as the lens of the eye and the testes, are the classic sensitive sites. OSHA’s old nonionizing standard sets a guide of 10 mW/cm² for 10 MHz to 100 GHz, averaged over any 0.1 hour (29 CFR 1910.97); current consensus limits from IEEE and ACGIH vary with frequency.

Laser hazards: output → wavelength → protection

1. Output mode: how quickly is energy delivered?

2. Wavelength: which eye structures are at risk?

Memory: 400–1,400 nm is the retinal hazard region. UV and longer-wave IR mainly affect the front of the eye, with the exact target depending on wavelength.

Sources: OSHA Technical Manual, laser chapter; Old Dominion University laser safety manual.

Check the actual output. A laser may emit several wavelengths or frequency-converted light, for example frequency-doubled Nd:YAG at 532 nm. Source: OSHA Technical Manual, laser chapter (wavelength and biological-effects tables).

MPE, NHZ and eyewear

The maximum permissible exposure (MPE) is the level the eye or skin can take without injury. The nominal hazard zone (NHZ) is the space where direct, reflected or scattered light exceeds the MPE; controls apply inside it. Eyewear is chosen for the laser’s wavelength and an optical density of at least:

$OD=\log_{10}\frac{H_0}{MPE}$, where $H_0$ is the worst-case exposure. Example: $H_0=1\ \text{W/cm}^2$, $MPE=0.0025\ \text{W/cm}^2$ → $OD=\log_{10}(400)=2.6$, so choose OD 3 or higher. Equation reference: optical density.

3. MPE and protective eyewear. The MPE depends on wavelength, exposure duration, pulse characteristics and exposure geometry. A repetitive-pulse laser may need a single-pulse check, an average-exposure check and the applicable multiple-pulse checks. Put beam enclosure, interlocks and beam stops first, and use eyewear where hazardous exposure remains. Source: Princeton EHS, Laser Control Measures.

$T=10^{-OD}$ (transmission). Use matching units in the ratio: irradiance over MPE irradiance, or radiant exposure over MPE radiant exposure.

Eyewear must give the required OD at every relevant wavelength, with suitable resistance to the anticipated laser exposure and adequate visibility. A rating at 10,600 nm does not establish protection at 1,064 nm, so check the certified wavelength coverage.

Laser safety distance: irradiance, divergence and the NOHD Calculated

A laser does not lose power as it travels: a 50 W beam still carries 50 W at a far wall. What changes is how tightly that power is squeezed. Distance protects the eye by spreading the same power over a larger area, until the intensity is below the exposure limit.

1. Irradiance: power per area

Injury depends on how concentrated the power is on the tissue, not on the machine’s total output alone. The beam spot is a circle, so its area comes from its diameter D.

$$E=\frac{\Phi}{A}\qquad A=\frac{\pi D^{2}}{4}$$

Here E is irradiance in W/cm² and Φ is the laser power in W.

2. The limit: MPE (written EL in the equation reference)

The maximum permissible exposure (MPE) is the irradiance the eye can take. Above it the beam is hazardous; at or below it the energy is too spread out to be hazardous. The value comes from the standard for the laser’s wavelength and exposure time, so a question will normally give it to you. Because power is fixed, the only thing you can change to lower the irradiance is the area.

3. Why the area grows: beam divergence

A laser beam spreads much less than a flashlight, but it is not perfectly parallel. Exit aperture (a) is the beam diameter where it leaves the laser. Divergence (φ) is the full angle of the spread, in radians; 1 mrad = 0.001 rad. At a distance r the beam diameter is (see laser beam diameter in the equation reference):

$$D(r)=\sqrt{a^{2}+\phi^{2}r^{2}}$$

Far from the aperture this is close to φr, so each metre of travel adds about φ × 1 m to the diameter:

Check the angle convention: if a value is defined as a half-angle, the diameter grows about twice as fast (6 mm per metre at 3 mrad). Beam diameter and divergence must be defined consistently. Source: OSHA Technical Manual, laser chapter.

4. The safe boundary: Nominal Ocular Hazard Distance (NOHD)

The NOHD is the distance r from the laser at which the irradiance has fallen to the MPE. Set the irradiance of the spread beam equal to the limit:

$$\frac{4\Phi}{\pi D(r)^{2}}=MPE\quad\text{with}\quad D(r)^{2}=a^{2}+\phi^{2}r^{2}$$

Solving for r gives the NOHD formula:

$$r_{NOHD}=\frac{1}{\phi}\left(\frac{4\Phi}{\pi\,MPE}-a^{2}\right)^{1/2}$$

This is the same form as the Nominal Hazard Zone and Ocular Hazard Distance equations in the CIH equation reference. More power or a smaller divergence (a tighter beam) means a longer NOHD. r is the distance from the laser out to the boundary. It is not the radius of the beam.

5. What the NOHD is used for

• Setting the controlled laser area: where to put barriers, interlocked doors and laser curtains.
• Deciding who needs eyewear: anyone who may be inside the boundary, in the beam path.
• Sizing the eyewear: the NOHD only locates the boundary. The lens density is then found from the exposure at the point of concern, as in the MPE card above: $OD=\log_{10}\frac{\text{exposure}}{MPE}$.

6. Worked example

A 50 W continuous laser leaves its aperture with a diameter a = 2 cm and a divergence of 2 mrad (0.002 rad). The applicable MPE is 0.1 W/cm². What is the NOHD?

Check the starting point. The area is $A=\frac{\pi(2)^2}{4}=3.14\ \text{cm}^2$, so the irradiance is $\frac{50}{3.14}\approx 15.9\ \text{W/cm}^2$, far above 0.1 W/cm².

$$\frac{4\Phi}{\pi\,MPE}=\frac{4\times 50}{\pi\times 0.1}=636.6\ \text{cm}^2$$

$$r_{NOHD}=\frac{1}{0.002}\left(636.6-2^{2}\right)^{1/2}=\frac{25.15}{0.002}\approx 12{,}600\ \text{cm}$$

NOHD ≈ 126 m. At that distance the beam is about 25 cm across and the 50 W is spread thinly enough to be at the limit.

A shortcut sometimes taught adds the divergence growth to the exit diameter in a straight line, $r=\frac{D-a}{\phi}$; here that gives about 116 m, a little short of the standard result. Use the formula above. The NOHD assumes a stated MPE and no focusing optics in the path; use the MPE and divergence values the question or the laser data sheet gives.

7. Second worked example: reflectivity and viewing angle given

Which formula? If the question gives a reflecting surface (reflectivity ρ) and a viewing angle (θ) instead of an aperture and a divergence, the hazard is the diffuse reflection off that surface, so use this form of the Nominal Hazard Zone equation, not the NOHD formula above:

$$r=\sqrt{\frac{\rho\,\Phi\cos\theta}{\pi\,MPE}}$$

ρ is the fraction of the power the surface sends back (70% = 0.70), Φ is the laser power in W, θ is the viewing angle, and the MPE (exposure limit) is in W/cm², so r comes out in cm.

Question. The radiant power of a laser beam is 1,500 W, with a viewing angle of 25°. The reflecting surface is 70% diffuse and the exposure limit is 0.25 W/cm². What is the nominal hazard zone?

$$r=\sqrt{\frac{0.70\times 1500\times\cos 25^{\circ}}{\pi\times 0.25}}=\sqrt{\frac{1050\times 0.9063}{0.7854}}=\sqrt{1212}\approx 35\ \text{cm}$$

NHZ ≈ 35 cm. Even a 1,500 W beam is only hazardous within about half a metre of a surface that scatters it this way.

Practice question. A 500 W laser strikes a surface that is 60% diffuse. The viewing angle is 30° and the exposure limit is 0.1 W/cm². What is the nominal hazard zone?

$$r=\sqrt{\frac{0.60\times 500\times\cos 30^{\circ}}{\pi\times 0.1}}=\sqrt{\frac{300\times 0.866}{0.3142}}=\sqrt{827}\approx 29\ \text{cm}$$

Two traps: convert the percent to a decimal (70% = 0.70), and keep W with W/cm² so the answer is in cm. This form applies to a diffusing surface, not a mirror-like one. The formula is the reflection form on the equation card.

Nonionizing controls in one line

Enclose or shield the source, interlock the access, use distance (fields and scattered light weaken quickly), limit time, and match the PPE to the wavelength: UV-filtering welding lenses, IR-filtering glass-furnace eyewear, laser eyewear with the right OD. Eyewear rated for one laser wavelength may give no protection at another.

Optical density: how much laser light gets through? Calculated

A laser filter cuts down the light that reaches the eye. Optical density (OD) states that reduction at one wavelength. It is not the thickness of the lens, and it is not how dark the lens looks.

$$OD=\log_{10}\!\left(\frac{E_{incident}}{E_{transmitted}}\right)\qquad E_{transmitted}=E_{incident}\times 10^{-OD}$$

Memory: every extra OD unit lets through one-tenth as much light.

Compare with shielding for ionizing radiation

One TVL and one OD unit are the same tenfold arithmetic, but they belong to different shielding systems: material thickness for ionizing radiation, a rated filter for laser light.

Practice: what OD is required?

A laser assessment gives an incident irradiance of 2 W/cm² and an applicable MPE of 0.001 W/cm² (a value assumed for this example).

$$OD_{min}=\log_{10}\!\left(\frac{2}{0.001}\right)=\log_{10}(2000)=3.30$$

The eyewear must give at least OD 3.30 at the laser wavelength. If the choices are OD 3 and OD 4:

• OD 3: 2 / 1,000 = 0.002 W/cm², which is above the MPE. Not enough.
• OD 4: 2 / 10,000 = 0.0002 W/cm², which is below the MPE. Choose this one.

Always round the required OD up to the next available rating, never down.

Selection check: match the wavelength, the required OD and the resistance to the expected exposure, and keep enough visibility to work. Use the same units in the ratio. For pulsed lasers use the radiant-exposure quantities and pulse criteria that apply. Eyewear supports beam enclosure and the other controls; it does not replace them. Same equation as the optical density card. Source: Princeton EHS, Laser Control Measures.